Question

You are considering buying a share of stock in a firm that has the following two possible payoffs with the corresponding probability of occurring. The stock has a purchase price of​ $15.00. You forecast that there is a​ 40% chance that the stock will sell for​ $30.00 at the end of one year. The alternative expectation is that there is a​ 60% chance that the stock will sell for​ $10.00 at the end of one year. What is the expected percentage oneminus−year return on this​ stock, and what is the return standard​ deviation?

Answer 1

Purchase price = $15.00

Forecasted price of $30.00 with probability of 40%:

Rate of Return = (Selling Price - Purchase Price) / Purchase Price
Rate of Return = ($30.00 - $15.00) / $15.00
Rate of Return = 100.00%

Forecasted price of $10.00 with probability of 60%:

Rate of Return = (Selling Price - Purchase Price) / Purchase Price
Rate of Return = ($10.00 - $15.00) / $15.00
Rate of Return = -33.33%

Expected Return = 0.40 * 1.0000 + 0.60 * (-0.3333)
Expected Return = 0.20 or 20.00%

Variance = 0.40 * (1.00 - 0.200)^2 + 0.60 * (-0.3333 - 0.200)^2
Variance = 0.426645

Standard Deviation = (0.426645)^(1/2)
Standard Deviation = 0.6532 or 65.32%