Even for a single option trade like that of example #1, a risk graph can be very useful in making decisions about exiting a trade. Knowing that the option will achieve a profit only if the stock price rises by a certain amount before a particular date can be crucial information.

For trades with multiple options, particularly where the options have different expiration dates, the risk graph provides information that is very difficult to otherwise determine. In example #2, the existence of a profit zone between \$33 and \$38 would be difficult to visualize without the benefit of the risk graph.

Note in both of the examples that the point on the initial time line corresponding to the stock price at the time of entry lies slightly to the left of the zero profit axis. That is, as soon as the trade is entered, it is showing a small loss. This is known as “slippage”. It results from the difference between the Bid and Ask prices for an option.

Risk graphs can also be adjusted to reflect the influence of other factors that affect the price of an option. Most notable are the changes in the risk graph due to a significant change in the volatility of the option prices.

In Fig 3-2, note that on the day this trade is initiated, it is shown to expire in 39 days. This is reflecting that the Jun 35 call will expired 39 days after the date it is sold in early May. The Nov 35 call doesn’t expire for another 150 days following the June expiration. This illustrates an important feature of risk graphs. They are only valid up until the expiration date of the earliest expiring option. To follow the progress of the trade after that date requires the calculation of a new risk graph.

From Fig 3-2, it is easy to see where you would like the price of XYZ stock to be when the Jun 35 call expires. The time lime representing the trade at the June expiration date crosses the zero profit axis at \$33 and \$38. Thus, this calendar trade returns a profit at the June expiration if the price of XYZ is between \$33 and \$38 with a maximum profit of \$95 if the stock price is exactly \$35.

This example of a calendar spread is presented and discussed in Chapter 12. Our goal here is just to look at the risk graph and see how to read it.

The stock price of XYZ is expected to trade within a narrow range around \$35 for the next several months. In early May with XYZ at \$34.70, the following trade is initiated. You buy 1 Nov 35 call for \$3.30 per share and sell 1 Jun 35 call for \$1.3 per share. Your net cost and maximum risk on this trade is \$200 [(3.30 –1.30) X 100 = 200].

See Fig 3-2 for a risk graph that depicts this calendar trade.

## Example #2

Next, let’s consider a trade involving two options. One option will be a long call that expires in a distant month and the other option will be a short call in a near month. Both options have the same strike price. This type of trade is known as a calendar spread.

In Fig 3-1, the price of XYZ stock is shown on the vertical axis. On the horizontal axis is the profit or loss in the value of the option with the zero point dividing the profit and loss regimes. The trade at the time of initiation is represented by the line labeled as “today: 17 days left”. The time line representing the trade at expiration is labeled as “Expiry: 0 days left”. In between are additional time lines for “12 days left” and “6 days left”.

This option seems cheap enough, but is it a good one to buy? To answer this question, let’s see what XYZ needs to do for this option to provide a reasonable profit.

The Apr 70 call expires in a little over two weeks. Since this option is out-of-the-money, all of its \$1.5 price is time value.

If XYZ rockets up to \$73 in one week, the option might become worth \$3.7 (\$3 intrinsic value and \$.70 time value). This represents a nice \$2.2 profit on a \$1.5 investment, but it required a 9% gain in the stock price in one week.

This profit information is found from the risk graph by moving horizontally along the stock price line for \$73 until a point is reached, between the 6 days and 12 days time lines that would represent 10 days left. Dropping down from that point to the horizontal axis indicates a profit in the trade of approximately \$220. Since this trade involves only one Apr 70 call contract purchased for \$150, this implies an option price of \$3.7 per share [(150 + 220)/100 = 3.7].

If XYZ only manages to rise gradually over the next two weeks to reach \$71.5 just at expiration, the option will be worth \$1.5 (all intrinsic value and no time value at expiration).  In this scenario, XYZ has gone up by 7% in three weeks, but you only break even on the option trade.

This information is found from the risk graph by noting that the time line at expiration crosses the zero profit axis at \$71.50.

Suppose XYZ barely edges up to \$68.50 with one week remaining. Then, this option might be worth only \$1.0 (all time value), because it is still out-of-the-money and has only one week of life remaining.  Now you have lost \$.50 per share on the option even though the stock has moved up slightly, and there is almost no time left to recover.

This information is found from the risk graph by moving horizontally along the stock price line for \$68.50 until a point is reached just to the right of the 6 days time line. Dropping down from that point to the horizontal axis indicates a loss in the trade of approximately \$50. This implies an option price of \$1.0 per share [(150 – 50)/ 100 = 1.0].

# Risk Graph

A well-known adage declares: “One picture is worth ten thousand words.” And so it is with understanding options trading. Since the value of an option depends upon several factors, it is difficult to appreciate the variety of ways its price can change without some kind of chart. The chart used to track the progress of an options trade is called a RISK GRAPH.

To follow the price movement of a specific option, the two factors of primary importance are the price of the underlying stock and the time remaining until expiration. The risk graph provides the visual means to comprehend how the profit or loss in an options trade is affected by changes in stock price as well as changes in time.

Basically, the risk graph is a two dimensional plot of stock price versus the profit or loss in the options trade. In the modern style of presentation, the stock price is shown on the vertical scale and the profit or loss in the trade is displayed on the horizontal scale. (The classical style of presentation interchanges these vertical and horizontal scales.)

The risk graph will display a variety of lines to illustrate the influence of time. One of these time lines always represents the current state of the trade. Another time line provides the projected profit or loss information at expiration. Other time lines provide the projected state of the trade at various times between the current state and expiration.

Risk graphs are particularly beneficial when depicting a trade that involves more than one option. Spread trades that are made up of two (or more) options with different strike prices and different expiration dates are especially difficult to evaluate without the aid of a risk graph.

How do you get access to risk graphs? Some brokers provide the technology to generate a risk graph. This capability is certainly worthy of consideration when selecting a broker. Also, there are independent charting firms that offer risk graph packages.

Let’s look at an example of a risk graph to illustrate a trade involving a single long call.

## Example #1

This example recalls example #3 from Chapter 2. We will use a risk graph to demonstrate how the information provided in that example was determined.

You think that XYZ is going to rise in price in the near to intermediate future. In early April, XYZ is at \$67.

You buy one Apr 70 call, which is priced at \$1.5 per share.

See Fig 3-1 for the risk graph that depicts this trade of being long one XYZ Apr 70 call with 17 days until the option expires.