Stat Review Homework

BM 410 HW #11

Free Response

1. BKM, chapter 3, #7 (page 85)

1. BKM, chapter 3, #8 (page 85)

1. Suppose that Intel currently is selling at $20 per share. You buy 1000 shares by using $15,000 of your own money (investment equity) and borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 8%. You are considering two possibilities:

Possibility 1: In one year, the price of Intel is 25.

Possibility 2: In one year, the price of Intel is 15.

a)For each case described above, what is the value of total assets, liabilities, and total investment equity in your portfolioin one year? What is the net return on equity?

b) For each case described above, find the net return on equity using portfolio weights. Show work. Your answers to part (a) and (b) should be the same.

c)Given that you expect Intel to return 10% with a standard deviation of 0.18, what is the expected return and standard deviation of your portfolio?

d)Given your answer in (c), what is your 5% Value-at-Risk?

e)What is your initial margin?

f)Assume the broker has established a maintenance margin of 30%. How far can the price fall immediately before you get a margin call?

g)Suppose the price falls to your answer in part (f). Describe the specifics of three transactions you can undertake satisfy the margin call. Assume that if you want to keep the margin position open, you must raise the margin to 50%.

1. Suppose that you sell short 1000 shares of Intel, currently selling for $20 per share, and deposit with your broker an additional $15,000 in your collateral account. Assume all cash in your collateral account earns an effective annual risk-free return of 4%. You are considering the following two possibilities:

Possibility 1: In one year, the price of Intel is 25.

Possibility 2: In one year, the price of Intel is 15.

a)For each case described above, what is the value of total assets, and total investment equity in your portfolio in one year? What is the percent change in equity (new equity divided by old equity minus one)?

b)For each case described above, find the percent change in equity using portfolio weights.

c)Given that you expect[1] Intel to return -10% with a standard deviation of 0.18, what is the expected return and standard deviation of your portfolio?

d)Given your answer in (c), what is your 5% Value-at-Risk?

e)What is your initial margin?

f)If the maintenance margin is 25%, how far can Intel's price increase immediately before you get a margin call? Ignore interest earned on collateral account.

g)Suppose the price increases to your answer in part (f). Describe the specifics of three transactions you can undertake to satisfy the margin call. Assume that if you want to keep the margin position open, you must raise the margin to 50%.

[1] Note that it would be very foolish to take a short position on stock if you expected the return to be positive.