Question

1. Following are the returns on two assets and three states of the economy

Economy Status	Probability	Stock    A RETURN          RA	Stock B RETURN          RB
BOOM	0.3	20%	6%
NORMAL	0.4	13%	7%
BUST	0.3	33%	11%

1. What are the expected returns and standard deviations for these two stocks?
2. What do you interpret? Which stock is riskier?

Answer 1

a: Expected returns

Stock A = 21.1%

Stock B= 7.90%

Standard deviations

Stock A= 8.31%

Stock B= 2.07%

b: Stock A is riskier since it has higher standard deviation

Workings

State	Probability	Stock A	X^2*P	B	X^2*P
Boom	0.30	20%	0.012	6%	0.00108
Normal	0.4	13%	0.00676	7%	0.00196
Bust	0.3	33%	0.03267	11%	0.00363
Expected return		21.10%		7.90%
Sum			0.05143		0.00667
Variance			0.006909		0.000429
SD			8.31%		2.07%