Master the essential metrics for robust investment strategy evaluation. This comprehensive guide distills years of practical experience and analytical rigor, providing a structured overview of the key backtest statistics and performance indicators critical for assessing any investment approach. From understanding general characteristics to deep dives into risk, efficiency, and attribution, this post serves as a valuable reference for financial professionals.
General Characteristics
Before diving into performance, understanding a strategy’s fundamental operational characteristics is paramount. These descriptive metrics provide context for its behavior and scalability:
- Time Range: The historical period over which the strategy has been simulated or observed.
- Average AUM (Assets Under Management): The typical capital size the strategy manages, providing insight into its scale.
- Capacity: The maximum AUM the strategy can effectively manage before its alpha may degrade due to market impact or liquidity constraints.
- Leverage: The degree to which borrowed capital is used to amplify returns, indicating potential risk magnification.
- Maximum Dollar Position: The largest absolute capital allocation to any single asset at a given time.
- Ratio of Longs: The proportion of long positions relative to total positions (longs + shorts), indicating directional bias.
- Frequency of Bets: How often the strategy initiates new positions or makes investment decisions (e.g., daily, weekly, monthly).
- Average Holding Period: The typical duration for which assets are held within the portfolio.
- Annualized Turnover: A measure of trading activity, representing the total value of assets bought or sold over a year, relative to AUM.
- Correlation to Underlying: The correlation of the strategy’s returns to its target market or a broad market index, indicating systemic exposure.
These metrics quantify the financial outcomes generated by the strategy:
- PnL (Profit and Loss): The absolute gain or loss over a period.
- PnL from Long Positions: The profit or loss specifically attributable to long positions, useful for dissecting performance sources.
- Annualized Rate of Return (Arithmetic/Geometric): The average return generated per year, often calculated using both arithmetic and time-weighted (geometric) methods for different insights.
- Time-Weighted Rate of Return: A geometric average that eliminates the effects of capital inflows/outflows, providing a true measure of investment compounding.
- Average Return from Hits: The average profit from winning trades.
- Average Return from Misses: The average loss from losing trades.
Run Statistics and Concentration
Beyond simple aggregates, understanding the pattern and concentration of returns is vital for assessing robustness and potential vulnerabilities:
- Returns Concentration:
- High Sharpe Ratio (often a goal): While a desired outcome, a high Sharpe must be investigated for its underlying drivers.
- High Number of Bets per Year: Indicates diversification across opportunities.
- High Hit Ratio: The percentage of winning trades.
- No Fat Tail: Implies that extreme negative returns are not disproportionately frequent or severe.
- Bets are not Concentrated in Time: Avoids over-reliance on specific periods, reducing time-series specific risk.
- Drawdown and Time Under Water:
- Drawdown: The peak-to-trough decline in value during a specific period.
- Time Under Water (TuW): The duration from the start of a drawdown until the previous peak is recovered.
- Runs Statistics for Performance Evaluation: These use statistical measures, often related to the Herfindahl-Hirschman Index (HHI), to assess concentration:
- HHI index on positive returns: Measures the concentration of profits in a few large winning trades.
- HHI index on negative returns: Measures the concentration of losses in a few large losing trades.
- HHI index on time between bets: Assesses if trades are clustered or evenly distributed over time.
- 95-percentile DD: The drawdown level that is worse than 95% of observed drawdowns, indicating extreme downside risk.
- 95-percentile TuW: The time under water duration that is longer than 95% of observed periods, indicating extreme recovery times.
Implementation Shortfall
These metrics quantify the costs and friction associated with executing a strategy in a live environment, comparing ideal performance to real-world outcomes:
- Broker Fees per Turnover: Direct costs paid to brokers relative to trading volume.
- Average Slippage per Turnover: The difference between the expected price of a trade and the actual price executed, normalized by trading volume.
- Dollar Performance per Turnover: The profit or loss generated per dollar of assets traded, considering all execution costs.
- Return on Execution Costs: A measure of how much return is generated for every unit of execution cost incurred.
Efficiency Metrics
Efficiency metrics evaluate the quality of risk-adjusted returns, providing a standardized way to compare strategies:
- Sharpe Ratio: Active return per unit of total risk (standard deviation of returns).
