This publication is part of a series of posts on the Greeks. These posts are a short summary of a part of the content of my book How to Calculate Options Prices and Their Greeks.
In the previous publication we’ve shown the difference in performance between the ‘tight’ hedger and the ‘wide’ hedger. The tight hedger was called the prudent trader; he was hedging his full gamma (2,000/ $) each dollar higher in the underlying, a trending asset which moved from $ 50 towards $ 55. The wide hedger didn’t do anything, he let the position run, therefore maximizing his return on his options portfolio. The two hedging strategies are shown below:
Tight hedging strategy:
Wide hedging strategy:
The wide hedger has a far better return on his position. However one needs to realise that we have to deal with the following circumstances when applying the most optimal strategy:
Applying the most optimal hedging strategy implies forecasting the market!
The tight hedging strategy almost always results in hedging too early
Hedging too early implies opportunity losses
The wide strategy almost always results in hedging too late, one cannot forecast tops and bottoms and hence one can miss the trade
Hedging too late implies opportunity losses as well
So it is difficult and sometimes frustrating when running a gamma book.
Therefore it is so important to have a proper hedging strategy in place, but one can be certain that it is (almost) never the most optimal.
We can derive two rules from the examples above:
A gamma short position demands a tight hedging strategy
When we would take theta (the timedecay of the options) into account, most probably the tight hedger, from the example above (being gamma long), wouldn’t have made any money with his position. His P&L can be easily washed away by the theta (which we set at $ 5,000 for this specific example). And at the same time the underlying has been trending! So actually, the trader had the right position in the most promising environment, because a trend of 10% was due. Still though, he ended with nothing because of the wrong hedging strategy.
What would have been his P&L when the asset would have been trading up a little and then retraced? Most probably he would have lost some.
What would have been his P&L when the asset would have been stuck at $ 50? He would have lost his full theta of approx $ 5,000
So in all three market scenarios, a trending, reverting and rangebound/ stuck market, the gamma long trader will not be able to produce a decent P&L when he applies a tight hedging strategy.
If this trader would have been a gamma short trader, he would have earned a P&L in two out of three scenarios AND he would have prevented a large loss in a real trending market!
Hence application of the tight hedging strategy is “mandatory” when being gamma short.
A gamma long position demands a wide hedging strategy
A gamma long position will only result in a decent P&L when there will be a large move in the underlying. Thus with a trending market and a market which is rangebound (in a fairly large range) with fairly large retracements the gamma long trader will be successful. With a market which is stuck at the initial level he will most definitely lose money.
Therefore, setting up a gamma long position must be the result of the view that the market will make a move. In markets which are rangebound (small range) and which hardly move the trader will lose money. Next to that, volatility has the tendency to come off; this adds another risk to the position.
So when entering a gamma long position the trader must have a conviction and he will only generate a good P&L when the market proves his conviction being the right one.
One could argue that intraday volatility also adds to the P&L. The problem is that when someone applies a wide hedging strategy he will not generate additional profits on the back of intraday volatility (he’s waiting for the large move and doesn’t want to hedge too early), one could call intraday volatility noise for the gamma long trader.
For the gamma short trader, intraday volatility comes at an extra cost.
So be cautious when choosing for running a gamma book (either long or short) it should be the result of careful consideration about the market. Hedges will almost always prove not to be optimal (either long or short gamma), intraday volatility is not contributing to your P&L when you need it the most (when gamma long and paying up for theta) and intraday volatility will be quite harsh for your position when being gamma short. It’s a tricky game!