Before implementing risk management techniques, Smitherspoon expresses confusion regarding some measures of risk management. "I know beta and standard deviation, but what is all this stuff about convexity, delta, gamma, and vega?

Mark Stober, William Robertson, and James McGuire are consultants for a regional pension consultancy. One of their clients, Richard Smitherspoon, chief investment officer of Quality Car Part Manufacturing, recently attended a conference on risk management topics for pension plans. Smitherspoon is a conservative manager who prefers to follow a long-term investment strategy with little portfolio turnover. Smitherspoon has substantial experience in managing a defined benefit plan but has little experience with risk management issues. Smitherspoon decides to discuss how Quality can begin implementing risk management techniques with Stober, Robertson, and McGuire. Quality’s risk exposure is evaluated on a quarterly basis.

Before implementing risk management techniques, Smitherspoon expresses confusion regarding some measures of risk management. "I know beta and standard deviation, but what is all this stuff about convexity, delta, gamma, and vega?" Stober informs Smitherspoon that delta is the first derivative of the call-stock price curve, and Robertson adds that gamma is the relationship between how bond prices change with changing time to maturity.

Smitherspoon is still curious about risk management techniques, and in particular the concept of VAR. He asks, "What does a daily 5% VAR of $5 million mean? I just get so confused with whether VAR is a measure of maximum or minimum loss. Just last month, the consultant from MinRisk, a competing consulting firm, told me it was ‘a measure of maximum loss, which in your case means we are 95% confident that the maximum 1-day loss is $5.0 million." McGuire states that his definition of VAR is that "VAR is a measure that combines probabilities over a certain time horizon with dollar amounts, which in your case means that one expects to lose a minimum $5 million five trading days out of every 100." Smitherspoon expresses bewilderment at the different methods for determining VAR. "Can’t you risk management types formulate a method that works like calculating a beta? It would be so easy if there were a method that allowed one to just use mean and standard deviation. I need a VAR that I can get my arms around."

The next week, Stober visits the headquarters of TopTech, a communications firm. Their CFO is Ralph Long, who prefers to manage the firm’s pension himself because he believes he can time the market and spot upcoming trends before analysts can. Long also believes that risk measurement for TopTech can be evaluated annually because of his close attention to the portfolio. Stober calculates TopTech’s 95% surplus at risk to be S500 million for an annual horizon. The expected return on TopTech’s asset base (currently at S2 billion) is 5%. The plan has a surplus of $100 million. Stober uses a 5% probability level to calculate the minimum amount by which the plan will be underfunded next year.

Smitherspoon asks Stober if it would be possible to calculate the VAR for each individual portfolio manager as well as the overall Quality fund. Determine which of Stober’s three responses is most incorrect.
A . "VAR is a universally accepted risk measure because it can be applied to practically any investment and is interpreted effectively the same way in each case; it is either the minimum or maximum loss at a given level of significance or confidence. For me to calculate the delta-normal VAR, you will need to provide me with each manager’s historical returns distribution and expected return, the time frame you wish to use, and the desired level of significance. I can then calculate VAR for each manager using historical standard deviations and expected returns."
B . "We can calculate VAR using the delta-normal method, which is also known as the mean variance approach, the historical method, or the Monte Carlo method. To calculate each manager’s 95% VAR, all we would have to do is use standard deviations and expected returns to calculate 90% confidence intervals."
C . "Because of the way it is calculated, individual mean-variance VARs can probably be calculated for each of our portfolio managers, regardless of their style or assets under management. The overall fund VAR is then the sum of the individual VARs. To calculate the fund VAR directly, we would have to measure the fund’s overall expected return and standard deviation. The problem with calculating it directly like this, however, is that to calculate the fund standard deviation we must consider the correlations of the managers’ returns."

View Answer

Answer: C

Explanation:

Response 1 is almost a definition of VAR. Response 2 might appear incorrect at first, because of the reference to the 90% confidence interval. Remember, however, that VAR considers only the lower tail of the distribution. To calculate the 95% VAR we use the Z-value corresponding to a 90% confidence interval (1.65), because that isolates the lower 5% of the distribution. Response 3 has an incorrect component. The last statement about calculating the overall VAR directly is correct; you must incorporate the correlations of the managers’ returns to calculate the overall fund standard deviation. That is the problem with using individual VARs to calculate a fund VAR; VAR is not additive. Adding individual VARs overstates the fund VAR, because adding them ignores the correlations of individual manager’s returns. (Study Session 14, LOS 40.d)