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
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