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Calls and Puts: Put-Call Parity – Options Basics

Put-call parity allows investors to protect their position in down markets through arbitrage techniques that sometimes come up in very illiquid markets.

Calls, puts, short positions and long positions in a particular security can be combined in varying proportions to achieve the risk or return exposures that the professional portfolio manager wishes to create. These exposures are often called “synthetic option positions.” One property of calls and puts is that one can be converted 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.

Let’s then suppose IBM stock traded up to $200 at some time before the option expired, and 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 and 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 a put-call parity 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 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.

With ABC at $150 on the spot market, a Put on ABC with a $100 strike price and expiry in June would have a price of roughly $5.00, and a June Call at $150 might be around $3.00. At expiry, if ABC.com’s stock price is $150, the call 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 created a synthetic 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 allows the call to expire worthless, and he no longer has a 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 will pick up on them and instantaneously eliminate the opportunity. 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 put-call parity to be a more cost-effective way of protecting an existing position.

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