Portfolio Return and Standard Deviation:

1. Security A has an expected return of 8%t and a standard deviation of 20%. Security B has an expected return of 10% and a standard deviation of 50%.

a) If you place half of your money in each stock, what is your expected return?

b) If you place 30% of your money in A and the remaining 70% in B, what is your expected return?

c) If the correlation between the returns of Securities A and B above is-0.5, what are the variance and the standard deviation of the returns of each of the two portfolios you found in parts a) and 1 b) above?

2.. Security C has an expected return of 6% and a standard deviation of 3% while security D has an expected return of 10% and a standard deviation of 7%. The correlation of returns between the two securities is -1.

a) If you place half of the money in each stock, then what is the expected return of this portfolio?

b) If you place 20% of the money in stock C and the remaining in stock D, then what is the expected return of the portfolio?

c) What is the portfolio standard deviation in b above?

SML and Required Rate of Return:

3. a) A security has a beta of 1.5 when the risk-free rate is 2.6 percent and the expected return on the market is 12 percent. Calculate the expected return on the security.

b) If the beta on the security in a) increases to 2.5, what is the new expected return? Why does the expected return increase as the beta increases?

Features Margin:

4. Zack Wheat has just sold four September 5,000-bushel corn futures contracts at $4.95 per bushel. The initial margin requirement is 4%.

a) How many dollars in initial margin must Zack put up?

b) If the September price of corn rises to $5.36, how much equity is in Zack's commodity account? Compute $ and % profit or loss.

c) If the September price of corn falls to $4.50, how much equity is in Zack's commodity account? Compute $ and % profit or loss.

Features Speculation:

5. Sullivan bought 10 number of December S&P 500 index futures contracts at 1975. If the index rises to 2000, what is Sleeper's dollar profit? The multiplier for the S&P 500 index futures contract is 250.

6. The margin requirements on the S&P 500 futures contract are 10%. If one sells the contract at 1,980, and each contract has a multiplier of 250, how much margin must be put up for each contract sold? If the futures price falls by 1.75% from the level of 1,980what will happen to margin account of the investor who holds one contract? What will be the investor's percentage return based on the amount put up as margin?

Features Hedging:

7. The S&P index is currently is at 1,990. You manage a $5 million indexed equity portfolio (Therefore, the beta of this portfolio is 1, same as the Market) The S&P 500 futures contract has a multiplier of 250.

a) If you are bearish on the stock market, how many contracts should you sell at 1,990 to fully eliminate your risk over the next 6 months?

b) How would your hedging strategy change if instead of holding an indexed portfolio, you hold a portfolio of socks with a beta of 1.5? How many contracts would now choose to sell? Would your hedged position be riskless?

Portfolio Performance Measures:

8. Given the following:

Portfolio Return Standard Deviation Beta

1 9% 5% 1.50

2 13% 7% 2.10

3 22% 16% 1.75

Market 12% 10% 1.00

Risk-Free Security 0.5%

Compute:

1. Sharpe Measure

2. Jensen Measure

3. Treynor Measure

And Rank the portfolios by each measure. Are the rankings consistent? Why or Why not?