Question

We know the following expected returns for stocks A and B, given different states of the economy:
States(s) Probability E(rAS) E(rB,)
Recession 0.2 -0.1 0.04
Normal 0.5 0.08 0.05
Expansion 0.3 0.1 0.07
1. What is the expected return for stock A?
2. What is the expected return for stock B?

Answer 1

Answer:

Expected Returns:

1. Stock A:

= (0.2 x 0.04) + (0.5 x 0.05) + (0.3 x 0.07)

= -0.02 + 0.04 + 0.12

= 0.14

= 14%

2. Stock B:

= (0.2 x -0.1) + (0.5 x 0.08) + (0.3 x 0.1)

= -0.008 + 0.025 + 0.021

= 0.054

= 5.4%

Explanation:

a) Data and Calculations:

States(s)                Probability       E(rAS)         E(rB,)

Recession                  0.2             -0.1             0.04

Normal                       0.5              0.08          0.05

Expansion                  0.3              0.1             0.07

b) An investor in Stock A's expected return is the sum of the returns under different economic scenarios of recession, normal economy, and expansion, weighed by the probabilities of each event, which the investor would expect to realize by making the investment in a security.  Stock A's expected return shows that the investor in the stock would expect a 14% return on the value of the investment.  Whereas, the same investor would expect a return of 5.4% in Stock B's investment.