Transparency is a feature. This page explains what these five risk-adjusted ratios measure and why we compute them — in plain terms. The precise formulas and numeric conventions are documented in our internal methodology; the summary here is deliberate, not an omission.
Each of these ratios answers a version of the same question: how much return did an investment earn for the risk it took? They are all annualized so figures at different frequencies (daily, monthly) can be compared on the same yearly scale. The frequency is always declared by whoever runs the calculation — we never guess it from the data. Returns are treated as simple period returns expressed as decimal fractions.
The Sharpe ratio measures excess return per unit of total volatility: it takes the average return above the risk-free rate and divides it by how much those excess returns swing around from period to period. Higher is better — more reward for each unit of overall risk. It is signed, so a negative Sharpe means the investment trailed the risk-free rate on average. It needs at least two periods to measure any variation, and if returns never move at all there is no volatility to divide by, so the ratio is undefined.
The Sortino ratio is a close cousin of Sharpe that only penalizes downside risk. Instead of dividing by total volatility, it divides the average return above a chosen minimum acceptable return by the downside deviation — the volatility computed from just the periods that fell short of that threshold. By default the threshold is zero, so only losing periods count as risk. Higher is better, and it is signed. If no period ever falls below the threshold there is no downside to divide by, so the ratio is undefined.
The Calmar ratio compares an investment's compound annual growth rate against its worst peak-to-trough loss (its maximum drawdown). It answers "how much did it grow relative to the deepest hole it dug?" Higher is better — more growth for each unit of worst-case pain. Both inputs are already annual or whole-horizon figures, so this one is not annualized further. The sign follows the growth rate, so a shrinking investment produces a negative Calmar. A flawless track record with no drawdown at all has nothing to divide by, so the ratio is undefined.
The Treynor ratio measures excess return per unit of market risk rather than total risk. It divides the average return above the risk-free rate by the investment's beta — its sensitivity to the benchmark. Because beta measures market exposure rather than volatility, Treynor is scaled up to an annual figure in direct proportion to the number of periods per year, differently from the volatility-based ratios above. Higher is better, and it is signed. If the investment has no market exposure (a beta of zero) there is no systematic risk to divide by, so the ratio is undefined.
The information ratio measures active return per unit of tracking error — how much a portfolio out- or under-performs its benchmark, relative to how consistently it does so. It divides the average active return (portfolio minus benchmark, period by period) by the volatility of that active-return series. Higher is better: it rewards steady outperformance and penalizes erratic bets. It is signed and antisymmetric, so swapping the portfolio and the benchmark simply flips its sign. The two return series must line up period for period and cover the same span, so a length mismatch is rejected rather than guessed at; it also needs at least two periods, and if the portfolio tracks the benchmark perfectly there is no active variation to divide by, so the ratio is undefined. Its close relatives are documented under tracking.
