Question #1
Calculate the number of S&P futures contracts to sell to hedge the market exposure of an equity portfolio value at $1m and with a of 1.5. The S&P is currently at 1000 and the contract multiplier is 250.
- A . 4
- B . 8
- C . 6
- D . 2
Correct Answer: C
C
Explanation:
Since the equity portfolio has a beta of 1.5, we need to sell short enough number of futures contracts as to have $1 x 1.5 = $1.5m short in notional. The value of one S&P futures contract is 1000 x 250 = $250,000, and therefore in order to be short $1.5m, we need to sell 6 contracts.
C
Explanation:
Since the equity portfolio has a beta of 1.5, we need to sell short enough number of futures contracts as to have $1 x 1.5 = $1.5m short in notional. The value of one S&P futures contract is 1000 x 250 = $250,000, and therefore in order to be short $1.5m, we need to sell 6 contracts.
Question #2
Calculate the fair no-arbitrage spot price of oil if the price of a one year forward is $75, the discrete one year interest rates are 6%, and annual storage costs are $4 per barrel paid at the end of the year.
- A . $70.75
- B . $74.53
- C . $71
- D . $66.98
Correct Answer: D
D
Explanation:
If $x be the spot price of oil, then in order for the forward price to be $75, the following relationship must hold: ($x + $4/(1.06))*(1 + 6%) = $75. Solving, we get x = $66.98
D
Explanation:
If $x be the spot price of oil, then in order for the forward price to be $75, the following relationship must hold: ($x + $4/(1.06))*(1 + 6%) = $75. Solving, we get x = $66.98
Question #3
Euro-dollar deposits refer to
- A . A deposit denominated in the ECU
- B . A US dollar deposit outside the US
- C . A Euro deposit convertible into dollars upon maturity
- D . A Euro deposit in the USA
Correct Answer: B
B
Explanation:
Eurodollar deposits refer to US dollar denominated deposits outside the US, for example in a banking center such as London, and held by a non-US bank or a foreign branch of a US bank. Choice ‘b’ is the correct answer.
B
Explanation:
Eurodollar deposits refer to US dollar denominated deposits outside the US, for example in a banking center such as London, and held by a non-US bank or a foreign branch of a US bank. Choice ‘b’ is the correct answer.
Question #4
If the 3 month interest rate is 5%, and the 6 month interest rate is 6%, what would be the contract rate applicable to a 3 x 6 FRA?
- A . 6%
- B . 6.9%
- C . 5.5%
- D . 5%
Correct Answer: B
B
Explanation:
The correct answer is Choice ‘b’, as this question is merely asking for the forward rate based on known spot rates. The forward rate applicable to the three month period commencing in 3 months time is given by [(1 + 6%*6/12)/(1 + 5%*3/12) – 1]*4 = 6.91%. Thus Choice ‘b’ is the correct answer.
Here is a step by step way to think about it: $1 invested now at 6% for 6 months grows to (1 + 6%*6/12)=1.03. At the same time, using the 3 month rate, $1 invested now at 5% for 3 months grows to (1 + 5%*3/12)=1.0125. Effectively, this means that the 1.0125 at the end of 3 months grow to 1.03 at the end of 6 months, implying the rate of interest during the 3 months from 3 to 6 months is (1.03/1.0125 – 1)*4 = 6.91%.
B
Explanation:
The correct answer is Choice ‘b’, as this question is merely asking for the forward rate based on known spot rates. The forward rate applicable to the three month period commencing in 3 months time is given by [(1 + 6%*6/12)/(1 + 5%*3/12) – 1]*4 = 6.91%. Thus Choice ‘b’ is the correct answer.
Here is a step by step way to think about it: $1 invested now at 6% for 6 months grows to (1 + 6%*6/12)=1.03. At the same time, using the 3 month rate, $1 invested now at 5% for 3 months grows to (1 + 5%*3/12)=1.0125. Effectively, this means that the 1.0125 at the end of 3 months grow to 1.03 at the end of 6 months, implying the rate of interest during the 3 months from 3 to 6 months is (1.03/1.0125 – 1)*4 = 6.91%.
Question #5
Which of the following statements is INCORRECT according to CAPM:
- A . expected returns on an asset will equal the risk free rate plus a compensation for the additional risk measured by the beta of the asset
- B . the return expected by investors for holding the risky asset is a function of the covariance of the risky asset to the market portfolio
- C . securities with a higher standard deviation of returns will have a higher expected return
- D . portfolios on the efficient frontier have different Sharpe ratios
Correct Answer: C
C
Explanation:
The return on an asset is a function of the covariance of the asset’s return to the returns of the market portfolio. They do not depend upon the standard deviation of the asset itself. Therefore Choice ‘b’ is correct and Choice ‘c’ is incorrect.
The expected returns on an asset are equal to the risk free rate plus the beta times the market risk premium, therefore Choice ‘a’ is correct.
Portfolios on the efficient frontier will all have a different Sharpe ratio, which is the ratio of excess returns to portfolio volatility.
Choice ‘c’ is the correct answer (note that the question is asking for an identification of the INCORRECT statement).
C
Explanation:
The return on an asset is a function of the covariance of the asset’s return to the returns of the market portfolio. They do not depend upon the standard deviation of the asset itself. Therefore Choice ‘b’ is correct and Choice ‘c’ is incorrect.
The expected returns on an asset are equal to the risk free rate plus the beta times the market risk premium, therefore Choice ‘a’ is correct.
Portfolios on the efficient frontier will all have a different Sharpe ratio, which is the ratio of excess returns to portfolio volatility.
Choice ‘c’ is the correct answer (note that the question is asking for an identification of the INCORRECT statement).
Question #6
A bank advertises its certificates of deposits as yielding a 5.2% annual effective rate.
What is the equivalent continuously compounded rate of return?
- A . 4.82%
- B . 5%
- C . 5.07%
- D . 5.20%
Correct Answer: C
C
Explanation:
The equivalent continuously compounded rate in this case can be calculated as ln(1+5.2%) = 5.07%. The other answers are incorrect.
Refer to the tutorial on interest rates for more details on how continuously compounded rates work.
C
Explanation:
The equivalent continuously compounded rate in this case can be calculated as ln(1+5.2%) = 5.07%. The other answers are incorrect.
Refer to the tutorial on interest rates for more details on how continuously compounded rates work.
Question #7
[According to the PRMIA study guide for Exam 1, Simple Exotics and Convertible Bonds have been excluded from the syllabus. You may choose to ignore this question. It appears here solely because the Handbook continues to have these chapters.]
What is the current conversion premium for a convertible bond where $100 in market value of the bond is convertible into two shares and the current share price is $50?
- A . 0.5
- B . 1
- C . 0
- D . None of the above
Correct Answer: C
C
Explanation:
Since $100 is convertible into two shares, the price upon conversion per share is $50,
which is the same as the current share price. Therefore there is no premium, and Choice ‘c’ is the correct answer.
C
Explanation:
Since $100 is convertible into two shares, the price upon conversion per share is $50,
which is the same as the current share price. Therefore there is no premium, and Choice ‘c’ is the correct answer.
Question #8
[According to the PRMIA study guide for Exam 1, Simple Exotics and Convertible Bonds have been excluded from the syllabus. You may choose to ignore this question. It appears here solely because the Handbook continues to have these chapters.]
Which of the following describes a ‘quanto’ instrument:
- A . options on options
- B . any two asset hybrid instrument
- C . correlation products
- D . any two asset instrument in which one asset is a foreign currency
Correct Answer: D
D
Explanation:
A quanto is any instrument in which one asset is a foreign currency. Examples include any option on a foreign currency asset with the strike price in foreign currency, and an option on a foreign currency asset with the foreign currency risk hedged.
Correlation products refer to credit products on a basket of credits. Options on options represent an option to buy or sell an option in the future, and they are not ‘quantos’. Similarly, not every two asset instrument is a quanto unless one of the two assets is a foreign currency.
D
Explanation:
A quanto is any instrument in which one asset is a foreign currency. Examples include any option on a foreign currency asset with the strike price in foreign currency, and an option on a foreign currency asset with the foreign currency risk hedged.
Correlation products refer to credit products on a basket of credits. Options on options represent an option to buy or sell an option in the future, and they are not ‘quantos’. Similarly, not every two asset instrument is a quanto unless one of the two assets is a foreign currency.
Question #9
A bullet bond refers to a bond:
- A . that carries no coupon payments during its lifetime
- B . that provides for fixed coupons and repayment of principal at maturity
- C . that is issued by a sovereign
- D . that provides for floating rate interest payments during its lifetime
Correct Answer: B
B
Explanation:
Choice ‘b’ represents a correct description of a bullet bond. All other choices are incorrect.
B
Explanation:
Choice ‘b’ represents a correct description of a bullet bond. All other choices are incorrect.
Question #10
The securities market line (SML) based upon the CAPM expresses the relationship between
- A . asset beta and expected returns
- B . asset standard deviation and expected returns
- C . excess returns from the asset and its standard deviation
- D . market returns and asset returns
Correct Answer: A
A
Explanation:
The security market line is generally shown graphically with returns on the y-axis and the asset’s beta on the x-axis. The correct answer is Choice ‘a’.
Note the difference between the SML and the CML (the capital markets line). The CML is the transformation line joining the risk free rate on the y-axis and the portfolio with the maximum Sharpe ratio on the efficient frontier, and expresses the relationship between risk and return.
A
Explanation:
The security market line is generally shown graphically with returns on the y-axis and the asset’s beta on the x-axis. The correct answer is Choice ‘a’.
Note the difference between the SML and the CML (the capital markets line). The CML is the transformation line joining the risk free rate on the y-axis and the portfolio with the maximum Sharpe ratio on the efficient frontier, and expresses the relationship between risk and return.
Question #11
Using covered interest parity, calculate the 3 month CAD/USD forward rate if the spot CAD/USD rate is 1.1239 and the three month interest rates on CAD and USD are 0.75% and 0.4% annually respectively.
- A . 1.1249
- B . 1.1229
- C . 1.1278
- D . 1.1200
Correct Answer: A
A
Explanation:
Forward rates can be calculated from spot rates and interest rates using the formula Spot x (1+domestic interest rate)/(1+foreign interest rate), where the ‘Spot’ is expressed as a direct rate (ie as the number of domestic currency units one unit of the foreign currency can buy). In this case the forward rate will be 1.1239 * (1 + 0.75%*90/360) / (1 + 0.4%*90/360) = 1.1249.
It can be confusing to determine which interest rate should be considered ‘domestic’, and which ‘foreign’ for this formula. For that, look at the spot rate. Think of the spot rate as being x units of one currency equal to 1 unit of the other currency. In this case, think of the spot rate 1.1239 as "CAD 1.1239 = USD 1". The currency that has the "1" in it is the ‘foreign’ and the other one is ‘domestic’.
It is also important to remember how exchange rates are generally quoted. Most exchange
rates are quoted in terms of how many foreign currencies does USD 1 buy. Therefore, a
rate of 99 for the JPY means that USD 1 is equal to JPY 99. These are called ‘direct rates’.
However, there are four major world currencies where the rate quote convention is the
other way round – these are EUR, GBP, AUD and NZD. For these currencies, the FX quote
implies how many US dollars can one unit of these currencies buy. So a quote of "1.1023"
for the Euro means EUR 1 is equal to USD 1.1023 and not the other way round.
A
Explanation:
Forward rates can be calculated from spot rates and interest rates using the formula Spot x (1+domestic interest rate)/(1+foreign interest rate), where the ‘Spot’ is expressed as a direct rate (ie as the number of domestic currency units one unit of the foreign currency can buy). In this case the forward rate will be 1.1239 * (1 + 0.75%*90/360) / (1 + 0.4%*90/360) = 1.1249.
It can be confusing to determine which interest rate should be considered ‘domestic’, and which ‘foreign’ for this formula. For that, look at the spot rate. Think of the spot rate as being x units of one currency equal to 1 unit of the other currency. In this case, think of the spot rate 1.1239 as "CAD 1.1239 = USD 1". The currency that has the "1" in it is the ‘foreign’ and the other one is ‘domestic’.
It is also important to remember how exchange rates are generally quoted. Most exchange
rates are quoted in terms of how many foreign currencies does USD 1 buy. Therefore, a
rate of 99 for the JPY means that USD 1 is equal to JPY 99. These are called ‘direct rates’.
However, there are four major world currencies where the rate quote convention is the
other way round – these are EUR, GBP, AUD and NZD. For these currencies, the FX quote
implies how many US dollars can one unit of these currencies buy. So a quote of "1.1023"
for the Euro means EUR 1 is equal to USD 1.1023 and not the other way round.
Question #12
A receiver option on a swap is a swaption that gives the buyer the right to:
- A . swap two options between the two counterparties
- B . receive the fixed rate and pay a variable rate
- C . receive the swap spread in effect on a future date and pay a variable underlying rate
- D . pay the fixed rate and receive a variable rate
Correct Answer: B
B
Explanation:
A swaption is an option to enter into a fixed for floating interest rate swap at a point in the future, with the fixed rate decided upfront. These options can be European, Bermudan or American, in terms of what dates the option can be exercised. A receiver option on a swap is an option that gives the buyer the right to enter into a swap and receive the fixed rate and pay the variable rate. In the case of a payer option, the buyer pays the fixed rate and receives the variable rate. One way to remember this is that receiving and paying are terms used with reference to the fixed rates.
B
Explanation:
A swaption is an option to enter into a fixed for floating interest rate swap at a point in the future, with the fixed rate decided upfront. These options can be European, Bermudan or American, in terms of what dates the option can be exercised. A receiver option on a swap is an option that gives the buyer the right to enter into a swap and receive the fixed rate and pay the variable rate. In the case of a payer option, the buyer pays the fixed rate and receives the variable rate. One way to remember this is that receiving and paying are terms used with reference to the fixed rates.
Question #13
[According to the PRMIA study guide for Exam 1, Simple Exotics and Convertible Bonds have been excluded from the syllabus. You may choose to ignore this question. It appears here solely because the Handbook continues to have these chapters.]
A company that uses physical commodities as an input into its manufacturing process wishes to use options to hedge against a rise in its raw material costs.
Which of the following options would be the most cost effective to use?
- A . Writer-extendible options
- B . Correlation options
- C . Vanilla options
- D . Average rate options
Correct Answer: D
D
Explanation:
Average rate options will be the most cost effective in this scenario as they are cheaper than vanilla options. Writer extendible options on commodities will be even more expensive, and correlation products are irrelevant to the manufacturing company’s hedging needs.
D
Explanation:
Average rate options will be the most cost effective in this scenario as they are cheaper than vanilla options. Writer extendible options on commodities will be even more expensive, and correlation products are irrelevant to the manufacturing company’s hedging needs.
Question #14
A company has a long term loan from a bank at a fixed rate of interest. It expects interest rates to go down.
Which of the following instruments can the company use to convert its fixed rate liability to a floating rate liability?
- A . A fixed for floating interest rate swap
- B . A currency swap
- C . A forward rate agreement
- D . Interest rate futures
Correct Answer: A
A
Explanation:
A fixed for floating interest rate swap would be the most appropriate to the company’s
needs. It will allow it to receive a fixed rate (which will offset the fixed payment it has to
make on the loan) and pay a floating rate which it expects will be lower than the fixed rates.
Choice ‘a’ is the correct answer.
A
Explanation:
A fixed for floating interest rate swap would be the most appropriate to the company’s
needs. It will allow it to receive a fixed rate (which will offset the fixed payment it has to
make on the loan) and pay a floating rate which it expects will be lower than the fixed rates.
Choice ‘a’ is the correct answer.
Question #15
A trader comes in to work and finds the following prices in relation to a stock: $100 spot, $10 for a call expiring in one year with a strike price of $100, and $10 for a put with the same expiry and strike. Interest rates are at 5% per year, and the stock does not pay any dividends.
What should the trader do?
- A . Buy the call, buy the put and sell the stock
- B . Buy the call, sell the put and sell the stock
- C . Buy the put, sell the call and buy the stock
- D . Do nothing
Correct Answer: B
B
Explanation:
The prices must satisfy the put-call parity, and if they do not, it means there is an arbitrage opportunity, The put-call parity is as follows. We plug in the values to check if the parity is maintainted.
Buying a call + Bank Deposit (PV of exercise price) = Buying the stock + Buying a put Thus the LHS = $10 + $100/(1 + 5%) = $105.24 and RHS = $100 + $10 = $110, ie the equality does not hold.
Since the trader can make a profit by buying low and selling high, and the set of positions on the left should be brought, and those on the RHS should be sold. Thus the trader should buy the call, sell the put and sell the stock to make a risk free profit. (There is no need to explicitly place a bank deposit at the risk-free rate).
B
Explanation:
The prices must satisfy the put-call parity, and if they do not, it means there is an arbitrage opportunity, The put-call parity is as follows. We plug in the values to check if the parity is maintainted.
Buying a call + Bank Deposit (PV of exercise price) = Buying the stock + Buying a put Thus the LHS = $10 + $100/(1 + 5%) = $105.24 and RHS = $100 + $10 = $110, ie the equality does not hold.
Since the trader can make a profit by buying low and selling high, and the set of positions on the left should be brought, and those on the RHS should be sold. Thus the trader should buy the call, sell the put and sell the stock to make a risk free profit. (There is no need to explicitly place a bank deposit at the risk-free rate).
Question #16
Which of the following does not explain the shape of an yield curve?
- A . Market segmentation theory
- B . The expectations hypothesis
- C . The efficient markets hypothesis
- D . The liquidity preference theory
Correct Answer: C
C
Explanation:
The efficient markets hypothesis states that all known information is captured in the prices of a security. It does not explain the shape of the yield curve.
The expectations hypothesis, the LPT and the market segmentation theory are all attempts to explain the shape of the term structure of interest rates.
Therefore Choice ‘c’ is the correct answer as it does not explain the shape of the yield curve.
C
Explanation:
The efficient markets hypothesis states that all known information is captured in the prices of a security. It does not explain the shape of the yield curve.
The expectations hypothesis, the LPT and the market segmentation theory are all attempts to explain the shape of the term structure of interest rates.
Therefore Choice ‘c’ is the correct answer as it does not explain the shape of the yield curve.
Question #17
If the quoted discount rate of a 3 month treasury bill futures contract is 10%, what is the price of a 3-month treasury bill with a principal at maturity of $100?
