Investment Analysis: HW week 11 Solutions
1. You are given the following information about some stocks:
Stock o (in %) 3 A 20 0.5 B 10 1 c 9 -.5 D 5 2
(a) Given the information above, sort the stocks in the order of the expected return you would need from them if you had to hold them:
i. individually (i.e., the stock would form your entire portfolio) ii. as part of a large, well-diversified portfolio resembling the market.
The point of this question is that investors should care about the mean and sigma (SD) of their portfolios. When you hold a stock by itself, i.e., the stock is your entire portfolio, then you need to care about the sigma of the stock. When the stock is part of a large portfolio, you only need to care about how much the stock adds to your portfolio's sigma- the stock's sigma is not relevant. As we saw in class, a stock increases your portfolio sigma by a lot if its beta is high. Therefore, for (i) the order is D (would demand smallest expected return), C, B A (would demand largest expected return). For (ii) the order is C (would demand smallest expected return), A, B, D (would demand largest expected return). (b) The risk-free rate is 0% and the expected return on the market is 10%. Assuming that you hold the stock as part of a well-diversified portfolio, which stocks would you buy if the expected return on the stocks were as below: Stock Expected return in % A 5 B 12 c 0 D 15 We can calculate what the CAPM says the expected return on these stocks should be, given their betas, using the SML:
1
E(Ri)=Rf+3i(E[Rm]-Rf
In this case,Rf =0 and E[Rm]= 10 Stock Expected return in % Expected return should be A 5 0 + 0.5 * 10= 5 B 12 0+1 *10=10 c 0 0 - .5 * 10 = -5 D 15 0 + 2 * 10 = 20 As you can see, stock A is fairly priced, since it is expected to pay 5%, and the CAPM says that, given its risk, it should be paying 5%. Stocks B and C have expected returns that are too high given their risk. Stock B, for instance, has an expected return of 12%, while the CAPM says that, given
is too high means the price is too low, this is the same thing as saying they are underpriced. Stock D has an expected return that is too low given its risk. Its expected return is 15%, while the CAPM says that, given its risk, its expected return should be 20%. Since an expected return that is too low means the price is too high, this is the same thing as saying this stock is overpriced. Thus, you would be indifferent to buying A (it is correctly priced), you would want to buy B and C, and you would not want to buy D (you