Risk of Ruin: The Chance Your Account Hits a Point of No Return
A system with an edge can still be ruined. A 500-trade simulation shows how risk per trade, payoff shape and losing regimes raise the odds of −30% and −50%.
- A useful definition of ruin is the level where you would stop or struggle to recover, such as −30% or −50%, not a zero balance
- With a +0.2R edge, risking 1% per trade gives about a 0.1% chance of touching −30% in 500 trades. Risking 5% raises it to 32.8%
- At the same edge, a system that wins rarely but big has drawdowns several times deeper than one that wins often but small
- Losses that cluster in market regimes make drawdowns almost twice as deep as a trade-by-trade shuffle suggests
- Choose risk per trade from the drawdown you can tolerate, divided by your system's 95th-percentile drawdown in R
Risk of ruin is the chance that an account reaches a point of no return before its edge has time to work. Many traders assume that a system with a positive average result will survive no matter what. But an edge is a long-run average, and your account has to live through the actual path one trade at a time. Risk too much per trade and a single bad stretch can take you there. This article runs 20,000 simulations per case to see what pushes that chance up or down.
Ruin doesn’t mean zero
In practice, most people don’t trade until the money is gone. They stop first, or the account is damaged so badly that recovery becomes very hard. So this article defines ruin at two levels:
- −30%: where many traders start abandoning their system. You need a 42.9% gain on what’s left to get back to even
- −50%: hard to come back from. You need a 100% gain. Try other numbers in the recovery calculator
There are two ways to measure it. The first is touching a level of the starting balance: start with 10,000 dollars and at some point fall to 7,000. The second is drawdown from the peak: climb to 15,000 and drop to 10,500, and that already counts as −30%. The second happens far more often and is closer to how it actually feels. If Balance versus Equity is still fuzzy, read How to read drawdown.
Gambler’s ruin: even a fair game ends broke
The classic version is gambler’s ruin. Flip a coin, win or lose 1 unit. If the game is fair (50%) and the other side has unlimited money, the player with limited money is certain to go broke eventually.
With an edge, a win probability p above 50%, the chance of going broke from a stake of a units is (q ÷ p) to the power a, where q = 1 − p.
| Win chance per flip | 10 units | 20 units | 50 units |
|---|---|---|---|
| 51% | 67.0% | 44.9% | 13.5% |
| 55% | 13.4% | 1.8% | under 0.01% |
Working the 55%, 10-unit cell: q ÷ p = 0.45 ÷ 0.55 = 0.818, and 0.818 to the power 10 = 0.134, or 13.4%.
Two lessons. An edge helps a lot, but the distance to ruin, measured in units risked per bet, matters just as much. In trading that unit is R, the amount you lose when one trade hits its Stop loss. If you can tolerate −30% and risk 2% per trade, the distance is 30 ÷ 2 = 15R. At 1% it becomes 30R straight away.
A 500-trade simulation: risk per trade is the biggest lever
Simulation setup: risk is a percentage of current equity on every trade, a loss costs exactly 1R, a win pays the RR, trades are independent, no costs. Each case runs 20,000 times, 500 trades per run. Every figure in this article comes from simulation, not from real trading.
Three systems for comparison:
- 40% wins at 2R: average per trade 0.4 × 2 − 0.6 × 1 = +0.2R
- 50% wins at 1.2R: 0.5 × 1.2 − 0.5 = +0.1R
- 50% wins at 1R: 0R, no edge
Chance of touching a level of the starting balance within 500 trades:
| Risk per trade | +0.2R touch −30% | +0.2R touch −50% | +0.1R touch −30% | +0.1R touch −50% | 0R touch −30% | 0R touch −50% |
|---|---|---|---|---|---|---|
| 0.5% | 0.0% | 0.0% | 0.0% | 0.0% | 0.1% | 0.0% |
| 1% | 0.1% | 0.0% | 0.2% | 0.0% | 12.5% | 0.2% |
| 2% | 4.0% | 0.2% | 6.5% | 0.4% | 48.9% | 16.4% |
| 3% | 12.7% | 1.9% | 17.7% | 3.5% | 68.3% | 40.0% |
| 5% | 32.8% | 12.1% | 39.4% | 17.2% | 85.2% | 69.8% |
0.0% means below 0.05%, not impossible.
