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Question 1

Let

E[X]=2,E[Y]=1,Var[X]=3,Var[Y]=2.5 $E[X] = 2, E[Y] = 1, Var[X] = 3, Var[Y] = 2.5$ and

Cov(X,Y)=.9 $Cov(X,Y) = .9$

(10) What is

E[.4X+.6Y] $E[.4X + .6Y]$ ?

2.1

1.4

1.5

Question 2

(10) What is

Var[.4X+.6Y] $Var[.4X + .6Y]$ ?

1.5

1.812

2.7

1.38

Question 3

(10) Suppose

X $X$ and

Y $Y$ are returns on two assets, and

w $w$ is your portfolio weight in asset

X $X$ with

(1−w) $(1-w)$ being the portfolio weight in asset

Y $Y$ . What value of

w $w$ minimizes the variance of your portfolio?

.605

.384

.432

.551

Question 4

(10) What is the variance of the portfolio with the weights you derived in the previous question?

2.046

1.808

3.366

1.214

Question 5

(10) What is the expected value of the portfolio with the weights you derived in the previous question?

1.567

1.432

1.622

1.4

Question 6

For the following questions, consider the AR(1) model:

Y t = 10 + .6 Y t - 1 + ϵ t ϵ t \sim N (0, 22)

$Y_t = 10 + .6Y_{t-1} +\epsilon_t \\ \epsilon_t \sim N(0, 2^2)$

(10) The process is covariance stationary.

False

True

Question 7

(10) What is the mean of this process?

Question 8

(10) What is the variance of the process?

6.25

8.5

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Introduction to Computational Finance and Financial Econometrics

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Introduction to Computational Finance and Financial Econometrics

Introduction to Computational Finance and Financial Econometricsby Eric Zivot

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Introduction to Computational Finance and Financial Econometrics
by Eric Zivot