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8007 Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Questions and Answers

Questions 4

Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24

Options:

A.

arithmetic sequence, common difference 2

B.

arithmetic sequence, common ratio 2

C.

geometric sequence, common ratio 2

D.

geometric sequence, common ratio 3

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Questions 5

What is the maximum value for f(x)= 8-(x+3)(x-3)?

Options:

A.

8

B.

-1

C.

17

D.

None of these

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Questions 6

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

Options:

A.

Normal distribution

B.

Student's t distribution

C.

F-distribution

D.

Binomial distribution

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Questions 7

A typical leptokurtotic distribution can be described as a distribution that is relative to a normal distribution

Options:

A.

peaked and thin at the center and with heavy (fat) tails

B.

peaked and thin at the center and with thin tails

C.

flat and thick at the center and with heavy (fat) tails

D.

flat and thick at the center and with thin tails

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Questions 8

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

Options:

A.

6.49

B.

5.03

C.

4.59

D.

4.54

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Questions 9

Variance reduction is:

Options:

A.

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

B.

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

C.

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

D.

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

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Questions 10

What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,…?

Options:

A.

1 048 574

B.

1 048 595

C.

2 097 170

D.

2 097 172

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Questions 11

Consider an investment fund with the following annual return rates over 8 years: +6%, -6%, +12%, -12%, +3%, -3%, +9%, -9% .

What can you say about the annual geometric and arithmetic mean returns of this investment fund?

Options:

A.

The arithmetic mean return is zero and the geometric mean return is negative

B.

The arithmetic mean return is negative and the geometric mean return is zero

C.

The arithmetic mean return is equal to the geometric mean return

D.

None of the above

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Questions 12

The Newton-Raphson method

Options:

A.

is based on finding a middle point between left and right end of the search interval

B.

is based on Taylor series and uses the first derivative

C.

can be used for continuous but not differentiable functions

D.

does provide an error bound along with every iteration

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Questions 13

The gradient of a smooth function is

Options:

A.

a vector that shows the direction of fastest change of a function

B.

matrix of second partial derivatives of a function

C.

infinite at a maximum point

D.

a matrix containing the function's second partial derivatives

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Questions 14

A quadratic form is

Options:

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.

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Questions 15

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 zero against the alternative that is less than zero?

Options:

A.

0.125

B.

2.5

C.

-1.25

D.

-2.5

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Questions 16

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:

Options:

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

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Questions 17

If a random variable X has a normal distribution with mean zero and variance 4, approximately what proportion of realizations of X should lie between -4 and +4?

Options:

A.

66.60%

B.

90%

C.

95%

D.

99%

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Questions 18

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

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Questions 19

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

Options:

A.

3.6 and 7.15

B.

3.4 and 3.84

C.

3.5 and 3.45

D.

None of these

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Exam Code: 8007
Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
Last Update: May 18, 2024
Questions: 132

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