Question

	Risk asset 1	Risk asset 2
Expected return	.12	.16
Standard deviation	.27	.89

If you wished to construct an optimal risky portfolio with these two assets, what is the percentage this portfolio would consist of for risk asset 1? And risk asset 2?

3.8% risk free rate and .009 coeficent correlation

Answer 1

Optimal risky portfoliom is the portfolio at which Portfolio risk is minimal.

Particulars	Amount
SD of A	27%
SD of B	89%
r	0.0090

Risk Aeest 1 = A

RIsk asset 2 = B

Weight in A = [ [ (SD of B)^2] - [ SD of A * SD of B * r(A,B) ] ] / [ [ (SD of A)^2 ]+ [ (SD of B)^2 ] - [ 2* SD of A * SD of B * r (A, B) ] ]

= [ [ (0.89)^2 ] - [ 0.27 * 0.89 * 0.009 ] ] / [ [ (0.27)^2 ] + [ ( 0.89 )^2 ] - [ 2 * 0.27 * 0.89 * 0.009 ] ]

= [ [ 0.7921 ] - [ 0.0021627 ] ] / [ [ 0.0729 ] + [ 0.7921 ] - [ 2 * 0.0021627 ] ]

= [ 0.7899373 ] / [ 0.8606746 ]

= 0.9178

Weight in B = [ [ (SD of A)^2] - [ SD of A * SD of B * r(A,B) ] ] / [ [ (SD of A)^2 ]+ [ (SD of B)^2 ] - [ 2* SD of A * SD of B * r (A, B) ] ]

= [ [ (0.27)^2 ] - [ 0.27 * 0.89 * 0.009 ] ] / [ [ (0.27)^2 ] + [ ( 0.89 )^2 ] - [ 2 * 0.27 * 0.89 * 0.009 ] ]

= [ [ 0.0729 ] - [ 0.0021627 ] ] / [ [ 0.0729 ] + [ 0.7921 ] - [ 2 * 0.0021627 ] ]

= [ 0.0707373 ] / [ 0.8606746 ]

= 0.0822