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: 3.1
Put price: p0 = 9
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 put, 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

The present value of the bond is [X - F(0, T)] / (1 + r)T = (60 - 55) / 1.04180/365 = 4.9.
The price of a synthetic put would be: p0 = short forward + c0 + [X - F(0, T)]/(1 + r)T = 0 + 3.1 + 4.9 = 8.
As the actual put is more expensive, we should sell the put and buy the synthetic put (long call, short forward and long bond).

The initial up-front cash is generated as -3.1 (long call) - 4.9 (long bond) + 0 (short forward) + 9 = 1.
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) - (ST - 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 1 up-front without any investment or any amount to pay back later.