Information Ratio

The information ratio formula is: IR = (Portfolio Return - Benchmark Return) / Tracking Error.

Active return: The numerator is simply how much you outperformed (or underperformed) the benchmark. If your portfolio returned 15% and the S&P 500 returned 10%, your active return is 5%.

Tracking error: The denominator measures the volatility of your active return — how consistently you outperform. If your excess returns are steady (+5%, +4%, +6% each year), tracking error is low. If they swing wildly (+20%, -10%, +15%), tracking error is high. Tracking error is calculated as the standard deviation of the differences between portfolio and benchmark returns.

Example: Portfolio return = 15%, benchmark = 10%, active return = 5%. Tracking error = 8%. IR = 5% / 8% = 0.625. This is a respectable IR — the strategy outperforms by more than half a standard deviation of its excess returns.

Benchmarks: IR above 0.5 = good. Above 0.75 = very good. Above 1.0 = exceptional and rare for sustained periods. The top decile of active fund managers historically achieve IRs of 0.5-0.7. An IR below 0 means you underperform the benchmark. An IR of exactly 0 means you match the benchmark — you could replace the strategy with an index fund.

IR vs Sharpe: The Sharpe ratio measures total return per unit of total risk. The IR measures excess return per unit of active risk. The Sharpe ratio is useful for comparing any two investments. The IR is specifically useful for evaluating whether active management adds value over passive indexing.

The information ratio is governed by the Fundamental Law of Active Management, formulated by Grinold and Kahn. The relationship is: IR ≈ IC × sqrt(BR), where IC is the Information Coefficient (the correlation between predicted and actual returns) and BR is Breadth (the number of independent investment decisions made per year).

This formula has profound implications for trading system design:

Information Coefficient (IC): Measures how accurate your signals are. An IC of 0.05 means your predictions explain 5% of the variance in subsequent returns — seemingly small, but statistically exploitable at scale. Most edge in trading comes from marginal IC improvements across hundreds of signals, not from finding one perfect predictor. An IC above 0.1 is considered excellent for a systematic strategy.

Breadth (BR): The number of independent bets placed per year. A day trader making 5 trades per day on 250 trading days has a breadth of 1,250 — far higher than a buy-and-hold investor making 10 annual decisions. Higher breadth means a lower IC can still produce a high information ratio. This is why high-frequency and systematic strategies can be profitable despite individual trade win rates near 50%.

The trade-off: You can improve IR by improving prediction accuracy (higher IC) or by making more independent bets (higher breadth). In practice, IC improvements are hard and degrade over time as markets adapt. Breadth improvements — trading more instruments, more timeframes, more strategies — are more tractable. This is why diversified systematic strategies with many uncorrelated signals often achieve higher sustained IRs than concentrated discretionary approaches.

Overcrowding effect: If many traders use the same signals, the IC of those signals declines toward zero because the edge gets arbitraged away. Unique data sources, proprietary signals, and faster execution maintain IC in competitive markets.

The information ratio is most valuable as a diagnostic tool, not just a ranking metric:

Rolling IR analysis: Calculate the IR over rolling 30, 60, and 90-day windows. A declining rolling IR suggests the edge is eroding — perhaps market conditions have changed, your signal is getting crowded, or execution quality has deteriorated. A rising rolling IR indicates improving skill or better-suited market conditions. The trend of the IR over time is more informative than any single calculation.

Statistical significance: A single quarter of outperformance does not establish skill. How many observations are needed to distinguish skill from luck? The approximate threshold is IR × sqrt(T) > 2, where T is the number of years of data. An IR of 0.5 requires 16 years of data to achieve 2-sigma significance. This is why most trading performance assessments are plagued by insufficient history — even professional fund managers cannot establish statistical skill within a typical 3-5 year track record.

IR decomposition: Decompose the information ratio into its sources. Which signals contribute most to active return? Which add tracking error without proportionate return? Eliminating low-IR signal components improves the overall portfolio IR. In a multi-strategy system like Tradewink, the strategies with the lowest rolling IR are candidates for deactivation or parameter adjustment.

Benchmark selection: The IR is only meaningful relative to an appropriate benchmark. Comparing a tech-heavy portfolio to the S&P 500 overstates active return during tech bull markets and understates it during sector rotation. A technology trader should compare to the XLK ETF; a small-cap trader to the IWM.