Look again at Tables 13.1 and 13.2. Suppose you think a boom will occur only 20 percent of the time instead of 50 percent. What are the expected returns on Stocks U and L in this case?
If the risk-free rate is 10 percent, what are the risk premiums?

Question

TABLE 13.1	States of the Economy and Stock Returns
State of Economy	Probability of State of Economy	Rate of Return If State Occurs
State of Economy	Probability of State of Economy	Stock L	Stock U
Recession	.50	−20%	30%
Boom	[latex]\underline{ .50}[/latex]	70	10
	1.00

TABLE 13.2	Calculation of Expected Return
		Stock L		Stock U
(1) State of Economy	(2) Probability of State of Economy	(3) Rate of Return If State Occurs	(4) Product (2) × (3)	(5) Rate of Return If State Occurs	(6) Product (2) × (5)
Recession	.50	−.20	−.10	.30	.15
Boom	[latex]\underline{ .50}[/latex]	.70	[latex]\underline{.35}[/latex]	.10	[latex]\underline{ .05}[/latex]
	1.00	[latex]E(R_{L})[/latex] = .25, or 25%		[latex]E(R_{U})[/latex] = .20, or 20%

Accepted Answer

The first thing to notice is that a recession must occur 80 percent of the time (1 − .20 = .80) because there are only two possibilities. With this in mind, we see that Stock U has a 30 percent return in 80 percent of the years and a 10 percent return in 20 percent of the years. To calculate the expected return, we again just multiply the possibilities by the probabilities and add up the results:

E(R[latex]_{U}[/latex]) = .80 × 30% + .20 × 10% = 26%

Table 13.3 summarizes the calculations for both stocks. Notice that the expected return on L is −2 percent.

TABLE 13.3	Calculation of Expected Return
		Stock L		Stock U
(1) State of Economy	(2) Probability of State of Economy	(3) Rate of Return If State Occurs	(4) Product (2) × (3)	(5) Rate of Return If State Occurs	(6) Product (2) × (5)
Recession	.80	−.20	−.16	.30	.24
Boom	.20	.70	[latex]\underline{.14}[/latex]	.10	[latex]\underline{ .02}[/latex]
		E(R[latex]_{L}[/latex]) = −.02, or −2%		E(R[latex]_{U}[/latex]) = .26 =, or 26%

The risk premium for Stock U is 26% − 10 = 16% in this case. The risk premium for Stock L is: −2% − 10 = −12%. This is a little odd; but, for reasons we discuss later, it is not impossible.

Question 13.1: Look again at Tables 13.1 and 13.2. Suppose you think a boom...

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