- Probabilistic Sharpe Ratio (PSR): A statistically robust version of the Sharpe Ratio that accounts for the number of trials and potential data mining, giving the probability that a strategy’s observed Sharpe Ratio is truly positive or above a certain threshold.
- Deflated Sharpe Ratio (DSR): Another advanced metric that adjusts the Sharpe Ratio for the impact of backtest overfitting, providing a more conservative and realistic estimate of out-of-sample performance.
- Information Ratio: Active return per unit of active risk (tracking error).
Classification Score (for ML-driven strategies)
For strategies employing machine learning classifiers, these metrics assess the performance of the prediction model itself:
- Accuracy: The proportion of correct predictions (both true positives and true negatives).
- Precision: Of all positive predictions, what proportion were actually correct (minimizes false positives).
- Recall: Of all actual positive cases, what proportion were correctly identified (minimizes false negatives).
- F1 Score: The harmonic mean of precision and recall, providing a balanced measure.
- Negative Log-Loss: A measure of prediction uncertainty and classification quality, penalizing confident wrong predictions more heavily.
Attribution
Attribution analysis dissects portfolio returns into components explained by specific factors (e.g., industry, style, country) and a residual, active component:
- Barra’s Multi-Factor Model: A widely used framework for attributing portfolio returns to systematic risk factors and manager-specific alpha, providing detailed insights into the sources of performance.
Risk Metrics
Comprehensive risk assessment goes beyond volatility to encompass benchmark-relative risk, capital preservation, and tail risk:
Volatility Risk
- Standard Deviation: The most common measure of total risk, quantifying the dispersion of returns around the mean.
- Downside Deviation: Measures only the volatility of negative returns, focusing on downside risk.
- Sharpe Ratio: As above, risk-adjusted return using total risk.
- Sortino Ratio: Risk-adjusted return using downside deviation, preferred for focusing on undesirable volatility.
Benchmark Risk
- Excess Return: The difference between the portfolio return and the benchmark return.
- Batting Average: The proportion of periods where the portfolio outperformed its benchmark.
- Up Capture: Measures how well the portfolio performs relative to the benchmark during periods of positive benchmark returns.
- Down Capture: Measures how much the portfolio declines relative to the benchmark during periods of negative benchmark returns.
- Alpha: The residual return not explained by systematic market risk, often derived from regression models (e.g., CAPM).
- Beta: A measure of a portfolio’s systematic risk, indicating its sensitivity to benchmark movements.
- R-squared: The proportion of the portfolio’s variance explained by the benchmark, indicating goodness of fit for regression models.
- Tracking Error: The standard deviation of the portfolio’s active returns (excess returns relative to the benchmark), representing active risk.
- Treynor Ratio: Excess return per unit of systematic risk (Beta), useful for diversified portfolios.
- Information Ratio: As above, active return per unit of active risk.
- M-squared (Modigliani-Modigliani Measure): A risk-adjusted return measure that scales the portfolio’s returns to have the same total risk as the market, allowing direct comparison with the market return.
Capital Preservation Risk
- Maximum Drawdown: The largest peak-to-trough decline in the portfolio’s value over a specified period, representing potential capital loss.
- Pain Ratio (Pain Index): A more nuanced measure of drawdown, accounting for both the magnitude and duration of losses.
- Calmar Ratio: Annualized return divided by maximum drawdown, offering a quick risk-adjusted return metric focused on capital preservation.
Tail Risk
- Skewness: Measures the asymmetry of the return distribution. Negative skewness indicates a higher probability of large negative returns.
- Kurtosis: Measures the “tailedness” of the return distribution. High kurtosis (leptokurtic distribution) indicates more frequent extreme events (both positive and negative) than a normal distribution.
- Omega Ratio: A risk-adjusted return measure that considers the entire return distribution, focusing on the likelihood of achieving returns above a minimum acceptable threshold.
- VaR (Value-at-Risk): A statistical measure of the maximum potential loss that a portfolio could incur over a given time horizon with a specified probability (e.g., 99% VaR over 1 day).
- CVaR (Conditional Value-at-Risk) / Expected Shortfall: The expected loss given that the loss exceeds the VaR, providing a more robust measure of tail risk than VaR alone.