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Consider two securities X and Y with the following 5 annual returns:

X: +10%, +3%, -2%, +3%, +5%

Y: +7%, -2%, +3%, -5%, +10%

In this case the sample covariance between the two time series can be calculated as:

A.

0.40729

B.

0.00109

C.

0.00087

D.

0.32583

Which statement regarding the matrix below is true?

A.

It is not positive definite

B.

It is positive semi-definite

C.

It is positive definite

D.

It is negative definite

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?

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

Every covariance matrix must be positive semi-definite. If it were not then:

A.

Some portfolios could have a negative variance

B.

One or more of its eigenvalues would be negative

C.

There would be no Cholesky decomposition matrix

D.

All the above statements are true

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

A.

8

B.

-1

C.

17

D.

None of these

The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is

A.

(0, 2, 1)

B.

(0, 0, 0)

C.

(1, 1, 1)

D.

(0, 1, -1)

Simple linear regression involves one dependent variable, one independent variable and one error variable. In contrast, multiple linear regression uses…

A.

One dependent variable, many independent variables, one error variable

B.

Many dependent variables, one independent variable, one error variable

C.

One dependent variable, one independent variable, many error variables

D.

Many dependent variables, many independent variables, many error variables

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 ?

A.

29

B.

-25

C.

1

D.

17

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

A.

E(exp(X)) = 1.6487

B.

E(exp(X)) = 1

C.

E(exp(X)) = 2.7183

D.

E(exp(X)) = 0.6065

Which of the following is not a sequence?

A.

, , , … , , …

B.

, , , , …

C.

, , , , , , …

D.

30