Optimal f Position Sizing and Look-Ahead Risk
Summary
The document investigates whether Vince’s optimal f can be used for futures position sizing without look-ahead bias. The author assumes log utility and is reluctant to estimate expected returns, then reproduces a historical profit-and-loss example in which optimal f is calculated using the largest observed loss. The stated result for that full sequence is an f of 0.24.
The central risk is that a sizing estimate based on a limited look-back may miss a larger future loss. In the example, sizing from an earlier subset produces an f of 0.64 and capital exposure based on a loss of five; the next observed loss is seventeen, which would exhaust the capital. The author notes that halving f would not prevent that outcome. This is an illustrative historical sequence, not a general proof about optimal sizing. The document poses open questions about bounded, no-look-ahead sizing and risk-only alternatives without answering them.
Key ideas
- Optimal f depends on the largest loss used in its calculation.
- Using only a look-back sample can underestimate a future loss and create ruin risk.
- The example’s smaller historical loss produces a higher f than the full sequence.
- Reducing the estimated f by half does not avert ruin in the stated example.
- The document asks about bounded sizing without look-ahead bias but offers no solution.
Tags
Full text
# Optimal f (position sizing) without look ahead bias # 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)?
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.