The above dialogue provides us with sufficient background to discuss the central issue involving money management-related stop placements — that of acting boldly, taking on too much risk and going bust; or trading too conservatively, which severely limits a trader’s ability to receive a good return on capital.
Let’s assume your trading strategy tends to win 53% of the time and lose 47% of the time, and that you have a $100,000 account. Playing it safe and risking $100 on each trade would minimize your chances of losing your initial stake, but given that the expected gain is 6% of $100 per trade, the returns would be too low to overcome transaction costs and trading overhead. Alternatively, if you risk all of your account on each trade, the probability you will be ruined moves toward certainty with each trade.
One way to maximize returns over the long run with acceptable risk is through use of the Kelly Criterion. This approach involves trading the same percentage of an account on each trade. To obtain the Kelly percentage, subtract the win/loss ratio from win probability [Kelly % = W – ((1 – W) / R)]. To calculate win probability, divide the number of trades with positive returns by the total number of winning and losing trades during this time period. To calculate the win/loss ratio, divide the average gains on winning trades by the average losses on losing trades.
The outcome of applying the Kelly formula is known among investment professionals as the "optimal geometric growth portfolio" because it promotes efficient diversification. In effect, as winnings accrue trade sizes increase, and as losses accrue, trade sizes decrease. As a result, the chance of ruin is small, although a run of bad luck on a series of trades could make it increasingly difficult to break even (see "Problem with percentages").
Of course the application of any system, including the Kelly Criterion, requires common sense. For example, if the Kelly percentage is 4% and you apply this parameter as a money management stop across 25 trades simultaneously, essentially your Value at Risk (VaR) is 100%. In practice, because over-trading is worse than under-trading, venturing a fraction of the amount recommended by the Kelly formula is suggested. This helps protect against errors in "edge" calculations, and helps reduce portfolio volatility.
Another consideration is trade frequency vs. magnitude of winnings. Said otherwise, the frequency of correctness does not matter, it is the magnitude of correctness that matters. In Nassim Taleb’s book, Fooled by Randomness, he provides a table, which highlights the difference between probability and expectations.
Outcomes are asymmetric. Even though there is a higher probability that the market will go up, the expectation is negative because if the market goes down, the magnitude will be greater. Using horse racing as an analogy, a horse with a high likelihood of winning can be a good or a bad bet — the difference being the odds. In other words, a 10-1 shot may be a better bet.