CFA Practice Question

There are 227 practice questions for this study session.

CFA Practice Question

A stock is worth $60 today. In a year the stock price can rise or fall by 15 percent. The interest rate is 6%. A call option expires in two years and has an exercise price of $55. Today at time 0, a risk-free hedge consists of a short position in 10,000 calls and a long position in ______ shares of the stock.
A. 5865
B. 7935
C. 8167
Explanation: The risk-neutral probability is π = (1.06 - 0.85) / (1.15 - 0.85) = 0.7, and 1 - π = 0.3.

Stock prices in the binomial tree one and two years from now are:
  • S+ = 60 (1.15) = $69
  • S- = 60 (0.85) = $51
  • S++ = 60 (1.15) (1.15) = $79.35
  • S+- = S-+ = 60 (1.15) (0.85) = $58.65
  • S-- = 60 (0.85) (0.85) = $43.35
Call option values at expiration two years from now are:
  • c++ = Max (0, 79.35 - 55) = $24.35
  • c+- = c-+ = Max (0, 58.65 - 55) = $3.65
  • c-- = Max (0, $43.35 - 55) = $0
The option prices at the end of year 1: c+ = (0.7 x 24.35 + 0.3 x 3.65)/(1.06) = $17.11.
c- = (0.7 x 3.65 + 0.3 x 0)/(1.06) = $2.41

At the current price of $60, n = (c+ - c-) / (S+ - S-) = (17.11 - 2.41) / (69 - 51) = 0.8167.

User Contributed Comments 5

User Comment
HenryQ Don't understand why d=0.85 instead of 1/1.15= 0.87...anyone?
heinzlive It is always u= 1+ upside potential in % and d= 1- downside potential in % thus, here u=1+0,15 = 1,15 and d= 1-0,15 = 0,85.
dblueroom somehow you can't use 1/1.15 (schweser uses this) however, here as well as CFA book only recognize an downside move 1-.15 in this case.
serboc I agree with DBlueroom
dakota6789 the reason I think you can't use 1/15 is that a 15% increase on a 15% decrease is not the same thing. If I lose 15% of 100, I'm left with 85. If I gain 15% of 85, that's less than 100.
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