Three things the table shows:
- Going from 1% to 2% risk changes the result more than losing half the edge. At the same risk, the +0.2R and +0.1R systems are not far apart
- With no edge, nearly half the runs at 2% risk touch −30% within 500 trades. Small risk only slows the decline, it doesn’t prevent it
- Most ruin happens early. For the +0.2R system at 3% risk, 9.6% touch −30% within the first 100 trades, 12.4% within 250, 12.8% within 500, and a 20,000-trade run still gives about 12.8%. Early on there are no accumulated profits to cushion the fall
Drawdown from the peak: trade long enough and you will see it
Measured from the peak instead, the picture changes a lot. The same +0.2R system (40% wins at 2R) over 500 trades:
| Risk per trade | DD reaches 30% | DD reaches 50% | Median max DD | 95th-percentile max DD |
|---|---|---|---|---|
| 0.5% | 0.0% | 0.0% | 8.2% | 13.4% |
| 1% | 1.5% | 0.0% | 15.7% | 25.4% |
| 2% | 46.1% | 2.2% | 29.4% | 45.4% |
| 3% | 91.9% | 21.6% | 41.4% | 60.8% |
| 5% | 100.0% | 84.5% | 60.9% | 81.4% |
At 2% risk, nearly half the runs see a 30% drawdown, while only 4% ever touch −30% of the starting balance. As the account grows, 2% per trade becomes more money, and drawdown from the peak never expires. The longer you trade, the more likely a deep drawdown becomes, however good the system. So every probability needs a time horizon attached.
Payoff shape changes the risk a lot
The same edge does not mean the same risk. Give every system +0.2R per trade and 2% risk per trade, but change the shape:
| System | SD per trade | Touch −30% | Touch −50% | DD reaches 30% | 95th-percentile max DD |
|---|---|---|---|---|---|
| 30% wins at 3R | 1.83R | 13.5% | 2.0% | 83.5% | 58.1% |
| 40% wins at 2R | 1.47R | 4.0% | 0.2% | 46.1% | 45.4% |
| 60% wins at 1R | 0.98R | 0.1% | 0.0% | 2.0% | 27.1% |
| 75% wins at 0.6R | 0.69R | 0.0% | 0.0% | 0.0% | 17.5% |
SD (standard deviation) measures how much the result per trade swings. A system that wins rarely but big is positively skewed: profit comes from a few large trades, and you sit through long losing streaks while waiting. Its swing per trade is larger, so it needs a smaller risk per trade to reach the same drawdown. More on streaks in Losing streaks are normal.
But the high-win-rate systems only look safe here because every loss is capped at 1R. Real trading has trades where price jumps past the Stop loss. Change the 75% system to 77% wins at 0.6R, 22% losses of 1R and another 1% losses of 4R. The edge stays at about +0.2R, but the 95th-percentile drawdown in R goes from 9.4R to 13.2R. A high-win-rate system with no real Stop loss is far riskier still. Read Fat tails and black swans and Grid and Martingale.
Losses that come in spells make ruin more likely
The simulation above assumes trades are independent. Real markets have stretches that suit a system and stretches that don’t. So here is a simulation with market regimes:
- Good spells: 50% wins at 2R (+0.5R per trade)
- Bad spells: 30% wins at 2R (0.3 × 2 − 0.7 = −0.1R per trade, a losing spell)
- Every trade has a 2% chance of switching spell, so a spell lasts 50 trades on average. Over the long run the system still averages 40% wins and +0.2R, the same as before
At 2% risk, the chance of touching −30% of the starting balance rises from 4.0% to 22.4%. If spells last 100 trades on average, it climbs to 30.6%. The interesting part is that the longest losing streak barely changes: the median goes from 11 to 12 trades. The damage doesn’t come from one streak. It comes from a long stretch with a negative average, lose, win a little, lose again, while the account slowly bleeds.
This matters for testing. A trade-by-trade shuffle, as in Monte Carlo strategy testing, breaks these spells apart, so the drawdowns it produces are shallower than reality. The usual fix is a block bootstrap: resample blocks of consecutive trades, for example 20 to 50 at a time, so good and bad spells stay intact. More on regimes in Market regimes and Volatility clustering.
A closed-form approximation, and its limits
If you don’t want to simulate, there is an approximation that treats the account as a random walk with drift. It works best when each trade is small compared with the distance to ruin, and it assumes you keep trading with no end date.
Fixed amount (for example, risking 200 dollars on every trade from a 10,000 start):
Risk of ruin ≈ e to the power (−2 × E × D ÷ V)
E = average result per trade (in R), V = variance per trade (in R²), D = distance to ruin (in R).
Example: 40% wins at 2R, risking 2% of the starting balance, ruin at −30%.
- E = 0.4 × 2 − 0.6 × 1 = 0.2R
- Average of the squared results = 0.4 × 4 + 0.6 × 1 = 2.2, so V = 2.2 − 0.2² = 2.16
- D = 30 ÷ 2 = 15R
- 2 × 0.2 × 15 ÷ 2.16 = 2.78, and e to the power −2.78 = 6.2%
Fixed fraction of current equity uses the same formula on log returns. A win is ln(1 + 2 × 0.02) = 0.0392, a loss is ln(0.98) = −0.0202. The mean is 0.00357, the variance 0.000847, the distance ln(1 ÷ 0.7) = 0.357. That gives 2 × 0.00357 × 0.357 ÷ 0.000847 = 3.00, and e to the power −3.00 = 5.0%.
