The Kelly criterion lets you determine the optimal amount of leverage which maximizes the long term growth of account. There is a lot more to it, as this maximization of growth comes with a very heavy penalty in terms of volatility and drawdowns. But essentially, this is what it's for: to figure out what leverage (i.e. position size) to use for every trade. The Kelly criterion for the cases involving two outcomes (a fixed-percentage loss or a fixed-percentage gain) is pretty simple, and can be solved analytically. If there is a continuous spectrum of outcomes (such as it is in trading), it can be solved numerically. Given a series of historical returns (from a trading system, for example), the Kelly fraction is determined by maximizing this quantity: G = Sum(Log(1 + r * L)) where L is leverage r is a return (such as a daily return) Sum is a sum of of the Log(1 + r * L) quantities for each return r So, you successively increase leverage L until the point when G becomes the highest. That gives you the answer L, which is the leverage. Beyond this value of L, as your leverage becomes higher, your total return actually becomes lower. Thus the term "optimal leverage" (aka Kelly fraction).
Thank you nonlinear5. So, Kelly does not minimize "ruin" and is good for someone with deep pocket. In general, should one "bet" using fraction Kelly, like 1/2 Kelly 1/4 Kelly? Can one numerically, i.e., using Monte Carlo to simulate risk of "ruin" using various fractional Kelly? What about "risk of ruin" in probability? Is that a good risk management/bet sizing value? Regards,
Anyone uses Kelly Criterion? Yes - I use my version of it modified for trading equities & ETFs as opposed to gambling which it was intended for. Max position size is 20% of capital (no margin loans!). I break each position into 4 separate trades of 5% of capital - layering in - adding only to winners. This keeps my loses much smaller than my winners and still allows for the equity curve to have stellar winning years and small draw downs on losing ones (<7%). My risk per trade is just under 1% of capital.
I set my overall system risk target with an eye on Kelly. I'm running at about a quarter Kelly (25% annualised risk target versus a backtested Sharpe Ratio of 1.0). I also size my bets proportionally according to inverse volatility (Kelly... but also Markowitz) and according to forecast strength (a.k.a. perceived 'edge') GAT
My futures trading system is based on the system as explained by @globalarbtrader in his book. This includes a Kelly analysis to determine bet sizes. I use 25% annualised risk target. I wanted to use the same "bet size calculation" for another system, which uses ETFs instead of futures. However, my account is not large enough to run at 25% risk (or, in other words: the ETF volatility is not large enough to reach 25%). The position sizes in the ETF system are therefore limited by account size, not by risk volatility.
Yea I used to run at 25% which maxes the gains but trimmed down just recently after I read this from Ed Thorpe - not willing to go down to %12.5 like he suggested but than again he has a huge amount of capital to deal with. Are you layering in to a position or going all in at once? if you bet half the Kelly amount, you get about three-quarters of the return with half the volatility. So it is much more comfortable to trade. I believe that betting half Kelly is psychologically much better. https://betyourbeliefs.wordpress.com/2017/02/27/ed-thorp-jack-schwager-and-the-kelly-criterion/
The futures system I'm referring to in my previous post is using something which you call "layering". It determines an amount of "confidence", or "strength", or whatever you would like to call it. If this value is higher, is a larger position size used. If this value is lower, is a smaller position size used.