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.
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.