# Expected return on a stock; Beta vs standard deviation

The stock of Uptown Men's Wear is expected to produce the following returns given the various states of the economy. What is the expected return on this stock?

Probabilities:

Recession:0.2

Normal:0.5

Boom:0.3

Returns:

Recession:-12%

Normal:13%

Boom:25%

Answer

12.6 percent

10.4 percent

7.9 percent

11.6 percent

9.1 percent

The difference between beta and standard deviation is best described as:

Answer

Beta measures the risk of the market as a whole, while standard deviation measures the risk of individual stocks.

Beta measures total volatility, while standard deviation measures total risk.

Beta measures the market risk premium, while standard deviation measures risk.

Beta measures the risk investors are compensated for, while standard deviation measures both systematic and unsystematic risk.

A company you are researching has common stock with a beta of 1.35. Currently, Treasury bills yield 2.5%, and the market portfolio offers an expected return of 11.5%. What is the required return on this common stock?

Answer

10.93%

11.86%

21.43%

14.65%

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#### Solution Preview

The stock of Uptown Men's Wear is expected to produce the following returns given the various states of the economy. What is the expected return on this stock?

Probabilities:

Recession:0.2

Normal:0.5

Boom:0.3 ...

#### Solution Summary

Expected return on a stock; Beta vs standard deviation; Required return on common stock

Expected Return, Standard Deviation, CAPM, Beta, CAL ( Capital Allocation Line)

1 Asset Expected Return Standard Deviation Weight

X 15% 22% 0.5

Y 10% 8% 0.4

Z 6% 3% 0.1

What is the expected return on this three -asset portfolio?

2) Karen Kay, a portfolio manager at Collins Asset Management, is using the capital asset pricing model for making recommendations to her clients. Her research department has developed the information shown in the following exhibit.

Forecasted returns, Standard deviations, and Betas

Forecasted return Standard deviation Beta

Stock X 14% 36% 0.8

Stock Y 17% 25% 1.5

Market Index 14% 15% 1

Risk-free rate 5%

a) Calculate the expected return on the stocks based on CAPM

b) Identify and justify which stock would be more appropriate for an investor who wants to

i) Add this stock to a well- diversified equity portfolio.

ii) Hold this stock as a single-stock portfolio

6. True or False and Explain

You can construct a portfolio with a Beta of .75 by investing .75 of the budget in T-Bills and the remainder in the market portfolio?

In problems 16-18 below, assume the risk-free rate is 8% and the expected rate of return on the market is 18%

16. A share of stock is now selling for $100. It will pay a dividend of $9 per share at the end of the year. Its beta is 1.0. What do the investors expect the stock to sell for at the end of the year.

18. A stock has an expected return of 6%. What is its beta?

For Problems 19-23, assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%.

19. a. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. What is the expected return and standard deviation of your client's portfolio?

b. Suppose your risky portfolio includes the following investments in the given proportions:

Stock A 27%

Stock B 33%

Stock C 40%

What are the investment proportions of your client's overall portfolio, including the position in T-bills?

c. What is the reward-to-variability ratio (S) of your risky portfolio and your client's overall portfolio?

d. Draw the CAL of your portfolio on an expected return/standard deviation diagram. What is the slope of the CAL? Show the position of your client on your fund's CAL.

Please see the attached file.

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