Although investing requires the individual to bear risk, the risk can be control

Question

Although investing requires the individual to bear risk, the risk can be controlled through the construction of diversified portfolios and by excluding any portfolio that offers an inferior return for a given amount of risk. While this concept seems obvious, one of your clients is considering purchasing a stock that you believe will offer an inferior return for the risk she will bear. To convince her that the acquisition is not desirable, you want to demontrate the trade-off between risk and return.

While it is impractical to show the drade-off for all possible combinations, you believe that illustrating several combinations of risk and return and applying the same analysis to the specific investment should be persuasive in discouraging the purchase. Currently, US Treasury billoffer 7 percent. Three possible stocks and their betas are as follows:

Security            ExpectedReturn                     Beta

StockA               9%                                    0.6

StockB                11                                    1.3

StockC                14                                    1.5

1. What will be the expected return and beta for each of thefollowing portfolio's?

a) Portfolio's 1-4 : All of the funds are invested soleyin one asset (the corresponding three stocks or the TreasuryBill)

b) Portfolio 5: One-quarter of the funds are invested in eachalternative.

c) Portfolio 6: One-half of the funds are invested in Stock Aand one-half in Stock C.

d) Portfolio 7: One-third of the funds are invested in eachstock.

2. Are any of the portfolio's inefficient?

3. Is there any combination of the Treasury Bill Stock C thatis superior to portfolio 6(i.e., half the funds in stock A and halfin stock C)?

4. Since your client's suggested stock has an anticipatedreturn of 12 percent and a beta of 1.4, does that information arguefor or against the purchase of the stock> Compare.

5. Why is it important to consider purchasing an asset as partof a portfolio and not as an independent act?

Explanation / Answer

Part A

Rp = sum of (weights x R)

Portfolio Return 1 = 9%

Portfolio Return 2 = 11%

Portfolio Return 3 = 14%

Portfolio Return 4 = 7%

Part B

Weight of each security would be 0.25.

Portfolio return 5 = 0.25 x 9% + 0.25 x 11% + 0.25 x 14% + 0.25 x 7%

                                    = 10.25%

Part C

Portfolio Return 6 = 0.50 x9% + 0.50 x 14%

                                    = 11.50%

Part D

Portfolio return = 9% x1/3    + 11%x 1/ 3   + 14% x 1 /3

                                = 11.33%

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