Question

You are considering investing $1,800 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 4% and a risky portfolio, P.constructed with two risky securities, X and Y. The optimal weights of X and Y in Pare 60% and 40% respectively. X has an expected rate of return of 13%, and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 7%, you should invest approximately in the risky portfolio. This will mean you will also invest approximately and of your complete portfolio in security X and Y respectively. Multiple Choice O 0% 60% 40% O 50% 30% 20% O 38% 23%, 15% O 23% 47% 30% < Prev 29 of 35 !!! Next >

Answer 1

Let's first find out the composite return of the risky portfolio

= 60%*13%+ 40%*10%

= 11.8%

Return of treasury bill = 4%

We want to have a total return of complete portfolio as 7%

Let's assume that investment in treasury bill is x. The total portfolio is 100%.

Hence investment in risky portfolio would be 100%-x

The equation comes out as follows

x* 4% + (100%-x)*11.8% = 7%

To solve for x, refer the attached photo.

11.84 71. 41. x 11.3 1- , 71. -7.810x . + 11.87 4.97 7.87. x 61.541.

Which gives us x = 61.54%

Therefore, you should invest approximately (100%-x) i.e. 38% in the risky portfolio. This means you would also invest approximately 38%* 60% and 38%*40% i.e. 23% and 15% of your complete portfolio in security x and y respectively.

Hence, option C is the correct option.