Question

Consider two risky investments with the following return distributions:

Probability	Return R1 (p.a.)
0.25 0.30 0.25 0.20	+12% +4% −5% −8%
Expected return	μ1 = 1.3500%
Volatility	σ1 = 7.6176%

Probability	Return R2 (p.a.)
0.30 0.30 0.20 0.20	+10% +8% +3% −15%
Expected return
Volatility

The correlation between the returns of the two investments is ρ₁₂ = 0.9.

1. (a) Calculate μ₂ and σ₂. (Read the Instructions carefully.)

2. (b) Express the portfolio squared volatility σP₂ in terms of w1, the weight of the first investment. (Round the coefficients to 6 decimals.)

3. (c) Using your answer in part (b), find the weight w₁ of the minimum-risk portfolio. Hence, find the expected return μ_P and volatility σ_P of the minimum-risk portfolio.

Answer 1

	Expected Return =Mean Return =SUMof ((Probability)*(Return))
	Variance of Return =Sum of(Probability* (Deviation ^2))
	Deviation =Return -Mean Return
	Standard Deviation of Return =Square Root of Variance of Return
	ANALYSIS OF ASSET 1
		p	R1	A1=R1*P	D1=R1-1.35	E1=(D1^2)	F1=p*E1
		Probability	Return(%)	Probability*Return(%)	Deviation(%)	Deviation Squared(%%)	Probability*Deviation Squared(%%)
		0.25	12	3	10.65	113.4225	28.355625
		0.30	4	1.2	2.65	7.0225	2.10675
		0.25	-5	-1.25	-6.35	40.3225	10.080625
		0.20	-8	-1.6	-9.35	87.4225	17.4845
			SUM	1.35		SUM	58.0275
	Expected Return =Mean return	1.35	%
	Variance of Return	58.0275	%%
	Standard Deviation of Return =SQRT(58.0275)=		7.6176	%
	ANALYSIS OF ASSET 2
		p	R2	A2=R2*p	D2=R2-2.65	E2=(D2^2)	F2=p*E2
		Probability	Return(%)	Probability*Return(%)	Deviation(%)	Deviation Squared(%%)	Probability*Deviation Squared(%%)
		0.25	10	2.5	7.35	54.0225	13.505625
		0.30	8	2.4	5.35	28.6225	8.58675
		0.25	3	0.75	0.35	0.1225	0.030625
		0.20	-15	-3	-17.65	311.5225	62.3045
			SUM	2.65		SUM	84.4275
	Expected Return =Mean return	2.65	%
	Variance of Return	84.4275	%%
	Standard Deviation of Return =SQRT(84.4275)=		9.1884	%
	Covariance between Return of Asset 1 and asset 2=Correlation*Standard Deviation of asset 1*Standard Deviation of asset 2
	Covariance between Return of Asset 1 and asset 2	62.9943	%%	(0.9*7.6176*9.1884)