Question

Consider two assets, A and B in three equally likely scenarios. In scenario 1, they earn 4% and 10%, respectively. In scenario 2, they both earn 5%. In scenario 3, they earn 6% and 0%, respectively. Find the expected rates of return for assets A and B. S1 S2 S3 Asset A 4% 5% 6% Asset B 10% 5% 0% Which asset would a risk-averse investor, who cares only about expected return and risk and can choose only one or the other, prefer?

Answer 1

Assets A
			Exp. Return	Variance
Scenario	Prob.	AR	AR * Prob.	(AR-ER)^2*Prob.
1	0.3333333	4	1.3333	0.3333
2	0.3333333	5	1.6667	0.0000
3	0.3333333	6	2.0000	0.3333
			5.0000	0.6667
ER = sum=	5.00%
Std. Dev.= SQRT(Variance)	0.82
Assets B
			Exp. Return	Variance
Scenario	Prob.	AR	AR * Prob.	(AR-ER)^2*Prob.
1	0.3333333	10	3.333333333	8.33333333
2	0.3333333	5	1.666666667	0
3	0.3333333	0	0	8.33333333
			5.00	16.67
ER = sum=	5.00%
Std. Dev.= SQRT(Variance)	4.08
Expected return of Both Asset A and B is 5%. But risk (Standard deviation) is less in case of Asset A (0.82%),
So Risk averse investor will always prefer Asset A.