Question

You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40%, respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. The dollar values of your positions in X, Y, and Treasury bills would be and respectively, if you decide to hold a complete portfolio that has an expected return of 8%. $162; $595; $243 $243; $162; $595 O $595; $162; $243 $595; $243; $162

Answer 1

Answer: Option 2 ($243, $162, $595)

Return from Risky portfolio P = w1 * r1 + w2 * r2

where w1 = % of investment in security X

r1 = return on investment in security X

w2 = % of investment in security Y

r2 = return on investment in security Y

Thus Return from Risky portfolio P = 0.60 * 14 + 0.40 * 10 = 12.40%

Let weight of investment in Treasury bill be w.

Thus investment in risky portfolio = 1 - w

Return from complete portfolio P = w1 * r1 + w2 * r2

where w1 = weight of investment in Treasury bill

r1 = return on investment in security Treasury bill

w2 = weight of investment in risky portfolio P

r2 = return on investment in Treasury bill

Thus 8 = w * 5 + (1 - w) * 12.40

8 = 5w + 12.40 - 12.40 w

7.4w = 4.4

w = 0.595 = 59.5% (weight of Treasury bill)

Thus weight of risky portfolio P = 40.5%

Thereby investment in treasury bill = $1000 * 59.5% = $595

Investment in risky portfolio P = $1000 - $590 = $405

Thus investment in security X = $405 * 60% = $243

Thus investment in security Y = $405 * 40% = $162