# On Delta Hedging

The broad trade-offs when trying to isolate volatility bets

Delta hedging is a trade-off between transaction costs (direct+slippage) and risk reduction. Some observations to help you think about it top-down:

- Delta hedging is sampling prices with trades instead of simple observation

When you compute realized volatility you choose a sampling period, say close-to-close. You can think of your delta hedges as samples. If you and I delta hedge at different prices we are sampling different volatilities. Close-to-close vol might not even correlate with our samples. So everyone’s lived experience of their attempted “market neutral” is different based on how their sampled vol compared with the implied. This is why delta hedging is bedeviling. - Delta hedging links implied vols to subsequent carry p/l

Delta hedging is the link between the implied vols you trade at and the subsequent p/l you realize regardless of what some objective measure of realized spits out. If you hedge a 1 month option 2x over its life you aren’t really trading vol since hedging that infrequently is going to generate a pretty random vol compared to the vol that’s realized by conventional measures. If you are trading implied vs realized strat you are mismatched. - Transaction cost vs risk trade-off

If you hedge hourly your sampled vol will land somewhere close to traditional measures of realized (assume no flash crashes or quick resolving discontinuities). But it costs you a few bps in slippage each time. Expensive. So you need to tolerate some delta, which means you don’t hedge “continuously” as the pricing models assume. How much you let your deltas run will depend on so many factors. Non-exhaustive list:

1. Tolerable p/l variance

2. How much gamma you have

3. Opinion of how returns are distributed.

Another thought. You could hedge more frequently but with a more liquid instrument like ES. So you are sampling vol more often, and saving on slippage, but increasing basis risk. (Be careful about taxes!…Futures are designated “1256” contracts and have specialized tax treatment which means you need to track p/l in different buckets for tax purposes.) - The reason to systematize your hedging rules

Once you tally all the considerations you just want to systematize the hedging. Fixed time intervals, time intervals divided in proportion to volume traded, just trade on the close, every time you go to the bathroom. Whatever. Just reduce the temptation to trade emotionally.

Why?

Cutting long gamma short and letting short gamma ride is the vol traders equivalent of being a loser in delta one trading. Be consistent about your rules whether you are short or long gamma. - Be realistic about what delta is capable of hedging.

Market making 101 — the only way to actually hedge an option is with another option. This is especially true with low delta or tail options.