- A . $90
- B . $110.00
- C . $102.50
- D . $97.50
Correct Answer: D
D
Explanation:
T-bill futures ‘discount’ can be converted to a price for the bill using the formula Price = [1 – discount * number of days/360]. In this case, this works out to (1- 10% *90/360) * 100 = $97.50. Choice ‘d’ is the correct answer.
D
Explanation:
T-bill futures ‘discount’ can be converted to a price for the bill using the formula Price = [1 – discount * number of days/360]. In this case, this works out to (1- 10% *90/360) * 100 = $97.50. Choice ‘d’ is the correct answer.
Question #18
[According to the PRMIA study guide for Exam 1, Simple Exotics and Convertible Bonds have been excluded from the syllabus. You may choose to ignore this question. It appears here solely because the Handbook continues to have these chapters.]
Which of the following statements relating to convertible debt are true:
I. A hard call protection means the bond cannot be called by the issuer till the share price reaches a threshold
II. It is advantageous for the issuer to call its convertible securities when the share price exceeds the conversion price
III. When the issuer’s share prices is very high, the convertible bond trades at a discount to the value of the shares it is convertible into
IV. Convertible bonds generally have to carry a higher coupon than on equivalent non-convertible securities to make them attractive to investors
- A . III and IV
- B . I and II
- C . I, III and IV
- D . II and III
Correct Answer: D
D
Explanation:
A ‘hard call protection’ means the bond cannot be called until a certain date, regardless of what the share price is. Therefore statement I is false. Also note that a ‘soft call protection’ means that a bond can be called only if the share price reaches a certain threshold.
It is advantageous for the issuer to call its convertible securities when the share price exceeds the conversion price – because these shares can instead be sold in the market at the higher share price than the lower conversion price. Statement II is true.
When the issuer’s share price is very high, the convertible bond trades at a discount to the share price because it is almost certain to be called by the issuer and be redeemed at par. Therefore statement III is right. Statement IV is incorrect because convertible bonds need to pay less coupon than equivalent non-convertible bonds because of the value of the option embedded in them.
D
Explanation:
A ‘hard call protection’ means the bond cannot be called until a certain date, regardless of what the share price is. Therefore statement I is false. Also note that a ‘soft call protection’ means that a bond can be called only if the share price reaches a certain threshold.
It is advantageous for the issuer to call its convertible securities when the share price exceeds the conversion price – because these shares can instead be sold in the market at the higher share price than the lower conversion price. Statement II is true.
When the issuer’s share price is very high, the convertible bond trades at a discount to the share price because it is almost certain to be called by the issuer and be redeemed at par. Therefore statement III is right. Statement IV is incorrect because convertible bonds need to pay less coupon than equivalent non-convertible bonds because of the value of the option embedded in them.
Question #19
For a stock that does not pay dividends, which of the following represents the delta of a futures contract?
- A . 0
- B . e^(rt)
- C . 1
- D . Futures contracts do not have a delta as they are not options
Correct Answer: B
B
Explanation:
The delivery price of a futures contract is given by Se^(rt), just as in the case of a forward contract. However, a key difference is that a forward is settled at maturity whereas a futures contract pays out the P&L daily. So if the spot price increases from S to S, the holder of a futures contract immediately receives the change in the delivery price without any discounting to the present. That is, the holder of the futures contract receives (S + S)e^(rt) – Se^(rt) = Se^(rt) right away. Therefore the delta of a futures contract is e^rt, which given positive non-zero values of r and t can only be greater than zero.
Therefore Choice ‘b’ is the correct answer. Note the difference from a forward contract where this difference is not received till the delivery date, therefore making the delta of the forward contract to be equal to 1.
B
Explanation:
The delivery price of a futures contract is given by Se^(rt), just as in the case of a forward contract. However, a key difference is that a forward is settled at maturity whereas a futures contract pays out the P&L daily. So if the spot price increases from S to S, the holder of a futures contract immediately receives the change in the delivery price without any discounting to the present. That is, the holder of the futures contract receives (S + S)e^(rt) – Se^(rt) = Se^(rt) right away. Therefore the delta of a futures contract is e^rt, which given positive non-zero values of r and t can only be greater than zero.
Therefore Choice ‘b’ is the correct answer. Note the difference from a forward contract where this difference is not received till the delivery date, therefore making the delta of the forward contract to be equal to 1.
Question #20
What is the fair price for a bond paying annual coupons at 5% and maturing in 5 years.
Assume par value of $100 and the yield curve is flat at 6%.
- A . $104.33
- B . $95.79
- C . $100.00
- D . $94.73
Correct Answer: B
B
Explanation:
The coupon payments can be considered an annuity which can be valued using the formula for the PV of annuities= annuity. Therefore the value of the five coupon payments is 5 * ((1-1/(1.06^5))/0.06) = $21.06 Similarly the principal payment at the end of 5 years can be valued as 100/1.065 = $74.73 Therefore the total value of the bond today is $95.79
B
Explanation:
The coupon payments can be considered an annuity which can be valued using the formula for the PV of annuities= annuity. Therefore the value of the five coupon payments is 5 * ((1-1/(1.06^5))/0.06) = $21.06 Similarly the principal payment at the end of 5 years can be valued as 100/1.065 = $74.73 Therefore the total value of the bond today is $95.79
Question #20
What is the fair price for a bond paying annual coupons at 5% and maturing in 5 years.
Assume par value of $100 and the yield curve is flat at 6%.
- A . $104.33
- B . $95.79
- C . $100.00
- D . $94.73
Correct Answer: B
B
Explanation:
The coupon payments can be considered an annuity which can be valued using the formula for the PV of annuities= annuity. Therefore the value of the five coupon payments is 5 * ((1-1/(1.06^5))/0.06) = $21.06 Similarly the principal payment at the end of 5 years can be valued as 100/1.065 = $74.73 Therefore the total value of the bond today is $95.79
B
Explanation:
The coupon payments can be considered an annuity which can be valued using the formula for the PV of annuities= annuity. Therefore the value of the five coupon payments is 5 * ((1-1/(1.06^5))/0.06) = $21.06 Similarly the principal payment at the end of 5 years can be valued as 100/1.065 = $74.73 Therefore the total value of the bond today is $95.79
Question #20
What is the fair price for a bond paying annual coupons at 5% and maturing in 5 years.
Assume par value of $100 and the yield curve is flat at 6%.
- A . $104.33
- B . $95.79
- C . $100.00
- D . $94.73
Correct Answer: B
B
Explanation:
The coupon payments can be considered an annuity which can be valued using the formula for the PV of annuities= annuity. Therefore the value of the five coupon payments is 5 * ((1-1/(1.06^5))/0.06) = $21.06 Similarly the principal payment at the end of 5 years can be valued as 100/1.065 = $74.73 Therefore the total value of the bond today is $95.79
B
Explanation:
The coupon payments can be considered an annuity which can be valued using the formula for the PV of annuities= annuity. Therefore the value of the five coupon payments is 5 * ((1-1/(1.06^5))/0.06) = $21.06 Similarly the principal payment at the end of 5 years can be valued as 100/1.065 = $74.73 Therefore the total value of the bond today is $95.79
Question #20
What is the fair price for a bond paying annual coupons at 5% and maturing in 5 years.
Assume par value of $100 and the yield curve is flat at 6%.
- A . $104.33
- B . $95.79
- C . $100.00
- D . $94.73
Correct Answer: B
B
Explanation:
The coupon payments can be considered an annuity which can be valued using the formula for the PV of annuities= annuity. Therefore the value of the five coupon payments is 5 * ((1-1/(1.06^5))/0.06) = $21.06 Similarly the principal payment at the end of 5 years can be valued as 100/1.065 = $74.73 Therefore the total value of the bond today is $95.79
B
Explanation:
The coupon payments can be considered an annuity which can be valued using the formula for the PV of annuities= annuity. Therefore the value of the five coupon payments is 5 * ((1-1/(1.06^5))/0.06) = $21.06 Similarly the principal payment at the end of 5 years can be valued as 100/1.065 = $74.73 Therefore the total value of the bond today is $95.79
Question #24
The yield-to-maturity on a 10 year coupon bearing bond
- A . 1, 2, 3
- B . 2, 1, 3
- C . 1, 3, 2
- D . 3, 2, 1
Correct Answer: B
B
Explanation:
This question highlights the difference between zero rates, yield-to-maturity and forward rates. Forward rates are from one point in time to another, for example say from year 4 to 5 in the future. A zero rate is from time 0, or now, to a point in time in the future. The zero rate is dependent on the forward rates for all the different periods from now to the future. The yield curve represents the various zero rates at different points in time, and if it is upward sloping it means forward rates for years further out are greater than the years prior. That is what causes the zero rate yields to increase over time and the curve to slope upwards. So the forward rate from year 9 to 10 will certainly be higher than the 10 year zero rate.
The yield-to-maturity for a bond is the rate at which the payments on the bond discount to be equal to the current bond price. It is therefore the average rate that applies to the bond. This average is based upon the different zero rates for the years in which bond holders receive payments. Since coupons are smaller than the payment at maturity, the zero rate that applies to the payment at maturity will have the most impact on the numerical value of the bond’s yield-to-maturity. Also affecting the yield-to-maturity will be the values of the coupon payments, which will be discounted at lower rates when the yield curve is upward sloping. So the yield-to-maturity will be an average lower than the 10 year zero. Since the 10 year zero will be lower than the forward rate from t=9-10, the yield-to-maturity will be the lowest rate of the three.
B
Explanation:
This question highlights the difference between zero rates, yield-to-maturity and forward rates. Forward rates are from one point in time to another, for example say from year 4 to 5 in the future. A zero rate is from time 0, or now, to a point in time in the future. The zero rate is dependent on the forward rates for all the different periods from now to the future. The yield curve represents the various zero rates at different points in time, and if it is upward sloping it means forward rates for years further out are greater than the years prior. That is what causes the zero rate yields to increase over time and the curve to slope upwards. So the forward rate from year 9 to 10 will certainly be higher than the 10 year zero rate.
The yield-to-maturity for a bond is the rate at which the payments on the bond discount to be equal to the current bond price. It is therefore the average rate that applies to the bond. This average is based upon the different zero rates for the years in which bond holders receive payments. Since coupons are smaller than the payment at maturity, the zero rate that applies to the payment at maturity will have the most impact on the numerical value of the bond’s yield-to-maturity. Also affecting the yield-to-maturity will be the values of the coupon payments, which will be discounted at lower rates when the yield curve is upward sloping. So the yield-to-maturity will be an average lower than the 10 year zero. Since the 10 year zero will be lower than the forward rate from t=9-10, the yield-to-maturity will be the lowest rate of the three.
Question #25
A stock sells for $100, and a call on the same stock for one year hence at a strike price of $100 goes for $35.
What is the price of the put on the stock with the same exercise and strike as the call? Assume the stock pays dividends at 1% per year at the end of the year and interest rates are 5% annually.
- A . $41.50
- B . $31.20
- C . $35
- D . $31.95
Correct Answer: B
B
Explanation:
We know from the put-call parity that:
Call – Put = Stock – Deposit
In the given situation,
Stock price = 100
call = 35
Put = ?
Exercise price = 100
However, we cannot use the stock price as-is, we need to adjust it for dividends that will be received during the period for which the option is valid. Dividends are $1, which need to be discounted to the present. In financial theory, dividends are often assumed to be continuously paid, though in reality they are single discrete payments at points in time. In this situation, for simplicity we assume that the dividend is paid at the end of the year, and needs to be discounted to the present and deducted from the spot price. Therefore:
Stock price adjusted for dividends = $100 – ($1/1.05) = $100 – $0.95 = $99.05
Similarly, the bank deposit amount, which is the PV of the exercise price, can be calculated as $100/1.05 = $95.24
We can now calculate the price of the put by plugging the numbers above in the put-call parity:
35 – Put = $99.05 – $95.24
Therefore the value of the put = 31.19, which is closest to 31.20 which therefore is the correct answer.
B
Explanation:
We know from the put-call parity that:
Call – Put = Stock – Deposit
In the given situation,
Stock price = 100
call = 35
Put = ?
Exercise price = 100
However, we cannot use the stock price as-is, we need to adjust it for dividends that will be received during the period for which the option is valid. Dividends are $1, which need to be discounted to the present. In financial theory, dividends are often assumed to be continuously paid, though in reality they are single discrete payments at points in time. In this situation, for simplicity we assume that the dividend is paid at the end of the year, and needs to be discounted to the present and deducted from the spot price. Therefore:
Stock price adjusted for dividends = $100 – ($1/1.05) = $100 – $0.95 = $99.05
Similarly, the bank deposit amount, which is the PV of the exercise price, can be calculated as $100/1.05 = $95.24
We can now calculate the price of the put by plugging the numbers above in the put-call parity:
35 – Put = $99.05 – $95.24
Therefore the value of the put = 31.19, which is closest to 31.20 which therefore is the correct answer.
Question #26
[According to the PRMIA study guide for Exam 1, Simple Exotics and Convertible Bonds have been excluded from the syllabus. You may choose to ignore this question. It appears here solely because the Handbook continues to have these chapters.]
Which of the following is not an approach to attempt to value to a convertible security:
- A . DCF analysis
- B . Bootstrapping
- C . Lower of bond value and value of converted shares
- D . Bond value plus equity option value
Correct Answer: B
B
Explanation:
Bootstrapping is not one of the various approaches to try to value a convertible security.
The rest of them are, and therefore Choice ‘b’ is the correct answer.
B
Explanation:
Bootstrapping is not one of the various approaches to try to value a convertible security.
The rest of them are, and therefore Choice ‘b’ is the correct answer.
Question #27
The two components of risk in a commodities futures portfolio are:
- A . Changes in the convenience yield and storage costs
- B . Changes in spot prices and carrying costs, also called commodity lease rates
- C . Changes in interest rates and spot prices
- D . The risk from change in basis and interest rates
Correct Answer: B
B
Explanation:
Commodity futures prices can be expressed as the summation of their spot prices and the carrying costs. Therefore any changes in either of these two would be a risk to the futures prices, and Choice ‘b’ is the correct answer. It is common to decompose complex commodity portfolios into underlying equivalent spot positions and the carrying costs, which includes interest, convenience yield and storage costs. For liquid commodities such as gold where changes of a short squeeze are low, interest costs dominate the carryings costs. Choice ‘b’ is the correct answer as it is most complete and covers the elements in the other choices. The ‘lease rate’ for a commodity is equivalent to (Fwd Price – Spot Price)/Spot Price, and comprises the interest and storage costs and the convenience yield. The other choices do not represent complete answers.
B
Explanation:
Commodity futures prices can be expressed as the summation of their spot prices and the carrying costs. Therefore any changes in either of these two would be a risk to the futures prices, and Choice ‘b’ is the correct answer. It is common to decompose complex commodity portfolios into underlying equivalent spot positions and the carrying costs, which includes interest, convenience yield and storage costs. For liquid commodities such as gold where changes of a short squeeze are low, interest costs dominate the carryings costs. Choice ‘b’ is the correct answer as it is most complete and covers the elements in the other choices. The ‘lease rate’ for a commodity is equivalent to (Fwd Price – Spot Price)/Spot Price, and comprises the interest and storage costs and the convenience yield. The other choices do not represent complete answers.
Question #28
Which of the following statements are true:
I. Protective puts are a form of insurance against a fall in prices
II. The maximum loss for an investor holding a protective put is equal to the decline in the value of the underlying
III. The premium paid on the put options held as a protective put is a loss if the value of the underlying goes up
IV. Protective puts can be a useful strategy for an investor holding a long position but with a negative short term view of the markets
- A . I and IV
- B . I, III and IV
- C . II and III
- D . I, II, III and IV
Correct Answer: B
B
Explanation:
A protective put is a put option purchased to protect against the fall in value of a long position. If the price of the underlying in respect of the long position goes down, the put options helps limit losses. If the price of the underlying goes up, the premium paid on the puts is lost but the investor gets to keep the entire upside from the rise in the price. Therefore statements I, III and IV are correct. Statement II is not correct as any decline in the value of the underlying is offset by the gain from the put, which is the entire idea behind a protective put.
B
Explanation:
A protective put is a put option purchased to protect against the fall in value of a long position. If the price of the underlying in respect of the long position goes down, the put options helps limit losses. If the price of the underlying goes up, the premium paid on the puts is lost but the investor gets to keep the entire upside from the rise in the price. Therefore statements I, III and IV are correct. Statement II is not correct as any decline in the value of the underlying is offset by the gain from the put, which is the entire idea behind a protective put.
Question #29
Which of the following is not a money market security
- A . Treasury notes
- B . Treasury bills
- C . Bankers’ acceptances
- D . Commercial paper
Correct Answer: A
A
Explanation:
A money market security is one that is initially issued with a maturity of less than one year. Treasury bills are short-term government securities with maturities ranging from a few days to 52 weeks. Bills are sold at a discount from their face value, and do not carry a coupon.
Treasury notes and treasury bonds are not money market instruments as they are issued for a maturity greater than a year. Treasury notes are issued with maturities of 2, 3, 5, 7, and 10 years and pay interest every six months. Treasury bonds pay interest every six months and mature in 30 years.
Commercial paper is issued by corporations to meet their short term funding needs and is a money market instrument. Bankers’ acceptances are short term loans to corporations that are guaranteed by a bank.
Of the given list, since treasury notes are the only instrument that are not money market securities, Choice ‘a’ is the correct answer.
A
Explanation:
A money market security is one that is initially issued with a maturity of less than one year. Treasury bills are short-term government securities with maturities ranging from a few days to 52 weeks. Bills are sold at a discount from their face value, and do not carry a coupon.
Treasury notes and treasury bonds are not money market instruments as they are issued for a maturity greater than a year. Treasury notes are issued with maturities of 2, 3, 5, 7, and 10 years and pay interest every six months. Treasury bonds pay interest every six months and mature in 30 years.
Commercial paper is issued by corporations to meet their short term funding needs and is a money market instrument. Bankers’ acceptances are short term loans to corporations that are guaranteed by a bank.
Of the given list, since treasury notes are the only instrument that are not money market securities, Choice ‘a’ is the correct answer.
Question #30
In terms of notional values traded, which of the following represents the largest share of total traded futures and options globally?
- A . interest rate products
- B . commodities
- C . foreign exchange futures and options
- D . equity futures and options
Correct Answer: D
D
Explanation:
Equity futures are by far the most traded futures contracts in terms of value, followed by interest rate products. Choice ‘d’ is the correct answer.
D
Explanation:
Equity futures are by far the most traded futures contracts in terms of value, followed by interest rate products. Choice ‘d’ is the correct answer.
