Stocks course · Section 6: Pro
Drawdowns and Risk of Ruin: The Maths of Surviving Bad Years
Why a 50% loss needs a 100% gain, how long losing streaks get, how risk per trade drives drawdowns, the Kelly formula and Monte Carlo tests of your trades.
Pro5 min read·6:14 video·Lesson 25 of 26·quiz: 4 questions
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A drawdown is the fall in a portfolio from its highest point to its lowest point before a new high, and because losses compound, a 50% drawdown needs a 100% gain just to get back to where you were. Risk of ruin is the chance that losses become so large that you cannot continue, or reach the level at which you would give up. Small risk per trade and limited leverage are the two decisions that keep both under control, and the maths below shows why.
Drawdowns and the recovery trap
Example
Your account peaks at $50,000 and falls to $37,500 before recovering. The drawdown is (50,000 - 37,500) / 50,000 = 25%. To get back to $50,000 from $37,500 you need a gain of 12,500 / 37,500 = 33.3%.
| Drawdown | Gain needed to recover |
|---|---|
| -10% | +11.1% |
| -20% | +25% |
| -30% | +42.9% |
| -50% | +100% |
| -75% | +300% |
| -90% | +900% |
Small drawdowns are repaired easily; large ones can take years or never be repaired. Drawdown duration, the time from one peak to the next, matters as much as depth: months or years spent below a previous high test anyone's patience.
Real markets have deep drawdowns
Broad indices, not just single stocks, have suffered severe falls. Roughly: the Nasdaq Composite lost about 78% from March 2000 to October 2002; the S&P 500 lost about 57% from October 2007 to March 2009, about 34% in a few weeks in early 2020, and about 25% during 2022. Individual stocks often fall much further. Any plan that cannot survive a fall like these, in the market or in your strategy, is not a complete plan.
Losing streaks are normal
If a strategy wins 45% of the time, the chance that the next 10 trades all lose is 0.55 to the power of 10, about 0.25%. That sounds rare. But over hundreds of trades, a long streak somewhere becomes likely: a rough rule of thumb puts the longest losing streak in n trades near ln(n) / ln(1 / loss rate).
Example
With a 45% win rate (55% loss rate) over 500 trades, the longest losing streak is typically about ln(500) / ln(1 / 0.55) = about 10 trades. With a 40% win rate over just 50 trades, it is about 7 or 8. A profitable strategy will still deliver streaks like these.
Risk per trade decides the damage
| Risk per trade | Account after 10 losses in a row |
|---|---|
| 0.5% | -4.9% |
| 1% | -9.6% |
| 2% | -18.3% |
| 5% | -40.1% |
| 10% | -65.1% |
At 1% per trade, a 10-loss streak is painful but recoverable with an 11% gain. At 10%, it needs a gain of almost 190%. This is why most of this course suggests 0.5-1% per trade (see position sizing and stop-losses). Gaps, correlated positions that stop out together, and leverage make real drawdowns worse than these tidy numbers.
Risk of ruin
Risk of ruin depends on three things: the edge (win rate and payoff), the size of each bet, and where you draw the "ruin" line. Even a strategy with a genuine edge can be ruined by betting too much, because a streak arrives before the edge has time to work.
Define ruin personally: the drawdown at which you would stop trading or lose sleep, perhaps 25% or 30%. Then design your sizing so that the chance of reaching it is small.
The Kelly formula and why traders use less
The Kelly criterion gives the fraction of capital to risk per bet that maximises long-run growth, if you know your edge exactly: f = W - (1 - W) / R, where W is the win rate and R the ratio of average win to average loss.
Example
W = 45% and R = 2. Kelly = 0.45 - 0.55 / 2 = 17.5% of the account at risk per trade. At that size, the 10-loss streak above would take the account down about 85%.
Real win rates and payoffs are estimates from limited data, and they change. Betting full Kelly on an overestimated edge leads to heavy losses. Many practitioners use a fraction of Kelly, and the 0.5-1% per trade common among traders is far below even that. Kelly is useful mainly as a warning of where the cliff edge is.
Monte Carlo: your backtest's other possible histories
A backtest is one sequence of trades. The same trades in a different order could produce a much deeper drawdown.
- Take the list of trade results from your backtest, in R.
- Shuffle the order randomly and recalculate the account curve at your chosen risk per trade.
- Repeat 1,000 times or more and record each run's maximum drawdown.
- Look at a bad case, such as the drawdown that 95% of runs stayed below.
Example
Your backtest's maximum drawdown was 15%. In 1,000 reshuffles, 95% of runs stayed under 24%. Plan for drawdowns of around 25%, not 15%. If 25% is more than you can stomach, cut risk per trade until the bad case is acceptable.
A spreadsheet can do this with a random-number column and sorting, or a short script in any programming language.
Drawdown controls
- Small risk per trade (0.5-1%) and a cap on total open risk.
- Limits on leverage, or none at all (see margin and short selling).
- Correlation limits, so several positions do not fail together.
- Drawdown-based de-risking: for example, halve risk per trade after a 10% drawdown and restore it after recovering half the loss.
- A kill-switch: stop and review if the drawdown exceeds the Monte Carlo bad case.
Risk
For long-term investors, a 50% fall in the stock market is a real possibility over a lifetime. Many advisers suggest that money you will need within the next few years should not be in stocks at all, so that a bear market never forces you to sell at the bottom.
Tip
Write your maximum acceptable drawdown at the top of your plan, then work backwards: from Monte Carlo results, choose the risk per trade that keeps your bad case below it. You will do exactly this in the capstone.
Next: the final lesson, where you put everything together in your complete trading plan.
Key takeaways
- A drawdown is the fall from a peak to a trough; recovering needs a bigger percentage gain than the loss.
- Long losing streaks are normal over hundreds of trades, even for profitable strategies.
- Risk per trade decides how deep streaks cut: 10 losses at 1% cost about 10%, at 10% about 65%.
- Full Kelly sizing is far too aggressive for real trading; most traders risk a small fraction of it.
- Reshuffling your trade list (Monte Carlo) shows drawdowns worse than the single path of your backtest.
Quiz: check what you learned
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