8007 PRMIA Exam II: Mathematical Foundations of Risk Measurement

Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

Last Update 2 hours ago Total Questions : 132

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Question # 1

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

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

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

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.

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.

Question # 2

The bisection method can be used for solving f(x)=0 for a unique solution of x, when

The function f(x) is continuous and monotonic

The function f(x) is differentiable

The function f(x) is differentiable and we have an explicit expression for the derivative

The function f(x) is continuous

Question # 3

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

0.095

0.905

0.95

0.100

Question # 4

Variance reduction is:

A technique that is applied in regression models to improve the accuracy of the coefficient estimates

A numerical method for finding portfolio weights to minimize the variance of a portfolio that has a given expected return

A numerical method for finding the variance of the underlying that is implicit in a market price of an option

A method for reducing the number of simulations required in a Monte Carlo simulation

Question # 5

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

x = 0 is a minimum

x = -3 is a maximum

x = 2 is a maximum

None of these

Question # 6

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?

0.75

1.125

0.3333

0.375

Question # 7

In a multiple linear regression, the significance of R2 can be tested using which distribution?

Normal distribution

Student ' s t distribution

F-distribution

Binomial distribution

Question # 8

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

(i) and (iv)

(i), (ii), and (iii)

(i), (iii), and (iv)

(i), (ii), (iii), and (iv)

Question # 9

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?

36%

36.33%

26.33%

20.78%

Question # 10

Assume that 40% of all financial organizations investigated by authorities turn out to be fraudulent.

What is the probability of randomly investigating 2 different organizations and finding that neither is fraudulent; and what is the probability of finding exactly one being fraudulent?

2/5 and 1/2

2/5 and 3/5

1/3 and 8/17

9/25 and 12/25