March Sale Special - Limited Time 65% Discount Offer - Ends in 0d 00h 00m 00s - Coupon code: top65certs

PRMIA 8007 Dumps

Page: 1 / 5
Total 132 questions

Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Questions and Answers

Question 1

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

Options:

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

Question 2

When a number is written with a fraction as an exponent, such as , which of the following is the correct computation?

Options:

A.

Take the square-root of 75 and raise it to the 5th power

B.

Divide 75 by 2, then raise it to the 5th power

C.

Multiply 75 by 2.5

D.

Square 75, then take the fifth root of it

Question 3

The fundamental theorem of analysis establishes a relation between

Options:

A.

First and second derivative of a function

B.

The derivative of a function and the slope of its graph

C.

Integration and differentiation of functions

D.

The derivative of a function and the derivative of its inverse function

Question 4

Over four consecutive years fund X returns 1%, 5%, -3%, 8%. What is the average growth rate of fund X over this period?

Options:

A.

2.67%

B.

2.75%

C.

2.49%

D.

None of the above

Question 5

Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

Options:

A.

E(exp(X)) = 1.6487

B.

E(exp(X)) = 1

C.

E(exp(X)) = 2.7183

D.

E(exp(X)) = 0.6065

Question 6

In a portfolio there are 7 bonds: 2 AAA Corporate bonds, 2 AAA Agency bonds, 1 AA Corporate and 2 AA Agency bonds. By an unexplained characteristic the probability of any specific AAA bond outperforming the others is twice the probability of any specific AA bond outperforming the others. What is the probability that an AA bond or a Corporate bond outperforms all of the others?

Options:

A.

5/7

B.

8/11

C.

6/11

D.

None of these

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

A 2-step binomial tree is used to value an American put option with strike 105, given that the underlying price is currently 100. At each step the underlying price can move up by 10 or down by 10 and the risk-neutral probability of an up move is 0.6. There are no dividends paid on the underlying and the continuously compounded risk free interest rate over each time step is 1%. What is the value of the option in this model?

Options:

A.

7.12

B.

6.59

C.

7.44

D.

7.29

Question 9

You want to test the hypothesis that a population parameter β of a regression model is zero. Your alternative hypothesis is that β≠0. Denote by SD(β) the estimated standard deviation of β, and by MEAN(β) the estimated mean of β. Which test statistic is appropriate, and what is its distribution?

Options:

A.

test statistic = SD(β)/MEAN(β), normal distribution

B.

test statistic = MEAN(β)/SD(β), normal distribution

C.

test statistic = SD(β)/MEAN(β), t distribution

D.

test statistic = MEAN(β)/SD(β), t distribution

Question 10

A linear regression gives the following output:

Figures in square brackets are estimated standard errors of the coefficient estimates.

What is the value of the test statistic for the hypothesis that the coefficient of is less than 1?

Options:

A.

0.32

B.

0.64

C.

0.96

D.

1.92

Question 11

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

Options:

A.

N(0) = 0.5

B.

N'(0) ≥ 0

C.

N(x) → 0 as x → ∞

D.

N'(x) → 0 as x → ∞

Question 12

You invest $2m in a bank savings account with a constant interest rate of 5% p.a. What is the value of the investment in 2 years time if interest is compounded quarterly?

Options:

A.

$2,208,972

B.

$2,210,342

C.

$2.205,000

D.

None of them

Question 13

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?

Options:

A.

The lattice will not recombine

B.

The probability of an up move will not be constant

C.

There will always be a downward drift in the lattice

D.

None of the above

Question 14

A bond has modified duration 6 and convexity 30. Find the duration-convexity approximation to the percentage change in bond price when its yield increases by 5 basis points

Options:

A.

10 basis point rise

B.

24 basis fall

C.

24 basis point rise

D.

30 basis points fall.

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

Find the first-order Taylor approximation p(x) for the function: at the point .

Options:

A.

-x

B.

-x+1

C.

x-1

D.

x+1

Question 17

An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European call option has a strike of 85 and a maturity of 40 days. Its Black-Scholes price is 15.52. The options sensitivities are: delta = 0.98; gamma = 0.006 and vega = 1.55. What is the delta-gamma-vega approximation to the new option price when the underlying asset price changes to 105 and the volatility changes to 28%?

Options:

A.

17.33

B.

18.75

C.

19.23

D.

20.54

Question 18

Find the roots, if they exist in the real numbers, of the quadratic equation

Options:

A.

4 and -2

B.

-4 and 2

C.

1 and 0

D.

No real roots

Question 19

Which of the following is not a direct cause of autocorrelation or heteroskedasticity in the residuals of a regression model?

Options:

A.

A structural break in the dependent variable

B.

A high positive correlation between two explanatory variables

C.

The omission of a relevant explanatory variable

D.

Using an inappropriate functional form in the model

Page: 1 / 5
Total 132 questions