Question

suppose asset a has an expected return of 10% and a standard deviation of 20% asset b has an expected return of 16% and a standard deviation of 40%.if the correlation between a and b is 0.6,what are the expected return and standard deviation for a prtifolio comprised of 40% asset a

Answer 1

Solution:
	Expected return of the portfolio	13.60	%
	Standard deviation of the portfolio	29.50	%
Working Notes:
Notes:	The portfolio consist of two asset A & asset B, and in the portfolio Asset A is 40% then balance of 60% out of 100% must be invested in Asset B
	We computed Expected return of the portfolio using formula where Expected return of portfolio = Weighted average expected return of Individual assets = Weight of stock A x ErA + Weight of stock B x ErB
	And standard deviation is computed using formula of computation of risk of a portfolio consisting of two risky assets.
(S.d of Port folio )^2 = (WA^2 x Sd. Of A^2) + (WB^2 x Sd. Of B^2) + 2 x WA x WB x Sd. Of A x Sd. Of B x rA,B
Data Given
	Standard deviation of the portfolio = S.d of Port folio =??
	Weight of asset A = WA = 40% =0.40
	Weight of asset B = WB = 60% =0.60
	Standard deviation of the asset A = S.d of A = 20%=0.20
	Expected return of Asset A = ErA = 10%
	Standard deviation of the Asset B = S.d of B = 40%=0.40
	Expected return of Asset B = ErB = 16%
	correlation coefficient (rA,B) = 0.60
First	Expected Return of the portfolio
Expected return of portfolio = Weighted average expected return of Individual assets
	= Weight of stock A x ErA + Weight of stock B x ErB
	=10% x 0.40 + 16% x 0.60
	=13.60%
Now	Standard deviation of the portfolio
(S.d of Port folio )^2 = (WA^2 x Sd. Of A^2) + (WB^2 x Sd. Of B^2) + 2 x WA x WB x Sd. Of A x Sd. Of B x rA,B
(S.d of Port folio )^2 = (0.4^2 x 0.20^2) + (0.60^2 x 0.40^2) + 2 x 0.40 x 0.60 x 0.20 x 0.40 x 0.60
	(S.d of Port folio )^2 = 0.08704
	S.d of Port folio = (0.08704)^(1/2)
	S.d of Port folio = 0.295025423
	S.d of Port folio = 29.5025423%
	S.d of Port folio = 29.50%
Please feel free to ask if anything about above solution in comment section of the question.