Question

ci. Consider the following data relating to the following securities. Return Variances and Covariances Security Α. B TC Expected Return 7.0% 5.0% 15.0% в C 0.040 0.015 0.022 0.250 0.031 1 0.090 Calculate the expected return and standard deviation of portfolios with the following weights. Weight in security A is 0.6 and weight in security C is 0.4. Weight in security A is 0.4, weight in security B is 0.2, and weight in security C is 0.4. Provide a brief comment on the risk characteristics of the above portfolios.

Answer 1

		Portfolio Return:
		w1*R1+w2*R2+w3*R3 +…....+wn*Rn
		w1,w2,w3 are weight of assets 1,2,3…n in the portfolio
		w1+w2+w3+…..+wn=1
		R1,R2,R3 …Rn=Returns of assets 1,2,3…n
		Portfolio Variance:
		(w1^2)*V1+(w2^2)*V2+(w3^2)*V3+…....+(wn^2)*Vn+2w1w2*Cov(1,2)+2w1w3*Cov(1,3)+2w2w3*Cov(2,3)+…................+2wnw(n-1)Cov(n,n-1)
		w1,w2,w3 are weight of assets 1,2,3…n in the portfolio
		w1+w2+w3+…..+wn=1
		V1,V2,V3….Vn are Variances of Assets 1,2,3…n
		Cov(1,2), Cov(1,3), ….(Cov(n,n-1) are covariance between asset pair
	a)	Expected Return:
		w1*R1+w2*R2=0.6*7+0.4*5=	6.20%
		Expected Variance:
		(w1^2)*V1+(w2^2)*V2+2w1w2*Cov(1,2)
		(0.6^2)*0.04+(0.4^2)*0.25+2*0.6*0.4*0.015=	0.0616
		Standard Deviation =Square Root of Variance
		Expected Standard Deviation:SQRT(0.0616)=	0.248193
		Expected Standard Deviation:	24.82%
	b)	Expected Return:
		w1*R1+w2*R2+w3*R3 =0.4*7+0.2*5+0.2*15=	6.80%
		Expected Variance:
		(w1^2)*V1+(w2^2)*V2+w3*V3+2w1w2*Cov(1,2)+2w1w3*Cov(1,3)+2w2w3*Cov(2,3)
		(0.4^2)*0.04+(0.2^2)*0.25+(0.2^2)*0.09+2*0.4*0.2*0.015+2*0.4*0.2*0.022+2*0.2*0.2*0.031=					0.0284
		Expected Portfolio Variance	0.0284
		Expected Standard Deviation:SQRT(0.0284)=	0.168523
		Expected Standard Deviation	16.85%
	c)	Portfolio b has higher diversification
		This has resulted in reduction of risk
		Risks are measured by standard deviation
		Also expected return of c is higher than b
		Hence, Return /Risk ratio has increased with more diversification