The first two articles in this series showed the profit and loss graphs for one of the two types of listed options – the Call option. If you didn’t catch these earlier lessons, here are links to Part 1 and Part 2.

Today, we’ll look at the diagram for the other kind of option – the Put Option.

When the price of a stock goes down, then the value of a Put on that stock goes up. So, when we buy a Put option, it is because we believe that the price of the underlying stock will go down. Buying a Put option is a way to make a bearish trade on the stock (a trade that makes a profit when the stock goes down, without selling the stock short). Puts have other uses too, but we’ll concentrate on that one for now.

The calculation of how much a put option’s price would go up for a given drop in the price of the underlying stock involves a good bit of calculus. It can’t be calculated without lots of computing horsepower, but fortunately, that is readily available. As described previously, all good option trading software platforms have the capability do complicated options calculations for you. The examples here are from the TradeStation platform.

Because we’ve been looking at options on the exchange-traded fund SPY up to now, we’ll continue with it.

As of the end of the day on July 16, 2018, SPY was at $279.07 per share. Let’s say that we thought that it had topped out for now (not a recommendation, just an example). We thought that it could easily drop back to the $270 level where it was just two weeks prior, or even to the $260 level where it was in May. We also noted a level of supply, or resistance overhead at about $283. If SPY rallied and exceeded that level, we would consider the bearish trade broken and exit from it. In planning our trade, we want to know how much we might make on a put option if we turn out to be right. Equally important, we need to know how much we could lose if we turn out to be wrong.

We chose a Put option at the $280 strike, very close to the current $279 price. We proposed to hold the put until SPY dropped down to our $270 target, or went up to $283, whichever came first. The price of the 280 Put with an expiration of October 2018 was $678.51 at the time, so if we wanted to play, that is what we would have to pay. Here is the P/L diagram for that trade:

Note these items about the P/L graph above:

- The graph has built into it the purchase price of the Put. This was $678.49 per contract, which rounds to $6.79 per share. $6.79 is the amount shown as Price near the bottom of the above illustration.

- The graph calculates the value that the Put would have if the stock moved to any specific level between $260 (far left side) and $295 (far right side). The farther SPY were to drop, the higher the price of the Put would be, and vice versa. The line on the graph does not actually plot the value of the Put at different a price of SPY; instead it shows how much the Put owner would make or lose, assuming that initial $678.49 cost of the put.

- We can add markers, or
*price slices*to the graph, to make the system calculate how much profit or loss would be made if the stock hit the price of the slice. In the above example, I put slices at $270.00 (our downside target); $279.07, (the current SPY price); and $283.00 (our stop-loss price). These prices are shown in the Price column of the table under the graph. Reading to the right across a line of the table, the column labeled Theo P/L gives the theoretical profit or loss on the trade if the stock were to be at that price.

- For example, if the underlying asset (SPY) were to drop to $270, the top line of the table shows a Theo P/L number of $581.11. That would be our target profit.

- We can see from the third line in the table that if SPY went up to our stop-loss price of $283.00, then the Theo P/L would be -$180.36. So, we could see from this analysis that we were risking that much in exchange for a possible profit of $581. If we liked those odds, then we had a trade.

Doing any kind of trading requires strict risk management – always risking less than we stand to make on the same trade. For option traders, the P/L graph is our primary tool for accomplishing that.