The cost of impatience

Vol #42 - June 11th, 2021

Impatience can be very expensive.

There’s a time for everything, good things come to those who wait, and patience is a virtue. We wouldn't need aphorisms if it was easy. 

Options are securities that by definition gain their value from time.  There’s no way to speed it up or slow it down, and their final value will only be determined at expiration.  

With zero time on the clock every option is worth parity. With infinite time remaining, their differences are a rounding error. What’s interesting is everything in between. 

Holders of options want stock to move before the final bell rings. Sellers of options bite their nails hoping that stock just sits still.  While there is a directional bias to most positions, how quickly that exposure changes is perhaps an even more important factor. 

Options traders define this effect as “gamma” or the rate of change of your delta as stock moves. Delta is the first order change of a position's value relative to stock price, and gamma is the second derivative of price movement. The more gamma a position has, the more quickly your delta (and PnL) will change as the underlying price changes.

When you buy a call option, you’re getting both long delta and long gamma. You’re long delta because you see positive PnL from the stock price going up. You’re long gamma, because your delta position gets longer as stock goes up, and shorter as stock goes down. 

Most active options traders will hedge their delta exposure, preferring to take a position on volatility or time rather than pure direction. Buying a call option would be hedged by selling some amount of stock against that. A forty delta call is hedged with forty shares of stock. 

If the stock drops, the delta of the option will fall - there’s now a lower chance of it landing in the money at expiration. If the call option falls to only twenty delta, the hedged options position is now net short deltas. It’s time to buy twenty shares of stock. 

You’ve sold stock higher as part of the initial hedge, and can now buy it back lower. If stock rallies back up, you’ll sell more deltas into a rising market. The dream scenario would be for this to continually happen until expiration, allowing you to ‘scalp’ the gamma from your position. 

Scalping gamma is an important part of managing an options position. On the long side, it helps pay for the theta or decay that buyers of options “lose” each day as time passes. With increasingly fewer days to expiration, the value of that optionality will continually fall. 

Sellers of options have the opposite problem. Short gamma positions get longer deltas as the stock is falling, and shorter deltas as the stock is rising. Hedging this too actively curses you to repeatedly buy high and sell low.

To compensate for this, option sellers realize positive theta every day. They slowly collect the premium from the decaying value of the insurance policy they’ve written.  If the option was priced appropriately, the premium collected should offset the realized cost of hedging and maintaining that position. 

Our internal psychology makes sitting on short gamma very difficult. Worse than watching paint dry, you’re perennially waiting for something not to happen.

Gamma management is an exercise in managing impatience. Traders with short options positions that try to constantly manage their risk will never see a large drawdown, but will guarantee many small losses. Conversely, long options positions that get too greedy about positive exposure will miss opportunities to lock in small gains. 

The correct answer for gamma management is only knowable ex-post, and in the meantime we’re left with a little bit of math, gut feelings, and rules of thumb. 

Managing uncertainty is a short gamma position, and must be a balance between the cost of reducing the uncertainty, and the benefits that may come from keeping your (pun intended) options open. Sometimes no-trade is the best trade.

On the long side, while we want to have exposure to many different possibilities, if we’re not able to manage them actively and “monetize our theta”, we risk seeing them decay as expiration approaches. There can be too much of a good thing. 

The best traders are willing to be both long and short gamma. It all depends on the context, the opportunity, and how ironclad your stomach is.