Totally random trading with a win percentage of 50% and an R multiple of 1 does not produce any advantage, as one would naturally expect. Remember that a multiple of R is the average profit 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. Fixed installment money management updates that dollar figure after each trade. Change the overall result after adding all the winners and all the losers. Remember that trading is the net result of several hundred trades or even thousands of trades. The power of a bet or position sizing 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 fixed percentage of the equity in the current account instead of the 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 carry a different amount of risk. A win on the previous trade would increase the account equity to $101,000. One percent of 101 grand is $1,010 of risk on the next trade. A huge ten dollar change.
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
Your multiple of R is 1.0
Win 50% of the time with no trade costs.
1% risk
A flip of heads means he wins. Lose when the corner falls tails.
The absolute worst outcome of playing 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 and brings it closer to the average. When an unfortunate and devastating drawdown occurs, the technique reduces the losses the trader experiences.
The best case scenario for fixed dollar risk is a return of $58,000 (58%). Adding money management to the system drastically extends the best case scenario further to the right. Improves to a return of $76,000 (76%). Good times get a lot better without changing anything at all about the trading system. The method stretches positive returns far from the average. The merchant walks away 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 the parameters that most traders consider critical, such as drawdowns and yield 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. The application of 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 a break-even point.
Random numbers occasionally follow a seemingly nonrandom pattern, such as win-loss-win-loss. When this occurs, the size of the losing trade is greater than the size of the winning trade. Even if the winning percentage is precisely 50%, those wins are slightly dwarfed 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
Red areas represent losing outcomes, 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 fractional money management moves the higher yield density slightly to the left. Doing so creates the trivial disadvantage of a slightly higher risk of negligible loss. Importantly, the extreme left (the worst-case loser) is drawn much closer to the average. The right winger (the winner at best) stretches much more than average. The tradeoff is a slightly higher risk of loss in exchange for better extreme results.