Question #31
Which of the following statements is not correct with respect to a European call option:
- A . A increase in the risk-free rate of interest always increases the value of the option
- B . An increase in the price of the underlying always increases the value of the option
- C . An increase in the time to expiry always increases the value of the option
- D . An increase in the volatility of the underlying always increases the value of the option
Correct Answer: C
C
Explanation:
An increase in volatility increases the value of the option, and so do increases in the price of the underlying and the risk free rate. However, since a European option can only be exercised at expiry, an increase in the time to expiry may not necessarily increase the value of the option as it may increase the uncertainty around a more certain payout. Consider the extreme case of a deep in the money European call option that has 1 day left to expiry, and a payout is certain. Now imagine the time to expiry is increased by say, 6 months. Now the payout is no longer certain as no one knows what the value of the underlying will end up at after 6 months. In such a case, the value of the option would decline. But this applies only to a European option. An American option, which can be exercised any time, will not be affected by this reasoning.
C
Explanation:
An increase in volatility increases the value of the option, and so do increases in the price of the underlying and the risk free rate. However, since a European option can only be exercised at expiry, an increase in the time to expiry may not necessarily increase the value of the option as it may increase the uncertainty around a more certain payout. Consider the extreme case of a deep in the money European call option that has 1 day left to expiry, and a payout is certain. Now imagine the time to expiry is increased by say, 6 months. Now the payout is no longer certain as no one knows what the value of the underlying will end up at after 6 months. In such a case, the value of the option would decline. But this applies only to a European option. An American option, which can be exercised any time, will not be affected by this reasoning.
Question #32
Which of the following expressions represents the Treynor ratio, where is the expected return, is the standard deviation of returns, rm is the return of the market portfolio and rf is the risk free rate:
A)
B)
C)
D)
- A . Option A
- B . Option B
- C . Option C
- D . Option D
Correct Answer: A
A
Explanation:
The Sharpe ratio is the ratio of the excess returns of a portfolio to its volatility. It provides an intuitive measure of a portfolio’s excess return over the risk free rate. The Sharpe ratio is calculated as [(Portfolio return – Risk free return)/Portfolio standard deviation].
The Treynor ratio is similar to the Sharpe ratio, but instead of using volatility in the denominator, it uses the portfolio’s beta. Therefore the Treynor Ratio is calculated as [(Portfolio return – Risk free return)/Portfolio’s beta]. Therefore Choice ‘a’ is the correct answer.
Jensen’s alpha is another risk adjusted performance measure. It considers only the ‘alpha’, or the return attributable to a portfolio manager’s skill. It is the difference between the return of the portfolio, and what the portfolio should theoretically have earned. Any portfolio can
be expected to earn the risk free rate (rf), plus the market risk premium (which is given by [Beta x (Market portfolio’s return – Risk free rate)]. Jensen’s alpha is therefore the actual return earned less the risk free rate and the beta return.
Refer to the tutorial on risk adjusted performance measures for more details
A
Explanation:
The Sharpe ratio is the ratio of the excess returns of a portfolio to its volatility. It provides an intuitive measure of a portfolio’s excess return over the risk free rate. The Sharpe ratio is calculated as [(Portfolio return – Risk free return)/Portfolio standard deviation].
The Treynor ratio is similar to the Sharpe ratio, but instead of using volatility in the denominator, it uses the portfolio’s beta. Therefore the Treynor Ratio is calculated as [(Portfolio return – Risk free return)/Portfolio’s beta]. Therefore Choice ‘a’ is the correct answer.
Jensen’s alpha is another risk adjusted performance measure. It considers only the ‘alpha’, or the return attributable to a portfolio manager’s skill. It is the difference between the return of the portfolio, and what the portfolio should theoretically have earned. Any portfolio can
be expected to earn the risk free rate (rf), plus the market risk premium (which is given by [Beta x (Market portfolio’s return – Risk free rate)]. Jensen’s alpha is therefore the actual return earned less the risk free rate and the beta return.
Refer to the tutorial on risk adjusted performance measures for more details
Question #33
Which of the following best describes the efficient frontier?
- A . The efficient frontier identifies portfolios with the lowest return per unit of volatility
- B . The efficient frontier identifies portfolios with the highest return per unit of volatility
- C . The efficient frontier identifies the market portfolio
- D . The efficient frontier identifies portfolios with the highest volatility for a given level of return
Correct Answer: B
B
Explanation:
The efficient frontier is plotted on a graph with portfolio return (mean) as the y-axis and portfolio volatility, or standard deviation, on the x-axis. For a given level of volatility, it identifies the portfolio with the maximum return. Therefore Choice ‘b’ is the correct answer. If a reading is taken from the y-axis (ie returns) by dropping a perpendicular line on to the efficient frontier, we can get the minimum risk portfolio for the given level of returns. So the efficient frontier can be used to identify either the highest return per unit of volatility, or the lowest volatility given a desired level of returns. The efficient frontier does not describe the market portfolio, though the market portfolio may be one of the many points on the efficient frontier. Thus the other choices are incorrect.
B
Explanation:
The efficient frontier is plotted on a graph with portfolio return (mean) as the y-axis and portfolio volatility, or standard deviation, on the x-axis. For a given level of volatility, it identifies the portfolio with the maximum return. Therefore Choice ‘b’ is the correct answer. If a reading is taken from the y-axis (ie returns) by dropping a perpendicular line on to the efficient frontier, we can get the minimum risk portfolio for the given level of returns. So the efficient frontier can be used to identify either the highest return per unit of volatility, or the lowest volatility given a desired level of returns. The efficient frontier does not describe the market portfolio, though the market portfolio may be one of the many points on the efficient frontier. Thus the other choices are incorrect.
Question #34
Profits and losses on futures contracts are:
- A . settled upfront
- B . settled upon the expiry of the contract
- C . settled by moving collateral
- D . settled daily
Correct Answer: D
D
Explanation:
Profits and losses on futures contracts are settled daily. (P&L on forward contracts is often settled upon the expiry of the contract, and may even be collateralized.) Therefore Choice ‘d’ is the correct answer.
D
Explanation:
Profits and losses on futures contracts are settled daily. (P&L on forward contracts is often settled upon the expiry of the contract, and may even be collateralized.) Therefore Choice ‘d’ is the correct answer.
Question #35
Determine the enterprise value of a firm whose expected operating free cash flows are $100 each year and are growing with GDP at 2.5%. Assume its weighted average cost of capital is 7.5% annually.
- A . $4,000
- B . $1,000
- C . $1,333
- D . $2,000
Correct Answer: D
D
Explanation:
The operating free cash flows can be considered a perpetual annuity with a given growth rate.
The value of a perpetuity of a periodic cash flow of ‘c’, with a discount rate ‘r’ and growth rate ‘g’ is given by c/(r – g). In the given case, the company can be considered as providing a perpetual annuity which provides an annual cash flow of $100 which are growing at 2.5% (equal to the GDP’s growth rate, as given), and whose cost of capital, or the discount rate to use, is 7.5%
Therefore the value of the firm in this case is given by $100/(7.5% – 2.5%) = $2,000. Recall that the value of the firm is equal to the Operating Free Cash Flow/Weighted Average Cost of Capital (OFCF/WACC). Therefore Choice ‘d’ is the correct answer.
D
Explanation:
The operating free cash flows can be considered a perpetual annuity with a given growth rate.
The value of a perpetuity of a periodic cash flow of ‘c’, with a discount rate ‘r’ and growth rate ‘g’ is given by c/(r – g). In the given case, the company can be considered as providing a perpetual annuity which provides an annual cash flow of $100 which are growing at 2.5% (equal to the GDP’s growth rate, as given), and whose cost of capital, or the discount rate to use, is 7.5%
Therefore the value of the firm in this case is given by $100/(7.5% – 2.5%) = $2,000. Recall that the value of the firm is equal to the Operating Free Cash Flow/Weighted Average Cost of Capital (OFCF/WACC). Therefore Choice ‘d’ is the correct answer.
Question #36
An investor in mortgage backed securities can hedge his/her prepayment risk using which of the following?
I. Long swaption
II. Short cap
III. Short callable bonds
IV. Long fixed/floating swap
- A . II and III
- B . I and III
- C . II and IV
- D . I and IV
Correct Answer: B
B
Explanation:
Mortgage backed securities carry prepayment risk as borrowers tend to prepay mortgages when rates fall, and substitute it with newer cheaper mortgages. This creates the issue of ‘negative convexity’ for mortgages, ie, they lose value when rates rise, but do not gain in value when rates fall.
Prepayment risk can be offset by instruments that also carry negative convexity. A swaption is an option to borrow in the future at an agreed rate, which may be fixed or floating. An option to borrow in the future paying floating and receiving fixed guards against losses when rates fall, as the option can be exercised for a profit when rates are declining and the mortgage portfolio is being prepaid. A callable bond is very similar to an MBS in that the issuer can call it back when rates fall. Thus a long position in an MBS can be offset by a short position in a callable bond. Thus I and III are valid choices.
A cap allows exchanging fixed for floating when interest rates rise above an agreed rate. A long cap position allows borrowing at a fixed rate in exchange for floating, and a short cap implies receiving fixed and paying floating when rates go above the strike rate. Prepayment risk arises from falling interest rates, therefore a short cap will not protect against such a risk as falling interest rates would mean that no payments would be exchanged. Thus II does not help hedge against the risk in question.
A long position in a fixed for floating swap would require paying fixed and receiving floating when rates are falling. This would just make the problem from prepayments worse as the position would pay fixed and receive a falling rate. Thus IV is not an appropriate way to hedge prepayment risk.
B
Explanation:
Mortgage backed securities carry prepayment risk as borrowers tend to prepay mortgages when rates fall, and substitute it with newer cheaper mortgages. This creates the issue of ‘negative convexity’ for mortgages, ie, they lose value when rates rise, but do not gain in value when rates fall.
Prepayment risk can be offset by instruments that also carry negative convexity. A swaption is an option to borrow in the future at an agreed rate, which may be fixed or floating. An option to borrow in the future paying floating and receiving fixed guards against losses when rates fall, as the option can be exercised for a profit when rates are declining and the mortgage portfolio is being prepaid. A callable bond is very similar to an MBS in that the issuer can call it back when rates fall. Thus a long position in an MBS can be offset by a short position in a callable bond. Thus I and III are valid choices.
A cap allows exchanging fixed for floating when interest rates rise above an agreed rate. A long cap position allows borrowing at a fixed rate in exchange for floating, and a short cap implies receiving fixed and paying floating when rates go above the strike rate. Prepayment risk arises from falling interest rates, therefore a short cap will not protect against such a risk as falling interest rates would mean that no payments would be exchanged. Thus II does not help hedge against the risk in question.
A long position in a fixed for floating swap would require paying fixed and receiving floating when rates are falling. This would just make the problem from prepayments worse as the position would pay fixed and receive a falling rate. Thus IV is not an appropriate way to hedge prepayment risk.
Question #37
A bank sells an interest rate swap to its client, with the client agreeing to pay the bank a fixed 4% and receive 3 month LIBOR + 100 basis points, payments due every quarter. After quarter 1, the 3 month LIBOR is 2% pa.
Which of the following payments will happen in respect of this swap, assuming the contract notional is $100m, and the rate convention is 30/360?
- A . Bank pays customer $1,000,000 and customer pays the bank $750,000
- B . Bank pays customer $250,000
- C . Customer pays bank $250,000
- D . Bank pays customer $1,000,000
Correct Answer: C
C
Explanation:
In an interest rate swap, only the net payment is made. In this case,
– the customer pays the bank 4%*(3/12)*$100m
– the bank owes the customer (2% + 100bp))*(3/12)*$100m
Therefore the customer pays (4% – (2% + 100bp))*(3/12)*$100m. 3/12 represents the 3 month time interval. This is equal to a net payment of $250k from the customer to the bank. Therefore Choice ‘c’ is the correct answer and the rest are incorrect.
C
Explanation:
In an interest rate swap, only the net payment is made. In this case,
– the customer pays the bank 4%*(3/12)*$100m
– the bank owes the customer (2% + 100bp))*(3/12)*$100m
Therefore the customer pays (4% – (2% + 100bp))*(3/12)*$100m. 3/12 represents the 3 month time interval. This is equal to a net payment of $250k from the customer to the bank. Therefore Choice ‘c’ is the correct answer and the rest are incorrect.
Question #38
Which of the following statements are true:
I. All investors regardless of their expectations face the same efficient frontier which is always the market portfolio
II. Investors will have different efficient frontiers based upon their views of expected risks, returns and correlations
III. Investors risk appetite will determine their choice of the combination of risk-free and risky assets to hold
IV. If all investors have identical views on expected returns, standard deviation and correlations, they will hold risky assets in identical proportions
- A . III and IV
- B . II, III and IV
- C . I and II
- D . I, II, III and IV
Correct Answer: B
B
Explanation:
Investors have differing view of the market, which means differing view of expected returns, correlations and volatilities. Not only do they have differing views, these views change frequently as new information reveals itself. Accordingly, each investor has their own version of the efficient frontier. Once investors have determined their efficient frontiers, they will determine the extent of risk they wish to hold. If they had identical views, they would have held the same portfolio. But they do not, and if they did, there would be very little trading in the markets.
All the above statements are true except statement I which is false due to differing investor expectations.
(Re statement IV: If investors have different risk appetites, their portfolio will vary in the split between the risky and the riskfree assets. But inside the ‘risky’ assets bundle the proportion of the assets will be identical. Ie, they would express their varying risk appetites by varying how much of the risky bundle and the riskfree asset they hold, but inside the risky bundle the proportion of the different risky assets will be the same.)
B
Explanation:
Investors have differing view of the market, which means differing view of expected returns, correlations and volatilities. Not only do they have differing views, these views change frequently as new information reveals itself. Accordingly, each investor has their own version of the efficient frontier. Once investors have determined their efficient frontiers, they will determine the extent of risk they wish to hold. If they had identical views, they would have held the same portfolio. But they do not, and if they did, there would be very little trading in the markets.
All the above statements are true except statement I which is false due to differing investor expectations.
(Re statement IV: If investors have different risk appetites, their portfolio will vary in the split between the risky and the riskfree assets. But inside the ‘risky’ assets bundle the proportion of the assets will be identical. Ie, they would express their varying risk appetites by varying how much of the risky bundle and the riskfree asset they hold, but inside the risky bundle the proportion of the different risky assets will be the same.)
Question #39
Which of the following statements is true in relation to an American style option:
I. Put-call parity applies to American options
II. An American put will never be cheaper than a European put
III. An American put option should never be exercised early for a non-dividend paying stock
IV. An American put option is always at least as valuable as its intrinsic value
- A . I, II and III
- B . II and III
- C . II and IV
- D . III and IV
Correct Answer: C
C
Explanation:
The put-call parity applies to European options and does not hold for American options because the latter can be exercised at any time up to expiry. Therefore statement I is false. An American put can not be cheaper than a European put is correct. This is because the American put will always be valued at at least its intrinsic value whereas a European value may be valued at less than intrinsic value if the exercise date is too far away in the future. This is because a long time interval will increase the chance that the intrinsic value may not be realized at expiry. Because the American put can be exercised anytime, it will always be at least equal to its intrinsic value because if it were to be cheaper than that, investors would immediately buy and exercise it, creating a riskless profit. Therefore statement II is correct, and statement IV is correct as well.
It may be optimal to exercise an American put (unlike an American call – note the difference!) before its expiry on a non dividend paying stock. This would be the case only when the put is deep in the money. If the option is really deep in the money (say, when the underlying’s price is down to zero), then it may be worthwhile to cash the option out prior to expiry as the upside might be lost if time were to be allowed to pass. Additionally, any further upside in the case of a deep in the money option may be zero or very little, and the time value of money would also make immediate exercise prefereable. Therefore statement III is not correct.
C
Explanation:
The put-call parity applies to European options and does not hold for American options because the latter can be exercised at any time up to expiry. Therefore statement I is false. An American put can not be cheaper than a European put is correct. This is because the American put will always be valued at at least its intrinsic value whereas a European value may be valued at less than intrinsic value if the exercise date is too far away in the future. This is because a long time interval will increase the chance that the intrinsic value may not be realized at expiry. Because the American put can be exercised anytime, it will always be at least equal to its intrinsic value because if it were to be cheaper than that, investors would immediately buy and exercise it, creating a riskless profit. Therefore statement II is correct, and statement IV is correct as well.
It may be optimal to exercise an American put (unlike an American call – note the difference!) before its expiry on a non dividend paying stock. This would be the case only when the put is deep in the money. If the option is really deep in the money (say, when the underlying’s price is down to zero), then it may be worthwhile to cash the option out prior to expiry as the upside might be lost if time were to be allowed to pass. Additionally, any further upside in the case of a deep in the money option may be zero or very little, and the time value of money would also make immediate exercise prefereable. Therefore statement III is not correct.
Question #40
The theta of a delta neutral options position is large and positive.
What can we say about the gamma of the position?
- A . The gamma must be large and positive
- B . The gamma must be large and negative
- C . The gamma must be small and positive
- D . The gamma must be small and negative
Correct Answer: B
B
Explanation:
The relationship between the value of an option, and its delta, gamma and theta is given by rV = + rS + 0.5(S)2, where V is the value of the option, r the risk-free rate, S the spot price of the underlying, and , & are the respective Greeks.
For a delta neutral portfolio, = 0 and this equation reduces to rV = + 0.5(S)2. Now rV is generally a small number, which means that if is large and positive, must be large and negative to offset that. Therefore Choice ‘b’ is the correct answer.
B
Explanation:
The relationship between the value of an option, and its delta, gamma and theta is given by rV = + rS + 0.5(S)2, where V is the value of the option, r the risk-free rate, S the spot price of the underlying, and , & are the respective Greeks.
For a delta neutral portfolio, = 0 and this equation reduces to rV = + 0.5(S)2. Now rV is generally a small number, which means that if is large and positive, must be large and negative to offset that. Therefore Choice ‘b’ is the correct answer.
Question #41
Which of the following statements is false:
- A . The value of an FRA at expiration is determined by the spot interest rate prevailing at expiration
- B . The value of an FRA (forward rate agreement) at inception is zero.
- C . An FRA can be valued at anytime in its lifetime using the spot interest rate for the period to which the FRA relates
- D . Notional principals are exchanged at the start and the end of an FRA to eliminate credit risk
Correct Answer: D
D
Explanation:
Notional principals are not exchanged at the start and the end of an FRA. In fact, if the notional principals were to be exchanged, it would increase credit risk and not decrease it by introducing settlement risk. Therefore Choice ‘d’ is incorrect.
