Question

States		Probability		Asset M Return		Asset N Return		Asset O Return
Boom		27​%		10%		21​%		2​%
Normal		50​%		8%		12​%		8%
Recession		23​%		2%		1​%		10​%

a. What is the expected return of investing equally in all three assets M, N, O?

b. What is the expected return of investing in asset M alone?

c. What is the standard deviation of the portfolio that invests equally in all three assets?

d. What is he standard deviation of asset M?

Answer 1

a.

Stock M
Scenario	Probability	Return	=rate of return * probability	Actual return -expected return(A)	(A)^2* probability
Recession	0.23	0.02	0.0046	-0.0516	0.000612389
Normal	0.5	0.08	0.04	0.0084	0.00003528
Boom	0.27	0.1	0.027	0.0284	0.000217771
	Expected return =	sum of weighted return =	0.0716	Sum=	0.00086544
			Standard deviation of stock A	=(sum)^(1/2)	0.029418362
Stock N
Scenario	Probability	Return	=rate of return * probability	Actual return -expected return(B)	(B)^2* probability
Recession	0.23	0.01	0.0023	-0.109	0.00273263
Normal	0.5	0.12	0.06	0.001	5E-07
Boom	0.27	0.21	0.0567	0.091	0.00223587
	Expected return =	sum of weighted return =	0.119	Sum=	0.004969
			Standard deviation of stock B	=(sum)^(1/2)	0.070491134
Stock O
Scenario	Probability	Return	=rate of return * probability	Actual return -expected return(C)	(C)^2* probability
Recession	0.23	0.1	0.023	-0.019	8.303E-05
Normal	0.5	0.18	0.09	0.061	0.0018605
Boom	0.27	0.02	0.0054	-0.099	0.00264627
	Expected return =	sum of weighted return =	0.1184	Sum=	0.0045898
			Standard deviation of stock C	=(sum)^(1/2)	0.067748063

Expected return=	Wt A*Return A+Wt B*Return B+Wt C*Return C
Expected return=	0.333333333333333*7.16+0.333333333333333*11.9+0.333333333333333*11.84
Expected return=	10.3

b.

Stock M
Scenario	Probability	Return	=rate of return * probability
Recession	0.23	0.02	0.0046
Normal	0.5	0.08	0.04
Boom	0.27	0.1	0.027
	Expected return =	sum of weighted return =	0.0716

=7.16%

c.

Variance=	=w2A*σ2(RA) + w2B*σ2(RB) + w2C*σ2(RC)+ 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB) + 2*(wA)*(wC)*Cor(RA, RC)*σ(RA)*σ(RC) + 2*(wC)*(wB)*Cor(RC, RB)*σ(RC)*σ(RB)
Variance=	0.001112151
Standard deviation=	(variance)^0.5
Standard deviation%=	3.33

d.

Stock M
Scenario	Probability	Return	=rate of return * probability	Actual return -expected return(A)	(A)^2* probability
Recession	0.23	0.02	0.0046	-0.0516	0.000612389
Normal	0.5	0.08	0.04	0.0084	0.00003528
Boom	0.27	0.1	0.027	0.0284	0.000217771
	Expected return =	sum of weighted return =	0.0716	Sum=	0.00086544
			Standard deviation of stock M	=(sum)^(1/2)	0.029418362

=2.94%