# Gamma hedging trading strategies : Part II

By Simon Gleadall, CEO of Volcube.

## Some gamma hedging strategies

With any trading strategy, the point is to achieve an objective. So ask yourself what you want to achieve with your strategy? A common answer here will involve the position theta ‘bill’. It could be that your objective is to try to ensure your gamma hedging will pay for all or most of the time decay that your position will experience. The output from the strategy however is basically a list of prices in the underlying at which you are intending to hedge your gamma. So let’s look at some typical ways of deciding those prices.

### Gamma hedging with break-even in mind

This is a common gamma hedging strategy. If the trader knows his theta bill, he can re-arrange the *Profits = ½ Γ x²* formula to calculate the distance he needs the spot price to move in order to break-even on his theta bill. In other words, he needs to find the change in the spot price, x, where the Profits are set equal to his theta bill. Here’s an example:

Assume the trader is paying $1000 per day (the theta bill) to be long 100 gamma. How far does he need the spot to move to break-even with a gamma hedge?

Answer: x= √[($1000 * 2)/100] = c.4.47 points. So the spot product needs to move by 4.47 points for a gamma hedge to cover this theta bill of $1000. Remember this does not assume any contract multiplier. When you make this calculation in your product, remember the size of the multiplier and make sure your answer makes intuitive sense.

So the strategy here might be to look to gamma hedge when the spot price has moved roughly 4.5 points and thus cover the theta decay.

### Gamma hedging with implied standard deviation in mind

Another measure some traders consider is the daily standard deviation implied by the options and to see if they can achieve that as a gamma hedging level. For example, if the underlying is trading at $100 and the trader is long some at-the-money options with an implied volatility of 25%, this suggests an expected daily standard deviation of $1.58. This comes from another formula worth memorising:

**Daily sd = Spot price * Implied Volatility / √[250]**

I always just used 15.8 for the square root of 250. 250 is also an approximation; it represents the number of trading days in the calendar year. Now if the returns of the underlying are log-normally distributed (as the standard Black-Scholes pricing model assumes even though it is generally not the case over the long term), then we can expect the underlying to achieve this standard deviation roughly 64% of the time. Remember, this is highly theoretical and in reality should only be used as a very rough and ready rule of thumb. Nevertheless, it can be a useful level to have up one’s sleeve. If the spot moves $1.58 in this case (especially on the open!), then a gamma hedge at this level is likely to cover a lot or more than all of the day’s theta bill. This is intuitive because this ‘size’ of move in the underlying is ‘expected’ so it seems ‘fair’ that the gamma profit should at this point roughly cover the theta bill. If the spot is consistently moving more than the daily sd number, it would suggest the actual volatility is greater than the implied volatility indicates and that profiting from gamma may be possible. That’s why traders will monitor this number, at least mentally, over the short term.

### Gamma hedging to ‘ensure’ at least partial cover of theta bill

This is a common strategy for traders who dislike being short gamma (because of the risk of explosive losses) but also dislike the theta bill associated with long gamma positions (because of the ‘bleed’ to their position). So it is quite common for market makers who expect to make profits during the day by scalping or trading volatility but who are core long gamma (and therefore experiencing a daily theta bleed from their position), to employ a strategy of gamma hedging reasonably ‘tightly’. This means hedging gamma at reasonably tight intervals. Remember though that the profits from a gamma hedge are *exponentially* related to the distance of the gamma hedge. So by hedging at closer intervals, the profits from each hedge are a lot lower. But, the positive side to this strategy is that you are more likely to at least cover *some *of the theta bill. Let’s take an example.

Spot is trading at $100. I calculate that to pay for my theta bill, I need a gamma hedge $1.50 away from here. So I could work gamma hedges at $98.5 and $101.50. However, this may feel a little “all-or-nothing”. If I fail to get those gamma hedges and the spot ends the day close to $100, I am likely to lose my entire theta bill. So maybe I will hedge 75 cents away instead. Remember however that a hedge $0.75 away will only be ¼ as profitable as a hedge $1.50 away. So now I need four such hedges to cover the theta bill.

Some traders will go further. They reason that it is better for them to hedge say every 20 cents and hope to get many, many hedges in the day. The idea here is to switch the risk from being binary (‘I cover my theta bill entirely / I cover 0% of my theta bill’) to something weighted toward ‘I cover some of my theta bill’. This is purely a matter of preference.

Another benefit to this strategy is that the chance of an occasional windfall is always there. Every so often the underlying product may move violently. The long gamma player will experience big pay-offs on such days.

Also remember the short gamma player can also employ this gamma hedging strategy in reverse. Negative gamma hedges little and often minimise the risk of very large losses (although they do not protect against gap moves such as in opening auctions). The short gamma player may hope to keep some of the daily theta decay from being short by preventing losses from short gamma spiralling. The risk to this approach is hedging too often and ‘eating up’ the premium he will collect from being short theta.

### Partial gamma hedging

Because the profits from gamma are exponentially increasing with the spot price moves, another strategy is to only partially gamma hedge and try to let the profits run on the remaining deltas. For example, if I have 100 gamma and the spot rallies 1 point, I will be long 100 deltas. Now I could gamma hedge here and sell all 100 deltas. However, I may feel that the spot is going to continue rallying. Of course, I could be wrong. If the spot simply drops back down to unchanged, I will have foregone the gamma profits if I failed to gamma hedge. If however I hedge, my delta is re-zeroed and although I will still profit from a further rally, it will not be nearly as profitable as if I had not yet hedged.

A third way then is to partially hedge. If say I sell 50 lots of my 100 long deltas, I will continue to carry the remaining 50 deltas higher if the spot rallies. Plus, (if I am still long gamma) I will pick up new long deltas along the way. Partial hedging can be a way to let some of the deltas continue running whilst locking in some profits from the initial move. If the spot falls back to its original level, at least by partially hedging I have made some gamma profits from the move.