# Expected returns and Alpha

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 14.0% 36% 0.8

Stock Y 17.0 25 1.5

Market index 14.0 15 1.0

Risk-free rate 5.0

a. Calculate expected return and alpha for each stock.

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.

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#### Solution Preview

a. Calculate expected return and alpha for each stock.

Alpha = Forecasted Return - Expected return

We calculate the expected return using CAPM

Expected return = Risk Free Rate + (Market return - risk free rate ) X beta

Stock X

Expected Return = 5% ...

#### Solution Summary

The solution explains the calculation of expected returns and alpha

1) The alpha of the stock is 2) The beta of the stock is 3) What is the proportion of stock A in the portfolio, so that the expected return of the portfolio is 16.4%? 4) If you expect stock A with a beta of 1.2 to offer a rate of return of 20%, then you should

1) Stock A has an estimated rate of return of 12% and a beta of 1.2. The market expected rate of return is 12% and the risk-free rate is 2%. The alpha of the stock is:

1. 0% 2. -2% 3. 2% 4. 4%

2) Stock A has an expected rate of return of 14%. The market expected rate of return is 12% and the risk-free rate is 2%. The beta of the stock is __________.

1. 1.2 2. 1.0 3. 0.8 4. 0.6

3) A portfolio is composed of two stocks, A and B. Stock A has an expected return of 10%, while stock B has an expected return of 18%. What is the proportion of stock A in the portfolio, so that the expected return of the portfolio is 16.4%?

1. 0.2 2. 0.8 3. 0.4 4. 0.6

4) The expected market rate of return is 14%, while the risk-free rate of expected return is 4%. If you expect stock A with a beta of 1.2 to offer a rate of return of 20%, then you should __________.

buy stock A because it is overpriced

buy stock A because it is underpriced

sell short stock A because it is overpriced

sell short stock A because it is underpriced