Question

We know the following expected returns for stock A and the market portfolio, given different states of the economy:

State (s)	Probability	E(rA,s)	E(rM,s)
Recession	0.2	-0.02	0.02
Normal	0.5	0.13	0.05
Expansion	0.3	0.21	0.09

The risk-free rate is 0.02.

Assuming the CAPM holds, what is the beta for stock A?

Answer 1

Expcted return on stock A
State	Probability	E(rA)	Expected return
a	b	c	d=b*c
Recession	0.2	-0.02	-0.004
Normal	0.5	0.13	0.065
Expansion	0.3	0.21	0.063
Total	1		0.124
State	Probability	E(rM,s)	Expected return
a	b	c	d=b*c
Recession	0.2	0.02	0.004
Normal	0.5	0.05	0.025
Expansion	0.3	0.09	0.027
Total	1		0.056
Calculation of beta
R = Rf+ B(Rm-Rf)
Where,
Rf = Risk Free Return
B= Beta
Rm = Market rate of return
Rm-Rf= Risk Premium
0.124=0.02+Beta*(0.056-0.02)
0.124=0.02+Beta*(0.036)
Beta = 2.89