Equity Curve

The slope of the equity curve represents the rate of capital appreciation. A linear upward slope indicates a constant rate of return, while a convex curve signals compounding and geometric growth. A flattening slope often precedes a performance plateau or regime shift.

• Linear Regression Slope: Quantifies the average profit per unit of time.
• R-squared: Measures how closely the curve adheres to a straight line; values near 1.0 indicate smooth, predictable growth.

Drawdown is the peak-to-trough decline in the equity curve, measuring the maximum capital lost before a new high-water mark is achieved. It is the most visceral measure of risk.

• Maximum Drawdown (MDD): The largest observed peak-to-trough percentage drop.
• Drawdown Duration: The time taken to recover from a trough to the previous peak. Long recovery times often signal a broken strategy.
• Ulcer Index: Measures the depth and duration of all drawdowns, penalizing prolonged retracements.

The roughness of the equity curve quantifies return volatility. A jagged, high-frequency oscillation indicates unstable P&L generation, even if the overall trend is positive.

• Standard Deviation of Daily Returns: The foundational measure of dispersion around the mean growth rate.
• Sharpe Ratio: Directly derived from the equity curve's slope (excess returns) divided by its roughness (standard deviation).
• Sortino Ratio: Focuses only on the downward deviations, ignoring upside volatility.

Sudden changes in the curve's gradient, known as inflection points, indicate the strategy's sensitivity to shifting market regimes. A robust strategy maintains a consistent slope across bull and bear cycles.

• Piecewise Linear Regression: Statistically identifies structural breaks in the curve's slope.
• Rolling Sharpe Analysis: Plots the Sharpe ratio over a moving window to detect periods of strategy decay.
• Correlation with Benchmark: A sudden divergence from a market index reveals whether alpha is truly uncorrelated.

The sequence of new high-water marks reveals the rhythm of profit realization. A strategy that makes new highs in tight clusters followed by long flat periods exhibits lumpy returns, which is undesirable for compounding.

• Time Between Highs: The average waiting period for a new equity peak.
• Run-Up Distribution: Analyzes the magnitude of gains between consecutive drawdowns to identify if profits are driven by a few outliers or consistent edge.

By resampling trade sequences, a probabilistic cone is projected around the historical equity curve. This visualizes the range of potential terminal wealth, distinguishing skill from luck.

• Confidence Bands: The 5th and 95th percentile paths show the worst-case and best-case scenarios.
• Terminal Wealth Dispersion: If the cone is wide, the strategy's outcome is highly path-dependent and fragile.
• Deflated Sharpe Ratio: Adjusts the probability that the observed curve's slope is statistically significant after accounting for multiple testing.

The peak unrealized loss experienced on a single trade before it is closed. Used to calibrate stop-loss levels and assess intra-trade risk tolerance.

• Plotted against Maximum Favorable Excursion (MFE) to visualize the strategy's ability to let winners run versus cutting losers.
• A tight cluster of low MAE values indicates disciplined risk control.

A strategy characteristic where the current trading decision is contingent on the sequence of prior events and executions. The equity curve is not just a sum of independent outcomes but a trajectory shaped by order.

• Requires precise state management in simulation.
• A path-dependent strategy may show identical final P&L but wildly different intra-period equity curves depending on trade sequencing.