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

a lump-sum payment of $22 500 on maturity (in five years)

an annually compounded rate of 4.15%

a quarterly-compounded rate of 4.1%

a continuously-compounded rate of 4%

One dependent variable, many independent variables, one error variable

Many dependent variables, one independent variable, one error variable

One dependent variable, one independent variable, many error variables

Many dependent variables, many independent variables, many error variables

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

matrix of second partial derivatives of a function

infinite at a maximum point

a matrix containing the function's second partial derivatives

Discrete and continuous compounding produce the same results if the discount rate is positive.

Continuous compounding is the better method because it results in higher present values compared to discrete compounding.

Continuous compounding can be thought as making the compounding period infinitesimally small.

The constant plays an important role in the mathematical description of continuous compounding.

$2,208,972

$2,210,342

$2.205,000

None of them

arithmetic sequence, common difference 2

arithmetic sequence, common ratio 2

geometric sequence, common ratio 2

geometric sequence, common ratio 3

the PDF is non-negative.

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

the CDF approaches 1 as its argument approaches infinity.

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

f has necessarily a minimum at this point

f has necessarily a maximum at this point

f has necessarily neither a minimum nor a maximum at this point

f might have either a minimum or a maximum or neither of them at this point

The distributions have the same kurtosis.

The normal distribution has higher kurtosis than the t distribution.

The normal distribution has lower kurtosis than the t distribution.

Which has the higher kurtosis depends on the degrees of freedom of the t distribution.

10

100

25

5

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

0.095

0.905

0.95

0.100

2

1.95

1.86

1.75

6.49

5.03

4.59

4.54

All three statements are correct

Statements 1 and 2 are correct

Statements 1 and 3 are correct

Statements 2 and 3 are correct

0.75

1.125

0.3333

0.375