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IntermediateRisk & PerformancePython

Run this module

cd "Finance - Information Ratio"
python "information_ratio.py"

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Information Ratio & Active Management Metrics

When a portfolio is judged against a benchmark, what matters is how much it beat the benchmark by — and how reliably. These are the core metrics of active management: active return, tracking error, Information Ratio, and the appraisal ratio.

Functions

Function Description
active_returns(portfolio, benchmark) Period-by-period excess over benchmark
tracking_error(portfolio, benchmark, periods) Annualised volatility of active returns
information_ratio(portfolio, benchmark, periods) Active return per unit of tracking error
appraisal_ratio(portfolio, benchmark, periods) Jensen's alpha ÷ residual vol, via CAPM regression

Key Concepts

  • Active return: r_portfolio − r_benchmark. The value the manager added (or lost) versus simply holding the benchmark.
  • Tracking error: the standard deviation of active returns, annualised. It is the risk of deviating from the benchmark.
  • Information Ratio (IR): annualised active return / tracking error. The benchmark-relative cousin of the Sharpe ratio. IR > 0.5 is good; > 1.0 is excellent and rare over long horizons.
  • Appraisal ratio: from r_p = α + β·r_b + ε, it is annualised α / σ(ε) — skill (alpha) per unit of idiosyncratic risk, isolating stock-picking from market exposure.

Example

import numpy as np
from information_ratio import information_ratio, tracking_error, appraisal_ratio

bench = np.random.default_rng(0).normal(0.0004, 0.011, 504)
port = 0.0002 + 1.05 * bench + np.random.default_rng(1).normal(0, 0.004, 504)

print(tracking_error(port, bench))     # annualised TE
print(information_ratio(port, bench))  # IR
print(appraisal_ratio(port, bench))    # alpha, beta, residual vol, appraisal ratio

Practical Notes

  • Annualisation uses mean × periods for return and std × √periods for volatility, so the IR scales by √periods.
  • Use periods=252 for daily data, 52 for weekly, 12 for monthly.
  • A high IR from a tiny tracking error can be statistically fragile — pair it with the [[bootstrap]] module to put a confidence interval around it.

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