8007 exam

In a portfolio there are 7 bonds: 2 AAA Corporate bonds, 2 AAA Agency bonds, 1 AA Corporate and 2 AA Agency bonds. By an unexplained characteristic the probability of any specific AAA bond outperforming the others is twice the probability of any specific AA bond outperforming the others ....

For the function f(x) =3x-x3 which of the following is true?A . x = 0 is a minimumB . x = -3 is a maximumC . x = 2 is a maximumD . None of theseView AnswerAnswer: D

Every covariance matrix must be positive semi-definite. If it were not then:A . Some portfolios could have a negative varianceB . One or more of its eigenvalues would be negativeC . There would be no Cholesky decomposition matrixD . All the above statements are trueView AnswerAnswer: D

Suppose I trade an option and I wish to hedge that option for delta and vega. Another option is available to trade. To complete the hedge I wouldA . trade the underlying in such a way as to make the portfolio delta and vega neutral.B . trade the other option...

What is a Hessian?A . Correlation matrix of market indicesB . The vector of partial derivatives of a contingent claimC . A matrix of second derivatives of a functionD . The point at which a minimum of a multidimensional function is achievedView AnswerAnswer: C

A simple linear regression is based on 100 data points. The total sum of squares is 1.5 and the correlation between the dependent and explanatory variables is 0.5 . What is the explained sum of squares?A . 0.75B . 1.125C . 0.3333D . 0.375View AnswerAnswer: D

I have $5m to invest in two stocks: 75% of my capital is invested in stock 1 which has price 100 and the rest is invested in stock 2, which has price 125. If the price of stock 1 falls to 90 and the price of stock 2 rises to...

A 2-year bond has a yield of 5% and an annual coupon of 5% . What is the Modified Duration of the bond?A . 2B . 1.95C . 1.86D . 1.75View AnswerAnswer: C

Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?A . the PDF is non-negative.B . the definite integral of the CDF from minus infinity to plus infinity is undefined.C . the CDF approaches 1 as its argument...

Which of the provided answers solves this system of equations? 2y C 3x = 3y +x y2 + x2 = 68A . x = 1; y = square root of 67B . x = 2; y = 8C . x = 2; y = -8D . x = -2; y...