# PRM Certification - Exam II: Mathematical Foundations of Risk Measurement v6.0 (8002)

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Total 137 questions

An asset price S is lognormally distributed if:

• A. the change in price (dS) is normally distributed
• B. 1/S is normally distributed
• C. ln(dS/S) is normally distributed
• D. ln(1+dS/S) is normally distributed

For the function f(x) =3x-x3 which of the following is true?

• A. x = 0 is a minimum
• B. x = -3 is a maximum
• C. x = 2 is a maximum
• D. None of these

Suppose we perform a principle component analysis of the correlation matrix of the returns of 13 yields along the yield curve. The largest eigenvalue of the correlation matrix is 9.8.
What percentage of return volatility is explained by the first component? (You may use the fact that the sum of the diagonal elements of a square matrix is always equal to the sum of its eigenvalues.)

• A. 64%
• B. 75%
• C. 98%
• D. Cannot be determined without estimates of the volatilities of the individual returns

An indefinite integral of a polynomial function is

• A. always positive
• B. always increasing
• C. always less than the function itself
• D. none of the above

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

• A. 2
• B. 1.95
• C. 1.86
• D. 1.75

You intend to invest \$100 000 for five years. Four different interest payment options are available. Choose the interest option that yields the highest return over the five year period.

• A. a lump-sum payment of \$22 500 on maturity (in five years)
• B. an annually compounded rate of 4.15%
• C. a quarterly-compounded rate of 4.1%
• D. a continuously-compounded rate of 4%

If the annual volatility of returns is 25% what is the variance of the quarterly returns?

• A. 0.1250
• B. 0.0156
• C. 0.0625
• D. None of the above

Let f(x) = c for x in [0,4] and 0 for other values of x.
What is the value of the constant c that makes f(x) a probability density function; and what if f(x) = cx for x in [0,4]?

• A. 1/4 and 1/7
• B. 1/7 and 1/9
• C. 1/4 and 1/6
• D. None of the above

Which of the following can be used to evaluate a regression model?
(i) Magnitude of R2
(ii) Magnitude of TSS (total sum of squares)
(iii) Tests for statistical significance
(iv) Sign and magnitude of each regression parameter

• A. (i) and (iv)
• B. (i), (ii), and (iii)
• C. (i), (iii), and (iv)
• D. (i), (ii), (iii), and (iv)

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 prices are stationary
• B. The commodity returns are stationary
• C. The commodity returns are integrated of order 1
• D. None of the above

What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,…?

• A. 1 048 574
• B. 1 048 595
• C. 2 097 170
• D. 2 097 172

Evaluate the derivative of exp(x2 + 2x + 1) at the point x = -1

• A. 0.5
• B. 0
• C. 1
• D. 2

Simple linear regression involves one dependent variable, one independent variable and one error variable. In contrast, multiple linear regression uses

• A. One dependent variable, many independent variables, one error variable
• B. Many dependent variables, one independent variable, one error variable
• C. One dependent variable, one independent variable, many error variables
• D. Many dependent variables, many independent variables, many error variables

Consider two securities X and Y with the following 5 annual returns:
X: +10%, +3%, -2%, +3%, +5%
Y: +7%, -2%, +3%, -5%, +10%
In this case the sample covariance between the two time series can be calculated as:

• A. 0.40729
• B. 0.00109
• C. 0.00087
• D. 0.32583