Question

There are only two risky assets (stocks) A and B in the market.

Asset A: Mean = 20% Standard Deviation = 10%

Asset B: Mean = 10% Standard Deviation = 5%

Returns on Assets have zero correlation.

A.Assume that there is no risk-free asset.

(i)Plot (sketch) the efficiency frontier (the investment opportunity set).

(ii)What is the expected return and the standard deviation of the minimum-variance-portfolio?

(iii)An investor would like to construct a portfolio that has a standard deviation of 8%. Aconsultant suggest the following portfolio: ????=−0.393,????=1.393. Is this a goodsuggestion? Explain.

Answer 1

	Expected Return of Stock A=R1	20%
	Expected Return of Stock Y=R2	10%
	S1=Standard Deviation of Stock A	10.00%
	S2=Standard Deviation of Stock B	5.00%
	Variance of Stock A=V1=(S1^2)	100	%%
	Variance of Stock B=V2=(S2^2)	25.00	%%
	Correlation (1,2)	0.00
	Covariance(1,2)=Correlation*S1*S2	0.00	%%
	w1=Investment in Stock A
	w2=Investment in Stock B
	Portfolio Return=Rp(Percentage)
	w1*R1+w2*R2=w1*20+w2*10			……..Equation (1)
	Vp=Portfolio Variance=(w1^2)*V1+(w2^2)*V2+2*w1*w2*Covariance(1.2)
	Vp=Portfolio Variance=(w1^2)*100+(w2^2)*25….....Equation(2)
	Sp=Portfolio Standard Deviation=Square root of Variance=SQRT(Vp)
	ALL POSSIBLE PORTFOLIOS
		w1	w2	Rp=w1*20+w2*10	Vp(Using Equation (2)	SP=Square Root(Vp)
		Weight of	Weight of
		Stock A	Stock B	Portfolio Return(%)	Portfolio Variance(%%)	Portfolio Standard Deviation(%)	Portfolio Return(%)
		0	1	10	25.00	5.0%	10.0%
		0.2	0.8	12	20.00	4.5%	12.0%
		0.3	0.7	13	21.25	4.6%	13.0%
		0.4	0.6	14	25.00	5.0%	14.0%
		0.5	0.5	15	31.25	5.6%	15.0%
		0.6	0.4	16	40.00	6.3%	16.0%
		0.7	0.3	17	51.25	7.2%	17.0%
		0.79	0.21	17.9	63.51	8.0%	17.9%
		0.8	0.2	18	65.00	8.1%	18.0%
		0.9	0.1	19	81.25	9.0%	19.0%
		1.00	0	20	100.00	10.0%	20.0%
		(0.39)	1.393	6.07	63.96	8.0%	6.1%
(ii)	Minimum Variance Portfolio
	Variance	20.00	%%
	Expected Return	12.0%
	Standard Deviation	4.5%
(iii)	8% Standard Deviation can be achieved by :
	Weight of A=0.79, Weight of B=0.21
	Expected Return of this portfolio	17.9%
	If you use:
	Weight of A=-0.393, Weight of B=1.393
	Standard Deviation	8.0%
	Expected Return of this portfolio	6.1%
	This is not a good suggestion
	Expected Return of this portfolio is much lower
	Weight of A=0.79, Weight of B=0.21
	Is a better solution for 8% standard Deviation
									Efficiency Frontier: X-axis:Standard Deviation; Y axis-Return 25.0% 20.0% 15.0% 10.0% 5.0% 0.0% 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% Ooo