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%. To form a complete portfolio with an expected rate of return of 11%, you should invest ________ of your complete portfolio in Treasury bills.

Answer 1

Answer:

amount invest in X   = $486

amount invest in Y = $324

Explanation:

given data

investing = $1,000

pay = 5%

weights of X = 60 %

weights of Y = 40%

X expected rate of return = 14%

Y expected rate of return = 10%

required return = 11%

solution

we get here first return from risky portfolio that is for X and Y is

return from risky portfolio = weight × return

return from risky portfolio X = 60% × 14% = 8.4 %

return from risky portfolio Y = 40% × 10% = 4%

total return from risky portfolio = 12.4 %

and

we consider investment in risky portfolio is = x

so risk free investment is = 1 - x

11% = 12.4 % × x + 5%  ( 1- x)

x = 0.810

so investment in risky portfolio = 0.810

and investment in risk free portfolio = 0.190

and

amount invest in risky portfolio is = 0.810 × 1000 = $810

amount invest is

amount invest in X  = $810 × 60% = $486

amount invest in Y  = $810 × 40% = $324