Loomis Rate Calculator

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Loomis Rate Calculator

Calculation Results

Expected Growth Rate:

function calculateLoomisRate() { var p = parseFloat(document.getElementById('winProbability').value); var w = parseFloat(document.getElementById('profitReturn').value); var l = parseFloat(document.getElementById('lossAmount').value); var resultDiv = document.getElementById('loomisResult'); var growthSpan = document.getElementById('growthRateValue'); var analysisP = document.getElementById('analysisText'); if (isNaN(p) || isNaN(w) || isNaN(l)) { alert("Please enter valid numbers in all fields."); return; } if (p > 100 || p 0) { analysisP.innerHTML = "Positive Loomis Rate: Based on these parameters, the strategy is expected to yield a geometric growth of " + growthPercentage + "% per trial. This suggests a sustainable edge."; } else if (growthRate < 0) { analysisP.innerHTML = "Negative Loomis Rate: This configuration leads to capital erosion over time. Even if the expected value is positive, the volatility drag results in a net loss of " + growthPercentage + "%."; } else { analysisP.innerHTML = "Neutral Loomis Rate: This strategy is at a break-even point where gains and losses cancel out the compound growth rate."; } }

Understanding the Loomis Rate in Finance and Probability

The Loomis Rate is a critical metric used by sophisticated investors, risk managers, and probability theorists to determine the geometric mean growth rate of a specific capital allocation strategy. Unlike a simple average (arithmetic mean), the Loomis Rate accounts for the "volatility drag" that occurs when capital is subject to compounding gains and losses.

How the Loomis Rate is Calculated

The calculation is based on the probability of success versus failure and the respective magnitude of those outcomes. The formula utilized in this calculator is:

G = (1 + Win%)P × (1 – Loss%)(1-P) – 1

Where:

  • G: The Loomis Growth Rate.
  • P: The probability of a winning outcome.
  • Win%: The percentage return gained on a win.
  • Loss%: The percentage of capital lost on a failure.

Practical Example: Strategic Edge Evaluation

Imagine a scenario where a trader has a strategy with a 60% Win Probability. On a win, they gain 5% of their capital, and on a loss, they lose 4%.

  1. Win Factor: 1 + 0.05 = 1.05
  2. Loss Factor: 1 – 0.04 = 0.96
  3. Calculation: (1.05)0.6 × (0.96)0.4 – 1
  4. Result: Approximately 0.0132 or 1.32% per trade.

While the arithmetic mean might suggest a higher return, the Loomis Rate provides the actual realized growth rate one would experience over thousands of trials, accounting for the mathematical reality that losses require a larger percentage gain to recover.

Why the Loomis Rate Matters

Using a Loomis Rate calculator helps in avoiding "Gambler's Ruin." Even if a strategy has a positive expected value, if the volatility (the loss percentage) is too high relative to the win percentage and probability, the Loomis Rate can become negative. This indicates that the portfolio will eventually trend toward zero despite having "winning" individual trades.

Risk managers use this rate to calibrate position sizes. If the Loomis Rate begins to drop despite a high win rate, it is often a signal that the "Loss on Failure" is too high and needs to be mitigated through tighter stop-losses or better diversification.

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