# Optimal f (position sizing) without look ahead bias

My goal is to identify a systematic way to position sizing in the futures market. Let assume that I'm an investor with log utility. In addition, let assume that I'm reluctant in estimating the expected return of a strategy. In Optimal f and the Kelly Criterion Vince states: "It is specifically because the optimal f calculation incorporates worst-case outcomes that it is bounded between zero and one inclusively". This is scary to me since in real life the next loss can be grater than the largest historical loss. So I've tested what would happen in this worst case scenario.

First, I've reproduced in Python the example in page 123 of Vince (1990) in order to make sure that the code works. In this example, the sequence of PnL is [9, 18, 7, 1, 10, -5, -3, -17, -7] and the largest Loss is -17. The resulting optimal f is 0.24. In real trading, we cannot observe the largest loss that we will face in future, so in practice it could make sense to use a look-back period to estimate the largest loss.

For example, the optimal f associated with the look-back period [9, 18, 7, 1, 10, -5, -3] where the largest loss is 5, we get f=0.64. The resulting capital to be invested in the next bet would be largest_loss / optimal_f = 5 / 0.64 = 7.81. However, the outcome of the next bet is -17, so we go broke. Note that even if we used the fractional optimal f, say half f, we would still go broke.

Questions:

• How to obtain the optimal f without introducing look-ahead bias and f bounded in [0, 1] while preserving the maximum long term geometric growth of capital?

• Is there any approach or extension that provide an optimal position sizing strategy without estimating the expected return of the strategy (i.e. position sizing taking into account for the risk only)?

• IMHO, instead of trying to find the 'optimal' amount of leverage to use, you should start with figuring out what percentage of your account you are willing to lose and use that as a constraint in finding your 'optimal' trade size. – amdopt May 23 '17 at 14:34
• Assuming that with "percentage of your account you are willing to lose" you are referring to the maximum drawdown, how would you proceed then? – MLguy May 23 '17 at 14:49
• Do you mean to ask how I would go about incorporating that constraint into a test? If so, there are many ways. That is something you would have to figure out on your own though. Assuming you have written some backtesting code, add the constraint as a variable and if the test parameters lead to that variable getting exceeded, try another set of parameters. That is the most basic way I can put it. Good luck :) – amdopt May 23 '17 at 15:10