Question

Harbin Manufacturing has 10 million shares outstanding with a current share price of $ 21.31 per share. In one​ year, the share price is equally likely to be $ 30 or $ 20. The​ risk-free interest rate is 6 %.

a. What is the expected return on Harbin​ stock?

b. What is the​ risk-neutral probability that​ Harbin's stock price will​ increase?

Answer 1

a). Expected Price in next year = [0.5 * 30] + [0.5 * 20]

= 15 + 10 = 25

Expected Return = [P1 - P0] / P0

= [$25 - $21.31] / $21.31 = $3.69 / $21.31 = 0.1732, or 17.32%

b). Up factor = Price in the up state / Current Price = 30 / 21.31 = 1.41

Down Factor = Price in the down state / Current Price

= 20 / 21.31 = 0.94

Risk-neutral probability = (1 + risk free rate - down factor) / (up factor - down factor)

= (1 + 0.06 - 0.94) / (1.41 - 0.94)

= 0.1215 / 0.4693

= 0.2589, or 25.89%