All other choices correctly describe various aspects of an FRA.
D
Explanation:
Notional principals are not exchanged at the start and the end of an FRA. In fact, if the notional principals were to be exchanged, it would increase credit risk and not decrease it by introducing settlement risk. Therefore Choice ‘d’ is incorrect.
All other choices correctly describe various aspects of an FRA.
Question #42
The value of which of the following options cannot be less than its intrinsic value
- A . a Bermudan put
- B . a European put
- C . an American put
- D . a European call
Correct Answer: C
C
Explanation:
Note that intrinsic value of an option is the difference between the value of the underlying and the strike price of the option.
European options can only be exercised at expiry, and Bermudan options only at certain dates during the life of the option. Therefore the option may be valued at less than intrinsic value if the earliest possible exercise date is not very close. An American option however can be exercised at any time prior to expiry, which means that its value can never fall below its intrinsic value. Because if it did, arbitrageurs would buy the option and immediately exercise it to get a risk free profit. It does not matter whether the option is a call or a put – therefore the correct answer is Choice ‘c’.
C
Explanation:
Note that intrinsic value of an option is the difference between the value of the underlying and the strike price of the option.
European options can only be exercised at expiry, and Bermudan options only at certain dates during the life of the option. Therefore the option may be valued at less than intrinsic value if the earliest possible exercise date is not very close. An American option however can be exercised at any time prior to expiry, which means that its value can never fall below its intrinsic value. Because if it did, arbitrageurs would buy the option and immediately exercise it to get a risk free profit. It does not matter whether the option is a call or a put – therefore the correct answer is Choice ‘c’.
Question #43
What is the yield to maturity for a 5% annual coupon bond trading at par? The bond matures in 10 years.
- A . Less than 5%
- B . Equal to 5%
- C . Greater than 5%
- D . Cannot be determined based on the given information
Correct Answer: B
B
Explanation:
The yield to maturity for a bond trading at par will be identical to its coupon. Therefore the yield to maturity for this bond will be 5%
B
Explanation:
The yield to maturity for a bond trading at par will be identical to its coupon. Therefore the yield to maturity for this bond will be 5%
Question #44
The LIBOR square swap offers the square of the interest rate change between contract inception and settlement date. If LIBOR at inception is y, and upon settlement is x, the contract pays (x – y)2 for x > y; and -(x – y)2 for x < y.
What of the following cannot be a value of the gamma of this contract?
- A . -2
- B . 1
- C . 2
- D . 0
Correct Answer: B
B
Explanation:
The LIBOR square is a (rare) derivative contract which pays, as mentioned in the question, the square of the interest rate move between two dates. If LIBOR at inception is y, and upon settlement is x, the contract pays (x – y)^2 for x > y; and -(x – y)^2 for x < y.
For any question that involves calculating delta or gamma, and the payoff is described in terms of variables as is the case here, remember that delta is always the first derivative and gamma is the second derivative.
For this question, let us calculate the second derivative and see what the gamma is:
If x > y, then the payoff is (x – y)^2
The first derivative wrt x is 2(x – y)
The second derivative wrt x is 2.
ie, the gamma is 2
If x < y, then the payoff is -(x – y)^2
The first derivative wrt x is -2(x – y)
The second derivative wrt x is -2.
ie, the gamma is -2
If x = y, then the payoff is 0. Both the first and the second derivatives are zero. ie the gamma is 0.
Based on the above, we see that the contract can have a gamma of either 0, +2 or -2. 1 is not a possible value for gamma, and therefore Choice ‘b’ is the correct answer.
B
Explanation:
The LIBOR square is a (rare) derivative contract which pays, as mentioned in the question, the square of the interest rate move between two dates. If LIBOR at inception is y, and upon settlement is x, the contract pays (x – y)^2 for x > y; and -(x – y)^2 for x < y.
For any question that involves calculating delta or gamma, and the payoff is described in terms of variables as is the case here, remember that delta is always the first derivative and gamma is the second derivative.
For this question, let us calculate the second derivative and see what the gamma is:
If x > y, then the payoff is (x – y)^2
The first derivative wrt x is 2(x – y)
The second derivative wrt x is 2.
ie, the gamma is 2
If x < y, then the payoff is -(x – y)^2
The first derivative wrt x is -2(x – y)
The second derivative wrt x is -2.
ie, the gamma is -2
If x = y, then the payoff is 0. Both the first and the second derivatives are zero. ie the gamma is 0.
Based on the above, we see that the contract can have a gamma of either 0, +2 or -2. 1 is not a possible value for gamma, and therefore Choice ‘b’ is the correct answer.
Question #45
An equity portfolio manager desires to be ‘market neutral’. His portfolio is valued at $10m and has a beta of 0.7 to the broad market index. The index is currently at 1000 and an index contract multiplier is specified as 250.
What should he do to make the beta of his portfolio zero?
- A . Sell 40 contracts of the index futures contract
- B . Buy 28 contracts of the index futures contract
- C . Buy 40 contracts of the index futures contract
- D . Sell 28 contracts of the index futures contract
Correct Answer: D
D
Explanation:
In terms of beta, his exposure is $10m*0.7 = $7m. This exposure is long. In order order to neutralize his long exposure, he needs to have an equal an identical short position with the same beta as this long position (of course, in the short direction). We need to figure out how many contracts will have a beta equal to his held position. (The beta of a futures contract is slightly different from 1 when compared to spot, but in the absence of other information in the question it is always okay to assume that the beta of the futures contract is 1. Such precision does not matter because of other errors such as rounding etc that cannot be anyway done away with.)
He needs to short futures contracts on the index with $7m in notional value. The value of each contract is currently 1000*250 =$250,000. He therefore needs to short $7m/$250,000 = 28 contracts to become market or beta neutral.
D
Explanation:
In terms of beta, his exposure is $10m*0.7 = $7m. This exposure is long. In order order to neutralize his long exposure, he needs to have an equal an identical short position with the same beta as this long position (of course, in the short direction). We need to figure out how many contracts will have a beta equal to his held position. (The beta of a futures contract is slightly different from 1 when compared to spot, but in the absence of other information in the question it is always okay to assume that the beta of the futures contract is 1. Such precision does not matter because of other errors such as rounding etc that cannot be anyway done away with.)
He needs to short futures contracts on the index with $7m in notional value. The value of each contract is currently 1000*250 =$250,000. He therefore needs to short $7m/$250,000 = 28 contracts to become market or beta neutral.
Question #46
[According to the PRMIA study guide for Exam 1, Simple Exotics and Convertible Bonds have been excluded from the syllabus. You may choose to ignore this question. It appears here solely because the Handbook continues to have these chapters.]
Which of the following statements is true?
I. Knock-out options start lifeless and convert to a plain vanilla option when the barrier is hit
II. Barrier options are cheaper than equivalent vanilla options
III. Average price options are more expensive than equivalent vanilla options
IV. Digital options have a high gamma close to the strike price
- A . II, III and IV
- B . II and IV
- C . I and III
- D . I, II and IV
Correct Answer: B
B
Explanation: :
Knock-out options start as plain vanilla options and are ‘knocked-out’, ie cease to exist, when the barrier is hit. Knock-in options start lifeless and ‘kick-in’, ie come into play as plain vanilla options when the barrier is hit. Therefore statement I is not correct.
Barrier options are certainly cheaper than equivalent vanilla options because vanilla options have a larger range of prices over which they pay out. Therefore statement II is correct.
Statement III is not correct. Average price options, also called Asian options, are less attractive to a buyer of options and therefore they are cheaper and not more expensive than vanilla options. This is because average prices are less volatile, and also when compared to a strip of equivalent vanilla options, some of the individual vanilla options in the strip may pay out whereas on the average nothing may pay out.
Digital options have a very high gamma close to the strike price as the option payout becomes uncertain and fluctuates sharply between 0 and 1. Therefore statement IV is correct.
B
Explanation: :
Knock-out options start as plain vanilla options and are ‘knocked-out’, ie cease to exist, when the barrier is hit. Knock-in options start lifeless and ‘kick-in’, ie come into play as plain vanilla options when the barrier is hit. Therefore statement I is not correct.
Barrier options are certainly cheaper than equivalent vanilla options because vanilla options have a larger range of prices over which they pay out. Therefore statement II is correct.
Statement III is not correct. Average price options, also called Asian options, are less attractive to a buyer of options and therefore they are cheaper and not more expensive than vanilla options. This is because average prices are less volatile, and also when compared to a strip of equivalent vanilla options, some of the individual vanilla options in the strip may pay out whereas on the average nothing may pay out.
Digital options have a very high gamma close to the strike price as the option payout becomes uncertain and fluctuates sharply between 0 and 1. Therefore statement IV is correct.
Question #47
What is the running yield on a 6% coupon bond selling at a clean price of $96?
- A . 5.70%
- B . 6.25%
- C . 6.30%
- D . 6.00%
Correct Answer: B
B
Explanation:
The ‘running yield’ refers to the coupon rate divided by the current price. In this case, it is 6/96 = 6.25%. Remember that the running yield is also called the current yield.
B
Explanation:
The ‘running yield’ refers to the coupon rate divided by the current price. In this case, it is 6/96 = 6.25%. Remember that the running yield is also called the current yield.
Question #48
An investor holds $1m in a 10 year bond that has a basis point value (or PV01) of 5 cents. She seeks to hedge it using a 30 year bond that has a BPV of 8 cents.
How much of the 30 year bond should she buy or sell to hedge against parallel shifts in the yield curve?
- A . Sell $1,600,000
- B . Sell $625,000
- C . Buy $1,000,000
- D . Buy $1,600,000
Correct Answer: B
B
Explanation:
When hedging one fixed income security with another, the question as to how much of the hedge to buy (or sell) (ie the hedge ratio) for a given primary position is determined by their respective basis point values, which in turn are determined by their duration. Therefore, when hedging a long maturity bond with a PV01 of $3 with a short maturity bond that has a PV of $1, we will need to buy 3 times the notional value of the short maturity bond to achieve the same sensitivity to interest rates as the longer maturity bond. Additionally, we may also expect the interest rates on the hedge to move differently from the interest rates on the primary instrument being hedged, and this needs to be accounted for as well as part of the hedge ratio calculation. This is called the yield beta and is calculated as change in yield for primary position/change in yield for the hedge security.
The hedge ratio is determined both by the yield beta and the BPVs of the two securities. In this case, the yield beta is 1 (as the question speaks of a parallel shift in the yield curve, ie all rates rise or fall together), and the ratio of the BPVs is 5/8. Therefore she should sell 5/8 x 1,000,000 = $625,000 of the 30 year bond. Choice ‘b’ is the correct answer.
B
Explanation:
When hedging one fixed income security with another, the question as to how much of the hedge to buy (or sell) (ie the hedge ratio) for a given primary position is determined by their respective basis point values, which in turn are determined by their duration. Therefore, when hedging a long maturity bond with a PV01 of $3 with a short maturity bond that has a PV of $1, we will need to buy 3 times the notional value of the short maturity bond to achieve the same sensitivity to interest rates as the longer maturity bond. Additionally, we may also expect the interest rates on the hedge to move differently from the interest rates on the primary instrument being hedged, and this needs to be accounted for as well as part of the hedge ratio calculation. This is called the yield beta and is calculated as change in yield for primary position/change in yield for the hedge security.
The hedge ratio is determined both by the yield beta and the BPVs of the two securities. In this case, the yield beta is 1 (as the question speaks of a parallel shift in the yield curve, ie all rates rise or fall together), and the ratio of the BPVs is 5/8. Therefore she should sell 5/8 x 1,000,000 = $625,000 of the 30 year bond. Choice ‘b’ is the correct answer.
Question #49
If the continuously compounded risk free rate is 4% per year, and the continuous rate of dividend on a broad market index is 1% annually, what is the no-arbitrage 6-month futures price of the index if its spot value is $1000?
- A . $1015.11
- B . $1015.00
- C . $1030.45
- D . $985.11
Correct Answer: A
A
Explanation:
The no-arbitrage futures price is given by exp(0.5*(4%-1%))*$1000 = $1015.11. Therefore Choice ‘a’ is the correct answer.
A
Explanation:
The no-arbitrage futures price is given by exp(0.5*(4%-1%))*$1000 = $1015.11. Therefore Choice ‘a’ is the correct answer.
Question #50
Backwardation can be explained by:
- A . expectations of oversupply in the future
- B . convenience yields being greater than the total carrying cost
- C . short term shortages in the spot markets
- D . all of the above
Correct Answer: D
D
Explanation:
When forward prices are greater than the spot prices, the market is said to be in contango. When forward prices are lower than spot prices, the market is said to be backwarded. A short squeeze may contribute to backwardation as shorts try to buy in the spot market to cover their short positions. Similarly, expectations of oversupply in the future, for example due to a bumper harvest may create situations where the forward prices fall below spot prices. Convenience yield is the benefit from having access to the commodity – and if the convenience yield is very high, for example in a market where manufacturers must never run out of a particular raw material, then these can switch the costs of carry (which include interest and storage costs, less convenience yields) to being negative.
Since all these factors can contribute to backwardation in the market, Choice ‘d’ is the correct answer.
D
Explanation:
When forward prices are greater than the spot prices, the market is said to be in contango. When forward prices are lower than spot prices, the market is said to be backwarded. A short squeeze may contribute to backwardation as shorts try to buy in the spot market to cover their short positions. Similarly, expectations of oversupply in the future, for example due to a bumper harvest may create situations where the forward prices fall below spot prices. Convenience yield is the benefit from having access to the commodity – and if the convenience yield is very high, for example in a market where manufacturers must never run out of a particular raw material, then these can switch the costs of carry (which include interest and storage costs, less convenience yields) to being negative.
Since all these factors can contribute to backwardation in the market, Choice ‘d’ is the correct answer.
Question #51
The yield to maturity for a zero coupon bond is equivalent to:
- A . short rates for the maturity of the bond
- B . the coupon rate for the bond
- C . forward rates for the maturity of the bond
- D . the spot rate from now till t years, where t is the maturity of the bond
Correct Answer: D
D
Explanation:
Since the zero coupon bond has no interim interest payments, its only cash flow is the final payment upon maturity. This would be identical to the spot rate from now till t years, where t is the maturity of the bond.
Forward rates are marginal rates that apply to individual years in a multi-period context. Short rates refer to short term interest rates in money market futures contracts. A zero coupon bond has no coupon.
D
Explanation:
Since the zero coupon bond has no interim interest payments, its only cash flow is the final payment upon maturity. This would be identical to the spot rate from now till t years, where t is the maturity of the bond.
Forward rates are marginal rates that apply to individual years in a multi-period context. Short rates refer to short term interest rates in money market futures contracts. A zero coupon bond has no coupon.
Question #52
If zero rates with continuous compounding for 4 and 5 years are 4% and 5% respectively, what is the forward rate for year 5?
- A . 5%
- B . 9%
- C . 9.097%
- D . 7%
Correct Answer: B
B
Explanation:
When rates are continuously compounded, we can calculate the marginal rate for year 5 as (5*5% – 4*4%) = 9%. (Note that things would be different if the rates were not continuously compounded, and they were annually compounded. In that case we would need to do a calculation of (1.05^5 / 1.04^4) – 1)
B
Explanation:
When rates are continuously compounded, we can calculate the marginal rate for year 5 as (5*5% – 4*4%) = 9%. (Note that things would be different if the rates were not continuously compounded, and they were annually compounded. In that case we would need to do a calculation of (1.05^5 / 1.04^4) – 1)
Question #53
According to the CAPM, the expected return from a risky asset is a function of:
- A . how much the risky asset contributes to portfolio risk
- B . diversifiable risk that the asset brings
- C . the riskiness, ie the volatility of the risky asset alone
- D . all of the above
Correct Answer: A
A
Explanation:
According to the CAPM, the expected return from a risky asset is a function of the contribution of the risky asset to the total risk of the market portfolio. Nothing else matters. All assets are priced according to the risk they bring to the market portfolio, regardless of their individual level of risk. An asset that is very volatile on its own, but has a negative correlation to the market may be priced high, ie have low expected return, because of its impact on the risk of the market portfolio. Therefore Choice ‘a’ is the correct answer, and the other options are incorrect.
Recall that according to the CAPM = covariancex, y / variancex, where x is the market portfolio and y is the risky asset.
The beta itself is a function of the covariance of the asset’s returns with market returns, and therefore only the driver of expected return for an asset is its beta, which is determined by the asset’s contribution to portfolio risk. ( = covariance(x, y) / variance(x), where x is the market portfolio and y is the risky asset. )
A
Explanation:
According to the CAPM, the expected return from a risky asset is a function of the contribution of the risky asset to the total risk of the market portfolio. Nothing else matters. All assets are priced according to the risk they bring to the market portfolio, regardless of their individual level of risk. An asset that is very volatile on its own, but has a negative correlation to the market may be priced high, ie have low expected return, because of its impact on the risk of the market portfolio. Therefore Choice ‘a’ is the correct answer, and the other options are incorrect.
Recall that according to the CAPM = covariancex, y / variancex, where x is the market portfolio and y is the risky asset.
The beta itself is a function of the covariance of the asset’s returns with market returns, and therefore only the driver of expected return for an asset is its beta, which is determined by the asset’s contribution to portfolio risk. ( = covariance(x, y) / variance(x), where x is the market portfolio and y is the risky asset. )
Question #54
A trader finds that a stock index is trading at 1000, and a six month futures contract on the same index is available at 1020. The risk free rate is 2% per annum, and the dividend rate is 1% per annum.
What should the trader do?
- A . Buy the index spot and sell the futures contract
- B . Buy the futures contract and sell the index spot
- C . Buy the index spot and buy the futures contract
- D . Sell the futures contract
Correct Answer: A
A
Explanation:
The fair price for the futures contract should be [1000 x ( 1 + (2%-1%)/2)] = 1005. This means the futures contract is ‘rich’ at 1020. The trader should therefore short the futures contract, and buy the index spot. To buy the spot index, he will incur a borrowing cost of 2%, which will be partly offset by the dividend yield of 1%, and at the end of six months he will owe a net amount of 1005 and hold the index. At the same time the futures contract would expire too, and he would be able to sell at the agreed price of 1020, making a risk free profit of 15.
