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Pillar Guide · 10 metrics

Risk-adjusted returns — the full landscape (2026).

A risk-adjusted return scales a portfolio's return by the risk taken to earn it — typically volatility (Sharpe, Sortino), drawdown (Calmar, Pain, Ulcer), the empirical distribution (Omega, Rachev), beta (Treynor) or active risk (Information Ratio). Each one measures a different definition of "risk", so the honest practice is to report the constellation. This pillar guide indexes the ten major metrics with formula, when to use each, and the failure mode of each.

The honest constellation

On every portfolio report, MEDGE Capital displays the four-line constellation:

  1. The Sharpe family: Sharpe + Sortino — the volatility-scaled view.
  2. The drawdown family: Calmar + Ulcer / Pain — the lived-experience view.
  3. The tail view: CVaR 95 + CVaR 99 — the institutional standard.
  4. The distribution view: Omega + Rachev — for asymmetric strategies.

When all four agree, the strategy is robust. When they disagree, the disagreement IS the information.

Volatility-scaled

Penalise some measure of return variability. The Sharpe family.

Sharpe Ratio

Formula

(R_p − R_f) / σ_p

When to use

Default risk-adjusted measure for Gaussian-distributed returns. Universally understood.

Pitfall

Treats upside volatility as risk. Ignores skew and tails — a Sharpe-2.0 short-volatility strategy is still short-volatility.

Full definition

Sortino Ratio

Formula

(R_p − T) / σ_down

When to use

When the strategy is intentionally asymmetric (trend-following, long convexity) or reporting to loss-averse investors.

Pitfall

Still silent on the magnitude of tail losses. Report alongside CVaR.

Full definition

M² (Modigliani-Modigliani)

Formula

(Sharpe_p × σ_b) + R_f

When to use

Communicating risk-adjusted return to a non-technical audience as a percentage rather than a ratio.

Pitfall

Mathematically equivalent to Sharpe rescaled — no information gain over Sharpe itself.

Full definition

Drawdown-scaled

Penalise the worst lived experience — Maximum Drawdown or its variants.

Calmar Ratio

Formula

CAGR / |Max Drawdown|

When to use

Retirement-target investors; strategies where the lived experience of drawdown matters more than vol.

Pitfall

Unstable when the window is short — one new low drives the metric. Use 5+ years minimum.

Full definition

Pain Ratio

Formula

(R_p − R_f) / Pain Index

When to use

When the worst drawdown is an outlier. Pain Index averages drawdown depth across the window.

Pitfall

Less prominent in literature; harder to communicate to non-technical audiences.

Full definition

Ulcer Performance Index

Formula

Excess return / Ulcer Index

When to use

Strategies where drawdown duration matters as much as depth. UPI = RMS of drawdowns.

Pitfall

Same drawback as Calmar plus a non-linear penalty that can over-weight deep drawdowns.

Full definition

Distribution-aware

Use the empirical return distribution; skew-aware, non-parametric.

Omega Ratio

Formula

∫_τ^∞ (1 − F(x))dx / ∫_-∞^τ F(x)dx

When to use

Asymmetric strategies; non-parametric — uses the full empirical distribution at a chosen threshold τ.

Pitfall

Sensitive to the threshold choice; defaults to zero hide cash-target investors.

Full definition

Tail-aware

Focus on the magnitude of left-tail losses (and sometimes right-tail gains).

Rachev Ratio

Formula

E[R | R ≥ VaR_α] / |E[R | R ≤ −VaR_β]|

When to use

When you care explicitly about left-tail vs right-tail symmetry. Defaults α = β = 0.95.

Pitfall

Ignores the bulk of the distribution; can prefer "rare big wins, many small losses" strategies.

Full definition

Beta-scaled

Penalise systematic risk only; idiosyncratic risk treated as diversified away.

Treynor Ratio

Formula

(R_p − R_f) / β_p

When to use

Ranking sleeves within an already-diversified portfolio (systematic risk relevant, idiosyncratic diversified away).

Pitfall

Assumes the portfolio is diversified — concentrated portfolios should use Sharpe instead.

Full definition

Active-risk-scaled

For active managers — penalise the volatility of return vs benchmark.

Information Ratio

Formula

α / Tracking Error

When to use

Active managers vs a benchmark. The Sharpe-equivalent for "alpha per unit of active risk".

Pitfall

Sensitive to the benchmark choice; α estimates are noisy on short windows.

Full definition

Frequently asked

What is a risk-adjusted return?
A risk-adjusted return is a portfolio's return scaled by a measure of the risk taken to earn it — typically volatility, drawdown, or a tail-loss metric. It answers the question "how much return per unit of risk?", letting two strategies with different risk profiles be ranked on the same scale. The most cited measure is the Sharpe Ratio (excess return divided by total volatility), but Sortino, Calmar, Omega, Rachev and others scale by different risk definitions.
Which risk-adjusted return is the best?
There is no single "best" measure — each measures risk differently. For a Gaussian return distribution Sharpe is sufficient. For asymmetric strategies (trend-following, options selling on the long side) Sortino is better because it ignores upside volatility. For retirement-target investors Calmar captures the lived experience (return per unit of drawdown) more honestly. For tail-aware allocators CVaR-based ratios (Min CVaR, Rachev) are coherent risk measures. The honest practice is to report the constellation, not pick one.
What is the difference between Sharpe and Sortino?
Sharpe uses TOTAL volatility (upside + downside) in the denominator. Sortino uses only DOWNSIDE deviation — the standard deviation of returns below a target. For a symmetric Gaussian distribution Sortino ≈ Sharpe × √2; for positively-skewed strategies Sortino can be materially higher than Sharpe; for negatively-skewed strategies (carry trades, short volatility) Sortino flatters the truth less.
What is the difference between Calmar and Sharpe?
Sharpe penalises volatility (week-to-week noise); Calmar penalises Maximum Drawdown (the worst experience). Two strategies with identical Sharpe can have wildly different Calmars: one suffers a single 50% drawdown over a long period (low Calmar) while the other has many small wobbles but never deep losses (high Calmar). Calmar is more representative of what an investor actually lives through.
How is CVaR used as a risk-adjusted return measure?
Most commonly via Min CVaR optimization (minimise the average loss in the worst α% of cases) and via the Rachev Ratio (expected gain above the upper VaR divided by expected loss below the lower VaR). Both are tail-aware and skew-aware in ways Sharpe / Sortino are not. CVaR-based measures are the institutional standard since Rockafellar-Uryasev (2000) showed CVaR minimisation is a convex problem.

Related reading

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