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

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Total 132 questions

Let N(.) denote the cumulative distribution function of the standard normal probability distribution, and N' its derivative. Which of the following is false?

A.

N(0) = 0.5

B.

N'(0) ≥ 0

C.

N(x) → 0 as x → ∞

D.

N'(x) → 0 as x → ∞

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

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

On average, one trade fails every 10 days. What is the probability that no trade will fail tomorrow?

A.

0.095

B.

0.905

C.

0.95

D.

0.100

A biased coin has a probability of getting heads equal to 0.3. If the coin is tossed 4 times, what is the probability of getting heads at least two times?

A.

0.7367

B.

0.3483

C.

0.2646

D.

None of these

Consider the linear regression model for the returns of stock A and the returns of stock B. Stock A is 50% more volatile than stock B. Which of the following statements is TRUE?

A.

The stocks must be positively correlated ( )

B.

Beta must be positive ( )

C.

Beta must be greater in absolute value than the correlation of the stocks ( )

D.

Alpha must be positive ( )

A quadratic form is

A.

defined as a positive definite Hessian matrix.

B.

an algebraic expression in two variables, x and y,involving , and terms.

C.

a specific solution of the Black-Scholes pricing formula

D.

an algebraic expression in two variables, x and y, involving , , and terms.

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

The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:

A.

f has necessarily a minimum at this point

B.

f has necessarily a maximum at this point

C.

f has necessarily neither a minimum nor a maximum at this point

D.

f might have either a minimum or a maximum or neither of them at this point

I have a portfolio of two stocks. The weights are equal. The one volatility is 30% while the other is 40%. The minimum and maximum possible values of the volatility of my portfolio are:

A.

30% and 40%

B.

5% and 35%

C.

10% and 40%

D.

10% and 70%