CFA Practice Question

There are 206 practice questions for this study session.

CFA Practice Question

Consider the following information on put and call options on an asset:

Call price: 2.6
Put price: p0 = 8
Exercise price: X = 60
Forward price: F(0, T) = 55
Days to option expiration: 180 days
The continuously compounded risk-free rate: r(c) = 4%

To make a risk-free profit using a synthetic call, you would ______.
A. long call and bond, short forward and put
B. long call and forward, short bond and put
C. long put and forward, and short call and bond
Explanation: The price of a synthetic call would be: c0 = long forward + p0 - [X - F(0, T)]/(1 + r)T = 0 + 8 - (60 - 55)/1.04180/365 = 3.10.
As the actual call is cheaper, we should buy the call and sell the synthetic call. The present value of the bond is [X - F(0, T)] / (1 + r)T = (60 - 55) / 1.04180/365 = 4.9.

The initial up-front cash is generated as -2.6 (long call) - 4.9 (long bond) + 0 (short forward) + 8 = 0.5.
At expiration, short forward would generate - (ST - 55), and long bond would generate (60 - 55).
  • If ST < 60, the portfolio would generate 0 (long call) - (STT - 55) (short forward) - (60 - ST) (short put) + (60 - 55) (long bond) = 0.
  • If ST >= 60, the portfolio would generate (ST - 60) (long call) - (ST - 55) (short forward) + 0 (short put) + (60 - 55) (long bond) = 0.
The strategy would generate 0.5 up-front without any investment or any amount to pay back later.

User Contributed Comments 4

User Comment
mghebrey To go short fwd as X>F.
dblueroom It's a lucky question, even if you used synthetic call using protective put - X/(1+r)^t, you still conclude synthetic call overpriced and would execute the same strategy. However, using Forward, synthetic call is closer to actual call price. Good question!
dblueroom make sure the bond in this case has a face value of (X-FP)
cschulz316 guess. study something else.
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