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%.
A. $162; $595; $243
B. $243; $162; $595
C. $595; $162; $243
D. $595; $243; $162

Answer 1

Answer:

amount to be investment in risky portfolio =  $405

amount invest in security x = $243

amount invested in security Y = $162

Explanation:

given data

investing = $1,000

Treasury bills = 5%

optimal weights of X = 60 %

optimal weights of Y = 40 %

expected rate of return x =  14%

expected rate of return y = 10%

solution

we know that

                      weight                     return                     return from risky port

X                     60 %                         14 %                       8.4 %

Y                     40 %                          10 %                       4%

total                                                                                 12.4 %

so here

return from risky portfolio is = 12.4 %

and

return from risk free investment = 5 %

so 'we consider here investment in risky portfolio = x

so investment in risk free  = 1 - x

so we can say that

12.4 % × x + 5 % × (1-x) = 8 %

solve we get

x = 0.405

so investment in risky portfolio = 0.405

so investment in risk free  =0.595

and

amount to be investment in risky portfolio = $1000 × 0.405

amount to be investment in risky portfolio =  $405

and

amount invest in security x = $405 × 60%

amount invest in security x = $243

and

amount invested in security Y = $405 × 60%

amount invested in security Y = $162