Risk of Ruin Probability

Risk of Ruin Probability is the statistical likelihood that a trading account will be wiped out — or breach a defined drawdown threshold — before a strategy’s edge has time to compound. Unlike win rate or expectancy, which describe average outcomes, ROR quantifies the worst-case tail risk sitting beneath every position sizing decision. It belongs to the risk category and is the one metric that directly dictates whether a position size is safe to trade.

Formula & Calculation

ROR = ((1 − A) / (1 + A))^C

Where:

• A = Edge = (Win Rate × Payoff Ratio) − Loss Rate
• C = Capital units = 1 ÷ Risk% per trade
• Win Rate = proportion of winning trades (e.g., 0.50 for 50%)
• Payoff Ratio = average winner ÷ average loser (e.g., 1.1 for $275 avg win / $250 avg loss)
• Loss Rate = 1 − Win Rate
• Risk% = fraction of account risked per trade (e.g., 0.02 for 2%)

To calculate ROR step by step:

1. Compute your edge: multiply win rate by payoff ratio, then subtract loss rate. A positive result means positive expectancy.
2. Compute capital units: divide 1 by your risk fraction (risking 2% gives C = 1 ÷ 0.02 = 50).
3. Form the base ratio: (1 − A) / (1 + A). A positive edge makes this ratio less than 1.
4. Raise the ratio to the power of C. A smaller ratio or larger C both drive ROR toward zero.

When A is zero or negative, the ratio (1 − A) / (1 + A) is 1 or greater, and ROR equals 100% — ruin is mathematically certain regardless of bet size.

Benchmarks

Level	Range	What It Means
Safe	Under 1%	Acceptable long-term ruin risk; standard position sizing target
Caution	1% – 5%	Elevated risk; reduce position size until ROR falls below 1%
High Risk	5% – 20%	Significant blowup probability; immediate review required
Critical	Above 20%	Ruin is likely over a full trading career; not sustainable

Practical Example

A trader opens a $25,000 account — the PDT minimum — to trade SPY 0DTE options. Their 90-day track record shows a 50% win rate, average winner $275, average loser $250 (payoff ratio 1.1:1).

Step 1 — Edge: A = (0.50 × 1.1) − 0.50 = 0.55 − 0.50 = 0.05

Step 2 — Base ratio: (1 − 0.05) / (1 + 0.05) = 0.95 / 1.05 = 0.9048

Step 3 — Apply across risk levels:

Risk %	$ Risk on $25k	C (Capital Units)	ROR
1%	$250	100	0.005%
2%	$500	50	0.68%
3%	$750	33	3.7%
5%	$1,250	20	13.6%
10%	$2,500	10	36.8%

At 2% risk ($500/trade), ROR sits at 0.68% — safely below the 1% threshold. At 5% risk ($1,250/trade), the same edge carries a 13.6% chance of a total blowup. That is a 20× increase from 2% to 5%, and a 2,700× increase from 1% to 5%. The non-linearity is critical: C appears as an exponent, so doubling risk does not double ruin probability — it can multiply it 10–50×.

The same trader with a 47% win rate instead of 50%: A = (0.47 × 1.1) − 0.53 = −0.013. The base ratio exceeds 1, and ROR = 100% at every bet size. Ruin is certain.

How to Track Risk of Ruin Probability

1. Log every trade with entry price, exit price, and dollar P&L — you need at least 50 trades to estimate win rate and payoff ratio reliably; 100+ is preferable.
2. Calculate edge A monthly — use a trailing 90-day window rather than your entire account history, since recent performance better reflects current market conditions.
3. Confirm your actual risk per trade — check your last 20 trades and compute average dollar risk as a percentage of account equity on each trade date; this is often higher than traders assume.
4. Paste the formula into Excel or Google Sheets — enter =((1-A)/(1+A))^C with your values substituted, and flag the cell red if the result exceeds 0.01 (1%).
5. Recalculate after significant changes — new strategy, different instruments, changed stop placement rules, or a 5%+ account equity change all warrant a fresh ROR calculation.

How to Improve Risk of Ruin Probability

1. Reduce risk per trade first — for a 50%/1.1:1 edge, dropping from 3% to 1% per trade cuts ROR from 3.7% to 0.005% with zero changes to trade selection or execution.
2. Widen average winners before sizing up — moving from 1.1:1 to 1.5:1 payoff (by letting winners run to 1.5× the initial stop distance) raises edge from 0.05 to 0.25, which drives ROR near zero even at 2–3% risk per trade.
3. Verify positive expectancy on a live sample — at 47% win rate and 1.1:1 payoff, A = −0.013 and ROR = 100%. Paper-trade or micro-size until the win rate or payoff ratio supports positive expectancy before risking normal size.
4. Solve backwards from a 1% ROR ceiling — rearrange: C = log(0.01) / log((1 − A) / (1 + A)). For A = 0.05, this gives C ≈ 46, setting the maximum risk per trade at 1/46 ≈ 2.2% of account equity.
5. Use Monte Carlo for prop firm accounts — if you trade a $100k funded account with a 10% max drawdown limit, simulate 10,000 equity paths over 500 trades. The percentage of paths that breach $10,000 drawdown is your effective ROR for that account, and it will often be higher than the closed-form result due to sequencing risk.

Common Mistakes

1. Win rate without payoff ratio — a 60% win rate with 0.5:1 payoff gives A = (0.60 × 0.5) − 0.40 = −0.10. ROR = 100%. Win rate alone tells you nothing about ruin risk.
2. Trading a negative-edge strategy — any A at or below zero guarantees ruin at every bet size. Reducing position size from 3% to 0.1% does not change the outcome — it only delays it. Fix the edge first.
3. Calculating ROR once and never updating — edge drifts as market conditions shift. A strategy that produced A = 0.08 last year may now sit at A = 0.02, pushing ROR above 1% at the same position size. Recalculate monthly.
4. Conflating ruin with drawdown — ROR measures blowup to zero (or a defined threshold), not a 15% or 20% equity decline. Prop firm traders need to define their ruin threshold as the firm’s max drawdown limit, then apply the formula to that dollar amount.
5. Using closed-form math for variable-size trading — if you size positions based on ATR, account heat, or setup tier, the fixed-bet assumption fails. The closed-form formula will underestimate true ruin risk; use Monte Carlo simulation instead.

How JournalPlus Calculates Risk of Ruin Probability

JournalPlus computes risk of ruin probability automatically on the analytics dashboard, pulling win rate, average winner, and average loser directly from your logged trade history. As each trade is recorded, the dashboard updates edge A in real time and recalculates ROR at your current average risk per trade. The performance charts flag any rolling 30-day period where position sizing pushed ruin probability above 1%, making it easy to identify when sizing crept up during a winning streak. You can filter by instrument, setup tag, or date range to compare ROR across different strategies — useful for determining which setups are safe to size up and which require tighter limits. The full calculation table is exportable as CSV for use in your own Monte Carlo model or prop firm drawdown analysis.

For the theoretical foundation underlying position sizing, see Kelly Criterion, which derives the optimal fraction to risk for maximum long-run growth. Risk per trade is the single variable with the most leverage over your ROR calculation. Expectancy determines whether edge A is positive — the prerequisite for any finite ruin probability. Maximum drawdown and portfolio heat round out the risk picture with realized and concurrent exposure metrics.