Fixed fractional money management

Trading in a totally random way with a profit percentage of 50% and a multiple R of 1 does not produce any advantage, as you would expect. Remember that a multiple R is the average profit divided by the average loss. Such a system has neither an advantage nor a disadvantage. The average result should be extremely close to the beginning balance.

Most traders focus on risking a certain dollar amount, such as $ 1,000, on a certain trade. Fixed fractional money management updates that dollar figure after each trade. Change the overall result after adding all the winners and all the losers. Remember that trade is the net result of several hundred exchanges or even thousands of exchanges. The power of position size or betting strategy comes into play as the number of trades increases.

Fixed fractional money management stretches some parts of the bell curve and compresses other regions. Before we get into that, it’s important to remember what fixed fractional money management means. It represents the idea of ​​risking a certain percentage of the capital in current account instead of the initial capital.

Consider an example where the account balance starts at $ 100,000 at a risk of 1%. Both methods risk the same amount on the first trade, $ 1,000. However, the next trade will produce a different amount of risk. A profit on the previous operation would increase the account’s principal to $ 101,000. One percent of $ 101,000 is $ 1,010 of risk on the next trade. A huge ten dollar change.

That may seem trivial. It is certainly not long term.

Examples of

Consider a merchant who plays a coin toss game and has a system with the following characteristics:

Starts with an account balance of $ 100,000

Its multiple R is 1.0

Win 50% of the time without commercial costs.

Risk 1%

A head turn means you win. Lose when corner lands cross.

The absolute worst result of playing the draw with a fixed dollar risk of $ 1,000 is a loss of $ 46,000. Adding fixed fractional money management during that difficult reduction improves the reduction to a less substantial loss of $ 37,500. The worst reduction goes from -46% to -37.5%. The method drags the worst case and brings it closer to the average. When a devastating and unfortunate drawdown occurs, the technique reduces the losses experienced by the trader.

The best scenario for fixed dollar risk is a return of $ 58,000 (58%). Adding money management to the system dramatically stretches the best-case scenario to the right. Upgrade to a return of $ 76,000 (76%). The good times get much better without changing anything at all about the trading system. The method stretches positive returns out of average. The merchant leaves with more money in his pocket.

The natural instinct is to conclude that fixed fractional money management is the way to go. I agree. Improves the risk-reward profile of a totally random strategy. Adding it to a real trading system should help control parameters that are considered critical by most traders, such as drawdowns and performance maximization.

However, an important consequence of using fixed fractional money management is that the odds of receiving a below-average return are slightly increased. The coin toss game underperformed 47% of the time. Applying fixed fractional money management increased the probability of a below average return to 53%. The effect is not so much. You are more likely to lose. But when it happens, the “loss” is so insignificant that it can be thought of as a breakeven point.

Random numbers occasionally follow a seemingly non-random pattern, like lose-win-lose-win. When this occurs, the trade size of the losses is larger than the trade size of the winners. Even if the winning percentage is exactly 50%, those wins are slightly overshadowed by the losers. That micro-effect of slightly larger losses than gains shows up as a slightly higher risk of not making as much money as expected.

Plot all results

The red areas represent the losing results, while the green areas represent the winners. Money management is really about maximizing the ratio of the green area to the red area. Random trades with no expectation of profit produce a standard bell curve.

Fixed fractional money management moves the higher density of returns slightly to the left. Doing so creates the trivial disadvantage of a slightly higher risk of negligible loss. Importantly, the far left (worst loser) is dragged much closer to average. The right winger (the best winner of the case) stretches much more than the average. The compensation is a slightly higher risk of loss in exchange for better extreme results.

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