Kelly criterion determines the optimal theoretical size for a trade based on historical data of trader.

However, I know many traders strongly recommend to not risk more than %1 of their balance and this is called 1% percent rule.

As you know, Kelly formula might obtain anything bigger than 1% (of course it depends on historical data). Therefore, it looks like a paradox for me. I mean, at the end, which option should i follow ? Half-Kelly or 1% ?

So, I am wondering if Kelly criterion has any advantages over 1% rule ?

• I haven’t voted on your question yet, but it seems like you have described 2 strategies that don’t really relate to each other: log of expected wealth vs less than 1% per investment. Perhaps if you explain why you think there should be a relationship between them, there would be more for the community to work on. Aug 30, 2021 at 15:54
• Per Wikipedia: "In probability theory, the Kelly criterion is a formula that determines the optimal theoretical size for a bet. It is valid when the expected returns are known." With stocks, expected returns are not known. The Kelly formula requires an accurate input of the probability of winning and losing. How does one know that for stocks??? Aug 30, 2021 at 16:08
• It also requires a binary outcome, e.g. p% chance of a% gain, (1-p)% change of b% loss. Stock returns do not fit the Kelly model without very generalizing assumptions. Aug 30, 2021 at 16:25
• A has an advantage over B if events favorable to A pan out. If not, B would have been the better choice. In some years, I have traded heavily and my rule of thumb has been to increase the size of the bet when I had an edge - not some arbitrary metric based on back testing (optimization and probability). Aug 30, 2021 at 16:51
• ‘However, I know many traders strongly recommend to not risk more than %1 of their balance’ how do you know that?
– quid
Aug 30, 2021 at 22:01

First, the Kelly criterion is only exact when the actual probabilities of outcomes are known (e.g. roulette). For uncertain probabilities (e.g. sports betting, investing), the criterion is invalid since you can't know the future probabilities, only guess them based on historical data.

In fact, the wiki page for the criterion explicitly states that the rule shouldn't be used for investing:

Note that the Kelly Criterion is only valid for known outcome probabilities, which is not the case with investments. Investing the full Kelly fraction is not recommended.

Second, the 1% "rule" is a risk-management guideline, not a magic or optimal threshold. It's a guideline that keeps traders from risking too much of their portfolio on one investment. Depending on the type of investment, the maximum investment would be increased. For example, one could have a rule that up to 10% could be invested in any one mutual fund, since funds are less risky than individual stocks. Traders can also employ stop losses, options, and other risk management measures to limit risk of loss.

So, can they be in conflict? Yes. What should you do if they are? Use your judgment. Do you have enough faith in the Kelly criterion to risk more than 1% of your portfolio? More than 10%? If the criterion says that you should bet 150%, should you borrow and use leverage to multiply your returns (and your risk)? That's not something than can be answered in a vacuum. One would have to look at the potential loss of an investment and determine how much risk they are comfortable with.

• But, you can never predict a random variable value, unless you try it many many times. Let's consider fliping a coin. You might say that it is 50% chance for each event. But, if you try it only 4 times, then your actual result might not be very compatible with 50%. The same for trading. You never know the probabilities unless you try it multiple time. Therefore, historical data of a given strategy clarifies the probability of the win. I guess, a trader should know how many percentage does he has a wining chance by a specific strategy ? I mean, if it is backtested well enough. Right ? Aug 30, 2021 at 16:25
• A coin toss absolutely has a 50% chance of heads and 50% chance of tails. That doesn't mean that I will always have 50% heads with an even number of throws, but statistically that's the probability of each outcome, which is what the Kelly criterion is based on. How do you measure the probability and magnitude of gain/loss for a financial investment? Aug 30, 2021 at 16:28
• I have the assumption that market behaves normally and if i see some strange signals i do not trade in that day. I also assume that I always use only one strategy. In that case, the wining probability is "number of trades with profit" devided by number of all the trades. Aug 30, 2021 at 16:34
• Beside this, the output of Kelly formula is a percentage, so it can never be 150%. Aug 30, 2021 at 17:04
• "This formula can result in Kelly fractions higher than 1. In this case, it is theoretically advantageous to use leverage to purchase additional securities on margin. " Aug 30, 2021 at 18:20