## 02 May 2008

### Understanding Risk Graphs

A risk graph is a diagram of the potential profit or loss of an option strategy. I actually prefer the term “payoff diagram”, but “risk graph” seems to have taken a firm hold in options trading vernacular.Many people avoid the use of risk graphs for one of two reasons. They either find them confusing, or they somehow equate the use of a risk graph to charting or technical analysis.

A risk graph is definitely not technical analysis. There is no prediction or analysis of share prices implied by the use of them. They simply make the calculation of potential profit and loss easier for those of us who are more visually oriented, or as a visual estimation tool to shortcut the need for a mathematical spreadsheet.

What I want to do here is to address the confusion factor in understanding risk graphs, by building some risk graphs from scratch.

I believe the confusion factor stems from what the x and y axes represent. Most of us have at least a basic grasp of a price chart, even if not chartists. Most people are aware of what the axes on a price chart represent. The x axis represents the passage of time and the y axis represents price.

However a risk graph does not have time represented on any axis, rather, it is a snapshot at a moment in time, usually at expiry of the option. The x axis, rather than representing time, represents price. The y axis, rather than representing price, represents profit or loss. Below is the risk graph of 100 common stock bought at \$50.00, which is represented by the blue line.

I have annotated the risk graph at 3 points. Point A represents the profit of the stock when trading at \$50. Because we bought the stock at \$50, of course there is no profit or loss. At \$56, because we bought 100 stock at \$50, there is \$600 of profit, which is plotted at point B. At \$46, there is a \$400 loss, plotted at point C.

Because we know there is a linear relationship between price and profit/loss, we can connect the dots and show the entire risk graph of the common by the blue line. “Passage of Time” is not involved here.

So we can now see what the “hockey stick” shaped risk graph of an option is portraying. Below is the risk graph, at expiry, of 1 x \$50 call option (expiry date etc is not important for this example) bought for \$2.50.

We can quickly ascertain, that if the option expires with the stock trading at anywhere from \$50.00 or less, our loss would be a maximum of \$250. We can also see that the stock is required to be trading at \$52.50 in order to break even as well as determining the exact profit at any point higher than \$52.50.

What about a risk graph of option values before expiry? We can, and should do that too. Below is the same option at the time of purchase, with the common trading at \$50.

This presents a somewhat different picture and demonstrates very clearly that the profit and loss picture of an option changes as time goes by. This demonstrates the time decay of long options. With the software I mentioned in an earlier section, we can view the risk graph at expiry, at analysis date and at any point in between, very handy.

The Hoadley software plots both the risk graph at analysis date and at expiry as default, and will perform an animation of the decay process up until expiry. This is very useful for if/then analysis without having to be a mathematics major.

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