Using Risk Management Ideas To Make Money With Options In Sideways, Volatile Markets

Trading and risk management are often at odds with one another but completely interdependent; good trades meet the approval of risk management and risk managers are necessitated through trading. Risk managers are like lawyers in that they're trained to say no. Often, tighter risk management policies mean less elbow room for traders, and thus, lower returns along with, hopefully, lower risk. Some concepts in risk management, however, actually imply ways to make money by carefully setting up proper hedges. Among these are convexity exposures and the options market is one medium through which you can exploit the idea for low risk gains.

Let's begin with an example. Say you buy an American call option on a stock price trading at $35 with a strike of $30 to expiry in 1 year. Let's further assume the risk free interest rate is 5%, the stock's volatility is 30% over the next year and no dividends are paid. The Black-Scholes-Merton model yields a theoretical price of $7.86. Let's also say that volatility turns out to be exactly implied volatility and the market's price is for the option is the same as the theoretical price.

You have 20 options on a stock providing the delivery of 20 x 100 = 2,000 shares at any time the stock may be in the money. How ought you hedge the position? A delta hedged position theoretically leaves you with no exposure to price movements. Here, the delta is 0.80, also given by the Black-Scholes-Merton model. According to the model, the option can be synthesized with 0.80 x 2,000 = 1,600 shares and some bonds. Therefore, you need to short 1,600 shares to hedge out exposure to the stock's price movements.

Now if the stock drops to $33 and then $30, the option delta changes along the way. At $33, you must be short 1,480 shares and 1,240 shares at $30. At the first price drop, you need to cover 120 shares. At the second, however, you must cover double that-240. Take a moment to think about your trading activity. You're buying a falling stock. More importantly, the faster and farther it falls the more you buy. It this a good thing? Of course, only to the extent you believe it will rise again. If the price does in fact go up the delta hedge will require you to short more shares. In other words, you're buying low and selling high just to maintain your hedge-said differently, as the stock price bounces around the hedge is paying you dividends.

The additional buying activity with changing prices is measured by gamma, one of the options greeks. Gamma is a measure of this convexity behavior as the stock price changes. The higher gamma, the more convex the option value is with respect to price changes, and that means greater fluctuations in delta. In other words, higher gamma positions create more instability in delta. As illustrated in my example, this is a good thing as long as the stock bounces around within a range, but a bad thing if the stock is trending in one direction or another.

Think about a delta-hedged options portfolio on Ambac or other bond insurers in recent months. As the stock fell from $60 to $50, you buy; it falls to $40, you buy; it falls to $30, you buy. Now the stock reaches a low of $8.15 on Friday, Feb 22. You might have softened the blow to some extent as the stock rallied on bail-out news that day, but overall you lost big time due to unstable deltas in the face of a trending stock.

High gamma positions can yield greater profits with high stock volatility and little trend-risk. Those profits aren't free, however. If volatility drops, gamma drops and the trading activity drops leading to less gain. More problematic, if the stock trends in a particular direction you may end up with a large position at unwanted prices. There's two ingredients to the trade here: volatility and trend. Stock volatility can easily be measured with past realized volatility or option-implied volatility. Stock trends on the other hand can be more difficult to measure. You can statistically measure trend by estimating an autoregressive model, analyzing correlation trends, or looking at cointegration with an exponential curve. These tests can only affirm looming danger-that is, they only detect the presence of trend, not the absence thereof. Hence trend patterns are usually best assessed qualitatively.

In sum, this kind of trading works very well in a market trending sideways. It works less well, in general, in a clear bull or a clear bear market. At the time this article was written, February 28, 2008, it appears to be a great asset to anyone's portfolio in the coming months.

Alan Illing