What is a Risk Graph?

Toni Henthorn

When analyzing the profit potential for stocks, an investor may use a two-dimensional diagram called a risk graph. An investor plots stock prices in ascending order for the underlying company along the horizontal axis and the potential profit or loss values along the vertical axis. He then draws a straight line from the lower left-hand corner of the risk graph to the upper right-hand corner. The exact midpoint on the horizontal axis represents the current price, with the corresponding profit on the vertical axis of zero. If the investor holds 100 shares, the risk graph will display a $100 US Dollar (USD) change in the profit or loss value for every one-dollar change in the price of the stock.

A risk graph will analyze the profit potential for stocks.
A risk graph will analyze the profit potential for stocks.

For example, imagine the stock price for ABC Company is currently $50 USD. If the stock price remains $50, the options trader breaks even, depicted by the zero value on the midpoint of the vertical axis. On the other hand, if the stock price increases to $52.50 USD, then the corresponding vertical axis value of 250 tells the investor that he will have a profit of $250 USD at that price. If the price drops to $45 USD, the investor can easily see that he will suffer a loss of $500 USD. In the single risk graph, he can demonstrate his greatest areas of risk exposure and his greatest profit potential.

In the setting of options trading, however, time also plays a key role in determining profit or loss. Options are dissipating assets that lose value as time passes. In order to track three variables on a two-dimensional risk graph for an option, the investor plots three curvilinear lines on the graph, each representing the profit or loss for a different date. If the stock price of the underlying security remains below the strike price of a long option, then the loss remains constant at the cost of the transaction, depicted by a relatively straight horizontal line. Conversely, when the stock price rises above the strike price, the plotted line slants upward, eventually crossing the break-even point and charting exponentially increasing profits.

For example, a long call on ABC Company stock with a strike price of $50 USD sells for $2.25 USD per share for 100 shares. The cost to buy the option is $230. A risk graph of the option shows that if the stock price remains at or below $50 USD, then the investor's loss remains stable at $230 USD. If the stock price rises to $52.25 USD, the investor breaks even, depicted by a linear trend rising to the zero value level. Any price above $52.23 USD plots on an upward slanting line that corresponds to progressively increasing profit values.

Plots for the profit or loss value at the time of purchase, at a point halfway between the current date and expiration, and at the expiration date will show progressive flattening of the curves on the risk graph as time passes. This reflects the accelerating deterioration of value over time. In addition to time decay, traders must account for the volatility of the stock. Unfortunately, volatility cannot be plotted on a risk graph that also plots time. The investor, however, can keep time constant and plot three lines representing incremental volatility changes to get an idea how such changes affect his position.

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