Gamma, Theta, and Volatility

Clearly, more volatile stocks are more profitable for gamma scalping, right? Well . . . maybe. Recall that the higher the implied volatility, the lower the gamma and the higher the theta of at-the-money (ATM) options. In many cases, the more volatile a stock, the higher the implied volatility (IV). That means that a volatile stock might have to move more for a trader to scalp enough stock to cover the higher theta.Let’s look at the gamma-theta relationship from another perspective.In this example, for 0.50 of theta, Harry could buy 2.80 gamma.

This relationship is based on an assumed 25 percent implied volatility. If IV were 50 percent, theta for this 20 lot would be higher, and the gamma would be lower. At a volatility of 50, Harry could buy 1.40 gammas for 0.90 of theta.The gamma is more expensive from a theta perspective, but if the stock’s statistical volatility is significantly higher, it may be worth it.

Gamma Hedging:Knowing that the gamma and theta figures of Exhibit 13.1 are derived from a 25 percent volatility assumption offers a benchmark with which to gauge the potential profitability of gamma trading the options. If the stock’s standard deviation is below 25 percent, it will be difficult to make money being long gamma. If it is above 25 percent, the play becomes easier to trade.

There is more scalping opportunity, there are more opportunities for big moves, and there are more likely to be gaps in either direction. The 25 percent volatility input not only determines the option’s theoretical value but also helps determine the ratio of gamma to theta.A 25 percent or higher realized volatility in this case does not guarantee the trade’s success or failure, however.

Much of the success of the trade has to do with how well the trader scalps stock. Covering deltas too soon leads to reduced profitability. Covering too late can lead to missed opportunities.Trading stock well is also important to gamma sellers with the opposite trade: sell calls and buy stock delta neutral. In this example, a trader will sell 20 ATM calls and buy stock on a delta-neutral ratio.

Sell 20 40-strike calls (50 delta) ———- (short 1,000 deltas) Buy 1,000 shares at $40 ——————- (long 1,000 deltas)This is a bearish position in realized volatility. It is the opposite of the trade in the last example. Consider again that 25 percent IV is the benchmark by which to gauge potential profitability. Here, if the stock’s volatility is below 25, the chances of having a profitable trade are increased. Above 25 is a bit more challenging.

In this simplified example, a different trader, Mary, plays the role of gamma seller. Over the same seven-day period as before, instead of buying calls, Mary sold a 20 lot. Exhibit 13.2 shows the analytics for the trade. For the purposes of this example, we assume that gamma remains constant and the trader is content trading odd lots of stock.

Day One:This was one of the volatile days. The stock rallied from $40 to $42 early in the day and had fallen back down to $40 by the end of the day. Big moves like this are hard to trade as a short-gamma trader. As the stock rose to $42,the negative delta would have been increasing. That means losses were adding up at an increasing rate. The only way to have stopped the hemorrhaging of money as the stock continued to rise would have been to buy stock.

Of course, if Mary buys stock and the stock then declines, she has a loser.Let’s assume the best-case scenario. When the stock reached $42 and she had a 2560 delta, Mary correctly felt the market was overbought and would retrace. Sometimes, the best trades are the ones you don’t make. On this day,Mary traded no stock. When the stock reached $40 a share at the end of the day, she was back to being delta neutral. Theta makes her a winner today.

Because of the way Mary handled her trade, the volatility of day one was not necessarily an impediment to it being profitable. Again, the assumption is that Mary made the right call not to negative scalp the stock. Mary could have decided to hedge her negative gamma when the stock reach $42 and the position delta was at 2$560 by buying stock and then selling it at $40.There are a number of techniques for hedging deltas resulting from negative gamma. The objective of hedging deltas is to avoid losses from the stock trending in one direction and creating increasingly adverse deltas but not to overtrade stock and negative scalp.