The Risk of Ruin (ROR) Calculator helps traders and investors estimate the probability of losing their entire trading capital based on their historical performance and risk management strategy. Use this tool to set appropriate position sizing and manage survival risk.
Risk of Ruin Calculator
Enter parameters and click ‘Calculate’.
—Risk of Ruin Calculator Formula
The calculation is based on the Gambler’s Ruin probability for a discrete, fixed-risk system, adapted for trading expectancy (Edge, $E$) and bankroll size ($A$).
$$E = (W \cdot R) - ((1 - W) \cdot 1)$$
$$\text{If } E > 0, \quad ROR = \left(\frac{1 - E}{1 + E}\right)^A \cdot 100\%$$
$$\text{If } E \leq 0, \quad ROR = 100\%$$
Variables Explained
- Win Rate (W): The historical or anticipated probability of a single trade resulting in a profit (expressed as a decimal, 0.55 for 55%).
- Reward/Risk Ratio (R): The average size of a winning trade divided by the average size of a losing trade (e.g., 2:1 ratio is R=2).
- Bankroll Units (A): The total number of maximum single-unit losses your bankroll can absorb. Calculated as $1 / (\text{Risk per Trade \%})$. For example, a 2% risk per trade means $A = 1/0.02 = 50$ units.
- Expectancy ($E$): The average profit or loss per dollar risked. A positive expectancy ($E > 0$) is required to have a ROR below 100%.
Related Calculators
Explore these related risk management tools:
- Kelly Criterion Calculator (Position Sizing Optimization)
- Compounding Interest Calculator (Growth Potential)
- Position Size Calculator (Trade Risk Management)
- Maximum Drawdown Calculator (Risk Exposure)
What is Risk of Ruin Calculator?
The Risk of Ruin Calculator is a crucial tool for quantitative finance and trading psychology. It provides a statistical estimate of the probability of experiencing a total loss of trading capital over an infinite number of trades, given the system’s edge and the trader’s risk management strategy (position sizing).
It fundamentally helps traders understand the delicate balance between profitability (Expectancy) and survival (Bankroll Units). While a high win rate or high R:R ratio might indicate a profitable system, excessive risk per trade (low Bankroll Units) dramatically increases the ROR. A ROR of 0% is statistically impossible, but most professional traders aim for a ROR far below 1%.
The formula simplifies a complex stochastic process, treating each trade as an independent Bernoulli trial. It highlights the non-linear relationship between risk percentage and ruin probability, demonstrating why even a slight increase in risk per trade can lead to a disproportionately large increase in ROR.
How to Calculate Risk of Ruin (Example)
Let’s use an example to calculate the Risk of Ruin:
- Define Inputs: Assume a trading system has a Win Rate ($W$) of 60%, a Reward/Risk Ratio ($R$) of 1.2, and the trader risks 2% of the bankroll per trade. Thus, Bankroll Units ($A$) is $1 / 0.02 = 50$.
- Calculate Expectancy (Edge): $E = (0.60 \cdot 1.2) – (0.40 \cdot 1) = 0.72 – 0.40 = 0.32$. The system has a positive edge.
- Apply ROR Formula: $\text{ROR} = \left(\frac{1 – 0.32}{1 + 0.32}\right)^{50}$.
- Solve the Base: $\left(\frac{0.68}{1.32}\right) \approx 0.51515$.
- Exponentiation: $\text{ROR} \approx (0.51515)^{50}$. This results in an extremely small number, indicating a near-zero risk of ruin.
- Conclusion: A profitable system ($E > 0$) with conservative risk per trade (high $A$) leads to a minimal Risk of Ruin.
Frequently Asked Questions (FAQ)
- What is a good Risk of Ruin percentage? A good ROR is generally considered to be below 1%, or ideally, near 0%. Anything above 5% is often considered too high for sustained professional trading.
- How does the Bankroll Units variable work? The Bankroll Units ($A$) represent how many maximum losses your total bankroll can withstand. If you risk 1% per trade, $A=100$. If you risk 5% per trade, $A=20$. Higher $A$ leads to a lower ROR.
- Does the Risk of Ruin calculator account for consecutive losses? Yes, the underlying mathematical model (Gambler’s Ruin) is specifically designed to assess the probability of a sequence of unfavorable outcomes leading to the depletion of capital.
- What happens if my Expectancy is negative? If your Expectancy ($E$) is zero or negative, the Risk of Ruin is mathematically 100%. A negative expectancy means that on average, you lose money per dollar risked, guaranteeing ruin over the long term.