Position Sizing When Payoff Estimates Have Low Predictive Power

Summary

The document raises a position-sizing problem: realized trade returns may correlate only weakly with estimated payoffs in advance. If that relationship is weak, sizing bets strictly according to a Kelly estimate could assign too much capital to trades with optimistic payoff estimates and too little to trades with modest estimates. The author asks whether sizing should adjust both upward and downward around Kelly recommendations.

It distinguishes this question from shrinkage methods that account for uncertainty in win rate and payoff by reducing Kelly-sized positions. A cited discussion suggests sizing in proportion to confidence and inversely to risk, while cautioning that confidence levels may be difficult to distinguish; equal weighting or risk parity are offered as alternatives. No empirical results, formal estimator, or sizing rule are developed, so the document serves as a research question and points to practical uncertainty in ranking trades by confidence.

Key ideas

• Weak correlation between estimated payoffs and realized returns can undermine Kelly-based sizing.
• The author asks about adjusting positions both above and below Kelly recommendations.
• Common shrinkage approaches described here reduce sizes to account for uncertainty in win rate and payoff.
• Confidence-based sizing depends on whether confidence levels can be meaningfully distinguished.
• Equal weighting and risk parity are mentioned as alternatives when confidence estimates are unreliable.

Tags

# Shrinkage estimates for position sizing


# Shrinkage estimates for position sizing












Problem: correlation between realized returns per trade and ex ante payoff is relatively low. Given that, it's possible that small (large) bets should be larger (smaller) than recommended by Kelly.

I have seen shrinkage estimators for Kelly which aim to take into account uncertainty about win rate and payoff but these all reduce the position sizes.

Is there any literature on adjusting position sizes up or down as mentioned in my problem statement above?

Thanks in advance.

EDIT: there are some relevant comments here https://mobile.twitter.com/macrocephalopod/status/1461456567522537473. In particular: "On trade sizing I think sizes should be proportional to confidence and inversely proportional to risk. That assumes you can meaningfully distinguish confidence levels! If not then equal weight or risk-parity weight is better than overthinking it"

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.