Risk
How much to risk on one trade
Run the same twenty trades at 1, 2 and 5 percent risk and you get three different accounts. The one that made the most also spent the middle of the run down 27 percent.
Position size is the one input a trader fully controls. The market decides whether a trade wins. You decide what it costs when it does not.
The size that puts a fixed fraction of the account at risk is:
f is the fraction of the account risked on this trade
The same trades, three ways
Here is a fixed sequence of 20 trades: 9 winners at twice the risked amount, 11 losers at exactly the risked amount, including a run of six losses in a row in the middle. The sequence never changes. Only f does.
| Risk per trade | Final account | Worst drawdown | Gain needed to recover it |
|---|---|---|---|
| 1% | +7.0% | 5.9% | 6.2% |
| 2% | +14.0% | 11.5% | 13.0% |
| 5% | +34.1% | 27.0% | 37.0% |
Five percent risk produced the best return. It also spent the middle of the run more than a quarter under water. Nothing about the strategy changed between those three columns.
The streak you should plan for
Six losses in a row sounds unlucky. It is not. If the loss rate is L, the expected length of the longest losing run in N trades is close to:
longest run of consecutive losses you should expect to see
At a 55 percent loss rate, which is what a 45 percent win rate implies:
| Trades | Longest streak to expect | Account left at 5% risk |
|---|---|---|
| 100 | 7.7 | 67% |
| 500 | 10.4 | 59% |
| 1,000 | 11.6 | 55% |
| 5,000 | 14.2 | 48% |
Over a thousand trades, a run of eleven or twelve losses is the expected case rather than the disaster case. At 5 percent risk that run costs about 45 percent of the account, and by the recovery arithmetic it then needs an 82 percent gain to get back.
This is why the sizing rule usually sits outside the strategy rather than inside it. The strategy decides what to trade. A separate limit decides how much of the account a bad run is allowed to remove.