# Stocks : Required Rate of Return and Expected Return

A stock has a beta of 1.5, the market risk premium is 9%, and the risk-free rate is 5%.

a. What is the required rate of return on this stock?

b. What is the expected return on the market?

c. If based on your personal opinion the stock will generate a return of 20%, is the stock over-valued or under-valued? Would you buy or sell the stock?

https://brainmass.com/statistics/central-tendency/required-rate-return-expected-return-example-235871

#### Solution Preview

Part A:

To find the required rate of return on a stock, you need to use the following formula:

Required Rate of Return = Risk Free Rate + (Beta * Market Risk Premium)

Now you plug in the numbers you already know:

Required Rate of Return = 5% + (1.5 * 9%)

Required Rate ...

#### Solution Summary

This solution explains how to calculate required rate of return and expected return on the market for a stock given the beta value, market risk premium, and the risk-free rate.

FIN500: Stock portfolio expected returns, beta, standard deviation

See attached file for proper format of the tables.

Please show all your work so I can understand everything.

1. Buxton Corporation is planning to invest in a security that has several potential rates of return. Using the following probability distribution of returns during different states of the economy, what is the expected rate of return on this investment? In addition, compute the standard deviation of the returns (σ). Finally, briefly explain what these numbers represent.

Probability Expected Return

0.10 -10%

0.20 5%

0.30 10%

0.40 25%

2. Using the capital asset pricing model (CAPM), estimate the appropriate required rate of return for the following three stocks, assuming that the risk-free rate (rRF) is 5 percent and the expected return for the market (rM) is 17 percent.

Stock Beta (β)

A 0.75

B 0.90

C 1.40

3. Based on the following table of actual (or ex post) returns for both Inquiry Corporation and the market from 2007 through 2010, calculate the average return and the standard deviation for both Inquiry and the market (keep in mind that this data is historical and not based on a probability distribution, so be sure to use the correct formulas).

Year Inquiry Corporation Market

2007 4% 2%

2008 6% 3%

2009 0% 1%

2010 2% -1%

4.

(a) Derive the expected return (rP) and beta (βP) for a portfolio based on the following information:

Stock Percentage of Portfolio Beta (β) Expected Return

1 40% 1.00 12%

2 25% 0.75 11%

3 35% 1.30 15%

(b) Given the information in the table above, present the equation for the security market line and explain where the return for this specific portfolio would lie (plot) relative to the SML (i.e., below or above the line). Assume that the risk-free rate (rRF) is 8 percent and that the expected return on the market portfolio (rM) is 12 percent.

5. Reliable Printing is evaluating a security. One-year Treasury bills (rRF) are currently paying 3.1 percent. Calculate the following investment's expected return and its standard deviation (σ). Should Reliable Printing invest in this security? Briefly explain.

Probability Expected Return

0.15 -1%

0.30 2%

0.40 3%

0.15 8%

6. You have researched the common stock of two companies (A and B) and have compiled the following information:

COMPANY A COMPANY B

Probability Return Probability Return

0.20 -2% 0.10 4%

0.50 18% 0.30 6%

0.30 27% 0.40 10%

0.20 15%

Calculate the expected return, standard deviation (σ), and the coefficient of variation (CV) for each stock and, based on the CV, which stock should you invest in? Briefly explain.

7. Assume you own a portfolio consisting of the following stocks:

Stock Percentage of Portfolio Beta (β) Expected Return

1 20% 1.00 16%

2 30% 0.85 14%

3 15% 1.20 20%

4 25% 0.60 12%

5 10% 1.60 24%

(a) Determine the expected return on your portfolio.

(b) Determine the portfolio beta (βP).

(c) Given the portfolio beta and the assumptions that the risk-free rate (rRF) is 7 percent and the expected return on the market portfolio (rMKT) is 15.5 percent, present the equation for the security market line (SML).

(d) Based on your equation for the SML and the expected returns from the data in the table, which stocks appear to be winners (i.e., underpriced) and which stocks appear to be losers (i.e., overpriced)?

8. The common stock for a particular company is known to have a beta (β) of 1.20. The expected return on the market (rM) is 9 percent and the risk-free rate (rRF) is 5 percent.

(a) Compute a fair rate of return based on this information.

(b) What would be a fair rate of return if the beta were 0.85?

(c) What would be a fair rate of return if the expected return on the market increased to 12 percent and the beta remained at 0.85?

9. The expected return for the general market (rMKT) is 12.8 percent, and the market risk premium (i.e., RPM) is 4.3 percent. Moe, Larry, and Curley have betas of 0.82, 0.57, and 0.68, respectively. What are the required rates of return for the three securities?

10. Hickory Stick's common stock has a beta (β) of 0.95. The expected return for the market (rM) is 7 percent and the risk-free rate (rRF) is 4 percent.

(a) What is the required rate of return based on this information?

(b) What would be the required rate of return if the beta were 1.25?

11. An exhaustive financial analysis has produced the following returns on two investments under three different scenarios:

Expected Returns

Scenario Probability Stock X Stock Y

S1 0.3 10% 8%

S2 0.4 16% 15%

S3 0.3 12% 20%

(a) Calculate the expected return on each investment.

(b) Calculate the standard deviations (σ) for both X and Y.

(c) Calculate the coefficient of variation (CV) for both X and Y.

(d) If you were to create a portfolio consisting of 67% of Stock X and 33% of Stock Y, what will be the expected return (rP) and the standard deviation (σP) for your portfolio?