Suppose the rate of return on short-term government securities (perceived to be risk-free) is about 6%. Suppose also that the expected rate of return required by the market for a portfolio with a beta of 1 is 16%. According to the capital asset pricing model: A. What is the expected return on the market portfolio?
B. What would be the expected return on a zero-beta stock?
C. The stock risk has been evaluated at beta = -.5. Is the stock overpriced or under-priced?

A. 16%

B. 6%

C. Underpriced. Note: This answer is based on the example we used to show how to complete solving this kind of question.

Explanation:

Given;

E(rM) = return required by the market for a portfolio = 16%, or 0.16

rf = rate of return on short-term government securities (perceived to be risk-free) = 6%, or 0.06

We can now proceed as follows:

A. What is the expected return on the market portfolio?

The formula for calculating the expected return on the market portfolio is as follows:

Expected return on the market portfolio = ([E(rM) - rf] / B) + rf

Where;

B = beta of the portfolio = 1

Substituting these values into the equation above, we have:

Expected return on the market portfolio = (0.16 - 0.06)/1 + 0.06 = 0.16, or 16%.

B. What would be the expected return on a zero-beta stock?

The formula for calculating the expected return on a zero-beta stock is as follows:

Expected return on a zero-beta stock = rf + B[E(rM) - rf]

Where;

B = beta of the portfolio = 0

Substituting these values into the equation above, we have:

Expected return on a zero-beta stock = 0.06 + 0[0.16 - 0.06] = 0.06, or 6%.

C. The stock risk has been evaluated at beta = -.5. Is the stock overpriced or under-priced?

In line with capital asset pricing model (CAPM), we have:

Expected return = E(r) = rf + B[E(rM) - rf]

B = beta of the portfolio = -0.5

Substituting these values into the equation above, we have:

E(r) =  0.06 - 0.5(0.16 - 0.06) = 0.06 - 0.05 = 0.01, or 1.00%

Note: To determine if a stock overpriced or under-priced, we make use of an example here by assuming buying a share of stock at $40 which is expected to pay $3 dividends next year and it is expected to sold then for $41.

In line with CAPM, the price must be:

Po = ($41 + $3) / [1 + E(r)] = $44 / (1 + 0.01) = $43.46

Since $43.46 is greater than purchase price of $40, the stock is underpriced.

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