Due: Oct 22, 10am in BrightSpace Dropbox (Assignment 1 Folder)

Problem 1 (5 Points) Find the price of a six-month (180-day) U.S. T-bill with a par value of $100,000 and a bank discount yield of 8.86 percent.

Problem 2 (15 Points)

Josh Next opened an account to short-sell 3,000 shares of Sun Spots Co.. The initial margin requirement is 50 percent. (The margin account pays no interest). A year later, the price of Sun Spots has risen from $45 to $50, and the stock has paid a dividend of $3 per share.

1. What is the remaining margin in the account (in dollars and percentage)?

2. If the maintenance margin requirement is 25 percent, will Josh Next receive a margin call?

3. What is the rate of return on the investment?

Problem 3 (7 Points) Consider the three stocks in the following table. Pt represents price at time t, and Qt represents shares outstanding at time t. Stock Omega splits two for one in the last period (at the end of the day 1, before open on day 2).

P0		Q0 P1 Q1 P2 Q2
Alpha Gamma Omega	88 48 102	100 200 200	94 46 110	100 200 200	96 45 55	100 200 400

1. Calculate the rate of return on a price-weighted index of the three stocks for the first period (t=0 to t=1).

2. What must happen to the divisor for the price-weighted index in year 2?

3. Calculate the price-weighted index for the second period (t=1 to t=2).

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Problem 4 (6 Points) Suppose that you sell short 300 shares of Starsnow, now selling at $80 per share.

1. What is your maximum possible loss?

2. What happens to the maximum loss if you simultaneously place a stop-buy order at $89?

Problem 5 (22 Points) Suppose the Xenon (XO) currently is selling at $90 per share. You buy 300 shares, using $20,000 of your own money, and borrow the remainder of the purchase price from your broker. The rate on the margin loan is 6 percent.

1. What is the percentage increase in the net wealth of your brokerage account if the price

   of XO immediately changes to (1)$98; (2)$90; (3)$82? What is the relationship between your percentage return and the percentage change in the price of XO (derive the formula in general terms, not only the numbers)?

2. If the minimum margin is 30 percent, how low can XOs price fall before you get a margin call?

3. How would your answer to (b) change if you had financed the initial purchase with only $15,000 of your own money?

4. What is the rate of return on your margined position (assuming again that you invest $15,000 of your own money) if XO is selling after one year at (1) $98; (2) $90; (3) $82? What is the relationship between your percentage return and the percentage change in the price of XO? Assume that XO pays no dividends.

5. Continue to assume that a year has passed. How low can XO price fall before you get a margin call?

Problem 6 (12 Points Total) Suppose that you sell short 300 shares of CYSCO (CY), currently selling for $90 per share, and give your broker $20,000 to establish your margin account.

1. If you earn no interest on the funds in your margin account, what will be your rate of

   return after one year if CY stock is selling at $98? Assume that CY pays no dividends.

2. If the minimum margin is 30 percent, how high can CYs price rise before you get a margin

   call?

3. Redo part (a) and (b), now assuming that CYs dividend (paid at year-end) is $3 per share.

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Problem 7 (25 Points) Suppose you find the following information for stock ORG:

• The minimum margin requirement =30%

• Current stock price = $50 per share

• No dividend is expected within a year

• The interest rate on a margin loan is 6% per annum

  You have an assessment of the ORG price probability distribution next year as below:

Bear Market Probability 0.2 ORG price 45

Normal Market

0.5 55

Bull Market

0.3 66

You bought 600 shares of the stock with $15,000 of your own funds.

1. a) What would be your rate of return on this investment if you sell the stock for $62.50 one year later?

2. b) What would be the stock price when a margin call occurs (assuming you do not pay any interest on the margin loan)?

3. c) What are the expected return and standard deviation of the stock, respectively (assuming the probability distribution given in table above)?

4. d) What are the expected return and standard deviation of your investment (assuming the probability distribution given in table above)?

Problem 8 (8 Points) You are considering the choice between investing $50,000 in a conventional 1-year bank CD offering an interest rate of 5% and a 1-year Inflation plus CD offering a 1.5% per year plus the rate of inflation. . Explain your answers clearly in words.

a). Which is the safer investment? b). Can you tell which offers the higher expected return? c). If you expect the rate of inflation to be 3% over the next year, which is the better investment? Why? d). If we observe a risk-free nominal interest rate of 5% per year and a risk-free real rate of 1.5% on inflation-indexed bonds, can we infer that the markets expected rate of inflation is 3.5% per year?