Adjustments in dynamic hedging do not alter the expected return; they simply reduce the short-term effects of good and bad luck

If a trader initiates a hedge but adjusts less frequently or does not adjust at all, how will this affect the outcome?

Because theoretical evaluation of options is based on the laws of probability, a trader who initiates a theoretically profitable hedge still has the odds on his side. Although he may lose on any one individual hedge, if given a chance to initiate the same hedge repeatedly at a positive theoretical edge, on average, he should profit by the amount predicted by the theoretical pricing model.

The adjustment process is simply a way of smoothing out the winning and losing hedges by forcing the trader to make more bets, always at the same favorable odds. A trader who is disinclined to adjust is at greater risk of not realizing a profit on any one hedge.

Adjustments do not in themselves alter the expected return; they simply reduce the short-term effects of good and bad luck.


This is one of the many passages and charts I find in books and articles on a daily basis. They span many disciplines, including:

I occasionally add a personal note to them.

The whole collection is available here.