Intraday trading is seldom entirely in one direction. A stock may close higher or lower, even sharply higher or lower, on the day, but during the day there is usually not a steady incremental rise or fall in the stock price. A typical intraday stock chart has peaks and troughs all day long. Delta-neutral traders who have gamma don’t remain delta neutral as the underlying price changes,which inevitably it will.
Delta-neutral trading is kind of a misnomer.In fact, it is gamma trading in which delta-neutral traders engage. For long-gamma traders, the position delta gets more positive as the underlying moves higher and more negative as the underlying moves lower. An upward move in the underlying increases positive deltas, resulting in exponentially increasing profits.
But if the underlying price begins to retrace downward,the gain from deltas can be erased as quickly as it was racked up.To lock in delta gains, a trader can adjust the position to delta neutral again by selling short stock to cover long deltas. If the stock price declines after this adjustment, losses are curtailed thanks to the short stock. In fact,the delta will become negative as the underlying price falls, leading to growing profits.
To lock in profits again, the trader buys stock to cover short deltas to once again become delta neutral.The net effect is a stock scalp. Positive gamma causes the delta-neutral trader to sell stock when the price rises and buy when the stock falls. This adds up to a true, realized profit. So positive gamma is a money-making machine, right? Not so fast. As in any business, the profits must be great enough to cover expenses.
Theta is the daily cost of running this gammascalping business.For example, a trader, Harry, notices that the intraday price swings in a particular stock have been increasing. He takes a bullish position in realized volatility by buying 20 off the 40-strike calls, which have a 50 delta, and selling stock on a delta-neutral ratio.Buy 20 40-strike calls (50 delta) (long 1,000 deltas) Short 1,000 shares at $40 (short 1,000 deltas)The immediate delta of this trade is flat, but as the stock moves up or down, that will change, presenting gamma-scalping opportunities.
Gamma scalping is the objective here. The position greeks in Exhibit 13.1 show the relationship of the two forces involved in this trade: gamma and theta. The relationship of gamma to theta in this sort of trade is paramount to its success. Gamma-scalping plays are not buy-and-hold strategies. This is active trading. These spreads need to be monitored intraday to take advantage of small moves in the underlying security. Harry will sell stock when the underlying rises and buy it when the underlying falls, taking a profit with each stock trade.
The goal for each day that passes is to profit enough from positive gamma to cover the day’s theta. But that’s not always as easy as it sounds. Let’s study what happens the first seven days after this hypothetical trade is executed. For the purposes of this example, we assume that gamma remains constant and that the trader is content trading odd lots of stock.Day One:The first day proves to be fairly volatile.
The stock rallies from $40 to $42 early in the day. This creates a positive position delta of 5.60, or the equivalent of being long about 560 shares. At $42, Harry covers the position delta by selling 560 shares of the underlying stock to become delta neutral again.Later in the day, the market reverses, and the stock drops back down to $40 a share. At this point, the position is short 5.60 deltas. Harry again adjusts the position, buying 560 shares to get flat.
The stock then closes right at $40.The volatility of day one led to it being a profitable day. Harry scalped 560 shares for a $2 profit, resulting from volatility in the stock. If the stock hadn’t moved as much, the delta would have been smaller, and the dollar amount scalped would have been smaller, leading to an exponentially smaller profit.If there had been more volatility, profits would have been exponentially larger.
It would have led to a bigger bite being taken out of the market.Day Two:The next day, the market is a bit quieter. There is a $0.40 drop in the price of the stock, at which point the position delta is short 1.12. Harry buys 112 shares at $39.60 to get delta neutral.Following Harry’s purchase, the stock slowly drifts back up and is trading at $40 near the close.
Harry decides to cover his deltas and sell 112 shares at $40. It is common to cover all deltas at the end of the day to get back to being delta neutral. Remember, the goal of gamma scalping is to trade volatility, not direction. Starting the next trading day with a delta,either positive or negative, means an often unwanted directional bias and unwanted directional risk. Tidying up deltas at the end of the day to get neutral is called going home flat.