# Statistics 430 Homework

## Homework 1

• Section 1.3 (p 10): 1, 2, 8, 11
• Section 1.4 (p 17): 1, 4, 7, 10
• Section 1.5 (p 23): 7, 9
• Section 1.2 (p 5): 6 (hardest problem, so out of order)

## Homework 2

• Section 2.2 (p 31): 1, 3, 7
• Section 2.3 (p 35): 7, 9
• Section 2.4 (p 40): 5
• Section 2.5 (p 44): 1, 3, 8

## Homework 3

• Section 2.6 (p 51): 1, 3, 5, 8, 11

## Practice questions for first midterm

• p 5: 2,5
• p 12: 10
• p 17: 6, 9
• p 23: 5,10
• p 31: 4,8
• p 35: 6
• p 44: 5, 6, 9
• p 51: 6, 9

## Homework 4

• Section 3.2 (p 70): 1, 5, 6, 7, 9

## Homework 5

• Section 3.3 (p 80): 3, 4, 5, 7
• Section 4.2 (p 107): 3, 4, 6

## Homework 6

• Section 4.3 (p 116): 1, 9, 11, 6
• Section 4.4 (p 124): 1, 2, 4, 5, 8

## Homework 7

1. Suppose you are working with your grandmother on how she should allocate the money she has saved. She is considering two investments, Tbill's which have a annual return of .03 and a variance of zero, and the market which she believes will have an annual return of .07 and a variance of .22. Suppose she is interested in maximizing her long run growth rate, then how should she allocate her money between t-bills and stocks? (Note: we are modeling her feelings of risk adversion by the fact that she expects the returns to be lower than the empircal average is.)

2. What is the optimal combination of Red, Green and White? What will its long run growth rate be? (Feel free to treat white as having zero mean and zero variance.)

3. The return on the Market is .07 per year with a variance of .04 per year. The return on Ford, is .09 with a variance of .06. The covariance between Ford and the market is .03.
• What is the beta for Ford? (Recall from class, the beta is defined as follows: Z = Ford - Beta * Market, such that Z and the market have zero covariance. Note: this corrects a previous statement in this hint.)
• What fraction should be put in Ford and what fraction should be put in the market?
• What is the resulting variance corrected growth rate?

4. This question will have you figure out what is the optimal fraction of money to put into Amazon.com. Use the web to find the growth rate of Amazon over the past year. Also find its beta with the market, its covariance with the market, and its variance (Note, you only need to find two of these and then compute the third one). Use a return of .09 for the market with a variance of .222. Now figure out the optimal fraction of money to invest in Amazon in order to maximize the long run growth rate.

5. section 4.4 (page 125): 9

## Homework 8

• Section 4.5 (p 132): 1 (Hint: use thm 4.5.2 to compute E(Y) and E(Y2, you might also need the fact that 1 + 2 + 3 + ... + n = n(n+1)/2 and 1 + 4 + 9 + 16 + ... + x^2 = x(x+1)(2x+1)/6.)
• 3, 4, 8, 9

## A few practice questions from the book for second exam

• Section 3.2: 3, 8
• Section 3.3: 2, 8
• Section 4.2 (p 107): 1, 2 (2 is very hard)
• Section 4.3 (p 116): 2, 7
• Section 4.4: no new ones
• Section 4.5: no new ones

## Homework 9

• Section 7.2 (p 233): 1, 2, 3, 8, 9

## Homework 10

• Section 6.2 (p 189): 3, 5, 7, 9
• Section 6.3 (p 198): 2, 5, 6

## Homework 11 (not to be collected)

• Section 6.5 (p 216): 1, 2, 7
• Section 7.4 (p 254): 3, 7 (4 is harder)