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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 one−year return on this​ stock, and what is the return standard​ deviation?

Respuesta :

Answer and Explanation:

The computation is shown below;

Purchase price = $15.00

Forecasted price of $30.00 with probability of 40%:

Now  

Rate of Return = (Selling Price - Purchase Price) ÷ Purchase Price

= ($30.00 - $15.00) ÷ $15.00

= 100.00%

And,

Forecasted price of $10.00 with probability of 60%:

Now

Rate of Return = (Selling Price - Purchase Price) ÷ Purchase Price

= ($10.00 - $15.00) ÷ $15.00

= -33.33%

Now  

Expected Return = 0.40 × 1.0000 + 0.60 × (-0.3333)

= 0.20 or 20.00%

and,

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

= 0.426645

Finally

Standard Deviation = (0.426645)^(1 ÷ 2)

= 0.6532 or 65.32%

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