# How to apply the Kelly criterion when expected return may be negative?

My concern is how to handle a negative value for the Kelly formula. Even when you have a system that has positive expectancy, you can (and usually will) sustain a number of losses, sometimes consecutively. This is usually most relevant at the beginning of trading system signals, each loss has a large impact on the formula. How would one handle trade signals when the Kelly formula turns negative? This is assuming a long only system. It seems to me if you ignore the trade signal you would never recover back to a positive probability since your choice to not take the trade would negate any chance to recover.

Some clarifications: I am writing software for a mechanical trading system. I can run backtest simulations to get a sense of historical "edge" and "odds". My confusion is how to apply the Kelly formula once the system goes live and I am making trades based on the system signals. I want to use actual trade data to calculate the Kelly %. Should I use backtest data for the previous x trades and then walk that data forward as I make new trades? Should I just use backtest odds and edge until I have enough live data to use?

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@user1443 Thanks for your answer. I would like to clarify some points in the above question. I am writing software for a mechanical trading system. I can run backtest simulations to get a sense of historical "edge" and "odds". My confusion is how to apply the Kelly formula once the system goes live and I am making trades based on the system signals. I want to use actual trade data to calculate the Kelly %. Should I use backtest data for the previous x trades and then walk that data forward as I make new trades? Should I just use backtest odds and edge until I have enough live data to use? –  user1748 Dec 5 '11 at 0:16
Well, first you have to be aware that no amount of backtesting will give you probabilities or confidence intervals that hold into the future. Second, if you genuinely have an edge because you know something the market doesn't, then the nature of that edge should dictate how to measure it. Finally, the Kelly Formula is correct in its closed form in poker and is only a hint in capital markets, because the payoff structures are different. You need to come up with a kelly-inspired optimization that corresponds to your trading strategy and market assumptions, and there's no pretty formula for that –  user1443 Dec 8 '11 at 4:54

You are trying to apply the Kelly Criterion, supposedly to maximize how aggressively to bet, and you are having trouble when the Kelly Value turns negative. The naive answer to your question is that when your kelly value turns negative, then $f=\frac{bp-q}{b}$ turning negative means the instantaneous expected return is negative, which means you should not bet any of your wealth at this moment if you don't have the ability to take the opposite bet (you said you're long only) or alter your instantaneous strategy or timing to change your estimated p, b and q.