A
Explanation:
The fair price for the futures contract should be [1000 x ( 1 + (2%-1%)/2)] = 1005. This means the futures contract is ‘rich’ at 1020. The trader should therefore short the futures contract, and buy the index spot. To buy the spot index, he will incur a borrowing cost of 2%, which will be partly offset by the dividend yield of 1%, and at the end of six months he will owe a net amount of 1005 and hold the index. At the same time the futures contract would expire too, and he would be able to sell at the agreed price of 1020, making a risk free profit of 15.
Question #55
A portfolio comprising a long call and a short put option has the same payoff as:
- A . a long underlying asset and a short bond position
- B . a short underlying asset and a short bond position
- C . a long underlying asset and a long bond position
- D . a short underlying asset and a long bond position
Correct Answer: A
A
Explanation:
To answer this question, we need to look at the put-call parity, which can be expressed as:
Value of call – Value of put = Spot price – Exercise price discounted to the present or, Value of call – Value of put = Stock – Bond with a future value equal to exercise price Therefore, a long call and a short put is equivalent to a long stock position and a short bond.
Choice ‘a’ is therefore the correct answer. (Alternatively, we could also have constructed a graph of the payoff profiles to arrive at the same answer).
A
Explanation:
To answer this question, we need to look at the put-call parity, which can be expressed as:
Value of call – Value of put = Spot price – Exercise price discounted to the present or, Value of call – Value of put = Stock – Bond with a future value equal to exercise price Therefore, a long call and a short put is equivalent to a long stock position and a short bond.
Choice ‘a’ is therefore the correct answer. (Alternatively, we could also have constructed a graph of the payoff profiles to arrive at the same answer).
Question #56
A utility function expresses:
- A . Risk probabilities
- B . Risk alternatives
- C . Risk assessment
- D . Risk attitude
Correct Answer: D
D
Explanation:
A utility function provides a description of an individual or a firm’s risk attitude. It expresses how risk seeking or risk averse a firm or an individual is. The utility function would explain differences between risk seeking and risk averse behavior, for example, as an individual becomes richer, he may seek (or shun) risk more than before. A utility function incorporates all of this, and therefore Choice ‘d’ is the correct answer.
D
Explanation:
A utility function provides a description of an individual or a firm’s risk attitude. It expresses how risk seeking or risk averse a firm or an individual is. The utility function would explain differences between risk seeking and risk averse behavior, for example, as an individual becomes richer, he may seek (or shun) risk more than before. A utility function incorporates all of this, and therefore Choice ‘d’ is the correct answer.
Question #57
What is the standard deviation (in dollars) of a portfolio worth $10,000, of which $4,000 is invested in Stock A, with an expected return of 10% and standard deviation of 20%; and the rest in Stock B, with an expected return of 12% and a standard deviation of 25%. The correlation between the two stocks is 0.6.
- A . $2,081
- B . $1,201
- C . $1,204
- D . $4,330,000
Correct Answer: A
A
Explanation:
Standard deviation of this portfolio can be calculated as SQRT(4000^2*20%^2 + 6000^2*25%^2 + 2*0.6*4000*6000*20%*25%), which is equal to $2,081. Choice ‘a’ is the correct answer. The other answers are incorrect.
A
Explanation:
Standard deviation of this portfolio can be calculated as SQRT(4000^2*20%^2 + 6000^2*25%^2 + 2*0.6*4000*6000*20%*25%), which is equal to $2,081. Choice ‘a’ is the correct answer. The other answers are incorrect.
Question #58
An investor has a bullish outlook on the market.
Which of the following option strategies would suit him?
I. Risk reversal
II. Collar
III. Bull spread
IV. Butterfly spread
- A . II and IV
- B . I, III and IV
- C . I and III
- D . I, II, III and IV
Correct Answer: C
C
Explanation:
The investor would benefit from the risk reversal and the bull spread as both these strategies have a payoff profile that benefit from rising prices of the underlying. The collar is the opposite of risk reversal, and benefits during a bear market, and the butterfly spread benefits when prices remain range bound. Therefore Choice ‘c’ is the correct answer.
C
Explanation:
The investor would benefit from the risk reversal and the bull spread as both these strategies have a payoff profile that benefit from rising prices of the underlying. The collar is the opposite of risk reversal, and benefits during a bear market, and the butterfly spread benefits when prices remain range bound. Therefore Choice ‘c’ is the correct answer.
Question #59
Suppose the S&P is trading at a level of 1000. Using continuously compounded rates, calculate the futures price for a contract expiring in three months, assuming expected dividends to be 2% and the interest rate for futures funding to be 5% (both rates expressed as continuously compounded rates)
- A . $1,007.50
- B . $1,000.00
- C . $1,007.53
- D . $1,012.58
Correct Answer: C
C
Explanation:
The futures price of the contract will be the future value of the spot price, calculated at a net rate equal to the cost of funding the futures position, less any dividends or other distributions. Also note that when rates are continuously compounded, Future Value = Present Value x (exp(rate x time)).
Therefore in this case the futures price for the S&P = 1000 * exp((5%-2%)*3/12) = 1007.53
C
Explanation:
The futures price of the contract will be the future value of the spot price, calculated at a net rate equal to the cost of funding the futures position, less any dividends or other distributions. Also note that when rates are continuously compounded, Future Value = Present Value x (exp(rate x time)).
Therefore in this case the futures price for the S&P = 1000 * exp((5%-2%)*3/12) = 1007.53
Question #60
How are foreign exchange futures quoted against the US dollar?
- A . Futures forex prices are always quoted as the number of units of the foreign currency that one US dollar can buy
- B . It depends upon the currency – futures forex prices follow the same convention as for spot prices
- C . Futures forex prices are always quoted as the number of US dollars one unit of the foreign currency can buy
- D . It can be quoted either way, based on whether the contract is for a short maturity or long
Correct Answer: C
C
Explanation:
Price quotes for futures where one of the currencies is the US dollar follow the convention of using the number of US dollars that one unit of the foreign currency can buy. (For JPY, 100 Yen is used.)
In the forward market, the convention used is the same as that used in the spot market.
In the spot market, prices are expressed as the number of units of the foreign currency that 1 USD can buy, except for GBP, EUR, AUD and NZD where it is the other way round (ie, number of USDs that 1 of each of these currencies can buy).
C
Explanation:
Price quotes for futures where one of the currencies is the US dollar follow the convention of using the number of US dollars that one unit of the foreign currency can buy. (For JPY, 100 Yen is used.)
In the forward market, the convention used is the same as that used in the spot market.
In the spot market, prices are expressed as the number of units of the foreign currency that 1 USD can buy, except for GBP, EUR, AUD and NZD where it is the other way round (ie, number of USDs that 1 of each of these currencies can buy).
Question #61
What is the duration of a 10 year zero coupon bond. Assume the bond is callable (ie, the issuer can buy it back) at face value at any time during its existence.
- A . 0 years
- B . 5 years
- C . 1 year
- D . 10 years
Correct Answer: D
D
Explanation:
The key point in this question is that the bond is zero coupon, and can only be called at face value. Since the bond is zero coupon, its value will always be less than its par value at any time during its existence (as any interest rate will be a positive number). Therefore the issuer will never exercise the call. Thus the bond will have a duration equal to what an equivalent non-callable bond would have.
Since zero coupon bonds have a duration equal to their maturity, the bond’s duration is 10 years.
D
Explanation:
The key point in this question is that the bond is zero coupon, and can only be called at face value. Since the bond is zero coupon, its value will always be less than its par value at any time during its existence (as any interest rate will be a positive number). Therefore the issuer will never exercise the call. Thus the bond will have a duration equal to what an equivalent non-callable bond would have.
Since zero coupon bonds have a duration equal to their maturity, the bond’s duration is 10 years.
Question #62
The forward price of a physical asset is affected by:
- A . the spot price, the risk-free rate, carrying costs, any other cash flows from holding the asset and the volatility of spot prices
- B . the spot price, the risk-free rate, carrying costs, any other cash flows from holding the asset and the time to maturity of the forward contract
- C . the spot price, the risk-free rate, carrying costs and any other cash flows from holding the asset
- D . The spot price of the asset and the market’s prevailing view of the commodity’s direction in the future
Correct Answer: B
B
Explanation:
Choice ‘b’ lists all the factors that affect the forward price of a physical asset and is the most complete answer. Forward prices for physical assets are not affected by volatility (only options are), nor are they arbitrarily decided by any prevailing ‘views’.
B
Explanation:
Choice ‘b’ lists all the factors that affect the forward price of a physical asset and is the most complete answer. Forward prices for physical assets are not affected by volatility (only options are), nor are they arbitrarily decided by any prevailing ‘views’.
Question #63
If the implied volatility for a call option is 30%, the implied volatility for the corresponding put option is:
- A . -70%
- B . 30%
- C . -30%
- D . 70%
Correct Answer: B
B
Explanation:
Implied volatilities are the same for calls and puts with similar exercise and strike prices. If not, it would offer an arbitrage opportunity. Therefore Choice ‘b’ is the correct answer.
B
Explanation:
Implied volatilities are the same for calls and puts with similar exercise and strike prices. If not, it would offer an arbitrage opportunity. Therefore Choice ‘b’ is the correct answer.
Question #64
Which of the following statements are true:
I. A deep in-the-money call option has a value very close to that of a forward contract with a forward price equal to the exercise price
II. If the volatility of a stock goes down to zero, the value of a call option on the stock will tend to be close to that of a forward contract so long as the option is in the money.
III. All other things remaining the same, the issue of stock warrants exercisable at a future date will cause a decline in the current stock price
IV. Implied volatilities are calculated from market prices of options and are forward looking
- A . I and IV
- B . II and III
- C . III and IV
- D . All of the above
Correct Answer: D
D
Explanation:
All the statements are correct, therefore Choice ‘d’ is the correct answer. Let us look at each of these statements one by one.
I. A deep in-the-money call option has a value very close to that of a forward contract with a forward price equal to the exercise price. This is true because a deep in the money call option is most likely to be exercised, and is therefore effectively like a forward contract to buy the stock at the exercise price.
We can also look at this using the BSM formula for a call option. If c be the value of a call option, and all other variables have their usual meaning (S0 is the spot price, K is exercise price, and t is time to expiry), then according to the Black Scholes model the value of a call is given by the following expression:
D
Explanation:
All the statements are correct, therefore Choice ‘d’ is the correct answer. Let us look at each of these statements one by one.
I. A deep in-the-money call option has a value very close to that of a forward contract with a forward price equal to the exercise price. This is true because a deep in the money call option is most likely to be exercised, and is therefore effectively like a forward contract to buy the stock at the exercise price.
We can also look at this using the BSM formula for a call option. If c be the value of a call option, and all other variables have their usual meaning (S0 is the spot price, K is exercise price, and t is time to expiry), then according to the Black Scholes model the value of a call is given by the following expression:
Question #64
Which of the following statements are true:
I. A deep in-the-money call option has a value very close to that of a forward contract with a forward price equal to the exercise price
II. If the volatility of a stock goes down to zero, the value of a call option on the stock will tend to be close to that of a forward contract so long as the option is in the money.
III. All other things remaining the same, the issue of stock warrants exercisable at a future date will cause a decline in the current stock price
IV. Implied volatilities are calculated from market prices of options and are forward looking
- A . I and IV
- B . II and III
- C . III and IV
- D . All of the above
Correct Answer: D
D
Explanation:
All the statements are correct, therefore Choice ‘d’ is the correct answer. Let us look at each of these statements one by one.
I. A deep in-the-money call option has a value very close to that of a forward contract with a forward price equal to the exercise price. This is true because a deep in the money call option is most likely to be exercised, and is therefore effectively like a forward contract to buy the stock at the exercise price.
We can also look at this using the BSM formula for a call option. If c be the value of a call option, and all other variables have their usual meaning (S0 is the spot price, K is exercise price, and t is time to expiry), then according to the Black Scholes model the value of a call is given by the following expression:
D
Explanation:
All the statements are correct, therefore Choice ‘d’ is the correct answer. Let us look at each of these statements one by one.
I. A deep in-the-money call option has a value very close to that of a forward contract with a forward price equal to the exercise price. This is true because a deep in the money call option is most likely to be exercised, and is therefore effectively like a forward contract to buy the stock at the exercise price.
We can also look at this using the BSM formula for a call option. If c be the value of a call option, and all other variables have their usual meaning (S0 is the spot price, K is exercise price, and t is time to expiry), then according to the Black Scholes model the value of a call is given by the following expression:
Question #66
Which of the following statements are true:
- A . Selling a call + Selling a put = Buying the stock + Bank deposit
- B . Buying a call + Bank Deposit = Buying the stock + Selling a put
- C . Buying a call + Selling a put = Buying the stock + Bank deposit
- D . Buying a call + Bank Deposit = Buying the stock + Buying a put
Correct Answer: D
D
Explanation:
The put-call parity can be expressed as:
Call C Put = Spot C PV of exercise price
Note that a negative sign above means a short position. The ‘term PV of exercise price’ is the same as a bank deposit placed today equivalent to the PV of the exercise price so that we will have the cash flow on the exercise date to exercise the option.
Therefore only Choice ‘d’ is the correct answer as rearranging the above gives us Buying a call + Bank Deposit = Buying the stock + Buying a put. Choice ‘d’ is therefore the correct answer.
D
Explanation:
The put-call parity can be expressed as:
Call C Put = Spot C PV of exercise price
Note that a negative sign above means a short position. The ‘term PV of exercise price’ is the same as a bank deposit placed today equivalent to the PV of the exercise price so that we will have the cash flow on the exercise date to exercise the option.
Therefore only Choice ‘d’ is the correct answer as rearranging the above gives us Buying a call + Bank Deposit = Buying the stock + Buying a put. Choice ‘d’ is therefore the correct answer.
Question #67
Futures initial margin requirements are
- A . determined based on the client’s credit history
- B . determined by the members based on the SPAN framework
- C . determined based on the length of the settlement period
- D . determined by the exchange
Correct Answer: D
D
Explanation:
Futures initial margins are determined by the exchange. SPAN is the name of a framework the CME uses to determine margins. Only Choice ‘d’ is correct.
D
Explanation:
Futures initial margins are determined by the exchange. SPAN is the name of a framework the CME uses to determine margins. Only Choice ‘d’ is correct.
Question #68
The relationship between covariance and correlation for two assets x and y is expressed by which of the following equations (where covarx,y is the covariance between x and y , x and y are the respective standard deviations and x,y is the correlation between x and y ):
A)
B)
C)
D)
None of the above
- A . Option A
- B . Option B
- C . Option C
- D . Option D
Correct Answer: B
B
Explanation:
Choice ‘b’ is the correct answer. The other relationships are not correct.
B
Explanation:
Choice ‘b’ is the correct answer. The other relationships are not correct.
Question #69
Which of the following are valid credit enhancements used for credit derivatives:
I. Overcollateralization
II. Excess spread
III. Cash reserves
IV. Margin requirements
- A . I, II and IV
- B . II, III and IV
- C . I, II and III
- D . I, II, III and IV
Correct Answer: C
C
Explanation:
Overcollateralization is when the notes issued by the special purpose vehicle are less in value compared to the underlying pool of assets, thereby providing a buffer to absorb losses. Excess spread implies that the notes issued carry a lower interest rate than the interest rate received on the underlying assets. Cash reserves are reserves intended to take first hits when losses happen. All of these are valid credit enhancements for structured products. Additionally, ‘insurance wraps’ are also used as a credit enhancement. Choice ‘c’ is the correct answer.
‘Margin requirements’ do not mean anything in this context and are not a valid credit enhancement used for credit derivatives.
C
Explanation:
Overcollateralization is when the notes issued by the special purpose vehicle are less in value compared to the underlying pool of assets, thereby providing a buffer to absorb losses. Excess spread implies that the notes issued carry a lower interest rate than the interest rate received on the underlying assets. Cash reserves are reserves intended to take first hits when losses happen. All of these are valid credit enhancements for structured products. Additionally, ‘insurance wraps’ are also used as a credit enhancement. Choice ‘c’ is the correct answer.
‘Margin requirements’ do not mean anything in this context and are not a valid credit enhancement used for credit derivatives.
Question #70
The gamma of a call option is 0.08.
What is the gamma of the corresponding put option?
- A . -0.08
- B . 0.92
- C . 0.08
- D . -0.92
Correct Answer: C
C
Explanation:
From the put-call parity, we know that Call – Put = Stock – Bank deposit. Since the bank deposit has a zero Gamma, and the Gamma of the Stock itself is also 0, we get the relationship Gamma of Call – Gamma of Put = 0. Therefore, if the Gamma of a call option is 0.08, the Gamma of the corresponding put option is also 0.08.
C
Explanation:
From the put-call parity, we know that Call – Put = Stock – Bank deposit. Since the bank deposit has a zero Gamma, and the Gamma of the Stock itself is also 0, we get the relationship Gamma of Call – Gamma of Put = 0. Therefore, if the Gamma of a call option is 0.08, the Gamma of the corresponding put option is also 0.08.
Question #71
For an investor short a bond, which of the following is true:
I. Higher convexity is preferable to lower convexity
II. An increase in yields is preferable to a decrease in yield
III. Negative convexity is preferable to positive convexity
- A . I and II
- B . II and III
- C . I, II and III
- D . I and III
Correct Answer: B
B
Explanation:
The effect of higher convexity is that when yields rise, the price decrease is lower than the increase in yields, and when yields fall, the increase in price is greater than the fall in yield. In either case, it benefits the holder of the fixed income instrument that carries such positive convexity. The converse is true for someone short a bond – such an investor would prefer lower convexity to higher convexity. Therefore statement I is not true for an investor who is short a bond.
An increase in yields makes bond prices decrease, something that would benefit the short.
Therefore statement II is true for an investor short a bond.
Negative convexity has exactly the opposite effect as the one described for positive convexity for statement I above. An investor short a bond would prefer negative convexity (which by the way is exhibited by very few fixed income instruments such as mortgages) to positive convexity, therefore statement III is true for such an investor. Choice ‘b’ is the correct answer.
B
Explanation:
The effect of higher convexity is that when yields rise, the price decrease is lower than the increase in yields, and when yields fall, the increase in price is greater than the fall in yield. In either case, it benefits the holder of the fixed income instrument that carries such positive convexity. The converse is true for someone short a bond – such an investor would prefer lower convexity to higher convexity. Therefore statement I is not true for an investor who is short a bond.
An increase in yields makes bond prices decrease, something that would benefit the short.
Therefore statement II is true for an investor short a bond.
