Stock/Bond Question #2?

1. Assume that the risk-free rate designated by r RF = 5%, the market risk premium designated by r M = 10%, and the expected rate of return for stock A is designated by r A = 12%,

a. What is the beta for Stock A?

b. If Stock A's beta was 2.0, what would be A's new required rate of return?

2. Assume that the risk-free rate is 5% and the market risk premium is 6%. What is the expected return for the overall stock market? What is the required rate of return for a stock that has a beta of 1.2%

3. Assume that the risk-free rate is 6% and the expected return on the market is 13%. What is the required rate of return on a stock that has a beta of 0.7%?

4. An individual has $35,000 invested in a stock which has a beta of 0.8 and $40,000 invested in a stock with a beta of 1.4. If these are the only two investments in her portfolio, what is the beta of her portfolio?

Use the capital asset pricing model (CAPM) to answer these questions:

E(R) = Rf + B(Rm - Rf)

E(R) is the expected return of a stock, or "what should this stock return this year?"
Rf is the risk-free rate, or "what does an investment with no risk at all pay me?" Usually this is the return on a 10-year US treasury bond.
B is the stock's beta, or "how much does the return of this stock vary up and down with the overall market?"
Rm is the expected return on the overall market.

1a.) In your case E(R) is 12%, Rf = 5% and Rm = 10%, so you have: 0.12 = 0.05 + B(0.10 - 0.05). Rearranging gives you: B 0.05B = 0.07. So B = 1.4.
1b.) If the beta were 2.0, this would give you:
E(R) = 0.05 + 2(0.10 - 0.05), so
E(R) = 0.15, or 15%

2. The expected return on the overall market is just the sum of the risk free rate and the market risk premium. Expected market return = market risk premium + risk-free rate. In this case that would give you 5% + 6% = 11% Now we plug this into CAPM for the second part. If a stock has a beta of 1.2, then E(R) = 0.05 + 1.2(0.11 - 0.05) = 0.122 or 12.2%.

3. There may be a typing error in this question, because betas aren't expressed in percent. So I'm assuming the beta is 0.7, not 0.7%.
E(R) = 0.06 + 0.7(0.13 - 0.06)
E(R) = 0.109, or 10.9%

4. The beta of a portolio is just the weighted-average of all of the stocks in the portfolio. The individual has a total of $75,000 invested, right? $35,000 in the stock with the 0.8 beta and $40,000 in the stock with the 1.4 beta. The beta contribution from the first stock will be:
(35,000/75,000) x 0.8 = 0.373
The beta contribution from the second stock will be:
(40,000/75000) x 1.4 = 0.747.
Add the two up, to give you the beta of the portfolio, which is:
0.373 + 0.747 = 1.12

Good luck!