Question

Assume that the economy could experience three possible "states," next year: High Growth, Normal Growth, and Recession; and that this table shows the probablilities of each state happening and the returns to the stock market if they happen:

State of the Economy	Probability	Return
High Growth	0.2	+30%
Normal Growth	0.7	+12%
Recession	0.1	-15%

Do EACH of the following calculations:

1. What is the expected payoff of a $1000 investment over the following year? What is the Expected Return to this investment over the following year? (2 points)
2. What is the Standard Deviation of those returns, expressed as a percentage of the investment? (1 point)
3. If the risk free rate is 5 percent, what is the RISK PREMIUM on this investment? (1 point)

Answer 1

Expected returns=Sum(Probability*Returns)=0.2*30%+0.7*12%+0.1*(-15%)=12.90000%

Standard deviation=Sqrt(Sum(probability*(returns-expected returns)^2))=Sqrt(0.2*(30%-12.90000%)^2+0.7*(12%-12.90000%)^2+0.1*(-15%-12.90000%)^2)=11.70000%

Risk Premium=Expected returns-risk free rate=12.90000%-5%=7.90000%