Kelly Sizing for Individual Trades and Multiple Trading Rules
Summary
The question considers how to apply the Kelly criterion when capital is allocated across several trading rules that generate multiple trades. It asks whether to assign capital to each rule in advance, size each trade according to its changing outlook, or combine both approaches. The setup also notes that strategies may have correlated signals and express forecasts as probability distributions.
The response distinguishes Kelly sizing from strategy combination. It describes Kelly as a way to choose leverage for a single strategy under log-wealth utility, while combining strategies requires considering their covariance as well as their expected returns. It also cautions that the basic Kelly-optimal leverage can be too high in practice. The exchange gives no allocation formula, empirical comparison, or detailed treatment of time-varying trade edges, so it frames the conceptual issue without providing a complete portfolio-sizing procedure.
Key ideas
- Kelly sizing concerns the leverage of a single strategy under log-wealth utility.
- Combining multiple trading rules requires considering covariance alongside expected returns.
- The basic Kelly-optimal leverage can be too aggressive in practice.
- The discussion does not provide a formula for allocating capital across changing trade opportunities.
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Full text
# Kelly Criterion at the individual trade level or the broader trade rule? # Kelly Criterion at the individual trade level or the broader trade rule? Suppose I've raised some initial capital, $C$. I would like to invest it according to three different trading rules, $T_1$, $T_2$, and $T_3$. Each of these rules will yield several trades over the course of a given year. Imagine I am relatively confident in my estimates of the edge for each of these rules. It is positive in all cases, but some rules are better than others. ### My question: what is the proper use of the Kelly criterion? - Do I divide $C$ among the trading rules in advance (i.e., Kelly at the "rule level")? For example, $T_1$ gets to wager at most $p_1C$ from now into eternity ($p_1$ ranging from 0 to 1). - Do I allocate portions of $C$ to an individual trade (i.e., at the "trade level")? For example, $T_1$ might return higher or lower expected returns from trade to trade. Intuitively, it makes sense to allocate more capital to cases where $T_1$ is more optimistic. - Are both of these the same? Am I totally misunderstanding the problem in the first place? A caveat: I know Kelly isn't the only game in town for things like position sizing. I'm open to alternatives, but can we stick to Kelly on this one for the sake of simplicity. I'm trying to understand the general nature of the problem. Additional assumptions: As pointed out in the comments, the trading strategies can be assumed to produce moderately correlated (r = .50) predictions about price movements. Moreover, their output will be continuous probability distributions about expected price movements. ## Answer by Michael Isichenko (score 0, accepted) https://quant.stackexchange.com/a/67984 As correctly pointed out in the first comment, the core question is about the covariance of your strategies (or trading rules if you prefer) in addition to their mean rates of return. Kelly criterion is not a tool for combining a set of strategies; it is about an optimal betting (leverage) level for a single strategy using a log wealth utility. Even then the Kelly-optimal leverage gives a simplistic result which tends to be too high. This point, as well as ways of combining strategies (involving less trivial math), are discussed in this book.
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