Question

The risky portfolio Q consists of 2,500 shares of Google and 7,500 shares of Yahoo. Assume that Google has a share price of $4, an expected return of 18 per cent, and a standard deviation of 25 per cent. Yahoo has a share price of $2, an expected return of 15 per cent, and a standard deviation of 20 per cent. The correlation between the two is 0.5, and the risk-free rate of interest is 2 per cent.

What fraction of your portfolio must you invest in risky portfolio of Q and risk-free to have a portfolio standard deviation of 12 per cent?

Answer 1

	S1=Standard Deviation of Google	25%
	S2=Standard Deviation of Yahoo	20%
	Total Portfolio Value=2500*4+7500*2=	$25,000
	w1=Weight of Google in the portfolio	0.40	(2500*4)/25000
	w2=Weight of Yahoo in the portfolio	0.60	(7500*2)/25001
	Covariance =Correlation*S1*S2
	Covariance =0.5*25*20	250	%%
	Portfolio Variance =Vp=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*Covariance*w1*w2
	Portfolio Variance =Vp=(0.4^2)*(25^2)+(0.6^2)*(20^2)+2*250*0.4*0.6=	364	%%
	Portfolio Standard Deviation=Square Root (Variance)
	Portfolio Standard Deviation=Square Root (364)=	19.08%
	W=Weight of Risky Portfolio Q
	(1-W)=Weight of Risk Free Asset
	S=Standard Deviation of Q=	19.08%
	Standard Deviation of Risk Free asset	0
	Covariance =0
	V=Variance of New Portfolio with Riskfree asset=	(W^2)*(19.08^2)
	S=Standard Deviation of New Portfolio =Square Root (V)
		W	1-W	V	S=SQRT(V)
		Weight of Q	Weight of Risk Feee	Portfolio Variance(%%)	Portfolio Std Deviation
		0.1	0.9	3.64	1.91%
		0.2	0.8	14.56	3.82%
		0.3	0.7	32.76	5.72%
		0.4	0.6	58.24	7.63%
		0.5	0.5	91	9.54%
		0.6	0.4	131.04	11.45%
		0.629	0.371	144.0133	12.00%
		0.7	0.3	178.36	13.36%
		0.8	0.2	232.96	15.26%
		0.9	0.1	294.84	17.17%
		1	0	364	19.08%
	Fraction of Portfolio in Q	0.629
	Fraction of Portfolio in Risk Free asset	0.371