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.