Problem 1: Optimal Risky Portfolio with Risk-Free Asset and Risky Asset (10 points)

You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 29%. The T-bill rate is 5%. Your clients degree of risk aversion is A = 2.5, assuming a utility function U = E(r) A. a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. What are the expected value and standard deviation of the rate of return on your clients optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Problem 2: Portfolio with two risky assets (10 points)

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 9%. The characteristics of the risky funds are as follows:

	Expected Return	Standard Deviation
Stock Fund (S)	17%	38%
Bond Fund (B)	13%	18%

The correlation between the fund returns is 0.12. Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Proportions:

Stock Fund
Bond Fund

Expected Return:

Standard Deviation

Problem 3: (10 points)

Suppose that you have $1 million and the following two opportunities from which to construct a portfolio:

1. Risk-free asset earning 10% per year.
2. Risky asset with expected return of 34% per year and standard deviation of 40%.

If you construct a portfolio with a standard deviation of 35%, what is its expected rate of return of the complete portfolio? (Do not round your intermediate calculations. Round your answer to 1 decimal place.)

Problem 4: (10 points)

Two investment advisers are comparing performance. One averaged a 16% rate of return and the other a 13% rate of return. However, the beta of the first investor was 1.6, whereas that of the second investor was 1. a. Can you tell which investor was a better selector of individual stocks (aside from the issue of general movements in the market)? (Please circle)

Cannot determine

First Investor

Second Investor b. If the T-bill rate was 8% and the market return during the period was 10%, which investor would be considered the superior stock selector? (Please show all the calculations)

Cannot determine

First Investor

Second Investor

Problem 5: (10 points)

Suppose the rate of return on short-term government securities (perceived to be risk-free) is about 7%. Suppose also that the expected rate of return required by the market for a portfolio with a beta of 1 is 14%. According to the capital asset pricing model: a. What is the expected rate of return on the market portfolio? (Round your answer to 2 decimal places.)

b. What would be the expected rate of return on a stock with = 0? (Round your answer to 2 decimal places.)

c. Suppose you consider buying a share of stock at $51. The stock is expected to pay $2 dividends next year and you expect it to sell then for $53. The stock risk has been evaluated at = .5. Is the stock overpriced or underpriced? (Please circle)

Overpriced

Underpriced

Extra Credit (3 possible points/ 1 for each)

• Name the Secretary of the US Treasury (1 point)
• In one word, describe the shape the UST yield curve? (1 point)
• Which of the major stock indexes which we report on every class for the Top Stories, would you deduce has the highest beta? (1 point)