Algorithm Performance Backtest

Financial Machine Learning

The Prediction Problem

Unlike traditional ML applications, financial markets exhibit several unique characteristics that make prediction exceptionally challenging:

• Low Signal-to-Noise Ratio: Asset returns contain predominantly noise, with predictive signals often explaining less than 5% of variance. A Spearman IC of 5-10% is considered excellent in practice.
• Non-Stationarity: Market dynamics evolve over time. Relationships that held in one regime may reverse in another, requiring adaptive models and careful validation.
• Adversarial Nature: Markets are competitive—profitable signals attract capital until arbitraged away. This 'alpha decay' means models require continuous research and refinement.

Cross-Validation in Finance

Standard k-fold cross-validation is inappropriate for time-series data due to temporal dependencies. We employ:

• Purged Cross-Validation: Eliminating samples near the train-test boundary to prevent information leakage from overlapping prediction horizons.
• Embargo Periods: Adding buffer zones between training and testing periods, typically equal to the prediction horizon length.
• Combinatorial Purged CV: Testing multiple train/test combinations while maintaining temporal integrity, providing robust out-of-sample estimates.

Feature Engineering

Raw price data must be transformed into stationary, predictive features. Common transformations include returns (arithmetic and logarithmic), z-scores, percentile ranks, and technical indicators. The choice of feature scaling and normalization significantly impacts model performance.

Financial Risk Management

Fundamental Risk Measures

Professional portfolio management requires rigorous risk quantification:

• Volatility (σ): The standard deviation of returns, typically annualized by multiplying by √252 for daily data. Measures total risk but doesn't distinguish between upside and downside.
• Maximum Drawdown: The largest peak-to-trough decline in portfolio value. Critical for understanding worst-case scenarios and investor psychology—a 50% drawdown requires a 100% gain to recover.
• Value at Risk (VaR): The maximum expected loss over a given time horizon at a specified confidence level (e.g., 95% VaR). Widely used but criticized for not capturing tail risk.
• Conditional VaR (Expected Shortfall): The expected loss given that losses exceed VaR. Addresses VaR's limitations by quantifying the severity of tail events.

The Sharpe Ratio

Defined as (Rp - Rf) / σp, the Sharpe ratio measures risk-adjusted returns—excess return per unit of volatility. A Sharpe ratio above 1.0 is generally considered good, above 2.0 is excellent. However, be cautious: Sharpe ratios can be artificially inflated by illiquidity, leverage, or short sample periods.

Systematic vs. Idiosyncratic Risk

Total risk decomposes into market risk (β × market movements) and company-specific risk. The Capital Asset Pricing Model (CAPM) suggests only systematic risk is compensated, as idiosyncratic risk can be diversified away. Modern factor models extend this to multiple risk factors (size, value, momentum, quality).

Portfolio Construction

Modern Portfolio Theory

Harry Markowitz's seminal work (1952) established that portfolio risk is not simply the weighted average of individual asset risks—correlations matter. Two assets with imperfect correlation (ρ < 1) combine to produce a portfolio with lower risk than either asset alone.

The Efficient Frontier

For any given return target, there exists a portfolio with minimum variance. The set of all such portfolios forms the efficient frontier—rational investors should only hold portfolios on this frontier. Points below the frontier are suboptimal (same risk, lower return), while points above are unattainable.

Optimization Challenges

Mean-variance optimization is notoriously sensitive to input estimates:

• Estimation Error: Expected returns are difficult to estimate accurately. Small errors in inputs can lead to dramatically different optimal portfolios.
• Concentration Risk: Unconstrained optimization often produces extreme positions. Practical implementations impose position limits and sector constraints.
• Regularization: Techniques like shrinkage estimators, Black-Litterman, and robust optimization help stabilize portfolio weights.

Equal-Weight vs. Optimized

The 1/N (equal-weight) portfolio often outperforms optimized portfolios out-of-sample due to estimation error. Our backtest uses equal 5% weights as a robust baseline. For enhanced portfolios, our optimizer applies constraints and regularization to improve real-world performance.

Long-Short Equity Strategies

Market Neutrality

A dollar-neutral long-short portfolio (equal long and short exposure) has zero net market exposure. This isolates the 'alpha' from stock selection while hedging market risk. The strategy profits when long positions outperform short positions, regardless of market direction.

Sources of Return

Long-short returns decompose into:

• Long Alpha: Outperformance of long positions versus the market.
• Short Alpha: Underperformance of short positions versus the market (we profit when shorts decline).
• Short Rebate: Interest earned on short sale proceeds (reduced by borrowing costs in practice).

Practical Considerations

Real-world implementation involves transaction costs (commissions, bid-ask spreads), market impact (moving prices against you), short-selling constraints (locate requirements, borrowing costs), and capacity limits. These frictions reduce realized returns from theoretical backtests.

Rebalancing Frequency

More frequent rebalancing captures alpha faster but incurs higher transaction costs. The optimal frequency balances signal decay against trading costs. For return predictions, monthly or quarterly rebalancing typically offers a favorable trade-off.

Factor Investing

What Are Factors?

Factors are systematic sources of return that explain why certain stocks outperform others over time. Unlike stock-picking based on individual company analysis, factor investing targets broad, persistent characteristics shared by groups of securities. Academic research has identified numerous factors, though only a handful have proven robust across markets and time periods.

The Classic Factors

• Market (β): Exposure to the overall equity market. The original factor from CAPM—stocks with higher beta move more with the market and historically earn higher returns (with higher risk).
• Size (SMB): Small-cap stocks tend to outperform large-cap stocks. Fama and French (1993) documented this 'small minus big' premium, though it has weakened in recent decades.
• Value (HML): Stocks with low price-to-book ratios outperform growth stocks over time. This 'high minus low' factor reflects buying cheap assets and selling expensive ones.
• Momentum (UMD): Stocks that performed well over the past 3-12 months tend to continue outperforming. Jegadeesh and Titman (1993) documented this 'up minus down' effect across markets.
• Quality (QMJ): Companies with high profitability, stable earnings, and low leverage outperform. Asness et al. (2019) formalized this 'quality minus junk' factor.
• Low Volatility: Paradoxically, low-risk stocks often deliver higher risk-adjusted returns than high-risk stocks, contradicting basic CAPM predictions.

Factor Models

Multi-factor models decompose returns into systematic components:

• Fama-French 3-Factor: Market + Size + Value. Explains ~90% of diversified portfolio returns.
• Carhart 4-Factor: Adds Momentum to the Fama-French model.
• Fama-French 5-Factor: Adds Profitability and Investment factors, though Momentum remains significant.

Factor Timing vs. Factor Exposure

Static factor exposure (always tilting toward value, momentum, etc.) has historically rewarded patient investors. Factor timing—dynamically adjusting factor weights—is far more difficult. Factors can underperform for years before reverting, and timing signals are notoriously unreliable. Most practitioners recommend diversified, consistent factor exposure rather than tactical allocation.

Machine Learning and Factors

Our prediction model implicitly captures factor exposures through its features. By learning patterns from fundamental data, price momentum, and market conditions, the model identifies stocks likely to outperform—effectively combining multiple factors in a data-driven way. This approach can discover non-linear factor interactions that traditional linear models miss.