The beta coefficient for Stock C is b C = 0.3, and that for Stock D is b D = - 0

Question

The beta coefficient for Stock C is bC = 0.3, and that for Stock D is bD = - 0.4. (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.)

I. In this situation, the expected rate of return = 7.90%. However, the required rate of return is 10%. Investors will seek to buy the stock, raising its price to $38.46. At this price, the stock will be in equilibrium.
II. In this situation, the expected rate of return = 10%. However, the required rate of return is 7.90%. Investors will seek to buy the stock, raising its price to $38.46. At this price, the stock will be in equilibrium.
III. In this situation, the expected rate of return = 10%. However, the required rate of return is 7.90%. Investors will seek to sell the stock, raising its price to $38.46. At this price, the stock will be in equilibrium.
IV. In this situation, the expected rate of return = 7.90%. However, the required rate of return is 10%. Investors will seek to sell the stock, raising its price to $38.46. At this price, the stock will be in equilibrium.
V. In this situation, both the expected rate of return and the required rate of return are equal. Therefore, the stock is in equilibrium at its current price.

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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