Question

1. Consider Asset A and B, which asset has higher systematic risk? Which one has higher total risk? Show your calculations. Assume the market risk premium is 8 percent, the risk-free rate is 4 percent, and the capital asset pricing model holds. (Rounding your answers to four decimal places)

State of Economy	Probability of State of Economy	Rate of Return if State Occurs
		Asset A	Asset B
Recession	0.10	0.02	-0.25
Normal	0.70	0.25	0.09
Irrational exuberance	0.20	0.05	0.40

Answer 1

Expected return = Recession probability x Return if recession occurs + Normal probability x Reurn in normal conditions + Irrational exuberance probability x Reurn in in such conditions

Expected return for asset A = 0.10 x 2% + 0.70 x 25% + 0.20 x 5%

Expected return for asset A = 18.7%

Expected return for asset B = 0.10 x (-25%) + 0.70 x 9% + 0.20 x 40%

Expected return for asset B = 11.8%

Beta is a measure of systematic risk. Beta can be calculated using CAPM model.

As per CAPM model :

Expected return = Risk free rate + Beta x Market risk premium

Where,

Expected return = Expected return on respective assets calculated above

Risk free rate = 4%

Market risk premium = 8%

Beta = ?

Hence, Beta of asset A :

18.7% = 4% + Beta x 8%

Beta = 1.8375 times

Beta of asset A is 1.8375 times

Beta of asset B :

11.8% = 4% + Beta x 8%

Beta = 0.975 times

Beta of asset B is 0.975 times

Hence, based on above Asset A has higher systematic risk because it has higher beta.

Standard deviation is a measure of total risk :

Standard deviation =

Standard deviation of asset A =

Standard deviation of asset A = 9.6545%

Standard deviation of asset B =

Standard deviation of asset B = 17.3194%

Hence, based on above total risk of Asset B is higher because of higher standard deviation.