Question

One share of stock Z is selling for $10. The stock has the following possible payoffs after one year:

Slump	Normal	Boom
$8	$12	$16

Calculate the expected rate of return offer by stock Z. Assume that the probability for slump is 25%, 50% for normal, and 25% for boom.

15%

12%

20%

16%

Answer 1

Answer is 20%

Slump:

Rate of Return = (Payoff - Selling Price) / Selling Price
Rate of Return = ($8 - $10) / $10
Rate of Return = -0.20

Normal:

Rate of Return = (Payoff - Selling Price) / Selling Price
Rate of Return = ($12 - $10) / $10
Rate of Return = 0.20

Boom:

Rate of Return = (Payoff - Selling Price) / Selling Price
Rate of Return = ($16 - $10) / $10
Rate of Return = 0.60

Expected Rate of Return = Probability of Slump * Rate of Return during Slump + Probability of Normal * Rate of Return during Normal + Probability of Boom * Rate of Return during Boom
Expected Rate of Return = 0.25 * (-0.20) + 0.50 * 0.20 + 0.25 * 0.60
Expected Rate of Return = 0.20 or 20%