Prerequisites: Ballast Management · Episode 6 — The Ballast Run · 18 min read
In Episode 6, Mike ran the ballast hard into biotech options. He knew his position size. He knew his stop. What he did not know was the probability that a string of losses would sink him before the tide turned. The Load Line would have shown him: at 35% win rate and 2:1 reward, his risk of ruin at 2% per trade was 12%. Not negligible. Not safe.
THE MEASUREMENT
Risk of ruin is the probability that a trader loses enough capital to be unable to continue trading. It is not the same as drawdown. Drawdown is what happened. Risk of ruin is what could happen — and the math that predicts it.
The Kelly Criterion tells you the optimal fraction of capital to risk on each trade. Most captains sail at Half Kelly: enough thrust to grow, enough margin to survive the squalls.
THE DERIVATION
Step 1: The Kelly Criterion
Developed by John Kelly at Bell Labs in 1956, the criterion maximizes the expected logarithm of wealth. For a trading system with known win rate and payoff ratio, the optimal bet size is:
Why Half Kelly?
Full Kelly is optimal for growth but brutal in drawdown. A 50% Kelly fraction reduces volatility by 50% while retaining 75% of growth. Most professional traders use Quarter to Half Kelly.
Step 2: Risk of Ruin
For a fixed-fraction system with positive edge, the probability of losing a fraction U of capital is:
The Edge Condition
Before calculating ruin, verify edge = (W × b) − L > 0. If not, no position size is safe. The formula becomes undefined because the base exceeds 1, and ruin probability approaches 100% regardless of how small you trade.
Step 3: Maximum Consecutive Losses
Before ruin math matters, know how many consecutive losses your hull can absorb:
WORKED EXAMPLE
Captain Vance runs a $100,000 account with a swing system: 45% win rate, $400 average win, $200 average loss (b = 2.0). He risks 2% per trade.
Kelly Fraction
f* = 0.45 − (0.55 / 2.0) = 0.45 − 0.275 = 0.175 (17.5%). Half Kelly = 8.75%. Vance's 2% risk is conservative — well below Half Kelly.
Risk of Ruin
Edge = (0.45 × 2.0) − 0.55 = 0.35 (positive). Base = 0.55 / (0.45 × 2.0) = 0.611. Exponent = 1 / 0.02 = 50. R = 0.611^50 = 0.0006%. At 2% risk, ruin is effectively zero.
At 5% Risk
Same system, but Vance sizes to 5% per trade. Exponent = 1 / 0.05 = 20. R = 0.611^20 = 0.13%. Still low, but 200× higher than at 2%.
At 10% Risk
Exponent = 10. R = 0.611^10 = 0.84%. Nearly 1 in 100 captains sink. The load line is breached.
THE INTERACTIVE CHRONOMETER
Enter your system parameters. The Load Line computes Kelly, ruin probability, and the maximum safe draft.
INTERPRETATION
| Risk of Ruin | Interpretation | Action |
|---|---|---|
| < 0.01%Safe | Ruin is statistically negligible. The hull is sound. | Standard sizing. Monitor for regime decay. |
| 0.01% – 0.5%Caution | Low but measurable. One in 200 captains sink. | Reduce to Half Kelly or lower. Increase diversification. |
| 0.5% – 5%Danger | Ruin is a real possibility over a career. | Cut risk fraction immediately. Verify edge. |
| > 5%Breach | The load line is breached. Do not sail. | Reduce size or fix the system. Edge may be negative. |
From the Logs
In Episode 11 — Driftwood and Diamonds, Hannah bought Exxon at 0.8x book with 8% of her account. She understood value. She did not understand that a 40% win rate with 1.5:1 payoff requires 2% risk to keep ruin below 1%. At 8%, her ruin probability was 4%. She got lucky. The Load Line does not rely on luck.
Related Guides
Ballast Management
Position sizing, cash allocation, and defensive positioning. The strategic companion to the Load Line's math.
The Astrolabe
Expectancy, win rate, and backtesting math. The foundation that feeds into Kelly and ruin calculations.
The Helm Response
Rolling Beta. Know when your portfolio moves with the market, inflating your perceived edge.
Episode 23 — When to Hold and When to Fold
The story of a captain who held through 18 consecutive losses because he never computed his ruin probability.