Objectives of money management

Besides simply placing an order to buy or sell, a trader also has to concern himself with how many units to place the transaction for. There are a number of motivations behind this concern. They include reducing the size of potential losses, avoiding margin calls, ensuring that additional funds remain for purposes of diversification, keeping drawdowns from getting out of hand, optimizing risk/reward ratios, and ensuring that position volatility is independent of market volatility.

Creating a basic framework

With the above goals in mind, one can consider certain factors that would call for increased or decreased position size. The table below lists topics affecting position size in two columns. The column on the left contains variables to which appropriate position size is directly proportionate. (When they go up, the number of units to purchase goes up) The column on the right lists variables to which position size is indirectly proportionate. (The ideal number of units to trade decreases as elements in the second column increase)

Getting Formal

With the above table, it is easy to get a rough idea at what an appropriate position size should look like. With more equity in the account, more tolerance for risk and more occurrence of winning trades, a trader can bet more. As market volatility, the risk in the trade itself or the price of the individual unit increase, the proper number of units to purchase decreases. However, for a truly systematic approach, it's necessary to transform these concepts into a mathematical model for determining how many units to buy or sell. Consider the equation below.

This formula is the ultimate in agressive trading. Just buy as many units, contracts or shares as the account equity will cover. Despite the imprudence of taking such a risk, at least this method ensures that the number of units bought is inversely proportionate to the price per unit and directly proportionate to trading capital. Time for some risk control!

As a wise trader always knows the worst case exit prior to entering any trade, it's trivial to calculate the actual risk of the trade itself. Because our strategy uses a volatility measurement in order to determine stop placement, this also ensures that position volatility is independent of market volatility.

For long trades:

For short trades:

In order to keep risks under control, our strategy involves using a renormalization coefficient which is obtained as follows using the trade risk and the maximum risk that the trader will take on a single trade.

This renormalization coefficient will decrease as the risk in the trade increases or increase as the maximum per trade risk is increased. This is the key to the final unit size formula.

Practical Application

Suppose a trader has $10,000 in trading funds and a market timing signal indicates that there is an opportunity to buy in stock XYZ which is currently trading at $40 per share. The volatility measure is $8, indicating that the trader's stop-loss point is $40 - $8, or $32. Using the formula for trade risk above, he performs the following calculation:

Now finding the renormalization coefficient only requires that the trader also know his maximum per trade risk. For example, suppose the trader is willing to risk no more than 1.5% of total equity per individual trade.

Now the trader can determine how many units constitute an appropriate position size

Since the trader cannot purchase fractional shares, he places his order for 18 shares of XYZ

The Benefit

Since our hypothetical trader only purchased 18 shares at $40, he only spent $720 leaving the remainder of his account to diversify his portfolio with through other investments. Additionally, if the price should fall to his stop of $32, he will only lose 1.5% of his own money while the actual stock loses 20%.

Choosing a Maximum Loss

As much as one would like to simply not have losses, they are an inevitable cost of doing business for the trader. What the trader can control is maximum drawdown by knowing what the odds of a win are and what percentage of drawdown will constitute an unacceptable loss. Suppose the trading system used produces winners 40% of the time. The trader has decided that after a drawdown of 25% he will close his trading account. Since the odds of a winning trade are 0.4, the odds of a losing trade are 1 - 0.4 or 0.6. From here the trader can figure out what length of a string of losses is mathematically sufficiently unlikely to be considered a serious risk. By using the formula

the trader can determine that a losing streak with 1 in 10000 odds of ever occurring will consist of 18 consecutive losses.

From here, the trader determines the amount to risk per trade which would develop into a 25% drawdown at 18 losses

Hence the trader establishes 1.5% as a maximum risk to take per trade.

Conclusions

In this article, we've covered money management issues in detail, showing the relationship between account equity, unit price, unit volatility, win / loss ratio, stop placement, drawdown tolerance and proper position size. Unless a system accounts for all of these factors in making money management decisions, it's not a complete trading system.

Additional reading

In addition to the material here, it may be helpful to know and understand some of the more common errors in money management. See this article on money management traps for more information.