Compared with the simulation (chance of touching −30% of the starting balance):
| Risk per trade | Fixed amount: formula | Fixed amount: simulated | Fixed fraction: formula | Fixed fraction: simulated |
|---|---|---|---|---|
| 1% | 0.4% | 0.3% | 0.2% | 0.1% |
| 2% | 6.2% | 5.4% | 5.0% | 4.0% |
| 3% | 15.7% | 14.3% | 15.0% | 12.7% |
| 5% | 32.9% | 31.4% | 36.2% | 32.8% |
In these cases the formula comes out slightly above the simulation, which makes it a good check on the order of magnitude. Risking a fixed fraction lowers the chance of a deep fall, because trades shrink as the account shrinks. At 3% risk, for example, touching −50% happens 1.9% of the time against 3.6% with a fixed amount. At 5% the two methods are close. Neither one rescues a risk per trade that is too large.
Over-betting has a hard ceiling. For 40% wins at 2R, the Kelly criterion stake is 0.4 − 0.6 ÷ 2 = 10% per trade. At 20% the log growth is almost zero, and at 25% it turns negative: the account shrinks in the long run despite the edge. Even half Kelly (5%) still gives an 84.5% chance of a 50% drawdown within 500 trades.
Limits of the formula:
- It assumes E is known exactly. If the true edge is +0.1R instead of +0.2R (same RR of 2, 36.7% wins), the example above jumps from 6.2% to 23.8%. Backtested edges are often too optimistic. Read Backtest versus live results
- It assumes independent trades, so it misses the regime effect from the previous section
- It ignores price jumping past the Stop loss, spread and slippage
- It has no time limit, and it only applies to touching a level of the starting balance, not to drawdown from the peak
Choose risk per trade from the drawdown you can tolerate
Instead of starting from “how much do I want to make”, start from “how deep a drawdown can I sit through and still follow the system”.
- Set your maximum tolerable drawdown: the number at which you would stop or start losing discipline, for example 20%
- Find the 95th-percentile drawdown in R from your own trade list, with a block-bootstrap Monte Carlo. Until you have one, use the chart above as a rough guide
- Divide: risk per trade ≈ tolerable drawdown ÷ drawdown in R
- Set a review point before that limit, such as halfway, and control each day with a daily loss limit
Example: you can tolerate 20%, and the 40%-at-2R system has a 95th-percentile drawdown of about 28R.
- 20 ÷ 28 = 0.71%, rounded down to 0.7% per trade
- Check: losing 28R at 0.7% of current equity leaves 0.993 to the power 28 = 0.821, a 17.9% fall, under 20% because trades shrink as the account falls
- If the system has regimes like the previous section, the drawdown is 52R, so 20 ÷ 52 ≈ 0.4% per trade (check: 0.996 to the power 52 is an 18.8% fall)
These numbers look smaller than what many traders use, but they line up with Why many traders risk only 1% per trade. To turn the risk into a lot size, see Position size from Stop loss.
The edge belongs to the market, but the risk per trade is yours alone. Pick one that lets you survive the longest bad stretch you can expect, with both money and nerve left over.
Common mistakes
- Believing a positive system can’t fail. An edge helps in the long run, but with a large risk per trade the chance of ruin before the long run arrives is still high. A +0.2R system at 5% risk touches −30% in 32.8% of 500-trade runs
- Trusting the drawdown of a single backtest. That path may have been a lucky one. Use the 95th percentile from a simulation
- Shuffling single trades and trusting the result. If the market has good and bad spells, real drawdowns can be almost twice as deep as the simulation
- Using the same risk for every system. A system that wins rarely but big needs a smaller risk per trade than one that wins often, to get similar drawdowns
- Raising risk after losses to win it back. It shortens the distance to ruin exactly when the account is thinnest, the opposite of what you should do
Frequently asked questions
What risk of ruin is acceptable?
There is no standard number. Many traders aim for under 1% to 5% chance of touching their stop-trading level over the period they plan for. But that figure is computed from an edge estimated on the past, which is often too optimistic, so leave extra room below your target.
If my system has an edge, does risk of ruin go to zero if I trade long enough?
Measured from the starting balance, most of the risk sits early on. Once profits build up, the chance of falling back to the original level drops sharply. But measured as drawdown from the peak, trading long enough always brings deeper drawdowns eventually. That is why every probability needs a time horizon attached.
Is the formula enough, or do I need to simulate?
The formula is good for intuition and quick checks, but it assumes trades are independent and the edge is known exactly. Real markets have good and bad spells, so simulate from your own trade list, resampling blocks of consecutive trades rather than single trades.
This is general education, not investment advice. Trading is risky and you may lose all of your capital.