Getting Graphic With Options

By John Succo  JUL 16, 2010 1:20 PM

Charts are a great tool in understanding options.


Editors note: This is the second in a six-part series.

The most valuable aspect of an option is that it breaks apart the risk-return profile of the underlying stock. This creates the flexibility to buy for a price the upside or downside of a stock with leverage and limited risk, or sell for a price the upside or downside while incurring undefined risk. It also creates the ability to design more complex strategies around various stock prices. Graphs are a great tool in understanding options. Once you understood these graphs, you will be able to develop and analyze strategies using various combinations of options and stock around an expected stock return profile.

Let’s begin by describing what an option is. A call option gives the buyer the right to buy a stock at a specific price (strike price) over a certain period of time (expiration). For that right the buyer pays the seller a premium or price. This is a sunk cost, but also the maximum loss, much like an insurance premium. It is the seller of the option who has undefined risk, like an insurance company. The following graph illustrates the return profile of a long (bought) call option on DuPont (DD:NYSE) stock at expiration:

The buyer pays $3.65 per share per option or $365 for 100 shares (each option contract represents 100 shares). This is the maximum loss and occurs at any point below $40 per share. It is depicted as a zero slope line up to the strike price. Because the buyer has the right to buy the stock at $40 per share, any price above this will give the option an “intrinsic” value that increases dollar for dollar with the stock price. This is depicted by a line with a slope of 1. The break-even stock price occurs at $43.65 where the intrinsic value equals the original cost. For every dollar that the stock goes up above this, the holder of the option makes $1 profit. As you can see, an option provides leverage: Instead of an investment of $40 x 100 shares or $4,000, a $365 investment makes an equivalent profit above a stock price of $43.65. As illustrated by the graph, the buyer of a call option is not only making the bet that the stock is going up, but that it will go up significantly and before the expiration date of the option. Time is against the buyer of the option.

The following graph illustrates the other side of the trade, the profit-loss graph for the seller of the call:

The seller collects the premium, which is the maximum profit and occurs as long as the option expires with the stock price below $40. Above $40 per share, the seller has the obligation to sell the stock to the call buyer at the strike price and begins to lose dollar for dollar. The graph indicates that the seller is making the bet that the stock will not go up, or at least not very much before the expiration of the option.

A put option gives the owner the right to sell the stock at the strike price anytime before the expiration of the option. The following graph illustrates the return profile at expiration of a long (bought) put on DuPont stock:

In this case, the buyer of the put pays a $2 per share premium for the right to sell the stock at the strike price of $40 until expiration. This premium is the maximum loss no matter how high the stock goes. The buyer of the put is making the bet that the stock price will drop significantly before expiration.

To complete the expiration graphing of options, the following illustrates the return profile for the seller of the put:

A subtle fact shown by these graphs is that the real value of options is to provide investors, traders, and speculators alike with flexibility. Options break apart into components the risk-return profile of the underlying asset. Combined with the underlying asset, various combinations of options can be used to create a desired return profile.

The following graph illustrates the return profile of long (bought) DuPont stock:

To illustrate that options break apart the risk-return profile of a stock, we can re-create the profile for long stock by using a combination of long calls and short puts of the same strike:


To combine the graphs, always start at the strike prices and calculate the net cost (see calculations above). 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.

Click here to read Part III: Options Pricing.

No positions in stocks mentioned.

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