To combine the graphs, always start at the strike prices and calculate the net cost. In this case, at $40 the cost of the call is netted against the profit of the put. We then adjust this by deducting the dividend not earned (the options position does not receive the dividend as the long stock would) and adding back the carry not incurred (the assumption is that when buying stock there is a borrow cost, which is not the case when margining the options).

The net cost then at $40 is $1.91: this is the starting point for the combined position. Below $40 the combined slope of the long call (slope is zero) plus the short put (slope is 1) is 1. We draw this as a black dashed line. Above $40 the combined slopes are also 1, and we continue the black dashed line. The resulting combined position (adjusted synthetic stock) is exactly equivalent to buying stock at $41.91. This illustrates that calls are priced mathematically against puts. This is called put-call parity. If the put price became more expensive because of supply-demand, the call would have to become more expensive as well or else there would be an arbitrage: we could sell the put, buy the call, and sell the stock short for a risk-less profit.

As we did above, we can now take various combinations of these five graphs to produce the desired return profile for any option strategy. One of the most popular strategies of options traders can be used as an example. Option traders often do not like to bet on the direction of a stock, but instead that the underlying stock will move a certain amount either up or down. By combining long stock and long puts on a ratio (long one share of stock versus 3 puts), the resulting strategy will make money if the stock moves dramatically either up or down:

This trade is done on a ratio (more puts than stock) and is a little more complicated. We are buying around 3 puts (300 shares) for every 100 shares of stock because the puts are out of the money (the strike price is below the stock price) and do not move as much as the stock unless the stock drops below the strike price. The graph makes this clear.

Again, let’s start at the $40 strike price and determine the profit loss at expiration. The $2 cost of the put is added to the 70-cent loss on the long stock (.37 shares bought at $41.91) to create a starting point of – $2.70. Under $40 the -1 slope of the put is netted against the .37 slope of the stock creating the dashed blue line with a -.63 slope. Above $40 the put has a 0 slope netted against the .37 slope of the stock to create the dashed line with a .37 slope. The break-even points are calculated above. Notice this strategy is profitable as the stock moves either up or down as long as it moves dramatically past the break-evens by expiration. This is called a back-spread and would be implemented by an option trader who anticipates that the stock will move dramatically with a small negative bias.

There are many other strategies that can be created with various combinations of options and stock. Now that you know how to create graphs and combine them, you should be able to design a strategy around your expected return profile.

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