8007試験無料問題集（133題）「PRMIA Exam II: Mathematical Foundations of Risk Measurement

出題：1

Suppose 60% of capital is invested in asset 1, with volatility 40% and the rest is invested in asset 2, with volatility 30%. If the two asset returns have a correlation of -0.5, what is the volatility of the portfolio?

A. 26.33%

B. 36%

C. 20.78%

D. 36.33%

正解：C 解答を投票する

出題：2

If a time series has to be differenced twice in order to be transformed into a stationary series, the original series is said to be:

A. integrated of order 2

B. non-functional

C. non-linear

D. differential

正解：A 解答を投票する

出題：3

In a quadratic Taylor approximation, a function is approximated by:

A. a parabola

B. a constant

C. a straight line

D. a cubic polynomial

正解：A 解答を投票する

出題：4

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

出題：5

Suppose a discrete random variable can take on the values -1, 0 and 1 each with a probability of 1/3. Then the mean and variance of the variable is

A. mean is 0, variance is 1/3

B. mean is 0, variance is 2/3

C. mean is 0, variance is 1/2

D. mean is 1/3, variance is 1/3

正解：B 解答を投票する

出題：6

You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:
Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of - 2.89)?

A. The commodity returns are stationary

B. The commodity returns are integrated of order 1

C. None of the above

D. The commodity prices are stationary

正解：C 解答を投票する

出題：7

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=2, a=0

B. b=0.5, a=1.5

C. b=2, a=4

D. b=0.5, a=2.5

正解：A 解答を投票する

出題：8

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

A. 2

B. 1.75

C. 1.86

D. 1.95

正解：C 解答を投票する

出題：9

Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?

A. 0.377

B. 2.362

C. 1.638

D. 1.623

正解：C 解答を投票する

出題：10

Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?

A. the definite integral of the CDF from minus infinity to plus infinity is undefined.

B. the definite integral of the PDF from minus infinity to plus infinity is zero.

C. the CDF approaches 1 as its argument approaches infinity.

D. the PDF is non-negative.

正解：B 解答を投票する

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