Put/call parity defines the pricing relationship between an underlying stock and all the calls and puts on that stock.

Let’s assume XYZ Co. is trading at $100 a share and pays no dividend. A one-year XYZ May 100 call is trading at $10 a share; a one-year XYZ May 100 put is trading at $9 a share.

On the surface, you might assume traders are bullish about XYZ, as they are willing to pay more for an at-the-money call than for an at-the-money put. In reality, the price differential has everything to do with put/call parity, and nothing to do with sentiment. Put/call parity effectively allows a market-maker to take offsetting, risk-free positions in order to facilitate a trade.

The concept is important for options traders because it lays the foundation for defining equivalent options strategies. Understanding that different options strategies have equivalent risk/reward characteristics helps define the risks unique to specific trades.

This is how it works: if you were to buy one XYZ share at $100, and one XYZ May 100 put at $9, your total investment would be $109 a share, or $10,900 for a 100-share position. This is known as a “married put” strategy.

Think about the trade in terms of risk and reward. With the put protecting the stock position, the downside risk is limited. The most you can lose on this trade is $9 a share, which is the premium paid for the put. If the stock declines to $50, you would simply exercise the put option and force the put writer to buy your shares at $100.

Your potential upside is unlimited. Of course, you are not in a profitable position at expiration unless the stock rises enough to overcome the $9 a share cost of the insurance. But, the married put strategy has unlimited upside potential and limited downside risk.

Now, let’s look at this from the call side of the equation. Instead of buying the stock plus a put, simply purchase one XYZ May 100 call at $10 a share. In this case, your maximum risk is limited to the cost of the call. Your potential upside is unlimited, once the stock climbs enough to recover the call’s cost. So, the long call position has unlimited upside potential with limited downside risk.

At first, it appears that the call buyer could lose $10 a share vs $9 a share for the married put strategy. For put/call parity to exist, two equivalent positions must have identical risk/return metrics; that is where we get into a “cost of carry” discussion.

The only difference between the two strategies is how we define the underlying position. With the married put strategy, you have to buy 100 shares at a cost of $10,000 and then buy a put option contract for $900. The total investment is $10,900. So, there is a cost of carry associated with that total investment.

Looking at the financial commitment from the call side, the total cost is only $1,000. The difference between the costs of buying the long call vs the married put strategy is $9,900. Assuming we took that $9,900 and invested it in a one-year treasury bill yielding slightly more than 1% a year, we would earn approximately $100 in interest over the next year. Subtract the $100 interest earned from the cost of the call and the worst-case scenario is now a risk of $900. That’s put/call parity. IE