Negative convexity has exactly the opposite effect as the one described for positive convexity for statement I above. An investor short a bond would prefer negative convexity (which by the way is exhibited by very few fixed income instruments such as mortgages) to positive convexity, therefore statement III is true for such an investor. Choice ‘b’ is the correct answer.
Question #72
Which of the following markets are characterized by the presence of a market maker always making two-way prices?
- A . Exchanges
- B . OTC markets
- C . ECNs
- D . Dark pools
Correct Answer: A
A
Explanation:
Over the counter and electronic communication networks match buyers and sellers. However, there is no market making function, ie, in periods of stress liquidity may completely disappear from these markets. Exchanges normally have market makers that are required to present two way quotes on the securities they are making the market for. Therefore Choice ‘a’ is the correct answer.
A
Explanation:
Over the counter and electronic communication networks match buyers and sellers. However, there is no market making function, ie, in periods of stress liquidity may completely disappear from these markets. Exchanges normally have market makers that are required to present two way quotes on the securities they are making the market for. Therefore Choice ‘a’ is the correct answer.
Question #73
A borrower pays a floating rate on a loan and wishes to convert it to a position where a fixed rate is paid.
Which of the following can be used to accomplish this objective?
I. A short position in a fixed rate bond and a long position in an FRN
II. An long position in an interest rate collar and long an FRN
III. A short position in a fixed rate bond and a short position in an FRN
IV. An interest rate swap where the investor pays the fixed rate
- A . None of the above
- B . I and IV
- C . I, II and IV
- D . II and III
Correct Answer: C
C
Explanation:
A short position in a fixed rate bond and a long position in an FRN has the effect of paying fixed and receiving floating. The floating received offsets the floating payment on the borrowing, leaving the borrower with just a fixed rate outflow. Therefore the combination identified in statement I can be used to achieve the objective of paying fixed. A collar is equivalent to a long position in an interest rate cap combined with a short position in an interest rate floor. This has the effect of setting a range within which the investor’s borrowing rate will vary. In the case where the cap and floor rates are the same, the combination of a collar and a long FRN effectively produces an outcome where the holder of such positions pays a fixed rate. Therefore, an interest rate collar can be used to convert the fixed payment to a floating rate payment. [Example: Assume current interest rate is 3%, and therefore the borrower has a liability of 3% on the FRN. Assume that the borrower now buys a collar at the strike rate of 4%. Now the borrower receives 0% (=Max(3% – 4%, 0)) on the cap part of the collar, and pays 1% on the floor part of the collar (=Max(4% – 3%, 0)). The net borrowing cost therefore is 3% paid on the FRN plus 1% paid on the collar, equal to 4%. Now if interest rates rise to say 6%, the borrower pays 6% on the FRN, and receives 2% from the collar (=Max(6% – 4%, 0) – Max(4% – 6%, 0)), creating a net cost of 6% – 2% = 4%.
A collar is often issued with an FRN to convert floating flows to fixed. Therefore combination II is an acceptable choice.
A short position in a fixed rate bond and a short position in an FRN produces a cash flow that does not produce a net fixed cash outflow when combined with the borrowing. Therefore statement III is not a valid combination.
An interest rate swap where the investor pays fixed and receives floating, when combined with a floating payment on an FRN leaves a net fixed payment, Therefore statement IV is a valid way to achieve the borrower’s objective.
C
Explanation:
A short position in a fixed rate bond and a long position in an FRN has the effect of paying fixed and receiving floating. The floating received offsets the floating payment on the borrowing, leaving the borrower with just a fixed rate outflow. Therefore the combination identified in statement I can be used to achieve the objective of paying fixed. A collar is equivalent to a long position in an interest rate cap combined with a short position in an interest rate floor. This has the effect of setting a range within which the investor’s borrowing rate will vary. In the case where the cap and floor rates are the same, the combination of a collar and a long FRN effectively produces an outcome where the holder of such positions pays a fixed rate. Therefore, an interest rate collar can be used to convert the fixed payment to a floating rate payment. [Example: Assume current interest rate is 3%, and therefore the borrower has a liability of 3% on the FRN. Assume that the borrower now buys a collar at the strike rate of 4%. Now the borrower receives 0% (=Max(3% – 4%, 0)) on the cap part of the collar, and pays 1% on the floor part of the collar (=Max(4% – 3%, 0)). The net borrowing cost therefore is 3% paid on the FRN plus 1% paid on the collar, equal to 4%. Now if interest rates rise to say 6%, the borrower pays 6% on the FRN, and receives 2% from the collar (=Max(6% – 4%, 0) – Max(4% – 6%, 0)), creating a net cost of 6% – 2% = 4%.
A collar is often issued with an FRN to convert floating flows to fixed. Therefore combination II is an acceptable choice.
A short position in a fixed rate bond and a short position in an FRN produces a cash flow that does not produce a net fixed cash outflow when combined with the borrowing. Therefore statement III is not a valid combination.
An interest rate swap where the investor pays fixed and receives floating, when combined with a floating payment on an FRN leaves a net fixed payment, Therefore statement IV is a valid way to achieve the borrower’s objective.
Question #74
Which of the following best describes a ‘when-issued’ market?
- A . where members of the syndicate bringing a bond issue to the market are obliged to not undercut the issue price till the first settlement date
- B . The when-issued market is one where dealers trade in a security after its price has been set but before the bonds are available for delivery
- C . The when-issued market is one where securities are traded on the OTC forward markets prior to their issue
- D . The when-issues market is one where the lead manager agreed to buy an entire bond issue at an agreed price, and having done so may sell them onwards to institutional or other investors
Correct Answer: C
C
Explanation:
Each of the choices describes various scenarios related to the issue of bonds. A when-issued market is a market in government securities where securities are traded as forward contracts prior to their issue. Choice ‘c’ is the correct answer.
Choice ‘d’ refers to a ‘bought deal’. Choice ‘b’ refers to the ‘grey market’, usually in corporate bonds. Choice ‘a’ refers to a fixed price re-offer mechanism.
C
Explanation:
Each of the choices describes various scenarios related to the issue of bonds. A when-issued market is a market in government securities where securities are traded as forward contracts prior to their issue. Choice ‘c’ is the correct answer.
Choice ‘d’ refers to a ‘bought deal’. Choice ‘b’ refers to the ‘grey market’, usually in corporate bonds. Choice ‘a’ refers to a fixed price re-offer mechanism.
Question #75
Which of the following statements is a correct description of the phrase present value of a basis point?
- A . It refers to the present value impact of 1 basis point move in an interest rate on a fixed income security
- B . It refers to the discounted present value of 1/100th of 1% of a future cash flow
- C . It is another name for duration
- D . It is the principal component representation of the duration of a bond
Correct Answer: A
A
Explanation:
This is a trick question, no great science to it. Remember that the ‘present value of a basis point’ refers to PV01, which is the same as BPV (basis point value) referred to in the PRMIA handbook. In other textbooks, the same term is also variously called ‘DV01’ (dollar value of a basis point). Remember these other terms too.
PV01, or the present value of a basis point, is the change in the value of a bond (or other fixed income security) from a 1 basis point change in the yield. PV01 is calculated as (Price * Modified Duration/10,000).
A
Explanation:
This is a trick question, no great science to it. Remember that the ‘present value of a basis point’ refers to PV01, which is the same as BPV (basis point value) referred to in the PRMIA handbook. In other textbooks, the same term is also variously called ‘DV01’ (dollar value of a basis point). Remember these other terms too.
PV01, or the present value of a basis point, is the change in the value of a bond (or other fixed income security) from a 1 basis point change in the yield. PV01 is calculated as (Price * Modified Duration/10,000).
Question #76
According to the dividend discount model, if d be the dividend per share in perpetuity of a company and g its expected growth rate, what would the share price of the company be. ‘r’ is the discount rate.
- A . https://riskprep.com/images/stories/questions/123.01.a.png
- B . https://riskprep.com/images/stories/questions/123.01.c.png
- C . https://riskprep.com/images/stories/questions/123.01.d.png
- D . https://riskprep.com/images/stories/questions/123.01.b.png
Correct Answer: A
A
Explanation:
According to the dividend discount model, the spot share prices represent the present value of all the future cash flows from the stock. If held till perpetuity, this becomes an annuity equal to the dividend, growing at its expected growth rate. Therefore Choice ‘a’ is the correct answer. Choice ‘c’ would represent the total market cap, and not the value per share that the question asks.
A
Explanation:
According to the dividend discount model, the spot share prices represent the present value of all the future cash flows from the stock. If held till perpetuity, this becomes an annuity equal to the dividend, growing at its expected growth rate. Therefore Choice ‘a’ is the correct answer. Choice ‘c’ would represent the total market cap, and not the value per share that the question asks.
Question #77
Which of the following statements are true?
I. The square-root-of-time rule for scaling volatility over time assumes returns on different
days are independent
II. If daily returns are positively correlated, realized volatility will be less than that calculated using the square-root-of time rule
III. If daily returns are negatively correlated, realized volatility will be less than that calculated using the square-root-of-time rule
IV. If stock prices are said to follow a random walk, it means daily returns are independent of each other and have an expected value of zero
- A . I, II and IV
- B . III and IV
- C . I and III
- D . All the statements are correct
Correct Answer: C
C
Explanation:
Statement I is correct. If daily returns are not independent, variances cannot simply be added up over the period, and the square root of time rule is not appropriate to use to scale volatility. Statement II is incorrect. Statement III is correct. If daily returns are positively correlated, it means that a high return on one day will likely cause a higher return the next day, and likewise for low or negative returns. Intuitively, it means that a ‘trend’ will be created and volatility will be higher than in a case where daily returns were not correlated. Therefore statement II is not correct. By the same logic, negative correlation between daily returns would mean a higher return on one day would likely be followed by lower returns the next day, ie a reversion to mean will result causing the volatility to be lower than the case when the returns are uncorrelated. (The correlation between the daily returns is called the ‘autocorrelation coefficient’.) Statement IV is false because while the random walk of prices does imply independence, it says nothing about the expected value of returns. It does not imply that the returns will have an expected value of zero (or any other value).Thus Choice ‘c’ is the correct answer and the rest are incorrect.
C
Explanation:
Statement I is correct. If daily returns are not independent, variances cannot simply be added up over the period, and the square root of time rule is not appropriate to use to scale volatility. Statement II is incorrect. Statement III is correct. If daily returns are positively correlated, it means that a high return on one day will likely cause a higher return the next day, and likewise for low or negative returns. Intuitively, it means that a ‘trend’ will be created and volatility will be higher than in a case where daily returns were not correlated. Therefore statement II is not correct. By the same logic, negative correlation between daily returns would mean a higher return on one day would likely be followed by lower returns the next day, ie a reversion to mean will result causing the volatility to be lower than the case when the returns are uncorrelated. (The correlation between the daily returns is called the ‘autocorrelation coefficient’.) Statement IV is false because while the random walk of prices does imply independence, it says nothing about the expected value of returns. It does not imply that the returns will have an expected value of zero (or any other value).Thus Choice ‘c’ is the correct answer and the rest are incorrect.
Question #78
An investor enters into a 4 year interest rate swap with a bank, agreeing to pay a fixed rate of 4% on a notional of $100m in return for receiving LIBOR.
What is the value of the swap to the investor two years hence, immediately after the net interest payments are exchanged? Assume the current zero coupon bond yields for 1, 2 and 3 years are 5%, 6% and 7% respectively. Also assume that the yield curve stays the same after two years (ie, at the end of year two, the rates for the following three years are 5%, 6%, and 7%
respectively).
- A . $2,749,326
- B . -$2,749,326
- C . $3,630,846
- D . – $3,630,846
Correct Answer: C
C
Explanation:
The swap can be valued by valuing the two individual components of the swap. The fixed rate bond equivalent in the swap is valued at =4/1.05 + 104/(1.06^2) = $96,369,154.
The FRN component will be valued at par as we are at a point where the rate has just been reset, ie $100m.
The investor is paying the fixed rate, and is therefore short the bond. He/she is receiving LIBOR, and is therefore long the FRN. The value of the swap to the investor therefore is +$100,000,000-$96,369,154 = $3,630,846
Detailed explanation:
An Interest Rate Swap exchanges fixed interest flows for floating rate flows. The floating rate leg is tied to some reference rate, such as LIBOR. The parties exchange net cash flows periodically. Conceptually, an interest rate swap is the combination of a fixed coupon bond and a floating rate note. The party receiving the fixed rate is long the fixed coupon bond and short the FRN, and the party receiving the floating rate is long the FRN and short the fixed coupon bond.
An interest rate swap can be valued as the difference between the two hypothetical bonds. FRNs sell for par at issue time as they pay whatever the current rate is, subject to periodic resets. Therefore immediately after a payment is made on a swap, the value of the FRN component is equal to its par value. The bond can be valued by discounting its cash flows. The difference between the two represents the value of the swap. When the swap is entered into, the fixed rate leg is set in such a way that the value of the hypothetical bond is equal to that of the FRN, and therefore the swap is valued at zero. The rate at which the fixed rate leg is set is called the swap rate. Over its life, market rates change and the value of the fixed coupon bond equivalent in our swap diverges from par (whereas the FRN stays at par – at least right after payments are exchanged and the new floating rate is set for the next period). Thus the swap acquires a non-zero value.
There are two ways to value a swap. If interest rates for the future are known, the bond and the FRN can be valued and their difference will be equal to the value of the swap. Sometimes, the current swap rates are known. In such a case, the swap can be valued by imagining entering into an opposite swap at the new swap rate, which will leave a residual fixed cash flow for the remaining life of the swap. This residual cash flow can be valued and that represents the value of the swap. For example, if a 4 year swap was entered into exchanging an annual fixed 5% payment on a notional of $100m for a floating payment
equal to LIBOR, and at the end of year 1 the swap rate is 6%, then the party paying fixed can choose to enter into a new swap to receive 6% and pay LIBOR. All cash flows between the old and the new swap will offset each other except a net receipt of 1% for the next 3 years. This cash flow can be valued using the current yield curve and represents the value of the swap.
C
Explanation:
The swap can be valued by valuing the two individual components of the swap. The fixed rate bond equivalent in the swap is valued at =4/1.05 + 104/(1.06^2) = $96,369,154.
The FRN component will be valued at par as we are at a point where the rate has just been reset, ie $100m.
The investor is paying the fixed rate, and is therefore short the bond. He/she is receiving LIBOR, and is therefore long the FRN. The value of the swap to the investor therefore is +$100,000,000-$96,369,154 = $3,630,846
Detailed explanation:
An Interest Rate Swap exchanges fixed interest flows for floating rate flows. The floating rate leg is tied to some reference rate, such as LIBOR. The parties exchange net cash flows periodically. Conceptually, an interest rate swap is the combination of a fixed coupon bond and a floating rate note. The party receiving the fixed rate is long the fixed coupon bond and short the FRN, and the party receiving the floating rate is long the FRN and short the fixed coupon bond.
An interest rate swap can be valued as the difference between the two hypothetical bonds. FRNs sell for par at issue time as they pay whatever the current rate is, subject to periodic resets. Therefore immediately after a payment is made on a swap, the value of the FRN component is equal to its par value. The bond can be valued by discounting its cash flows. The difference between the two represents the value of the swap. When the swap is entered into, the fixed rate leg is set in such a way that the value of the hypothetical bond is equal to that of the FRN, and therefore the swap is valued at zero. The rate at which the fixed rate leg is set is called the swap rate. Over its life, market rates change and the value of the fixed coupon bond equivalent in our swap diverges from par (whereas the FRN stays at par – at least right after payments are exchanged and the new floating rate is set for the next period). Thus the swap acquires a non-zero value.
There are two ways to value a swap. If interest rates for the future are known, the bond and the FRN can be valued and their difference will be equal to the value of the swap. Sometimes, the current swap rates are known. In such a case, the swap can be valued by imagining entering into an opposite swap at the new swap rate, which will leave a residual fixed cash flow for the remaining life of the swap. This residual cash flow can be valued and that represents the value of the swap. For example, if a 4 year swap was entered into exchanging an annual fixed 5% payment on a notional of $100m for a floating payment
equal to LIBOR, and at the end of year 1 the swap rate is 6%, then the party paying fixed can choose to enter into a new swap to receive 6% and pay LIBOR. All cash flows between the old and the new swap will offset each other except a net receipt of 1% for the next 3 years. This cash flow can be valued using the current yield curve and represents the value of the swap.
Question #79
The price of an interest rate cap is determined by:
I. The period to which the cap relates
II. Volatility of the underlying interest rate
III. The exercise or the strike rate
IV. The risk free rate
- A . I, II, III and IV
- B . I, II and III
- C . II, III and IV
- D . I, II and IV
Correct Answer: B
B
Explanation:
The price of an interest rate cap is affected by all of the listed choices except the risk free rate. The risk free rate does not come into play in the pricing of caps, and therefore Choice ‘b’ is the correct answer.
B
Explanation:
The price of an interest rate cap is affected by all of the listed choices except the risk free rate. The risk free rate does not come into play in the pricing of caps, and therefore Choice ‘b’ is the correct answer.
Question #80
Which of the following correctly describes a "reverse repo"?
- A . An asset swap that is offset by an identical but opposite swap
- B . Lending cash with securities as a collateral
- C . Borrowing cash while posting securities as a collateral
- D . A repo with an undefined maturity period
Correct Answer: B
B
Explanation:
A repo, or a repurchase agreement, is the lending of securities in return for cash, with an agreement to buy the securities back at a later date at the borrowed amount plus interest. It is a form of collateralized borrowing. A ‘reverse repo’ is exactly the opposite of a repo transaction, ie where cash is lent and securities borrowed. Therefore Choice ‘b’ is the correct answer. In any repo transaction, the counterparty will therefore always have a ‘reverse repo’ position.
A reverse repo is a useful transaction – not merely for the purpose of lending short term funds, but more importantly to enable short positions. For example, if an investor wishes to short a bond, he can borrow the bond on a ‘reverse repo’ and sell it. Of course, he will have to return the bond when the reverse repo matures, but hopefully by that time prices of the bond would have fallen to allow him to do so profitably. Short positions in physical bonds are nearly always facilitated by reverse repos.
B
Explanation:
A repo, or a repurchase agreement, is the lending of securities in return for cash, with an agreement to buy the securities back at a later date at the borrowed amount plus interest. It is a form of collateralized borrowing. A ‘reverse repo’ is exactly the opposite of a repo transaction, ie where cash is lent and securities borrowed. Therefore Choice ‘b’ is the correct answer. In any repo transaction, the counterparty will therefore always have a ‘reverse repo’ position.
