Question

Harbin Manufacturing has 10 million shares outstanding with a current share price of $22.28 per share. In one year, the share price is equally likely to be $28 or $19. 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) Return if price go up to $28 = ($28 - $22.28) / 22.28 * 100 = 25.67%

Return if price go down to $19 = ($19 - $22.28) / 22.28 * 100 =-14.72%

Expected Return = Sum (Return * Probability)

Expected Return = (25.67% * 0.5) + (-14.72% * 0.5) = 5.475%

b) Under Risk neutral mode

So = spot price = $22.28 per share

Risk free rate = 6%

Normal return = $22.28 * 6% = $1.3368

Profit if price goes up = $28 - $22.28 = $5.72

Loss if price goes down = $19 - $22.28 = -$3.28

Lets 'P' be probability of Price of Harbin stock will increase

Lets '1 - P' be probability of Price of Harbin stock will decrease

$1.3368 = ($5.72 * P) + (-$3.28 * (1-P))

= 5.72P + 3.28P - 3.28

4.6168 = 9P

P = 4.6168 / 9 = 0.513 = 51.3%

Probability of Price of Harbin stock will increase is 0.513