Question

Consider the following information on Stocks A, B, C and their returns (in decimals) in each state: State Prob. of State A B C Boom 20% 0.34 0.2 0.14 Good 45% 0.13 0.09 0.08 Poor 25% 0.01 0.01 0.04 Bust 10% -0.08 -0.03 -0.03 If your portfolio is invested 25% in A, 40% in B, and 35% in C, what is the standard deviation of the portfolio in percent? Answer to two decimals, carry intermediate calcs. to at least four decimals.

Answer 1

A
Scenario	Probability	Return	=rate of return * probability	Actual return -expected return(A)	(A)^2* probability
Boom	0.2	0.34	0.068	0.219	0.0095922
Good	0.45	0.13	0.0585	0.009	3.645E-05
Poor	0.25	0.01	0.0025	-0.111	0.00308025
Bust	0.1	-0.08	-0.008	-0.201	0.0040401
	Expected return =	sum of weighted return =	0.121	Sum=	0.016749
			Standard deviation of A	=(sum)^(1/2)	0.129417928
			Coefficient of variation=	STD DEV/RETURN=	1.06956965
B
Scenario	Probability	Return	=rate of return * probability	Actual return -expected return(B)	(B)^2* probability
Boom	0.2	0.2	0.04	0.12	0.00288
Good	0.45	0.09	0.0405	0.01	4.5E-05
Poor	0.25	0.01	0.0025	-0.07	0.001225
Bust	0.1	-0.03	-0.003	-0.11	0.00121
	Expected return =	sum of weighted return =	0.08	Sum=	0.00536
			Standard deviation of B	=(sum)^(1/2)	0.073212021
			Coefficient of variation=	STD DEV/RETURN=	0.915150261
C
Scenario	Probability	Return	=rate of return * probability	Actual return -expected return(C)	(C)^2* probability
Boom	0.2	0.14	0.028	0.06	0.00072
Good	0.45	0.08	0.036	0	0
Poor	0.25	0.04	0.01	-0.04	0.0004
Bust	0.1	-0.03	-0.003	-0.11	0.00121
	Expected return =	sum of weighted return =	0.071	Sum=	0.00233
			Standard deviation of C	=(sum)^(1/2)	0.048270074
			Coefficient of variation=	STD DEV/RETURN=	0.679860191
Covariance A B:
Scenario	Probability	Actual return -expected return(A)	Actual return -expected return(B)	(A)*(B)*probability
Boom	0.2	0.2190	0.12	0.005256
Good	0.45	0.009	0.01	0.0000405
Poor	0.25	-0.11	-0.07	0.0019425
Bust	0.1	-0.201	-0.11	0.002211
			Covariance=sum=	0.00945
		Correlation A&B=	Covariance/(std devA*std devB)=	0.997366949
Covariance A C:
Scenario	Probability	Actual return -expected return(A)	Actual return -expected return(C)	(A)*(C)*probability
Boom	0.2	0.219	0.06	0.002628
Good	0.45	0.009	0	0
Poor	0.25	-11.10%	-0.04	0.00111
Bust	0.1	-0.201	-0.11	0.002211
			Covariance=sum=	0.005949
		Correlation A&C=	Covariance/(std devA*std devC)=	0.952295138
Covariance B C:
Scenario	Probability	Actual return -expected return(B)	Actual return -expected return(C)	(A)*(B)*probability
Boom	0.2	0.12	0.06	0.00144
Good	0.45	0.01	0	0
Poor	0.25	-0.07	-0.04	0.0007
Bust	0.1	-0.11	-0.11	0.00121
			Covariance=sum=	0.00335
		Correlation B&C=	Covariance/(std devB*std devC)=	0.947947863
	Expected return=	Wt A*Return A+Wt B*Return B+Wt C*Return C
	Expected return=	0.25*12.1+0.4*8+0.35*7.1
	Expected return=	8.71
	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=	0.006058913
	Standard deviation=	(variance)^0.5
	Standard deviation%=	7.78