In this case, what is being mimicked is a long position on a stock by selling a put and buying a call at the same strike price and expiry (usually at the money). Here’s how it works in more detail:
A Long Stock, purchased at $50 has the following payoff diagram:
As you would expect if the stock rises above $50 the ‘position’ is profitable and gets more profitable as the stock rises further. And the converse is true too: below $50 the stock is unprofitable and gets worse as the stock price falls.
In order to place a synthetic stock, it’s important to remember one of the key principles of options trading: if the pay-off diagrams of two positions are the same then they are, in effect, the same trade.
Therefore all we need to do is construct an options spread that has the same pay-off (or ‘P&L’) diagram as the above and we have ‘synthetically’ created a long call.
And the spread that does the job is to buy an at the money call and sell an at the money put. Both should have the same expiry date.
The long call has the following P&L diagram:
And here’s the short put’s pay-off:
And when put together they produce:
Which is, of course, the same pay-off diagram as the Long Stock above, and therefore the same trade.
Why would you go to the bother of putting on the synthetic version of a bought stock when you could quite easily just buy the stock? Here are a couple of reasons:
To own stock you require the capital to purchase the shares. Even if you’re buying stock on margin you still need to deposit 50% of the purchase price with your broker.
The margin requirements for the ‘sell put and buy call’ strategy is much smaller and therefore less cash is required.
Because options are involved a sophisticated trader has more, well, options to manage the trade.
For example if the stock price drops, therefore increasing the price of the short put, it could be rolled down (ie sold at a lower price point) or out (buying back the put and selling a put of a later expiry date).
With all options trades there is a downside to consider to placing the synthetic version of the long call. Here are a few:
The required margin is lower than a purchased stock as we’ve seen. However, because the trade includes an uncovered sold put, your broker will recalculate your margin requirements daily. If the stock has moved down significantly you’ll be asked to post more margin immediately.
For a smaller amount of capital you’re being exposed to the full risk profile of the stock. Therefore, when compared to the capital outlay you have more risk.
This is the flip side of being able to put the trade on for less capital: you’ve effectively leveraged yourself to the stock price. You could get more return (on your capital requirement) but for a greater risk.
The ‘Sell Put And Buy Call’ strategy, the sell of an ATM put coupled with the purchase on an ATM call, is a way of creating a synthetic long stock position. It requires a lower capital outlay than simply purchasing the stock, but also exposes you to the same risk.
About the Author: Chris Young has a mathematics degree and 18 years finance experience. Chris is British by background but has worked in the US and lately in Australia. His interest in options was first aroused by the ‘Trading Options’ section of the Financial Times (of London). He decided to bring this knowledge to a wider audience and founded Epsilon Options in 2012.