Question

Asked Jul 5, 2019

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A stock with a beta of 0.8 has an expected rate of return of 12%. If the market return this year turns out to be 5 percentage points below expectations, what is your best guess as to the rate of return on the stock?

Step 1

Recall the famous CAPM equation to estimate the expected rate of return on a stock:

R = R_{f} + β x (R_{m} – R_{f})

Where R = expected return on the stock, R_{f} = Risk free rate, R_{m} = expected return from the market and β = Beta of the stock

Step 2

A stock with a beta of 0.8 has an expected rate of return of 12%. We can place this in CAPM to get our first equation:

12% = R_{f} + 0.8 x (R_{m} – R_{f}) -------------- Eqn (1)

Now, this year, expected return from the market turns out to be 5 percentage points below expectations. Hence, for this year, we will put R_{m} = R_{m} – 5% in CAPM. Application of CAPM will give us the second equation as:

R = R_{f} + 0.8 x (R_{m} – 5% - R_{f}) ----------------- Eqn (2)

Step 3

Eqn (2) - Eqn (1) gives us:

R - 12% = - 0.8% x 5%...

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