## Further talk on money management, money management styles

### You will learn about the following concepts

- Money management strategies
- Fixed ratio
- Fixed fractional
- Martingale style
- Kelly criterion

In the previous article we dug a bit deeper into money management and discussed a couple of calculations that can help us project what earnings we might expect from our trading strategy and money management system, as well as a general oversight of what the risk of going bankrupt is. Now we will turn our attention to some of the most common money management styles traders use in order to improve their performance.

## Fixed ratio

The first money management system we will discuss is the so-called fixed ratio management system, developed by Ryan Jones. It helps you determine the optimal number of contracts to trade as a function of profit and loss, thus rewarding better performance. It uses the following calculation:

– N is the number of contracts you should trade

– P is your accumulated profit up to date

– ∆ (delta) is the amount of money you will need before trading a second contract

Traders are using the fixed ratio money management system in order to safely increase their market exposure, while also protecting their accumulated profits. Let us assume that the minimum margin for a futures contract is $1 000. This means you will need to have another $1 000 at your disposal, if you want to trade a second contract. This means that for the fixed ratio calculation your delta is $1 000.

This system is suitable for traders starting with smaller accounts, because it requires less profits at the start in order to increase the position sizes. Generally it implies that traders are willing to risk more at the start to spur initial growth, but as their account equity surges, traders are prepared to take less risk. The Fixed Ratio system takes advantage of winning streaks, in that it encourages more aggressiveness during consecutive winnings, but as the the capital grows, the system allows for the position size growth to slow down. This averages the risk-versus-aggressiveness ratio over the course of the accounts equity growth.

## Fixed fractional

The fixed fractional money management system was developed by Ralph Vince and assumes that the number of traded units is based on the risk of the trade. It defines the trade risk as a fraction of the equity. The risk of a trade is the amount of capital the trader is risking to lose with each trade, if it is a loser. This of course is adjusted for trading systems, which use protective stops.

Basically the risk remains the same percentage (fraction) of the trading capital. This way, the risked absolute amount of money remains proportional to the equity and rises and declines as the equity itself rises or falls after successful and unsuccessful trades. Here is the formula:

f x (equity/|trade risk|) = N, where

– f is the fixed fraction of your account you have decided to risk with a trade

– equity is the value of your total trading capital

– trade risk is the amount of money you could lose in the transaction. Because the trade risk value signifies a loss, which should be a negative value, in order for our calculation to work you need that to be in absolute value (thus in ||).

– N is the number of contracts you should share.

If youve decided to risk not more than 5% of your account equity per trade, and, like the example above, you are trading a futures contract at the price of $3 500, and you have $50 000 dollars in your trading account, then the calculation will look as follows:

0.05 x (50 000/3 500) = 0.714 contracts

However, since you cant trade less than one contract, you will need to round that up to 1 contract.

### Drawback

One of the biggest advantages of this money management system is its compounding effect. It means that as the trader scores successful trades and his trading capital increases, his position size is also gradually increased. This way, if that market players trading strategy continues to be successful, he will gradually continue to increase his profits (he will achieve geometric growth). Logically, when the trader enters a losing streak and his account equity shrinks, he will automatically begin using a smaller position size and each further losses will be narrowing proportionally to his account balance.

The proportional adjustment of the position size also means that when you have chosen to risk a small amount of your equity, each winning or losing streak will have a smaller impact on your equity curve, leading to smoother capital appreciation.

One of the main problems this money management system encounters is with small account sizes. First, you will experience difficulties in fine-tuning your position size due to the lots you are forced to work with. Also, even if you think that you are ready to increase your position size, but you havent achieved good enough results yet, you will need to first attain a very high return so that your account balance grows. If you dont wait and decide to go ahead and increase your position size, you will be risking too much.

Another drawback of the fixed fractional system is the difficult recovery from a losing streak, because your position size will respectively also decline (this opposes the martingale money management style, which will be discussed next).

There is also a problem with winning streaks. As you score more and more winning trades, your position size will keep growing. Eventually, in the absence of drawdowns, your trading capital will soar to a point that your position size may be well above the level you can calmly and adequately manage. One of the ways to handle such a high risk is to withdraw money from your trading account each time it reaches a critical mass (according to your own standards). This way you will: 1. lock in profits and touch the money youve earned; 2. reduce the risk of operating with a very large position size, thus ensuring smaller future losses.

## Martingale style

The martingale money management style is a betting strategy, used widely by many gamblers, especially in casinos, but also by some investors. Its goal is to improve your earnings in games, at which you have even odds to win, or the odds are in your favor. And because day trading is a zero sum game, i.e. each winner comes on the back of losing counterpart, the martingale system is found suitable by some traders.

Under this strategy, when a trader bets, if he gets it wrong, then he should immediately bet in the same direction again, but doubling his position size. This way, if the second time he is right, the second position would offset the first ones losses. For example, if you enter a trade with $100 and your trade succeeds, you should trade another $100. However, if you lose on the first trade, you should immediately re-enter the market in the same direction with $200 and win back the money lost. If you lose again, then you should trade $600 dollars etc.

The martingale system relies in probability numbers and assumes that as long as you have at least even odds, you will eventually come to be right and one winning trade will offset all the previous ones losses.

The main problem about this money management strategy is that a long losing streak might cause you to lose all your money before being able to win it back. You will surely avoid such a scenario, if you have an infinite amount of capital, but you dont. In contrast, the market as a whole, has what you can call infinite resources (at least when compared to yours), thus it in theory it can drive you down to bankrupt, while you cant do the opposite.

## Kelly Criterion

The Kelly Criterion is a formula which investors and gamblers use to calculate the ideal percentage of their portfolio to put at risk in order to maximize long-term growth. In order to determine what part of their capital should be committed to each positions, traders need to know their winning trades percentage, the profit from a winning trade and the ratio performance of winning to losing trades. The formula used looks like this:

Kelly % = W – [(1-W)/R], where

– W is the winning probability factor (the percentage of winning trades). This is the probability of a trade to have positive return.

– R is the win/loss ratio and is calculated by dividing the total positive trade amounts by the total negative trade amounts. The result of the calculation tells investors what fraction of their trading capital they should invest in each trade.

Using the same numbers from the example in the previous article, we calculate the following percentage:

Kelly % = 0.55 – [(1-0.55)/(0.012/0.01)] = 0.175 = 17.5%

According to the results, you should theoretically not run out of money as long as you limit your trades to maximum 17.5% of your trading capital. Some traders however use a variation of this strategy, limiting the position size to half of the Kelly percentage as a way to avoid incurring heavy losses. This is commonly used when the Kelly formula generates a number larger than 20%.