The beta coefficient for Stock C is bC = 0.4 and that for Stock D is bD. (Stock

Question

The beta coefficient for Stock C is bC = 0.4 and that for Stock D is bD. (Stock D's beta is negative, indicating that its rate of return rises whenever returns on most other stocks fall. There are very few negative-beta stocks, although collection agency and gold mining stocks are sometimes cited as examples.) a. If the risk-free rate is 9% and the expected rate of return on an average stock is 13%, what are the required rates of return on Stocks C and D? b. For Stock C, suppose the current price, Po,is $25; the next expected dividend, D1, is $1.50; and the stock's expected constant growth rate is 4%. Is the stock in equilibrium? Explain, and describe what would happen if the stock were not in equilibrium.

Explanation / Answer

a) use CAPM...E(r) = RFR + Beta(Rm - RFR) Stock C: E(r) = 0.09 + 0.4(0.13 - 0.09) = 0.106 Stock D: E(r) = 0.09 + [ -0.5(0.13 - 0.09)] = 0.07 b) P0 (according to Gordon growth model) = 1.50/(0.106 - 0.04) = $22.73 but P0 = $25, so the stock is not in equilibrium...the stock is "oversold" and the price should fall (at 1.50/25 = 0.06, with a growth rate of 4%, the 6% here implies a required return of 10%) The stock is thus priced (returning) below the Security Market Line, indicating it is oversold/overpriced...sell short...arbitrage will drive the price back to equilibrium...at least according to theory.

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