(Portfolio selection problem) Daniel Grady is the financial advisor for a number

Question

(Portfolio selection problem) Daniel Grady is the financial advisor for a number of professional ath- letes. An analysis of the long-term goals for many of these athletes has resulted in a recommendation to purchase stocks with some of their income that is set aside for investments. Five stocks have been identified as having very favorable expectations for future performance. Although the expected return is important in these investments, the risk, as measured by the beta of the stock, is also important. (A high value of beta indicates that the stock has a relatively high risk.) The expected return and the betas for five stocks are as follows: 2

Explanation / Answer

(1) Formulation Suppose in Each Case amt. Invested = 20% i.e Equally

So Weight of Investment is X1, X2, X3, X4, X5

So 0.11X1 + 0.09X2+0.065X3+.15X4+0.13X5>0.11

X1,X2,X3,X4,X5<0.35

X1,X2,X3,X4,X5>0

(2) Expected Return of Portfolio Consisting Equal investment i.e. 20% in Each Stock

Weighted average of all the returns

11%*0.20+9.00%*0.20+6.50%*0.20+15.00*0.20+13.00%*0.20

= 10.90%

Beta of portfolio = Weighted Avg beta of All Stocks

1.20*0.20+0.85*0.20+0.55*0.20+1.40*0.20+1.25*0.20

= 1.05

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