Question

3. Expected return and CAPM Suppose the risk-free rate is 4% and the market portfolio and stock j have the following return distributions: Probability in tot Market return -.15 .05 .15 .20 Return for i --30 .00 .20 .50 a. Find the expected market return, Im. b. Find the variance of the market return, c. Find the expected return for stock j, r;. d. Find the covariance of j and the market, Oim. e. What is J's beta?

Answer 1

Probability	Rm	Rj	Rm*p	Rj*p	Rm-ERm	Rj-ERj	(Rm-ERm)2*p	(Rj-ERj)2*p	(Rm-ERm)*(Rj-ERj)*p
0.10	-0.15	-0.30	-0.02	-0.03	-0.25	-0.45	0.006250	0.020250	0.011250
0.30	0.05	0.00	0.02	0.00	-0.05	-0.15	0.000750	0.006750	0.002250
0.40	0.15	0.20	0.06	0.08	0.05	0.05	0.001000	0.001000	0.001000
0.20	0.20	0.50	0.04	0.10	0.10	0.35	0.002000	0.024500	0.007000
Total			ERm = 0.10	ERj= 0.15			$\sigma$m2=0.010000	$\sigma$j2=0.052500	Covariance = 0.0215
							$\sigma$m=0.10	$\sigma$j=0.229129

J's Beta = Covariance/ $\sigma$ _m² = 0.0215/0.01 = 2.15