8007無料問題集「PRMIA Exam II: Mathematical Foundations of Risk Measurement

質問 1

Stress testing portfolios requires changing the asset volatilities and correlations to extreme values. Which of the following would lead to a non positive definite covariance matrix?

（A）Changing all the correlations to be zero

（B）Changing the volatilities to be greater than 100%

（C）All of the above

（D）Changing all the correlations to be unity

正解：D 解答を投票する

質問 2

A 2-year bond has a yield of 5% and an annual coupon of 5%. What is the Modified Duration of the bond?

（A）1.75

（B）1.86

（C）2

（D）1.95

正解：B 解答を投票する

質問 3

Let N(.) denote the cumulative distribution function and suppose that X and Y are standard normally distributed and uncorrelated. Using the fact that N(1.96)=0.975, the probability that X 0 and Y 1.96 is approximately

（A）0.25%

（B）0.495%

（C）0.488%

（D）0.49%

正解：C 解答を投票する

質問 4

In a 2-step binomial tree, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of d = 1/u. The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. Use the Cox, Ross, Rubinstein parameterization to find the risk neutral probability and hence find the value of a European put option with strike 102, given that the underlying price is currently 100.

（A）5.19

（B）5.66

（C）4.18

（D）6.31

正解：D 解答を投票する

質問 5

A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates.
Which of the following is an approximate 95% confidence interval for the true value of the coefficient of ?

（A）[1, 2]

（B）[0, 1.5]

（C）None of the above

（D）[0, 3]

正解：D 解答を投票する

質問 6

You are to perform a simple linear regression using the dependent variable Y and the independent variable X (Y = a + bX). Suppose that cov(X,Y)=10, var(X)= 5, and that the mean of X is 1 and the mean of Y is 2. What are the values for the regression parameters a and b?

（A）b=0.5, a=2.5

（B）b=2, a=4

（C）b=2, a=0

（D）b=0.5, a=1.5

正解：C 解答を投票する

質問 7

Which of the following statements is true for symmetric positive definite matrices?

（A）Its eigenvalues are all positive

（B）If a is its eigenvalue, then is also its eigenvalue

（C）One of its eigenvalues equals 0

（D）If a is its eigenvalue, then -a is also its eigenvalue

正解：A 解答を投票する

質問 8

An indefinite integral of a polynomial function is

（A）always increasing

（B）none of the above

（C）always positive

（D）always less than the function itself

正解：B 解答を投票する

質問 9

Which statement regarding the matrix below is true?

（A）It is positive definite

（B）It is positive semi-definite

（C）It is negative definite

（D）It is not positive definite

正解：D 解答を投票する

質問 10

What is the maximum value of the function F(x, y)=x2+y2 in the domain defined by inequalities x 1, y -2, y-x 3 ?

（A）17

（B）1

（C）29

（D）-25

正解：C 解答を投票する

8007 無料問題集「PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition」

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