# Estimating Risk and Return Assessment

1. Explain how differences in allocations between the risk-free security and the market portfolio can determine the level of market risk.

2. Based on the probability and percentage of return for the three economic states in the table below, compute the expected return.

Economic State Probability Percentage of Return

Fast Growth 0.10 60

Slow Growth 0.50 30

Recession 0.40 -23

3. If the risk-free rate is 7 percent and the risk premium is 4 percent, what is the required return?

4. Suppose that the average annual return on the Standard and Poor's 500 Index from 1969 to 2005 was 14.8 percent. The average annual T-bill yield during the same period was 5.6 percent. What was the market risk premium during these 10 years?

5. Conglomco has a beta of 0.32. If the market return is expected to be 12 percent and the risk-free rate is 5 percent, what is Hastings' required return? Use the capital asset pricing model (CAPM) to calculate Conglomco's required return.

6. Calculate the beta of a portfolio that includes the following stocks:

- Conglomco stock, which has a beta of 3.9 and comprises 35 percent of the portfolio.

- Supercorp stock, which has a beta of 1.7 and comprises 25 percent of the portfolio.

- Megaorg stock, which has a beta of 0.3 and comprises 40 percent of the portfolio.

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#### Solution Preview

1) A risk-free security has zero risk, i.e. Beta = 0. A market portfolio has market risk, i.e. Beta = 1. By observing the differences in the allocations between the risk-free security and market portfolio, the level of market risk can be determined. For example, if 25% of the market is invested in risk-free securities, while 75% of the portfolio is invested in the market, then the portfolio will have Beta = 75%.

2) Expected return = (probability of Fast Growth * % Return of Fast ...

#### Solution Summary

This solution answers various questions involving risk and return assessment in 372 words. Formulas and step-by-step computations are shown.

You are given the following long-run annual rates of return for alternative investment instruments:

? US Government T-Bills 3.5%

? Large-cap common stocks 12.1%

? Long-term corporate bonds 6.2%

? Long-term government bonds 5.6%

? Small-capitalization common stock 14.6%

The annual rate of inflation during the period was 2.9%. Compute the real rate of return on these investment alternatives.

Assignment #2: Risk Assessment, Portfolio Management

1. You are given the following long-run annual rates of return for alternative investment instruments:

? US Government T-Bills 3.5%

? Large-cap common stocks 12.1%

? Long-term corporate bonds 6.2%

? Long-term government bonds 5.6%

? Small-capitalization common stock 14.6%

The annual rate of inflation during the period was 2.9%. Compute the real rate of return on these investment alternatives.

2. The following are the monthly rates of return for TECO Electric and Gold Hill

Using an excel spreadsheet, compute the following:

a. Average monthly rate of return for each stock

b. Standard deviation of returns for each stock

c. Covariance between the rates of return

d. The correlation coefficient between the rates of return

3. Based on five years of monthly data, you derive the following information for the companies listed:

a. Compute the beta coefficient for each stock

b. Assuming a risk free rate of 5 percent and an expected return for the market portfolio of 12 percent, compute the expected (required) return for all the stocks.

c. Plot the following estimated returns for the next year on the SML and indicate which stocks are undervalued or overvalued.

? Johnson and Johnson-15%

? Exxon Mobil-10%

? Pfizer-13%

? Microsoft-20%

4. The following are the historic returns for the Columbia Sportswear Company (COLM) and the General Index:

Based on this information, and using an excel software, compute the following:

a. The correlation coefficient between COLM and the General Index.

b. The standard deviation for the company and the Index

c. The beta for the COLM.