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

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Total 132 questions

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

A.

the PDF is non-negative.

B.

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

C.

the CDF approaches 1 as its argument approaches infinity.

D.

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

What is the indefinite integral of the function f(x) = ln(x), where ln(x) denotes the natural logarithmic function?

A.

x ln(x) - x

B.

ln(x) - x

C.

1/x

D.

exp(x)

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 2/3

B.

mean is 0, variance is 1/3

C.

mean is 0, variance is 1/2

D.

mean is 1/3, variance is 1/3

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?

A.

0.75

B.

1.125

C.

0.3333

D.

0.375

Suppose I trade an option and I wish to hedge that option for delta and vega. Another option is available to trade. To complete the hedge I would

A.

trade the underlying in such a way as to make the portfolio delta and vega neutral.

B.

trade the other option in such a way as to make the portfolio delta and vega neutral.

C.

trade the other option in such a way as to make the portfolio vega neutral, and then trade the underlying in such a way as to make the portfolio delta neutral.

D.

trade the underlying in such a way as to make the portfolio delta neutral, and then trade the other option in such a way as to make the portfolio vega neutral.

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

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

Kurtosis(X) is defined as the fourth centred moment of X, divided by the square of the variance of X. Assuming X is a normally distributed variable, what is Kurtosis(X)?

A.

0

B.

3

C.

2

D.

1

Consider the following distribution data for a random variable X: What is the mean and variance of X?

A.

3.6 and 7.15

B.

3.4 and 3.84

C.

3.5 and 3.45

D.

None of these

Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by

A.

F(x)G(x)

B.

F(x)g(x) + f(x)G(x)

C.

F(x)g(x) - ∫F(x)g'(x)dx

D.

f(x)G(x) - ∫F(x)g'(x)dx

An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European put option has a strike of 105 and a maturity of 90 days. Its Black-Scholes price is 7.11. The options sensitivities are: delta = -0.59; gamma = 0.03; vega = 19.29. Find the delta-gamma approximation to the new option price when the underlying asset price changes to 105

A.

6.49

B.

5.03

C.

4.59

D.

4.54