Need assistnace with solving the following. 8. Write out the Security Market Lin

Question

Need assistnace with solving the following.

8. Write out the Security Market Line (SML) equation and use it to calculate the required rate of return on each alternative. Compare the expected rates of return with the required rates of return. How do these perform against your predictions?

9. Does the fact that Repo Men has an expected rate of return less than the T-bill rate of return make any sense? Why or why not?

10. What would be the market risk and the required return of a 50-50 portfolio of Alta Industries and Repo Men? Or of Alta Industries and American Foam? Based on your analysis and conclusions, which would you recommend to your client

Explanation / Answer

Answer:8

Here is the SML equation:

                                                       ri = rrf + (rm - rrf)bi.

If we use the t-bill yield as a proxy for the risk-free rate, then rRF = 8%. Further, our estimate of rm =is 15%. Thus, the required rates of return for the alternatives are as follows:

Alta Inds: 8% + (15% - 8%)1.29 = 17.03% » 17.0%.

Market:                  8% + (15% - 8%)1.00 = 15.0%.

Am Foam :            8% +(15% - 8%)0.68 = 12.76% » 12.8%.

T-Bills:                  8% + (15% - 8%)1.29 = 17.03% » 17.0%.

Repo Men:            8% + (15% - 8%)-0.86 = 1.98% » 2%.

Answer:9 Repo Men is an interesting stock. Its negative beta indicates negative market risk— including it in a portfolio of “normal” stocks will lower the portfolio’s risk. Therefore, its required rate of return is below the risk-free rate. Basically, this means that Repo Men is a valuable security to rational, well-diversified investors. To see why, consider this question: would any rational investor ever make an investment that has a negative expected return? The answer is “yes”—just think of the purchase of a life or fire insurance policy. The fire insurance policy has a negative expected return because of commissions and insurance company profits, but businesses buy fire insurance because they pay off at a time when normal operations are in bad shape. Life insurance is similar—it has a high return when work income ceases. A negative beta stock is conceptually similar to an insurance policy.

Answer:10

Note that the beta of a portfolio is simply the weighted average of the betas of the stocks in the portfolio. Thus, the beta of a portfolio with 50 percent Alta Inds and 50 percent Repo Men is:

bp = 0.5(bAlta) + 0.5(bRepo) = 0.5(1.29) + 0.5(-0.86)

     = 0.215,

rp = rRF + (rM - rRF)bp    = 8.0% + (15.0% - 8.0%)(0.215)

                                          = 8.0% + 7%(0.215) = 9.51% » 9.5%.

For a portfolio consisting of 50% Alta Inds plus 50% Am. Foam, the required return would be 14.9%:

bp = 0.5(1.29) + 0.5(0.68) = 0.985.

rp = 8.0% + 7%(0.985) = 14.9%.

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