Finance HW questions

please show work

Fin 3312 Fall 2013

Your name: ______________________________________

Note:

1. Type your answer in the space provided following each question.

2. Save the file under your name and course number plus class time (eg, Jim Spence, file name will be spencefin33121040).

1. Suppose a stock is trading at $100 per share. You ask your broker to sell short 1,000 shares. Assume your broker has a 50% margin requirement on short sales and requires a 30% maintenance margin. Ignore commissions and interest.

a. Suppose the price goes down to $70. Are you making money or losing money? How much? What is your rate of return?

b. How far can the price go up before you get a margin call?

2. If a mutual fund has an initial NAV of $20 at the start of the month, makes income distribution of $0.15 and capital gain distribution of $0.05, and ends the month with NAV of $21.10. What is your monthly rate of return?

3. The Equity Fund sells Class A shares with a front-end load of 6% and Class B shares with 12-1 fees of 1.0% annually as well as redemption fees that start at 5% and fall by 1% for each full year the investor holds the portfolio (until the fifth year). Assume the rate of return on the fund portfolio is 10% annually. What will be the value of $10,000 investment in Class A and Class B shares if the shares are redeemed after:

a. 1 year?

b. 4 years?

c. 8 years?

4. Suppose you observe the investment performance of 200 fund managers and rank them by investment returns during the year. Of the managers in the top half of the sample, 40% are truly skilled, but the other 60% fall in the top half purely because of good luck. What fraction of these top-half managers would you expect to be top-half performers next year?

5. Answer the following:

a. Suppose the real interest rate is 3% per year, and the expected inflation rate is 8%. What is the nominal interest rate?

b. Suppose the expected inflation rate rises to 10%, but the real rate is unchanged. What happens to the nominal interest rate?

6. Suppose the risk premium on the market portfolio is estimated at 8% with a standard deviation of 22%. What is the risk premium on a portfolio invested 25% in GM with a beta of 1.15 and 75% in Ford with a beta of 1.25?

7. Answer the following:

a. Stock XYZ has an expected return of 12% and beta of 1.0. Stock ABC is expected to return 13% with a beta of 1.5. The market’s expected return is 11% and Treasury bills return is 5%. According to the CAPM, which stock is a better buy? What is the alpha of each stock?

b. The risk-free rate is 8% and the expected return on the market portfolio is 16%. A firm considers a project with an estimated beta of 1.3. What is the required rate of return on the project? If the IRR of the project is 19%, what is the project alpha?

8. If the weak form of the efficient market hypothesis is valid, must the strong form also hold? Conversely, does the strong form efficiency imply weak form efficiency? Briefly explain.

9. What would happen to market efficiency if all investors attempt to follow a passive strategy? Briefly explain.

10. Answer the following:

a. The stock of Biversy went from $60 to $66 last year. The firm also paid 80 cents in dividends. Compute the rate of return.

b. During the next year, the dividend paid was $1.60 per share and the stock closed at $62, down from $66 per share. Compute the annual gain or loss for the second year holding period.

11. Assume a portfolio has the probability of returning 6%, 9%, 10%, or 15% with the likelihood of 20 percent, 30 percent, 25 percent, and 25 percent respectively. What is the expected return of the portfolio?

12. An investment has the following range of outcomes and probabilities:

Outcomes (%) probabilities

3% 0.15

7% 0.70

16% 0.15

Calculate the expected value and the standard deviation.