A reverse repo is a useful transaction – not merely for the purpose of lending short term funds, but more importantly to enable short positions. For example, if an investor wishes to short a bond, he can borrow the bond on a ‘reverse repo’ and sell it. Of course, he will have to return the bond when the reverse repo matures, but hopefully by that time prices of the bond would have fallen to allow him to do so profitably. Short positions in physical bonds are nearly always facilitated by reverse repos.
Question #81
A bond with a 5% coupon trades at 95. An increase in interest rates by 10 bps causes its price to decline to $94.50. A decrease in interest rates by 10 bps causes its price to increase to $95.60. Estimate the modified duration of the bond.
- A . 5
- B . 5.79
- C . 5.5
- D . -5
Correct Answer: B
B
Explanation:
In this case, we can estimate the duration of the bond as follows: we know that a 10 bps increase in rates causes the price to move to $94.50, and a 10 bps decrease causes the price to increase to $95.60. Thus, over the range of the 20 bps, the average change in price per basis point is ($95.60 – $94.50)/20 bps = $1.10/20 = $0.055/basis point, or $0.055* 100 = $5.5 for 100 basis points (ie 1%). We know that modified duration is equivalent to the percentage change in the bond price as a result of a 1% change in interest rates. A 1% change in the interest rates leading to a $5.5 change in a bond priced at $95 equates to $5.5/$95 = 5.79%, in other words the modified duration is roughly equal to 5.79 years.
In fact if we know the price of a bond at any two different interest rates, we can make an estimate of modified duration. Modified duration is just the first derivative with respect to price, and given two prices and the associated yields, we can easily calculate modified duration to be the ratio of the change in price to the change in interest rates. In this question, we are given both an up move and a down move. Using this estimation, only one data point (ie, either the up price or the down price) in addition to the starting point ($95) would have been enough to come to a rough estimate of modified duration. You will notice that the modified duration would be slightly different if we were to use the high point and the starting point (ie $95.60 and $95), and the starting point and the lower point ($95 and $94.50). The difference is due to convexity. The decrease in price is lower than the increase in price – and this is due to the convexity of the bond.
B
Explanation:
In this case, we can estimate the duration of the bond as follows: we know that a 10 bps increase in rates causes the price to move to $94.50, and a 10 bps decrease causes the price to increase to $95.60. Thus, over the range of the 20 bps, the average change in price per basis point is ($95.60 – $94.50)/20 bps = $1.10/20 = $0.055/basis point, or $0.055* 100 = $5.5 for 100 basis points (ie 1%). We know that modified duration is equivalent to the percentage change in the bond price as a result of a 1% change in interest rates. A 1% change in the interest rates leading to a $5.5 change in a bond priced at $95 equates to $5.5/$95 = 5.79%, in other words the modified duration is roughly equal to 5.79 years.
In fact if we know the price of a bond at any two different interest rates, we can make an estimate of modified duration. Modified duration is just the first derivative with respect to price, and given two prices and the associated yields, we can easily calculate modified duration to be the ratio of the change in price to the change in interest rates. In this question, we are given both an up move and a down move. Using this estimation, only one data point (ie, either the up price or the down price) in addition to the starting point ($95) would have been enough to come to a rough estimate of modified duration. You will notice that the modified duration would be slightly different if we were to use the high point and the starting point (ie $95.60 and $95), and the starting point and the lower point ($95 and $94.50). The difference is due to convexity. The decrease in price is lower than the increase in price – and this is due to the convexity of the bond.
Question #82
What can the buyer of a 6 x 12 FRA expect to receive (or pay) if the contracted rate is 10% and the settlement rate is 12%? Assume contract notional is $100m.
- A . Pay $1,000,000
- B . Receive $1,000,000
- C . Pay $943,396
- D . Receive $943,396
Correct Answer: D
D
Explanation:
The buyer of the FRA gets to borrow $100m at 10% per annum for 6 months at the end of 6 months from the contract date. Thus, the interest due is $100m * 10% * 6/12 = $5m. However, at the end of the 6 months (when the notional borrowing period begins), the spot rate is 12%. The interest due on a borrowing at the spot rate would be $100m * 12% * 6/12
= $6m. Since the buyer gets to borrow cheaper than the going rate, he or she has made a gain of $1m on the FRA. However, this amount is not due immediately, it is due at the end of the 6 month borrowing period (ie, 12 months from the date the contract was entered into). The seller of the FRA can make the buyer whole by paying the buyer the present value of $1m due in 6 months time, which is $1m/(1 + 12%*6/12) = $1m/1.06 = $943,396. Thus, Choice ‘d’ is the correct answer. Remember that the FRA gets settled at the beginning of the notional borrowing period as all future cash flows, and the applicable
discount rates are known with certainty. The buyer and the seller do not need to wait for the entire period to get over first. The cash settlement allows the buyer to borrow at the market rate and still have the same net borrowing cost as he or she had initially contracted for in the FRA.
D
Explanation:
The buyer of the FRA gets to borrow $100m at 10% per annum for 6 months at the end of 6 months from the contract date. Thus, the interest due is $100m * 10% * 6/12 = $5m. However, at the end of the 6 months (when the notional borrowing period begins), the spot rate is 12%. The interest due on a borrowing at the spot rate would be $100m * 12% * 6/12
= $6m. Since the buyer gets to borrow cheaper than the going rate, he or she has made a gain of $1m on the FRA. However, this amount is not due immediately, it is due at the end of the 6 month borrowing period (ie, 12 months from the date the contract was entered into). The seller of the FRA can make the buyer whole by paying the buyer the present value of $1m due in 6 months time, which is $1m/(1 + 12%*6/12) = $1m/1.06 = $943,396. Thus, Choice ‘d’ is the correct answer. Remember that the FRA gets settled at the beginning of the notional borrowing period as all future cash flows, and the applicable
discount rates are known with certainty. The buyer and the seller do not need to wait for the entire period to get over first. The cash settlement allows the buyer to borrow at the market rate and still have the same net borrowing cost as he or she had initially contracted for in the FRA.
Question #83
[According to the PRMIA study guide for Exam 1, Simple Exotics and Convertible Bonds have been excluded from the syllabus. You may choose to ignore this question. It appears here solely because the Handbook continues to have these chapters.]
Which of the following best describes a shout option?
- A . an option in which the holder of the option has the right to reset the strike price to be at-the-money once during the life of the option
- B . an option which kicks in as a plain vanilla option if the underlying hits an agreed threshold
- C . an option in which the buyer of the option has the option to extend the expiry of the option upon the payment of an extra premium
- D . an option whose expiry is automatically extended if it finishes out of the money.
Correct Answer: A
A
Explanation:
Choice ‘c’ correctly describes a ‘holder extendible option’. Choice ‘d’ describes a ‘writer extendible option’. Choice ‘a’ describes a ‘shout option’. Choice ‘b’ describes a ‘knock in’ option.
A
Explanation:
Choice ‘c’ correctly describes a ‘holder extendible option’. Choice ‘d’ describes a ‘writer extendible option’. Choice ‘a’ describes a ‘shout option’. Choice ‘b’ describes a ‘knock in’ option.
Question #84
Which of the following statements is false:
- A . Forward contracts are settled at the end of the contract while futures gains and losses are settled daily
- B . Futures are OTC instruments with transparent pricing while forward contracts are not
- C . Forward contracts, unless collateralized, carry credit risks while the exchange practically eliminates the credit risk on a futures contract.
- D . Forward and futures prices differ due to differences in the timing of cash flows
Correct Answer: B
B
Explanation:
This question addresses the key differences between futures and forward contracts. Forward contracts are over the counter (OTC) instruments, while futures are exchange traded. Therefore Choice ‘b’ is not a true statement.
Futures contracts require an initial margin to be paid to the exchange, and gains and losses to be settled daily, while forward contracts generally settle only at the maturity of the contract. Therefore Choice ‘a’ is a true statement.
The exchange is the counterparty in a futures contract, and through its system of initial and variation margins guarantees the performance of the contract. Futures therefore have very little credit risk when compared to forwards. Therefore Choice ‘c’ is a true statement.
Because futures gains and losses give rise to daily cash flows, while the P&L on forward contracts is settled only at the end of the contract, the timing differences create small pricing differences between the two. Therefore Choice ‘d’ is a true statement.
B
Explanation:
This question addresses the key differences between futures and forward contracts. Forward contracts are over the counter (OTC) instruments, while futures are exchange traded. Therefore Choice ‘b’ is not a true statement.
Futures contracts require an initial margin to be paid to the exchange, and gains and losses to be settled daily, while forward contracts generally settle only at the maturity of the contract. Therefore Choice ‘a’ is a true statement.
The exchange is the counterparty in a futures contract, and through its system of initial and variation margins guarantees the performance of the contract. Futures therefore have very little credit risk when compared to forwards. Therefore Choice ‘c’ is a true statement.
Because futures gains and losses give rise to daily cash flows, while the P&L on forward contracts is settled only at the end of the contract, the timing differences create small pricing differences between the two. Therefore Choice ‘d’ is a true statement.
Question #85
What kind of a risk attitude does a utility function with downward sloping curvature indicate?
- A . risk mitigation
- B . risk averse
- C . risk seeking
- D . risk neutral
Correct Answer: B
B
Explanation:
A utility function is graphed with utility on the y-axis and the variable driving utility (generally wealth) along the x-axis.
A concave utility function, ie a function with a downward sloping curve, indicates risk aversion. A convex utility function indicates a risk seeking attitude and a straight line (ie no curvature) indicates a risk neutral attitude.
B
Explanation:
A utility function is graphed with utility on the y-axis and the variable driving utility (generally wealth) along the x-axis.
A concave utility function, ie a function with a downward sloping curve, indicates risk aversion. A convex utility function indicates a risk seeking attitude and a straight line (ie no curvature) indicates a risk neutral attitude.
Question #86
A normal yield curve is generally:
- A . Flat
- B . Humped
- C . Downward sloping
- D . Upward sloping
Correct Answer: D
D
Explanation:
A normal yield curve is generally upward sloping. Downward sloping, humped or flat yield curves are less common and indicate exceptional market conditions.
D
Explanation:
A normal yield curve is generally upward sloping. Downward sloping, humped or flat yield curves are less common and indicate exceptional market conditions.
Question #87
The quote for which of the following methods of physical delivery of a futures contract would be the cheapest?
- A . Free on board
- B . Free alongside ship
- C . In store
- D . Cost, insurance and freight
Correct Answer: C
C
Explanation:
‘In store’ delivery is for delivery in a standardized location, and the buyer is handed a ‘warrant’ that allows him to pick the goods up. This is the cheapest means of physical delivery. The other prices will be higher as they involve more costs for the seller who has to get the goods on board a ship, or to the docks, or insurance and freight as well. Choice ‘c’ is the correct answer.
C
Explanation:
‘In store’ delivery is for delivery in a standardized location, and the buyer is handed a ‘warrant’ that allows him to pick the goods up. This is the cheapest means of physical delivery. The other prices will be higher as they involve more costs for the seller who has to get the goods on board a ship, or to the docks, or insurance and freight as well. Choice ‘c’ is the correct answer.
Question #88
The greatest risk in energy derivatives trading comes from:
- A . interest rate risks
- B . risk of default by derivatives’ counterparties
- C . hedging risk
- D . price volatility
Correct Answer: D
D
Explanation:
Energy derivative markets are still not very liquid, and experience high price volatility. This high volatility is responsible for most of the risk in these markets. Choice ‘d’ is the correct answer.
D
Explanation:
Energy derivative markets are still not very liquid, and experience high price volatility. This high volatility is responsible for most of the risk in these markets. Choice ‘d’ is the correct answer.
Question #89
Which of the following statements is true:
I. The maximum value of the delta of a call option can be infinity
II. The value of theta for a deep out of the money call approaches zero
III. The vega for a put option is negative
IV. For a at the money cash-or-nothing digital option, gamma approaches zero
- A . I and IV
- B . III only
- C . II and III
- D . II only
Correct Answer: D
D
Explanation:
The maximum value for delta of a call option is 1 and not infinity. The value of theta for a deep out of the money call option does indeed approach zero as the value of the option is hardly affected by the passage of time. Vega measures the sensitivity of option prices to the volatility of the underlying, an increase in vega increases the price of the option regardless of whether it is a call option or a put option. (Vega is identical and positive for both calls and puts). Gamma changes very rapidly and reaches its maximum (& not zero) close to the strike price, including for a digital option. Therefore statement II is true and the rest are incorrect.
D
Explanation:
The maximum value for delta of a call option is 1 and not infinity. The value of theta for a deep out of the money call option does indeed approach zero as the value of the option is hardly affected by the passage of time. Vega measures the sensitivity of option prices to the volatility of the underlying, an increase in vega increases the price of the option regardless of whether it is a call option or a put option. (Vega is identical and positive for both calls and puts). Gamma changes very rapidly and reaches its maximum (& not zero) close to the strike price, including for a digital option. Therefore statement II is true and the rest are incorrect.
Question #90
A bank holding a basket of credit sensitive securities transfers these to a special purpose vehicle (SPV), which sells notes based on these securities to third party investors.
Which of the following terms best describes this arrangement?
- A . n-th to default swap
- B . A credit default swap purchase
- C . A synthetic CDO creation
- D . A collateralized debt obligation issuance
Correct Answer: D
D
Explanation:
A traditional collateralized debt obligation (CDO) involves the complete transfer of securities to an SPV, which then issues notes or securities to investors. Therefore Choice ‘d’ is the correct answer.
A synthetic CDO achieves the same result as a traditional CDO, but uses credit derivatives to synthetically create the same economic effect as a traditional CDO.
A credit default swap is a derivative instrument that pays in the event of the occurrence of agreed credit events. The arrangement described in the question is not a credit default swap purchase. n-th to default swap arrangements are similar to CDSs, but on a portfolio with the first ‘n’ losses being covered by the swap.
D
Explanation:
A traditional collateralized debt obligation (CDO) involves the complete transfer of securities to an SPV, which then issues notes or securities to investors. Therefore Choice ‘d’ is the correct answer.
A synthetic CDO achieves the same result as a traditional CDO, but uses credit derivatives to synthetically create the same economic effect as a traditional CDO.
A credit default swap is a derivative instrument that pays in the event of the occurrence of agreed credit events. The arrangement described in the question is not a credit default swap purchase. n-th to default swap arrangements are similar to CDSs, but on a portfolio with the first ‘n’ losses being covered by the swap.
Question #91
An investor expects stock prices to move either sharply up or down.
His preferred strategy should be to:
- A . buy a butterfly spread
- B . buy a condor
- C . buy a collar
- D . buy a straddle
Correct Answer: D
D
Explanation:
Straddles and strangles are strategies that would benefit from sharp movement in option prices, regardless of direction. These comprise a long call and a long put, which would benefit regardless of whether prices rise or fall. The only time they would lose money would be when prices stay constant.
A collar would gain when stock prices fall, and not when they rise. Since our investor does not have a view on the direction of the movement, this strategy will not work for him.
A butterfly spread or a condor would gain when prices stay range-bound, so that cannot be a useful strategy.
Therefore Choice ‘d’ is the correct answer.
D
Explanation:
Straddles and strangles are strategies that would benefit from sharp movement in option prices, regardless of direction. These comprise a long call and a long put, which would benefit regardless of whether prices rise or fall. The only time they would lose money would be when prices stay constant.
A collar would gain when stock prices fall, and not when they rise. Since our investor does not have a view on the direction of the movement, this strategy will not work for him.
A butterfly spread or a condor would gain when prices stay range-bound, so that cannot be a useful strategy.
Therefore Choice ‘d’ is the correct answer.
Question #92
For a forward contract on a commodity, an increase in carrying costs (all other factors remaining constant) has the effect of:
- A . increasing the forward price
- B . decreasing the forward price
- C . increasing the spot price
- D . decreasing the spot price
Correct Answer: A
A
Explanation:
The forward price for a commodity is nothing but the spot price plus carrying costs till the maturity date of the forward contract. Any increase in carrying costs therefore has the effect of increasing the forward price. Note that carrying costs include interest cost in respect of funding the position, costs of storage, less any convenience yield. Increase in the carrying costs will not affect the spot prices.
A
Explanation:
The forward price for a commodity is nothing but the spot price plus carrying costs till the maturity date of the forward contract. Any increase in carrying costs therefore has the effect of increasing the forward price. Note that carrying costs include interest cost in respect of funding the position, costs of storage, less any convenience yield. Increase in the carrying costs will not affect the spot prices.
Question #93
What would be the expected return on a stock with a beta of 1.2, when the risk free rate is 3% and the broad market index is expected to earn 8%?
- A . 7%
- B . 7.4%
- C . 9%
- D . 9.6%
Correct Answer: C
C
Explanation:
The stock has a beta of 1.2, therefore intuitively it can be expected to earn more than the broad market index. It will earn the risk free rate, ie 3%, and 1.2 times the equity risk premium of 5% (8% – 3%). The expected returns from the stock therefore are 3% + (8% – 3%)*1.2 = 9%
C
Explanation:
The stock has a beta of 1.2, therefore intuitively it can be expected to earn more than the broad market index. It will earn the risk free rate, ie 3%, and 1.2 times the equity risk premium of 5% (8% – 3%). The expected returns from the stock therefore are 3% + (8% – 3%)*1.2 = 9%
Question #94
Which of the following statements are true:
I. A credit default swap provides exposure to credit risk alone and none to credit spreads
II. A CDS contract provides exposure to default risk and credit spreads
III. A TRS can be used as a funding source by the party paying LIBOR or other floating rate
IV. A CLN is an unfunded security for getting exposure to credit risk
- A . I, III and IV
- B . II, III and IV
- C . II and IV
- D . II and III
Correct Answer: D
D
Explanation:
A CDS contract provides exposure to default risk and the credit spread for a particular credit. It does not provide an exposure to the risk of interest rates going up or down. It is an instrument that allows institutions to take a view on the price of credit risk alone. Therefore statement I is false and statement II is true.
A total return swap (TRS) exchanges the return from an asset for a fixed or floating exchange rate. It is in essence a financing arrangement where one party pays the other interest to earn a return on an asset that it does not wish to hold itself, perhaps for liquidity reasons. The financed asset is held by the party paying the asset’s returns, effectively creating a ‘collateral’. Therefore statement III is correct.
A credit linked note is a funded instrument where the sellers of the protection have put up the money upfront in the form of a subscription to a note in case the credit losses are realized. Therefore statement IV is not correct.
