Question

1) Consider the following two assets that have rates of return in three equally likely scenarios:

Scenario	M (market)	A
Strong Growth	15	9
Weak Growth	5	-5
Recession	-5	5

a) What is the expected return of each asset?

b) What is the risk of each asset when viewed in isolation (standard deviation)?

c) Assuming that investors currently hold asset M, what is the risk of asset A in the portfolio sense (beta)?

Answer 1

M (Market):
Scenario	Return [r]	Probability [p]	r*p	dM=r-E[r]	dM^2	p*dM^2
Strong growth	15	0.3333	5.00	10	100	33.33
Weak growth	5	0.3333	1.67	0	0	0.00
Recession	-5	0.3333	-1.67	-10	100	33.33
			5.00			66.67
Expected return = 5%
Standard deviation = 66.67^0.5 =		8.17
A:
Scenario	Return [r]	Probability [p]	r*p	dA=r-E[r]	dA^2	p*dA^2
Strong growth	9	0.3333	3.00	6	36	12.00
Weak growth	-5	0.3333	-1.67	-8	64	21.33
Recession	5	0.3333	1.67	2	4	1.33
			3.00			34.67
Expected return = 3%
Standard deviation = 34.67^0.5 =		5.89
CORRELATION (M,A)
dM*dA	dM*dA*p
60	20.00		`
0	0.00
-20	-6.67
	13.33
Correlation (M,A) = dM*dA*p/(SDM*SDA) = 13.33/(8.17*5.89) =				0.28
ANSWERS:
Expected return:
M (Market) = 5%
A = 3%
SD:
M = 8.17%
A = 5.89%
Beta of A = COR(M,A)*SDA/SDM = 0.28*5.89/8.17 =			0.20