# Calculating expected return and standard deviation

An analyst believes that the economic conditions during the next year will either be Strong, Normal or Weak and she thinks that the Simpson Company's returns will have the following probability distribution. What's the standard deviation of Simpson's returns as estimated by this analyst?

PROBABILITY RETURN

STRONG 30% 24%

NORMAL 40% 15%

WEAK 30% -10%.

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Solution:

Economic conditions Probability Return

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#### Solution Summary

Solution describes the steps to calculate expected returns and standard deviation of returns.

Calculate expected return, standard deviation and coefficient of variation.

1. 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, and the coefficient of variation (CV) for each stock and. Based on the CV, which stock should you invest in? Briefly explain.

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

Stock Percentage of Portfolio Beta 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.

(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., under priced) and which stocks appear to be losers (i.e., overpriced)?

3. The common stock for a particular company is known to have a beta (?) 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?

4. 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?

5. Hickory Stick's common stock has a beta (?) 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 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 for your portfolio?