D
Explanation:
A CDS contract provides exposure to default risk and the credit spread for a particular credit. It does not provide an exposure to the risk of interest rates going up or down. It is an instrument that allows institutions to take a view on the price of credit risk alone. Therefore statement I is false and statement II is true.
A total return swap (TRS) exchanges the return from an asset for a fixed or floating exchange rate. It is in essence a financing arrangement where one party pays the other interest to earn a return on an asset that it does not wish to hold itself, perhaps for liquidity reasons. The financed asset is held by the party paying the asset’s returns, effectively creating a ‘collateral’. Therefore statement III is correct.
A credit linked note is a funded instrument where the sellers of the protection have put up the money upfront in the form of a subscription to a note in case the credit losses are realized. Therefore statement IV is not correct.
Question #95
An investor enters into a 4 year interest rate swap with a bank, agreeing to pay a fixed rate of 4% on a notional of $100m in return for receiving LIBOR.
What is the value of the swap to the investor two years hence, immediately after the net interest payments are exchanged? Assume the 2 year swap rate is 5%, and the yield curve is also flat at 5%
- A . $1,859,410
- B . $1,904,762
- C . -$1,859,410
- D . -$1,904,762
Correct Answer: A
A
Explanation:
The swap can be valued by using the new swap rate of 5%. The investor is paying fixed and receiving LIBOR, and can effectively get out of his position by entering into a swap to receive 5% and pay LIBOR. This will leave him/her with a net cash flow of 1% for two years, ie $1m for 2 years that can be discounted to the present using the rates provided, ie =(1/1.05 + 1/(1.05^2)) = $1,859,410.
Detailed explanation:
An Interest Rate Swap exchanges fixed interest flows for floating rate flows. The floating rate leg is tied to some reference rate, such as LIBOR. The parties exchange net cash flows periodically. Conceptually, an interest rate swap is the combination of a fixed coupon bond and a floating rate note. The party receiving the fixed rate is long the fixed coupon bond and short the FRN, and the party receiving the floating rate is long the FRN and short the fixed coupon bond.
An interest rate swap can be valued as the difference between the two hypothetical bonds. FRNs sell for par at issue time as they pay whatever the current rate is, subject to periodic resets. Therefore immediately after a payment is made on a swap, the value of the FRN component is equal to its par value. The bond can be valued by discounting its cash flows. The difference between the two represents the value of the swap. When the swap is entered into, the fixed rate leg is set in such a way that the value of the hypothetical bond is equal to that of the FRN, and the swap is valued at zero. The rate at which the fixed rate leg is set is called the swap rate. Over its life, market rates change and the value of the fixed coupon bond equivalent in our swap diverges from par (whereas the FRN stays at par – at least right after payments are exchanged and the new floating rate is set for the next period). Thus the swap acquires a non-zero value.
There are two ways to value a swap. If interest rates for the future are known, the bond and the FRN can be valued and their difference will be equal to the value of the swap. Sometimes, the current swap rates are known. In such a case, the swap can be valued by imagining entering into an opposite swap at the new swap rate, which will leave a residual fixed cash flow for the remaining life of the swap. This residual cash flow can be valued and that represents the value of the swap. For example, if a 4 year swap was entered into exchanging an annual fixed 5% payment on a notional of $100m for a floating payment equal to LIBOR, and at the end of year 1 the swap rate is 6%, then the party paying fixed can choose to enter into a new swap to receive 6% and pay LIBOR. All cash flows between the old and the new swap will offset each other except a net receipt of 1% for the next 3
years. This cash flow can be valued using the current yield curve and represents the value of the swap.
A
Explanation:
The swap can be valued by using the new swap rate of 5%. The investor is paying fixed and receiving LIBOR, and can effectively get out of his position by entering into a swap to receive 5% and pay LIBOR. This will leave him/her with a net cash flow of 1% for two years, ie $1m for 2 years that can be discounted to the present using the rates provided, ie =(1/1.05 + 1/(1.05^2)) = $1,859,410.
Detailed explanation:
An Interest Rate Swap exchanges fixed interest flows for floating rate flows. The floating rate leg is tied to some reference rate, such as LIBOR. The parties exchange net cash flows periodically. Conceptually, an interest rate swap is the combination of a fixed coupon bond and a floating rate note. The party receiving the fixed rate is long the fixed coupon bond and short the FRN, and the party receiving the floating rate is long the FRN and short the fixed coupon bond.
An interest rate swap can be valued as the difference between the two hypothetical bonds. FRNs sell for par at issue time as they pay whatever the current rate is, subject to periodic resets. Therefore immediately after a payment is made on a swap, the value of the FRN component is equal to its par value. The bond can be valued by discounting its cash flows. The difference between the two represents the value of the swap. When the swap is entered into, the fixed rate leg is set in such a way that the value of the hypothetical bond is equal to that of the FRN, and the swap is valued at zero. The rate at which the fixed rate leg is set is called the swap rate. Over its life, market rates change and the value of the fixed coupon bond equivalent in our swap diverges from par (whereas the FRN stays at par – at least right after payments are exchanged and the new floating rate is set for the next period). Thus the swap acquires a non-zero value.
There are two ways to value a swap. If interest rates for the future are known, the bond and the FRN can be valued and their difference will be equal to the value of the swap. Sometimes, the current swap rates are known. In such a case, the swap can be valued by imagining entering into an opposite swap at the new swap rate, which will leave a residual fixed cash flow for the remaining life of the swap. This residual cash flow can be valued and that represents the value of the swap. For example, if a 4 year swap was entered into exchanging an annual fixed 5% payment on a notional of $100m for a floating payment equal to LIBOR, and at the end of year 1 the swap rate is 6%, then the party paying fixed can choose to enter into a new swap to receive 6% and pay LIBOR. All cash flows between the old and the new swap will offset each other except a net receipt of 1% for the next 3
years. This cash flow can be valued using the current yield curve and represents the value of the swap.
Question #96
Which of the following expressions represents Jensen’s alpha, where is the expected return, is the standard deviation of returns, rm is the return of the market portfolio and rf is the risk free rate:
- A . https://www.riskprep.com/images/stories/questions/102.12.b.png
B)
https://www.riskprep.com/images/stories/questions/102.12.d.png
C)
https://www.riskprep.com/images/stories/questions/102.12.c.png
D)
https://www.riskprep.com/images/stories/questions/102.12.a.png - B . Option A
- C . Option B
- D . Option C
- E . Option D
Correct Answer: C
C
Explanation:
The Sharpe ratio is the ratio of the excess returns of a portfolio to its volatility. It provides an intuitive measure of a portfolio’s excess return over the risk free rate. The Sharpe ratio is calculated as [(Portfolio return – Risk free return)/Portfolio standard deviation].
The Treynor ratio is similar to the Sharpe ratio, but instead of using volatility in the denominator, it uses the portfolio’s beta. Therefore the Treynor Ratio is calculated as [(Portfolio return – Risk free return)/Portfolio’s beta]. Therefore Choice ‘a’ is the correct answer.
Jensen’s alpha is another risk adjusted performance measure. It considers only the ‘alpha’, or the return attributable to a portfolio manager’s skill. It is the difference between the return of the portfolio, and what the portfolio should theoretically have earned. Any portfolio can
be expected to earn the risk free rate (rf), plus the market risk premium (which is given by [Beta x (Market portfolio’s return – Risk free rate)]. Jensen’s alpha is therefore the actual return earned less the risk free rate and the beta return. Choice ‘c’ is the correct answer. Refer to the tutorial on risk adjusted performance measures for more details.
C
Explanation:
The Sharpe ratio is the ratio of the excess returns of a portfolio to its volatility. It provides an intuitive measure of a portfolio’s excess return over the risk free rate. The Sharpe ratio is calculated as [(Portfolio return – Risk free return)/Portfolio standard deviation].
The Treynor ratio is similar to the Sharpe ratio, but instead of using volatility in the denominator, it uses the portfolio’s beta. Therefore the Treynor Ratio is calculated as [(Portfolio return – Risk free return)/Portfolio’s beta]. Therefore Choice ‘a’ is the correct answer.
Jensen’s alpha is another risk adjusted performance measure. It considers only the ‘alpha’, or the return attributable to a portfolio manager’s skill. It is the difference between the return of the portfolio, and what the portfolio should theoretically have earned. Any portfolio can
be expected to earn the risk free rate (rf), plus the market risk premium (which is given by [Beta x (Market portfolio’s return – Risk free rate)]. Jensen’s alpha is therefore the actual return earned less the risk free rate and the beta return. Choice ‘c’ is the correct answer. Refer to the tutorial on risk adjusted performance measures for more details.
Question #97
When graphing the efficient frontier, the two axes are:
- A . Asset beta and standard deviation of the market portfolio
- B . Expected return and asset’s beta
- C . Portfolio return and market standard deviation
- D . Portfolio return and portfolio standard deviation
Correct Answer: D
D
Explanation:
The efficient frontier is plotted on a graph with portfolio return (mean) as the y-axis and portfolio volatility, or standard deviation, on the x-axis. Asset beta and standard deviation of the market portfolio have nothing to do with the determination of the efficient portfolio. Therefore Choice ‘d’ is the correct answer, and the rest of the choices are incorrect.
D
Explanation:
The efficient frontier is plotted on a graph with portfolio return (mean) as the y-axis and portfolio volatility, or standard deviation, on the x-axis. Asset beta and standard deviation of the market portfolio have nothing to do with the determination of the efficient portfolio. Therefore Choice ‘d’ is the correct answer, and the rest of the choices are incorrect.
Question #98
Backwardation can happen in markets where
- A . convenience yield is less than the total interest and carrying costs
- B . convenience yields are greater than the total interest, storage and other carrying costs
- C . convenience yields are positive
- D . convenience yields are zero
Correct Answer: B
B
Explanation:
Convenience yield is the benefit from having access to the commodity – and if the convenience yield is very high, for example in a market where manufacturers must never run out of a particular raw material, then these can switch the total cost of carry (which include interest and storage costs, less convenience yields) to being negative. This causes forward prices to become lower than spot prices, a phenomenon known as backwardation. Therefore Choice ‘b’ is the correct answer. If convenience yields are less than other carrying costs, then backwardation will not happen. The sign of convenience yields does not matter, what matters is their relative magnitude when compared to the other costs of carry.
To understand this in an intuitive way, consider that forward prices are nothing but spot prices, plus interest, plus storage costs, less convenience yields. If interest and storage costs are less than the convenience yield, the market will be backwarded.
B
Explanation:
Convenience yield is the benefit from having access to the commodity – and if the convenience yield is very high, for example in a market where manufacturers must never run out of a particular raw material, then these can switch the total cost of carry (which include interest and storage costs, less convenience yields) to being negative. This causes forward prices to become lower than spot prices, a phenomenon known as backwardation. Therefore Choice ‘b’ is the correct answer. If convenience yields are less than other carrying costs, then backwardation will not happen. The sign of convenience yields does not matter, what matters is their relative magnitude when compared to the other costs of carry.
To understand this in an intuitive way, consider that forward prices are nothing but spot prices, plus interest, plus storage costs, less convenience yields. If interest and storage costs are less than the convenience yield, the market will be backwarded.
Question #99
If the spot price for a commodity is lower than the forward price, the market is said to be in:
- A . contango
- B . backwardation
- C . a short squeeze
- D . disequilibrium
Correct Answer: A
A
Explanation:
When the forward prices are greater than the spot prices, the market is said to be in contango. When forward prices are lower than spot prices, the market is said to be backwarded. A short squeeze may contribute to backwardation. Choice ‘a’ is the correct answer.
A
Explanation:
When the forward prices are greater than the spot prices, the market is said to be in contango. When forward prices are lower than spot prices, the market is said to be backwarded. A short squeeze may contribute to backwardation. Choice ‘a’ is the correct answer.
Question #100
The cheapest to deliver bond for a treasury bond futures contract is the one with the :
- A . the lowest yield to maturity adjusted by the conversion factor
- B . the lowest coupon
- C . the lowest basis when comparing cash price to the futures spot price adjusted by the conversion factor
- D . the highest coupon
Correct Answer: C
C
Explanation:
Treasury bond futures do not specify which bond can be used to effect delivery, but allow the seller to pick from a number of available bonds. As a result, one of these eligible bonds emerges as being the ‘cheapest’ to deliver, and this CTD bond is determined by the basis between the cash price of the bond and the futures spot price as adjusted by the conversion factor for this specific bond. (ie, basis = Cash Price of the Bond – Futures Price
x Conversion Factor)
The bond with the lowest basis is generally the CTD – therefore Choice ‘c’ is the correct answer.
C
Explanation:
Treasury bond futures do not specify which bond can be used to effect delivery, but allow the seller to pick from a number of available bonds. As a result, one of these eligible bonds emerges as being the ‘cheapest’ to deliver, and this CTD bond is determined by the basis between the cash price of the bond and the futures spot price as adjusted by the conversion factor for this specific bond. (ie, basis = Cash Price of the Bond – Futures Price
x Conversion Factor)
The bond with the lowest basis is generally the CTD – therefore Choice ‘c’ is the correct answer.
Question #101
Credit risk in the case of a CDO (Collateralized Debt Obligation) is borne by:
- A . The sponsoring institution
- B . Investors
- C . The reference entity
- D . The Special Purpose Vehicle (SPV)
Correct Answer: B
B
Explanation:
Investors in CDOs bear credit risk. The SPV is merely a conduit that owns the underlying assets on which the sponsoring institution has bought protection. The investors have sold them this protection, and are on the hook for defaults or other credit events. The reference entity is relevant only to CDSs, not CDOs. Choice ‘b’ is the correct answer.
B
Explanation:
Investors in CDOs bear credit risk. The SPV is merely a conduit that owns the underlying assets on which the sponsoring institution has bought protection. The investors have sold them this protection, and are on the hook for defaults or other credit events. The reference entity is relevant only to CDSs, not CDOs. Choice ‘b’ is the correct answer.
Question #102
An investor believes that the market is likely to stay where it is.
Which of the following option strategies will help him profit should his view be proven correct (assume all strategies described below are long only)?
- A . Strangle
- B . Collar
- C . Butterfly spread
- D . Straddle
Correct Answer: C
C
Explanation:
Only the butterfly spread has a payoff profile that benefits when prices do not move much. The collar benefits during declining markets, the straddle and the strangle benefit from sharp movements in the markets. Therefore Choice ‘c’ is the correct answer.
C
Explanation:
Only the butterfly spread has a payoff profile that benefits when prices do not move much. The collar benefits during declining markets, the straddle and the strangle benefit from sharp movements in the markets. Therefore Choice ‘c’ is the correct answer.
Question #103
Caps, floors and collars are instruments designed to:
- A . Hedge against credit spreads changing
- B . Hedge gamma risk in option portfolios
- C . Hedge interest rate risks
- D . All of the above
Correct Answer: C
C
Explanation:
Interest rate caps are effectively call options on an underlying interest rate that protect the buyer of the cap against a rise in interest rates over the agreed exercise rate. As with options, the premium on the cap depends upon the volatility of the underlying rates as one of its variables. A floor is the exact opposite of a cap, ie it is effectively a put option on an underlying interest rate that protects the buyer of the floor against a fall in interest rates below the agreed exercise rate.
A cap protects a borrower against a rise in interest rates beyond a point, and a floor protects a lender against a fall in interest rates below a point.
A collar is a combination of a long cap and a short floor, the idea being that the premium due on the cap is offset partly by the premium earned on the short floor position. Therefore a collar is less expensive than a cap or a floor.
Caps, floors and collars provide a hedge against interest rate risks, but do not protect against changes in credit spreads unless the reference rate already includes the spread (eg, by reference to the corporate bond rate), and they certainly do not have anything to do with gamma risk. Therefore Choice ‘c’ is the correct answer.
C
Explanation:
Interest rate caps are effectively call options on an underlying interest rate that protect the buyer of the cap against a rise in interest rates over the agreed exercise rate. As with options, the premium on the cap depends upon the volatility of the underlying rates as one of its variables. A floor is the exact opposite of a cap, ie it is effectively a put option on an underlying interest rate that protects the buyer of the floor against a fall in interest rates below the agreed exercise rate.
A cap protects a borrower against a rise in interest rates beyond a point, and a floor protects a lender against a fall in interest rates below a point.
A collar is a combination of a long cap and a short floor, the idea being that the premium due on the cap is offset partly by the premium earned on the short floor position. Therefore a collar is less expensive than a cap or a floor.
Caps, floors and collars provide a hedge against interest rate risks, but do not protect against changes in credit spreads unless the reference rate already includes the spread (eg, by reference to the corporate bond rate), and they certainly do not have anything to do with gamma risk. Therefore Choice ‘c’ is the correct answer.
Question #104
Which of the following are true:
I. A interest rate cap is effectively a call option on an underlying interest rate
II. The premium on a cap is determined by the volatility of the underlying rate
III. A collar is more expensive than a cap or a floor
IV. A floor is effectively a put option on an underlying interest rate
- A . I, II, III and IV
- B . I, II and III
- C . III and IV
- D . I, II and IV
Correct Answer: D
D
Explanation:
Interest rate caps are effectively call options on an underlying interest rate that protect the buyer of the cap against a rise in interest rates over the agreed exercise rate. As with options, the premium on the cap depends upon the volatility of the underlying rates as one of its variables. A floor is the exact opposite of a cap, ie it is effectively a put option on an underlying interest rate that protects the buyer of the floor against a fall in interest rates below the agreed exercise rate.
A cap protects a borrower against a rise in interest rates beyond a point, and a floor protects a lender against a fall in interest rates below a point.
A collar is a combination of a long cap and a short floor, the idea being that the premium due on the cap is offset partly by the premium earned on the short floor position. Therefore a collar is less expensive than a cap or a floor.
D
Explanation:
Interest rate caps are effectively call options on an underlying interest rate that protect the buyer of the cap against a rise in interest rates over the agreed exercise rate. As with options, the premium on the cap depends upon the volatility of the underlying rates as one of its variables. A floor is the exact opposite of a cap, ie it is effectively a put option on an underlying interest rate that protects the buyer of the floor against a fall in interest rates below the agreed exercise rate.
A cap protects a borrower against a rise in interest rates beyond a point, and a floor protects a lender against a fall in interest rates below a point.
A collar is a combination of a long cap and a short floor, the idea being that the premium due on the cap is offset partly by the premium earned on the short floor position. Therefore a collar is less expensive than a cap or a floor.