gbos, Thanks for this link. I'll check it out. I also noticed several other interesting titles from your root link: http://money-management.martinsewell.com
dougcs, Kelly criterion gives you the percentage of your account that you should risk if you want to get the best compounded return. It needs the probability of win and the ratio averageWin / averageLoss. You could verify that this optimum risk percentage gives you the best return by playing with some numbers in an Excel spreadsheet. See the attached graphs. <img src=http://www.elitetrader.com/vb/attachment.php?s=&postid=929130>
Bernard111, The most important MM papers I reviewed are referenced in this thread. The charts I was referring were the result of my playing with numbers in Excel spreadsheets like the ones I just posted, or the one attached. Sometimes a picture tells more than a bunch of numbers. <img src=http://www.elitetrader.com/vb/attachment.php?s=&postid=929141>
No, this is a common misunderstanding but it is wrong. You can apply the Kelly criterion no matter what the distribution of returns. You can apply Kelly for lognormal, normal, uniform, triangular, discrete or whatever other distribution. You just don’t apply the same formula as in the Bernoulli case. In Thorp’s paper has an example for the normal distribution case. He uses matrix algebra to determine the capital allocation between assets with normally distributed returns. Even in the case that no analytical solutions are available a simple optimization algorithm will do the job. The required calculations can be done easily within excel.
An interesting link that has some references to money management: John Hill's "A Response To Mike Covel and Trend Trading"
No wonder why recently so many posts on ET mentioning and promoting "Kelly". Q Has anyone used the Edge/Odds formula in investing? http://www.amazon.com/gp/discussion...09046377&store=books&cdThread=Tx2J6Y8YS9500TB This famous formula seems simple enough [Edge/Odds]. However, it seems rather inpractical for investment purpose. This is because you typically have no edge within an efficient market. And, the odds are truly uncertain. It is a random variable with an undefined distribution (it is not normal). This formula, per the author, also suggests that there is an optimal level of risk beyond which you are going to get hurt and wipe out your capital. This is contrary to investment theory that suggests that additional risk should always be compensated with extra return otherwise no investors would be willing to take on this additional risk. In view of the above, has anyone figured out how to find the optimal risk level. UQ
More comments regarding the limitations of Kelly value from the same author/ book/ chapter above: Q However, the Kelly formula is only applicable to strategies where every winner is the same size and every loser is the same size - hardly the case in actual trading. ~ snip ~ As already mentioned, the major flaw of the Kelly formula is that it assumes two outcomes only - a winner of a certian magnitude and a loser of a certain magnitude. Trading, with its virtually infinite number of potential outcomes per trade, is not such a simple game, however. The Kelly formula should, therefore, be used only for initial research and experimentation. For a better approximation of the optimal trade size, one should determine what is popularly known as the optimal f, which requires a slightly more complex calculation. UQ
Q Money Management Traps http://www.isigmasystems.com/mm2.html Novice errors Out of all the mistakes in money management, by far the most common is to take recklessly large positions. This typically occurs where a trader decides an instrument looks like a favorable profit opportunity and proceeds to accumulate the largest position his total equity will cover. Our money management article addresses this type of error in greater detail and provides a mathematical explanation for a wiser approach to issues of position sizing. Trading recklessly large positions, however, is not the only error traders make in money management. Drawdowns: duration or severity? There exists a common misconception that the way to control drawdown is to reduce position size in response to losing streaks. A popular version if this idea says to reduce position sizes by 20% for every 10% in losses. A more mathematically sophisticated (but equally wrongheaded) approach would be to modify the formula Units to Buy = (Renormalization Coefficient * Equity) / Unit Price to be proportionate to the ratio between current equity and historical maximum equity Units to buy = (Equity / Max Equity) (Renorm Coeff * Equity) / Price Effectively, this would mean that during sequential losses a trader would become more and more risk averse. During the series of losses, this might seem like the wisest idea, to trade the least when things aren't going well. Where this method fails in in real trading. When the losing period comes to an end, the trader is now constrained to trading a tiny fraction of the original position size so that the successful trades which recover from the losing streak are transacted at such a small size that it take the trader considerably longer to recover and begin generating profits again. Raising the stakes A less common, but more dangerous approach is to start trading bigger as losses mount. The assumption behind such a strategy is that drawdowns can be made shorter if winning trades, when they happen, are executed with large position size. Mathematically, this could be expressed as Units to buy = (Max Equity / Equity) (Renorm Coeff * Equity) / Price So for example, if equity should fall to 50% of it's historical high, the trader will now trade at twice the level of risk as before. Eventually, such practice will lead to a situation where a trader is taking positions large enough to entirely wipe out the trading account. Optimization Errors Many "gurus" recommend position sizing using something called the Kelly Formula. The formula, originally developed to solve problems in signal transmission, is quite sound from a mathematical standpoint. It states Optimal Risk = Win Rate - [ (1 - Win Rate) / (Avg Win / Avg Loss) ] In trading, however, the Kelly formula frequently suggests taking on dangerously large risks which can lead to severe drawdowns and potential margin calls. In addition to the Kelly formula, there are a number of other concepts of optimal position size. All such methods are similarly problematic for the same reasons as the Kelly formula, i.e., the focus is solely on maximization of profit while risk management is neglected. Conclusions Despite the good intentions behind the money management approaches listed here, none of them are particularly advisable. Cutting back serves to make drawdowns shallow but prolongs them at the expense of total returns. Raising the stakes shortens drawdowns most of the time, but the exceptions result in blowouts. Optimization formulas provide a solid basis for producing maximal returns, but they neglect to control the downside risks. What all of these methods have in common is that they address one aspect of money management while neglecting all the other aspects. The solution: Use a money management strategy which deals with all aspects of proper position sizing. UQ
Odd - Interesting insights. Thank you. So, if increasing size on draw down is risky, and reducing size on draw down leads to a less timely return to profit, perhaps a fixed size is the answer - related to units equal to starting capital? ST