Treynor ratio and information ratio

The Sharpe and Sortino ratios divide excess return by total risk. Two further ratios change the denominator to answer different questions.

Treynor ratio: reward per unit of market risk

The Treynor ratio divides excess return by beta rather than volatility:

Treynor ratio = (portfolio return minus risk-free rate) / beta

The logic: if a portfolio is one slice of a larger, well-diversified holding, its own stand-alone volatility is irrelevant — only the systematic risk it adds (its beta) matters, because the diversifiable part washes out. Treynor measures return per unit of that non-diversifiable risk.

Portfolio: 11 percent return, beta 1.1, risk-free 2 percent
    Treynor = (11 - 2) / 1.1 = 8.18

Use Sharpe when the portfolio is your whole wealth; use Treynor when it is one component among many.

Information ratio: skill relative to a benchmark

The information ratio measures how consistently a manager beats a specific benchmark:

information ratio = (portfolio return minus benchmark return) / tracking error

Tracking error is the standard deviation of the difference between the portfolio and its benchmark each period. The numerator (active return) is the average outperformance; the denominator is how erratic that outperformance is.

Manager beats benchmark by 3 percent per year on average
Tracking error of that gap = 5 percent
    Information ratio = 3 / 5 = 0.60

A high information ratio means steady, repeatable outperformance — the signature of genuine skill rather than one lucky bet. An IR around 0.5 is respectable; above 1.0 is rare and excellent.

The shared caveat

Every one of these ratios is computed from a historical sample and depends on choices — the benchmark, the beta estimate, the period length. They are tools for comparison and humility, not certificates of skill. A manager can look brilliant over three years and ordinary over ten.