The Kelly Criterion II
p(b +1)!1 b
The Kelly criterion gives the mathematically optimal, in the sense that it maximizes long term growth, portion of ones bankroll to bet on a wager that pays out b to 1 with probability p. Thus it is a way to turn our probabilities of success into actions, and, in practice, it will lead us to making small trades with a large number of occurrences.
For example, selling a vertical spread with strikes width K 1 K 0 for c credit, c b = K 1! K 0! c and so the Kelly criterion says that you should invest c! (1! p)(k 1! K 0 ) c of your bankroll in this strategy.
In an efficient market, we should expect this number to be very close to 0, which allows us to make many many trades.
While in it s purest sense the Kelly criterion applies to casino style gambling, if we keep in mind the differences between trading and playing roulette (other than the negative expected value for roulette), we can see how and when to apply it to putting on trades.
The first assumption of the Kelly criterion is that the trade has only two possible outcomes: success and failure. While no option strategy has only two possible values at expiration, strategies with defined maximum loss and profit such as verticals or iron condors are well described by their maximum profit and loss, especially if the strikes are close together and so the Kelly criterion can be used to decide how large a trade to put on in those cases.
The more difficult assumption of the Kelly criterion is that separate trades succeed or fail independently. For example, in the casino if the Kelly criterion said.05 for some bet, then the correct behavior would be to bet 1/20th of your bankroll on 20 separate bets, but in trading that 20 means we need new uncorrelated underlyings and/or new expirations and so can t expect such simple prescribed behavior.
So using the Kelly criterion helps us trade in two ways. Firstly, it gives specific, generally very small, amounts to put into specific trades. More importantly, it reminds us that selling the same option twice doesn t count as making two trades for getting up your number of occurrences. We need to constantly be searching for new trades.
Otherwise, we can never get to the long term where following the Kelly criterion guarantees the optimal growth for a portfolio and can instead wind up losing out to short term randomness (which just means a low number of occurrences).
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