Question

Being a sharp analyst, you have narrowed the possible outcomes for two potential investments as follows (also included is your estimate of the returns on the market):
State of the
Return (%)
Economy
Probability
Stock A
Stock B
Market
1 (great)
0.30
25
20
18
2 (good)
0.50
16
14
16
3 (mediocre)
0.20
8
12
14
a. Calculate the expected returns for stocks A and B and the market.
b. Calculate the standard deviation of returns for stocks A and B and the market.
c. Find the covariance between stock A and the market, and between stock B and the market.
d. Find the correlation coefficients between stock A and the market and between stock B and the market.

Answer 1

a

Stock A
Scenario	Probability	Return	=rate of return * probability
Great	0.3	0.25	0.075
Good	0.5	0.16	0.08
Mediocre	0.2	0.08	0.016
	Expected return =	sum of weighted return =	0.171

Stock B
Scenario	Probability	Return	=rate of return * probability
Great	0.3	0.2	0.06
Good	0.5	0.14	0.07
Mediocre	0.2	0.12	0.024
	Expected return =	sum of weighted return =	0.154

b

Stock A
Scenario	Probability	Return	=rate of return * probability	Actual return -expected return(A)	(A)^2* probability
Great	0.3	0.25	0.075	0.079	0.0018723
Good	0.5	0.16	0.08	-0.011	6.05E-05
Mediocre	0.2	0.08	0.016	-0.091	0.0016562
	Expected return =	sum of weighted return =	0.171	Sum=	0.003589
			Standard deviation of Stock A	=(sum)^(1/2)	0.059908263
Stock B
Scenario	Probability	Return	=rate of return * probability	Actual return -expected return(B)	(B)^2* probability
Great	0.3	0.2	0.06	0.046	0.0006348
Good	0.5	0.14	0.07	-0.014	9.8E-05
Mediocre	0.2	0.12	0.024	-0.034	0.0002312
	Expected return =	sum of weighted return =	0.154	Sum=	0.000964
			Standard deviation of Stock B	=(sum)^(1/2)	0.031048349

c & d

Covariance Stock A Market:
Scenario	Probability	Actual return -expected return(A)	Actual return -expected return(C)	(A)*(C)*probability
Great	0.3	0.079	0.026	0.0006162
Good	0.5	-0.011	0.006	-0.000033
Mediocre	0.2	-9.10%	-0.014	0.0002548
			Covariance=sum=	0.000838
		Correlation A&C=	Covariance/(std devA*std devC)=	0.867502261
Covariance Stock B Market:
Scenario	Probability	Actual return -expected return(B)	Actual return -expected return(C)	(A)*(B)*probability
Great	0.3	0.046	0.026	0.0003588
Good	0.5	-0.014	0.006	-0.000042
Mediocre	0.2	-0.034	-0.014	9.52E-05
			Covariance=sum=	0.000412
		Correlation B&C=	Covariance/(std devB*std devC)=	0.822947301