Assignment 3: Computations Help Center

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Warning: The hard deadline has passed. You can attempt it, but you will not get credit for it. You are welcome to try it as a learning exercise.

Question 1

Consider the following joint distribution of X and Y:

X/Y 1 2 3
1 0.1 0.2 0
2 0.1 0 0.2
3 0 0.1 0.3

Find the marginal distributions of X and Y.
(10) Using the table above, compute E[X].

Question 2

(10) Using the table from question 1, compute E[Y].

Question 3

(10) Using the table from question 1, compute the variance of X.

Question 4

(10) Using the table from question 1, compute the variance of Y.

Question 5

(10) Using the table from question 1, compute the standard deviation of X.

Question 6

(10) Using the table from question 1, compute the standard deviation of Y.

Question 7

(10) Using the table from question 1, what is the covariance of X and Y?

Question 8

(10) Using the table from question 1, what is the correlation of X and Y?

Question 9

(10) X and Y are independent.

Question 10

Let r denote the continuously compounded monthly return on Microsoft stock and let W0 denote initial wealth to be invested over the month. Assume that r∼ iid N(0.04,(0.09)2) and that W0 = $100,000.
(10) Determine the 1% and 5% value-at-risk (VaR) over the year on the investment. Hint: to answer this question, you must determine the normal distribution that applies to the annual (12 month) continuously compounded return. This was done as an example in class.
    
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