# Expected rate of return on the market portfolio

Suppose the rate of return on short-term government securities (perceived to be risk-free) is 5%. Suppose also that the expected rate of return required by the market for a portfolio with a beta of 1 is 12%. According to the CAPM

1. What is the expected rate of return on the market portfolio?

2. Suppose you consider buying a stock which does not pay a dividend. The current price is $50, and in one year, you expect the price to be $57.50, giving a rate of return of 15%. The stock has a ? which you calculate to be 0.75. Assuming your estimate of the stockâ??s price in one year is correct, is the stock currently overpriced or underpriced according to the CAPM? Explain thoroughly, using the ideas and formulas.

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#### Solution Preview

1. According to CAPM

Required return on stock = Rf + (Rm-Rf) beta

In this question

Required return = 12%

Rf = risk free rate = 5%

Rm = Expected rate of return on market which is to be found

beta = 1

12% = 5% + (Rm-5%) X 1

Rm = (12%-5%) + 5% = 12%

Expected return on market portfolio = 12%

2. The beta of stock ...

#### Solution Summary

Expected rate of return on the market portfolio is calculated.

A portfolio that combines the risk-free asset...

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 22 percent and a standard deviation of 5 percent. The risk-free rate is 4.9 percent, and the expected return on the market portfolio is 19 percent. Assume the capital-asset-pricing model holds.

What expected rate of return would a security earn if it had a 0.6 correlation with the market portfolio and a standard deviation of 3 percent?

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