One property of calls and puts is that they can be converted one into the
other, using a property known as put-call parity. Imagine that you have a call
on IBM stock, giving you the right to purchase 100 shares at a price of $200
for expiry in three month's time. If IBM stock were to trade up to $200 at any
time before the option expired, let's say that you sold the full 100 shares of
the stock at $200.
You now effectively have a put on IBM stock with a strike price of $200.
The combined portfolio of the call option and the short position have the same
payoff profile at expiry and the same intermediate behavioural characteristics
as a portfolio consisting of a put on 100 shares of IBM with a strike price of
$200 for the same expiry date. If IBM's stock at expiry is above $200, you
exercise the call option, buy the stock at $200. This long position offsets
your short position and your profit and loss is simply the loss of the premium
you initially paid for the call option. If IBM's stock at expiry is below $200,
you do not exercise the call option and you are short IBM stock at $200 (from
your sale of 100 shares at $200 against your option position).
Why is this important? There may be cases when
illiquid equity markets can be arbitraged. Let's say that you're an investor
who is concerned about a sudden downfall in the equity markets. You own 100
shares of ABC.com stock, purchased at a price of $100. The stock price is now
$150. You want to buy downside protection with a put on your particular stock
but the price is too expensive for your tastes. Instead of buying the put on
ABC.com stock, you could buy the in-the-money option with the same strike and
maturity and simultaneously sell the ABC stock in the spot market.
ABC.com stock
price=$150 ABC.com June $100 put=$5 ABC.com June $100 call=$53. The ABC.com
June $100 call has $50 of intrinsic value and a remainder of $3 of value,
called time value. At expiry, if ABC.com's stock price is $150, the option will
still be worth $50 but its time value will have wasted away to zero. By
simultaneously buying the June $100 call for $53 and selling the stock at a
price of $150, the investor has purchased the put for $2 less than if he had
simply purchased the put. At expiry, if the ABC.com stock price is above $100,
the investor exercises the call and is long the stock again. If the ABC.com
stock price is below $100, the investor does nothing with the call and he has
not position in the stock, having sold his position at $150.
As long as the stock price is below $97 ($150 less the $53 premium), the
investor is better off than if he had done nothing. In practice, these
arbitrage opportunities do not present themselves in anything but the most
illiquid markets. Sophisticated investors (like the readers of the Financial
Pipeline) will pick up on them and close them out. But if it is difficult to
short the stock (for example, because of funding difficulties or problems
finding stock to borrow), then investors looking for downside protection might
find this to be a more cost-effective way of protecting an existing position.
Article by Chand Sooran, Principal, Victory
Risk Management Consulting, Inc. |