Performance evaluation

Performance evaluation is the art and science of deciding whether a fund manager, strategy, or sub-portfolio has actually delivered value — beyond what could be explained by passive exposure to factors, luck, or fees. This is the question every allocator has to answer with limited data and asymmetric information.

Returns vs alpha vs information ratio

• Total return: raw fund return. Misleading because it conflates beta and skill.
• Excess return: return - benchmark. The right starting point.
• Alpha: the intercept of a regression of returns on factor exposures. The most-quoted 'skill' measure.
• Information ratio: alpha / tracking-error. The Sharpe ratio of the active-return stream.

Sharpe ratio

SR = (μ_p - r_f) / σ_p. Universal benchmark. Excellent funds run at SR 1.5-3 over long horizons; the average actively managed mutual fund has historic SR around 0.3-0.5; passive equity index SR has been ~0.4 long-run.

Sortino ratio

(μ_p - r_f) / σ_down. σ_down is the semi-deviation — standard deviation of returns below the minimum acceptable return (often zero or r_f). Penalises only downside vol. Favoured for asymmetric strategies (option selling, momentum).

Treynor ratio

(μ_p - r_f) / β_p. Excess return per unit of systematic risk. Used when a portfolio is part of a larger diversified portfolio, so idiosyncratic risk doesn't matter — only its CAPM beta does.

Information ratio (IR)

IR = (μ_p - μ_benchmark) / σ_(p - benchmark). Active return over the volatility of the active return. Industry-standard benchmark for active management; long-only US mutual funds average IR around 0 (post-fees); best hedge funds run IR 1-2.

Alpha and its standard error

From a single-factor regression: R_p,t - r_f,t = α + β (R_M,t - r_f,t) + ε_t. The intercept α̂ has standard error roughly σ_ε / √T. For T = 60 months (5 years) and σ_ε ≈ 4% per month, SE(α̂) ≈ 0.5%/month = 6%/year. To declare α at 95% confidence requires α̂ > 12%/year — a very high bar. Most 'alpha' is statistically indistinguishable from zero over 3-5 year windows.

Sharpe ratio standard error (Lo 2002)

SE(SR̂) ≈ √((1 + SR²/2) / T)
(T in years for annual SR estimation)

For SR ≈ 1 and T = 3 years: SE ≈ √(1.5/3) ≈ 0.71. 95% CI is roughly [SR̂ - 1.4, SR̂ + 1.4]. A Sharpe of 1 over 3 years has confidence interval crossing zero — i.e., not statistically different from no skill.

Multi-factor benchmarks

If a manager's alpha vanishes once you adjust for size, value, momentum, profitability exposures, then they aren't a skill provider — they are a smart-beta provider. FF3, FF5, FF6 (with momentum) are the dominant adjusting frameworks. A persistently positive 6-factor alpha is the gold standard.

Tear-sheet checklist

• Total and excess return over benchmark, by year, since inception.
• Annualised volatility, Sharpe, Sortino, max drawdown.
• Beta, alpha, and information ratio against CAPM, FF3, FF5, FF6 — multiple benchmarks.
• Up-capture / down-capture: fraction of benchmark gains/losses captured.
• Worst 5 months / worst calendar quarter / longest drawdown duration.
• Annualised turnover, fees, expense ratio.
• Survivorship and selection bias disclosures.

Risk-adjusted return decomposition

Brinson-Fachler attribution decomposes excess return into (1) asset allocation, (2) security selection, (3) interaction. Useful for distinguishing 'good asset class call' from 'good stock picks'. Modern multi-factor attribution decomposes excess return across factor exposures, allowing 'this manager outperformed because they had a tilt to small-cap value'.