Question

You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081.

What would be the dollar value of your positions in X, Y, and the T-bills, respectively, if you decide to hold a portfolio that has an expected outcome of $1,120?

Multiple Choice

• Cannot be determined.

• $568; $54; $378

• $568; $378; $54

• $378; $54; $568

• $108; $514; $378

Answer 1

Option 2

Return of portfolio P= weighted average of return of individual securities=06*.14+0.4*.1=0.124=12.4%

Let weight of investment in T-bills be.a

then in risky portfolio P=1-a

Expected outcome=$1120

Hence return on $1000=$1120-1000=$120=$120/1000*100=12%

Return on 12% will be achieved by investing in T bills and P in such a way that the weighted average of their return gives 12%

Hnece, weight of tbill*0.05+weight of P*12.4%=12%

or, a*0.05+(1-a)*0.124=0.12

or, 0.05a+0.124-0.124a=0.12

or, 0.004=.124a-0.05a

or,a=0.004/0.074=0.054

1-a=0.946

Hence weight of Tbill=$1000*a=$1000*0.054=$54

Weight of P=$1000-54=$946

Now in P, weight of X=60%=946*60%=$568

weight of Y=40%=946*40%=$378