Does Kelly method practically work for trading? According to Lawrence McMillan (options guru, with applied mathematics background), "In reality, the Kelly System was designed only for use on terms that have only two results (win or lose, true or false, on or off, etc.). This works very well for gamgling, but not so well for the stock market. ... The Kelly formula can't be directly applied to the stock market, because results are more complicated. Each trade doesn't produce a complete loss or 100 percent profit, less commissions, as sports or casio betting does. A stock, futures, or option trade can have an infinite number of outcomes." Any comments?

A static linear system trying to work in a dynamic, non-linear environment. Market geometry changes too much to apply a static system to.

Assuming you mean Kelly ratio [http://www.gummy-stuff.org/kelly-ratio.htm], it is flawed. So is optimal F. There are several position sizing methods that are better. Bob Spear(s?) had one. There is also Fixed Ratio and Fixed Fractional (probably the simplest and best).

I don't see why Kelly should not work. The inputs are your avg win, avg loss and win ratio... if those change throughout the day, why not break them down to different time periods of the day, maybe conditions change from the first half hour, the next hour and a half, midday and last half hour... use your averages from each time period to calculate bet size... I don't use Kelly because I'm trading just one fut contract but I'd backtest it before I dismissed it on anybody's word..

He misses the point because he is looking at %Kelly from the point of view of the market rather than from the trading system's. A trading system has only two outcomes, win or loss. %Kelly maximizes the geometric growth of the equity curve of a trading system, not of the market. It is an approximation that works well if the expectancy is proven to be positive, although it may be changing slightly over time. I gave a link in another thread to an excellent article on this subject: http://www.tradingpatterns.com/Kelly.pdf For trading systems with no proven expectancy, the fixed percent method is more appropriate: http://www.tradingpatterns.com/PositionSizing.pdf Again, the "guru" you mentioned seems not to understand what %Kelly does. It applies to the trading system, not to the market. It applies to the two outcomes avg. win and avg. loss. This is an approximation that works well in high frequency trading with fixed stops apllied.

Try not to focus to much on the 'general' formulas; it is better to understand the principles behind the kelly criterion. Even the simple binary model is not perfect, since it uses probabilities to model the win/loss frequencies. Hence, the optimal pt will shift depending on the real outcome distribution. In my experience, using avg win and loss is not a good substitute for approximating return distribution for kelly criterion. A simple way to look at this is to generate some number of arbitrary returns (say, 100), both positive and negative. Then take (1+avg win)^nwins and (1-avg loss)^nlosses, multiply to get terminal wealth vs. f. You'll see that the optimal pk is very different vs the true compounded individual returns. It's useful to run monte carlo simulations of expected continuous returns (even though they are not binary), to get a feel for the optimal fraction. However, you will find that due to the random nature of returns, the optimal point shifts (much more than the binary model, since the distribution is more complex). That's why it's better to look at it from the perspective of a range or region of optimality. The closer your distribution models the real returns, the better your assessment of the true optimal fraction mesa will be. Also, don't get caught up in the notion of position sizing and scaling of optimal f as it is commonly employed in trading books. This has major problems as many have discovered. You will find plenty of detractors, as it suffers from the same problems as all parametric type estimations do (VAR for example); namely that of fat tails. The key is to understand that, and find a way to utilize the concept with that in mind. What makes the kelly criterion so powerful, is simply the fact that compounded terminal wealth has a quadratic profile and not uniform vs. fractional bet sizing; thus the idea of an optimal point or region to scale bets. There are other methods to spread and dampen risk of fat tails. Be creative.

There is a chasm like the Grand Canyon between traders with a system with proven expectancy and all the rest... the rest have to work on psychology and money management, and finding an edge. Tharp said as much very plainly at times. He said that all the people that he coached really didn't have a system. Tharp's money management ideas can take a very marginal system and improve it. They won't do much for a really robust system that gains all the time, Kelly would apply to that probably, like I said, it would be very easy to backtest it with any software that does portfolio backtests well...

I see the cardboard shill generator hasn't been updated yet. http://elitetrader.com/vb/showthread.php?s=&threadid=170253&perpage=6&pagenumber=2 Is trade martingale equal not improvement or quantum discrete position entanglement? Elaborate? Turing would be proud.

The problem with Kelly sizing is misapplication. This is not an inherent flaw of the Kelly criterion, it is a failure to fully understand it. There is more than one Kelly formula in the public domain and what almost all have in common is this: they were designed only for simple binary-outcome casino-type betting. They fail when applied to multiple-outcome scenarios like trading. The whole idea behind the parameters winrate, average gain and average loss is to force-fit the square peg of binary-outcome Kelly sizing into the round hole of trading. Unsurprisingly this usually does not bode well. There are robust multi-outcome Kelly formulae that are extant. But they are not known to the general public, nor should they be. If you have a firm grasp on differential calculus, you can with some effort devise your own robust Kelly formula. But as stated elsewhere, all it takes is "some assembly required" to stop most ETers cold. Sorry, no silver platter service here. Do the work or go without. For what it's worth, most quants are no better at this game than non-quants, and they have far less excuse (they do know calculus). Most seem to have unskeptically embraced what is arguably the worst Kelly formula in the public domain, probably because it's been advocated by Edward Thorp. And so it goes.