Harbin Manufacturing has 10 million shares outstanding with a current share pric

Question

Harbin Manufacturing has 10 million shares outstanding with a current share price of $20.36 per share. In one year, the share price is equally likely to be $28 or $19. The risk-free interest rate is 5%. a. Using the risk-neutral probabilities, what is the value of a one-year call option on Harbin stock with a strike price of $25? b. What is the expected return of the call option? c. Using the risk-neutral probabilities, what is the value of a one-year put option on Harbin stock with a strike price of $25? d. What is the expected return of the put option?

Explanation / Answer

a)

payoff in upper side = max(28 - 25,0) = 3

payoff in down side = max(19 - 25,0) = 0

hedge ratio = (3 - 0) / (28-19) = 0.33

Sell one call buy 0.33 shares

-C + 0.33*S

Value after 1 year in upside = -3 + 0.33*28 = 6.33

Downside = 0 + 0.33*19 = 6.33

PV of portfolio = 6.33 / (1+5%) = 6.0317

current value of portfolio = -C + 0.33*20.36 = -C + 6.7867

-C + 6.7867 = 6.0317

C = 6.7867 - 6.0317 = 0.7549

b)

expected return = 0.5*3 + 0.5*0 = 1.5

call cost = 0.7549

return = (1.5 - 0.7549) / 0.7549 = 98.7%

c)

payoff in upper side = max(25 - 28,0) = 0

payoff in down side = max(25 - 19,0) = 6

hedge ratio = (0 - 6) / (28-19) = -0.67

buy one put and buy 0.67 shares

P + 0.67*S

Value after 1 year in upside = 0 + 0.67*28 = 18.67

Downside = 6 + 0.67*19 = 18.67

PV of portfolio = 18.67 / (1+5%) = 17.78

current value of portfolio = P + 0.67*S = P + 0.67*20.36

P + 13.57 = 17.78

P = 4.2044

d)

expected return = 0.5*0 + 0.5*6 = 3

call cost = 4.2044

return = (3 - 4.2044 ) / 4.2044 = -28.65%

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.