The Flaw in the Kelly Criterion – Betting Under Uncertainty

Many traders know the about the Kelly Criterion, but do you know why this formula is not commonly used to actually determine bet sizes in quant trading firms? Let’s dive into the 4 main reasons that firms will use not be using the full Kelly Criterion size.

The Kelly Criterion is a bet-sizing formula developed by John L. Kelly Jr. in 1956 at Bell Labs. It has since been adapted by traders seeking to allocate capital / size bets efficiently when they believe they have a statistical edge.

The intuition of the Kelly Criterion is clear:

• the higher the win probability the more you bet
• the higher the odds, the more you bet
• the lower the loss, the more you bet

The Kelly Criterion is balancing between two possible errors: overbetting (which risks ruin or large drawdowns) and underbetting (which stifles growth).

Reason 1: Insane Leverage

Playing around with the slider above, you can see that small partial losses result in insane leverage being required, more than is actually feasible!

Reason 2: You Only Live Once

Can you live with a 30% drawdown on your net worth? Imagine you spend your entire life accumulating a nice nest egg and then you blow 30% of it trading. Will you keep going?

Kelly maximizes expected log‑growth of wealth. It doesn't actually maximize on your median performance, so there are situations where your outcomes are very right-tailed and your median outcome isn't actually all that great. For example, if I spend 40% of all my money repeatedly buying the Mega Millions Lottery tickets, even if it is positive expected value (e.g. payout is $1 billion with 1 in 300 million chance of winning, at $2 a ticket is positive expected value), I will be penniless 99.99% of the time, and fabulously wealthy that other small fraction - positive expectancy doesn't mean I should blow all my money on that infinitesimal probability!

It might be worth building some intuition as to how it actually feels to be betting. This coin flipping game demonstrates "trading" with a "small" edge. Can you beat my best of winning in 9 clicks? (this took hundreds of tries where I lost my entire bankroll - something you should probably not do in real life!)

Hint: use the calculator above to get an optimal Kelly bet

You can see that in playing this game, if you're too aggressive and lose money early, the betting gets quite oppressive and you need to click a lot, so it's important that early on, when we do not have as much information, that we are more conservative with our betting. However, as the picture gets clearer and our bankroll gets bigger, it becomes more optimal to bet bigger size.

Also, if I play with the mindset that I cannot go broke, as opposed to getting to $1M with minimal clicks, that changes my strategy completely.

If we're trying to minimize the number of clicks, given that you know the coin is weighted, we should be betting some amount to compound our money (but not too much). Given that each coin flip imparts new information for us, we should be updating our understanding of the coin while betting.

For reference, in a 2016 betting experiment Victor Haghani and Richard Dewey gave 61 quantitatively trained participants $25 and a 60 ⁄ 40 biased coin for 30 minutes to make even odds bets. Around 20 of the participants went broke despite the clear edge!

Another simulation: the below graph simulates Kelly betting, but with a stop at a 30% drawdown. You can see that betting less size will outperform full Kelly betting under these conditions because a ridiculous percent of the Full Kelly betting simulations will hit the drawdown limit!

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Reason 3: Fat Tails and Noisy Edge

You don't actually know the underlying distribution of the payoffs and the probabilities, and also, they are constantly changing. What might seem like a straightforward bet might have some fat tails (e.g. every 2008 financial crisis level event, your strategy loses 50%) that can dramatically change the expected value of the trade (almost always for the worse!).

You can account for not knowing the full probability distribution of the betand the distribution constantly changing by applying a statistical shrinkage (ie use fractional Kelly). In simpler terms, you can statistically justify betting less (applying a shrinkage) because you are uncertain about the probability distribution of the bet winning.

A question you will face when losing money is: "has my strategy decayed or am I going through a drawdown?" (AQR has some writings on this topic).

In other words, has the underlying probability distribution fundamentally changed or am I just getting unlucky? Not betting full Kelly gives you more runway to correctly deduce whether to shut down a strategy because it has decayed as opposed to being forced to shut it down because you're losing too much money.

Reason 4: Real‑World Frictions & Risk Limits

• Slippage & fees: Each bet’s expected value is shaved by spreads, commissions, and price impact. Fees are guaranteed, profit is not!
• Liquidity caps: Big positions move the market; Kelly ignores impact‑adjusted sizing.
• Drawdown limits: Multi‑manager pods are often cut at <10 % intramonth; full‑Kelly’s 35 %+ worst‑case is career‑ending.
• Portfolio interaction: Positions co‑move; edge isn’t independent across trades.
• Adverse selection: Most positions that you can naively put on for huge size are likely being offered by the market because they are toxic or unfavorable. You have to respect that other market professionals also are trading with you because they think they will make money doing so.

How Modern Quants Actually Size Risk

Quant trading firms generally do not directly use the Kelly criterion in its classical form - but they do use Kelly Criterion inspired principles.

• Risk parity / volatility targeting – Replace p with Sharpe; size so that each sector contributes equal vol.
• Inventory limits – Hard caps on gross and net exposures regardless of theoretical edge.
• Opportunity‑constrained EV‑maximisation – At mega‑shops like Susquehanna (SIG) and Jane Street, due to their years of successful trading, their bankroll often exceeds their capacity for edge. They size every fill to the venue’s liquidity/impact ceiling, effectively taking the entire opportunity set and focusing on aggregate expected value rather than per‑trade Kelly sizing.

Also, generally, if a strategy is really good, your bankroll will eventually grow to the point to where Kelly sizing will exceed the available liquidity given by the market, so in that sense you will be betting some fraction of full Kelly.

Key Takeaways

The Kelly Criterion teaches that sizing should scale with edge and inverse payoff, but raw formulas ignore a couple of factors.

• Insane Leverage: not possible (nor suggestible) to get 30x levered
• You Only Live Once: This formula is maximizing the logarithmic growth of capital NOT the expected value / nor the median outcome. If you cannot handle a massive drawdown then Kelly is too aggressive.
  
• Fat Tails and Noisy Edge he model assumes a consistent, measurable edge and independent trade outcomes - conditions rarely met in live trading. There are very complex payoff distributions, and adverse selection. You rarely know the full distribution, and the distribution generally is constantly changing with the state of the world.

• Real‑World Frictions & Risk Limits: adverse selection, slippage, risk limits will prevent you from ever realizing the long term growth.

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Only in venues with genuinely binary payoffs and knowable probabilities, and sports books, prediction markets, the Kelly Criterion might explicitly be used.

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If you're developing a strategy and want to understand your edge and risk exposure more clearly, the Architect brokerage is designed to help you test, size, and manage trades systematically.

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References: Another good article on Kelly Criterion.

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