8007 PRMIA Exam II: Mathematical Foundations of Risk Measurement

Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

Last Update 3 hours ago Total Questions : 132

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Question # 21

What is the maximum value of the function F(x, y)=x2+y2 in the domain defined by inequalities x ≤ 1, y ≥ -2, y-x ≤ 3 ?

-25

Question # 22

Consider a binomial lattice where a security price S moves up by a factor u with probability p, or down by a factor d with probability 1 - p. If we set d > 1/u then which of the following will be TRUE?

The lattice will not recombine

The probability of an up move will not be constant

There will always be a downward drift in the lattice

None of the above

Question # 23

When the errors in a linear regression show signs of positive autocorrelation, which of the statements below is true?

The regression coefficient will be too high and the standard error of the regression coefficient will be understated

The regression coefficient will be too low and the standard error of the regression coefficient will be overstated

The regression coefficient will be unbiased, but the standard error of the regression coefficient will be understated

The regression coefficient will be unbiased, but the standard error of the regression coefficient will be overstated

Question # 24

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?

0.7367

0.3483

0.2646

None of these

Question # 25

For each of the following functions, indicate whether its graph is concave or convex:

Y = 7x2 + 3x + 9

Y = 6 ln(3x)

Y = exp(-4x)

concave, concave, concave

concave, convex, convex

convex, concave, concave

convex, convex, concave

Question # 26

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

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

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

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

A Type I occurs whenever data series are serially correlated

Question # 27

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

1.95

1.86

1.75

Question # 28

Maximum likelihood estimation is a method for:

Finding parameter estimates of a given density function

Estimating the solution of a partial differential equation

Solving a portfolio optimization problem

Estimating the implied volatility of a simple European option

Question # 29

What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?

1 / (x+y)

(∆x + ∆y) / (x+y)

-∆x/(x+y) - ∆y/(x+y)

ln(x+y) ∆x + ln(x+y) ∆y

Question # 30

In a 2-step binomial tree, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of d = 1/u. The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. Use the Cox, Ross, Rubinstein parameterization to find the risk neutral probability and hence find the value of a European put option with strike 102, given that the underlying price is currently 100.

5.19

5.66

6.31

4.18