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  4. 8002 - PRM Certification - Exam II: Mathematical Foundations of Risk Measurement

PRMIA 8002 PRM Certification - Exam II: Mathematical Foundations of Risk Measurement Exam Practice Test

Demo: 19 questions
Total 132 questions
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PRM Certification - Exam II: Mathematical Foundations of Risk Measurement Questions and Answers

Question 1

I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 100%. The volatility of my portfolio is

Options:

A.

4%

B.

14.4%

C.

20%

D.

24%

Question 2

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

Options:

A.

0.1250

B.

0.0156

C.

0.0625

D.

None of the above

Question 3

You are investigating the relationship between weather and stock market performance. To do this, you pick 100 stock market locations all over the world. For each location, you collect yesterday's mean temperature and humidity and yesterday's local index return. Performing a regression analysis on this data is an example of…

Options:

A.

Simple time-series regression

B.

Multiple time-series regression

C.

Simple cross-section regression

D.

Multiple cross-section regression

Question 4

What can be said about observations of random variables that are i.i.d. a normally distributed?

Options:

A.

The estimated mean divided by the estimated variance has a t-distribution

B.

The estimated mean divided by the estimated variance has a Chi2-distribution

C.

The estimated mean divided by the estimated standard deviation has a t-distribution

D.

The estimated mean divided by the estimated standard deviation has a Chi2-distribution

Question 5

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)?

Options:

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

Question 6

Exploring a regression model for values of the independent variable that have not been observed is most accurately described as…

Options:

A.

Estimation

B.

Regression

C.

Hypothesis testing

D.

Prediction

Question 7

Your stockbroker randomly recommends stocks to his clients from a tip sheet he is given each day. Today, his tip sheet has 3 common stocks and 5 preferred stocks from Asian companies and 3 common stocks and 5 preferred stocks from European companies. What is the probability that he will recommend a common stock AND/OR a European stock to you when you call and ask for one stock to buy today?

Options:

A.

11/16

B.

7/8

C.

9/16

D.

None of these

Question 8

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.)

Options:

A.

64%

B.

75%

C.

98%

D.

Cannot be determined without estimates of the volatilities of the individual returns

Question 9

Maximum likelihood estimation is a method for:

Options:

A.

Finding parameter estimates of a given density function

B.

Estimating the solution of a partial differential equation

C.

Solving a portfolio optimization problem

D.

Estimating the implied volatility of a simple European option

Question 10

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

Options:

A.

Its eigenvalues are all positive

B.

One of its eigenvalues equals 0

C.

If a is its eigenvalue, then -a is also its eigenvalue

D.

If a is its eigenvalue, then is also its eigenvalue

Question 11

The natural logarithm of x is:

Options:

A.

the inverse function of exp(x)

B.

log(e)

C.

always greater than x, for x>0

D.

46

Question 12

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?

Options:

A.

0.75

B.

1.125

C.

0.3333

D.

0.375

Question 13

Every covariance matrix must be positive semi-definite. If it were not then:

Options:

A.

Some portfolios could have a negative variance

B.

One or more of its eigenvalues would be negative

C.

There would be no Cholesky decomposition matrix

D.

All the above statements are true

Question 14

What is a Hessian?

Options:

A.

Correlation matrix of market indices

B.

The vector of partial derivatives of a contingent claim

C.

A matrix of second derivatives of a function

D.

The point at which a minimum of a multidimensional function is achieved

Question 15

Let X be a random variable normally distributed with zero mean and let . Then the correlation between X and Y is:

Options:

A.

negative

B.

zero

C.

not defined

D.

positive

Question 16

Which of the following is consistent with the definition of a Type I error?

Options:

A.

The probability of a Type I error is 100% minus the significance level

B.

A Type I error would have occurred if the performance of a stock was positively correlated with the performance of a hedge fund, but in a linear regression, the hypothesis of positive correlation was rejected

C.

A Type I error would have occurred if the performance of a stock was positively correlated with the performance of a hedge fund, but in a linear regression, the hypothesis of no correlation was rejected

D.

A Type I occurs whenever data series are serially correlated

Question 17

Let A be a square matrix and denote its determinant by x. Then the determinant of A transposed is:

Options:

A.

x -1

B.

x

C.

ln(x)

D.

-x

Question 18

Every covariance matrix must be positive semi-definite. If it were not then:

Options:

A.

Some portfolios could have a negative variance

B.

It could not be used to simulate correlated asset paths

C.

The associated correlation matrix would not be positive semi-definite

D.

All the above statements are true

Question 19

Which of the following statements is true?

Options:

A.

Discrete and continuous compounding produce the same results if the discount rate is positive.

B.

Continuous compounding is the better method because it results in higher present values compared to discrete compounding.

C.

Continuous compounding can be thought as making the compounding period infinitesimally small.

D.

The constant plays an important role in the mathematical description of continuous compounding.

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