Trading completely randomly with a win rate of 50% and an R multiple of 1 produces no advantage, as one would naturally expect. Remember that a multiple of R is the average win divided by the average loss. Such a system presents neither an advantage nor a disadvantage. The average result should be extremely close to the opening balance.
Most traders focus on risking a fixed dollar amount, such as $1,000 on a given trade. The fixed fractionalized money administration updates that figure in dollars after each operation. Change the overall result after adding all the winners and all the losers. Remember that trade is the net result of several hundred trades or even thousands of trades. The power of a position sizing 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 split money management means. It represents the idea of risking a fixed percentage of your checking account equity instead of your initial equity.
Consider an example where the account balance starts at $100,000 risking 1%. Both methods risk the same amount on the first trade, $1,000. The next trade, however, will generate a different amount of risk. A win on the previous trade would increase the account equity to $101,000. One percent of 101 big is $1,010 risk on the next trade. Huge change for ten bucks.
That may seem trivial. It’s certainly not long term.
examples
Consider a trader who plays a coin toss game and has a system with the following characteristics:
Start with an account balance of $100,000
Its multiple of R is 1.0
Win 50% of the time with no trading costs.
1% risk
A head toss means he wins. He loses when the corner falls tails.
The absolute worst outcome of playing a coin toss with a fixed dollar risk of $1,000 is a loss of $46,000. Adding fixed fractional money management during that difficult withdrawal improves the withdrawal to a less substantial loss of $37,500. The worst reduction goes from -46% to -37.5%. The method drags the absolute worst case scenario closer to the average. When an unfortunate and devastating drawdown occurs, the technique reduces the losses that the trader experiences.
The best case scenario for fixed dollar risk is a return of $58,000 (58%). Adding money management to the system dramatically extends the best case scenario further to the right. Improves 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 away from the 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 most traders consider critical, such as drawdowns and maximizing performance.
However, one important consequence of using fixed split 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. Losing is more likely. But when it does happen, the “loss” is so insignificant that it can be considered as breaking even.
Random numbers occasionally follow an apparently non-random pattern, such as loss-win-loss-win. When this occurs, the trade size of losses is greater than the trade size of winners. Even if the win percentage is precisely 50%, those wins are slightly dwarfed by the losers. That micro effect of slightly higher losses than gains shows up as a slightly higher risk of not making as much money as expected.
Graph all results
Red areas represent losing results, while green areas represent winners. Money management is really about maximizing the ratio between the green area and the red area. Random trades with no expectation of profit produce a standard bell curve.
Fixed split 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 left winger (the worst-case underdog) gets dragged much closer to average. The right winger (the winner at best) stretches much more than average. The trade off is a slightly higher risk of loss in exchange for better extreme results.