Portfolio Performance Ratios

Portfolio Performance Ratios (Portfolio Performance Ratios) are quantitative metrics that allow the assessment of the returns of an investment portfolio adjusted for the risk taken. A simple comparison of absolute portfolio returns without accounting for risk is a major mistake: a portfolio with a return of 15% and volatility of 30% is significantly less attractive than a portfolio with a return of 10% and volatility of 8%. Performance ratios formalize this intuition, enabling proper comparison of strategies, managers, and asset classes with different risk profiles. For a large capital manager, understanding the nuances of each ratio is not an academic exercise, but a practical tool for decision-making: selection of managers, allocation between strategies, assessment of personal tactical decisions.

Sharpe Ratio (Sharpe Ratio)

The Sharpe Ratio (Sharpe Ratio), proposed by William Sharpe in 1966, is the most widely used risk-adjusted return metric. The formula: Sharpe Ratio = (Rp – Rf) / σp, where Rp is the portfolio return, Rf is the risk-free rate (usually the yield of 3-month Treasury Bills), σp is the standard deviation (volatility) of portfolio returns.

The Sharpe Ratio measures excess return (Excess Return) per unit of total risk. Interpretation: Sharpe 1.5 — exceptional (and requires increased skepticism — possible overstatement due to smoothing, illiquidity, or leverage).

Key nuances of Sharpe Ratio, critically important for practical application.

Period dependence: The Sharpe Ratio varies significantly depending on the chosen evaluation period. A manager with Sharpe 1.5 for 2017–2019 (period of low volatility) and Sharpe 0.3 for 2020–2022 (period of high volatility) might have Sharpe 0.7 for the full cycle. Recommendation: assess Sharpe over a full market cycle (5–7 years, including both bull and bear markets).

Normality problem: Sharpe Ratio assumes a normal distribution of returns and does not distinguish “good” volatility (upward deviations) and “bad” volatility (downward deviations). For strategies with positive skewness (Long Volatility, Trend Following) Sharpe Ratio understates efficiency; for strategies with negative skewness (Short Volatility, Credit Carry) — overstates.

Annualization: to convert from daily to annual Sharpe Ratio, multiply by √252 (number of trading days); from monthly — multiply by √12. Important: annualized Sharpe is correct only with no autocorrelation in returns (which is violated for many alternative strategies).

Sortino Ratio (Sortino Ratio)

The Sortino Ratio (Sortino Ratio) eliminates the main drawback of the Sharpe Ratio — an identical treatment of upward and downward deviations — by replacing overall volatility with downside deviation (downward deviation).

The formula: Sortino Ratio = (Rp – MAR) / σd, where MAR (Minimum Acceptable Return) is the minimum acceptable return (usually the risk-free rate or zero), σd is the downside deviation — the standard deviation of only negative deviations from MAR.

Sortino Ratio assesses excess return per unit of “harmful” risk — only those deviations that incur losses for the investor.

For an investor with large capital, Sortino is more informative than Sharpe: the main task is to avoid major losses, and positive volatility (unexpectedly high returns) is not a risk but a benefit.

Comparing Sharpe and Sortino reveals valuable information about the strategy’s character.

If Sortino is significantly higher than Sharpe — the strategy has positive skewness (Positive Skew): volatility is mostly “good” (large positive surprises with limited losses). Typical examples: Trend Following (CTA) strategies, Long Volatility funds, Tail Risk Hedging.

If Sortino is close to Sharpe or lower — the strategy has symmetric or negatively skewed distribution. Typical examples: Short Volatility (selling options), Credit Carry (arbitrage on credit spreads).

When choosing managers and strategies, it is recommended to: (1) compare both ratios — Sharpe and Sortino; (2) give preference to strategies where Sortino > Sharpe (positive skewness); (3) be cautious with high Sharpe and low Sortino — a sign of potentially catastrophic tail risk.

Calmar Ratio (Calmar Ratio)

The Calmar Ratio (Calmar Ratio) measures returns relative to maximum drawdown (Maximum Drawdown, MDD) — the greatest drop in portfolio value from peak to trough.

The formula: Calmar Ratio = Annualized Return / |Maximum Drawdown|.

For example, a portfolio with an average annual return of 12% and a maximum drawdown of –25% has Calmar = 12/25 = 0.48.

Calmar Ratio is especially valuable for evaluating strategies with a long track record, as Maximum Drawdown reflects the worst realized scenario, not a statistical abstraction.

Benchmarks: Calmar > 1.0 — excellent return/drawdown ratio; Calmar 0.5–1.0 — good; Calmar < 0.5 — insufficient.

Maximum Drawdown (MDD) — key metric for UHNWI investors for several reasons.

Psychological: a –40% drawdown requires +67% growth to recover, –50% requires +100%, –60% requires +150% — the math is ruthless and exponential.

Practical: deep drawdown may coincide with the need to fund expenses (lifestyle, capital calls of PE funds, tax obligations), forcing asset sales at the bottom.

Reputational: for a family office or manager of large capital, loss of 40–50% of capital is not just a financial shock, but possibly the end of a career.

Recovery Time — additional critically important metric: S&P 500 required 5.5 years to recover after the 2000–2002 crash and 4 years after the 2008–2009 crisis. For large private capital with obligations (lifestyle spending, commitments) such timelines may be unacceptable.

Volatility vs Downside Risk: Practical Differences

The fundamental difference between volatility (Volatility, standard deviation of returns) and downside risk (risk of decline) determines the choice of portfolio assessment metrics.

Volatility (σ) — a symmetric measure: it accounts for both upside (Upside Volatility) and downside (Downside Volatility) deviations equally. For the investor who “lives” in the portfolio (and not evaluating it ex-post in an academic paper), upside deviations are a “good” surprise, and downside deviations are real risk.

Semi-Deviation measures only deviations below the mean or a given threshold; Downside Deviation — standard deviation of negative deviations from MAR; Maximum Drawdown — the worst realized result.

For portfolio optimization, the choice of objective function determines the outcome.

Optimization by Sharpe Ratio (maximizing Return/Volatility) leads to a portfolio that ignores distribution skewness.

Optimization by Sortino Ratio (maximizing Return/Downside Deviation) builds a portfolio minimizing “harmful” volatility.

Optimization by CVaR (minimizing expected tail losses) focuses on extreme scenarios.

Conditional Drawdown at Risk (CDaR) — a metric combining CVaR and Drawdown approaches: minimizes the expected drawdown depth beyond a set threshold.

Portfolio Optimization and Practical Recommendations

For the manager of large capital, it is recommended to use the Dashboard approach with parallel monitoring of several metrics.

Level one (Daily): VaR(95%, 1 day), CVaR(95%, 1 day), current drawdown from the latest peak, current realized volatility (20-day and 60-day).

Level two (Monthly): Sharpe Ratio (trailing 12M), Sortino Ratio (trailing 12M), Calmar Ratio (trailing 36M), Information Ratio vs benchmark, tracking error.

Level three (Quarterly): Performance Attribution (Brinson-Fachler), factor exposure analysis, stress test results, liquidity analysis.

When selecting external managers: request the full set of metrics (Sharpe, Sortino, Calmar, MDD, Recovery Time) for at least 5 years (including crisis periods); compare Sortino/Sharpe ratio to assess skewness; prefer managers with Calmar > 0.7 and Recovery Time < 2 years; be skeptical about high Sharpe/Calmar ratios (Sharpe > 2.0, Calmar > 2.0) — possible smoothing (smoothing of illiquid asset valuations), survivorship bias or leverage.