Portfolio & Risk Indicators

Portfolio and risk indicators measure a whole portfolio rather than one security: its exposure (gross, net, beta-adjusted, factor), its concentration (Herfindahl index, effective number of bets, diversification ratio), its loss profile (drawdown, downside deviation, value at risk and its components) and its return quality against a benchmark (alpha, tracking error, capture ratios, the Sterling, Martin and gain-to-pain ratios). They are read to size risk and to judge whether a return was earned or borrowed.

What do Portfolio & Risk indicators have in common?

Every indicator in this category takes the portfolio's holdings or its return series as input rather than a price chart. Some are accounting identities computed from weights and betas, such as gross and net exposure or the Herfindahl concentration index. Some are statistics of the return series, such as drawdown, downside deviation, tracking error and the historical value at risk. Some come from a model, such as parametric and Monte Carlo VaR, Jensen's alpha, the risk-parity and maximum-diversification weights and the Kelly fraction.

The category divides into four groups. Exposure measures (gross, net and beta-adjusted exposure, factor exposure, portfolio beta) say how much market and factor risk is held. Concentration measures (the Herfindahl index, the effective number of bets, the diversification ratio, correlation concentration, risk contribution and its marginal, volatility and factor versions) say how many independent sources of risk the portfolio really has, which is usually fewer than its number of positions.

Loss measures (current drawdown, drawdown duration and contribution, recovery time, downside deviation, downside capture, historical, parametric and Monte Carlo VaR with marginal, incremental and component VaR) describe how bad it has been or could be. Return-quality measures (alpha and Jensen's alpha, risk-adjusted return, tracking error, active share, upside capture, the Sterling, Burke, Martin, gain-to-pain and ulcer performance ratios, portfolio turnover) ask whether the return paid for the risk and the cost.

What they share is a published origin: Jensen's alpha, value at risk as codified in the RiskMetrics technical document, active share, the diversification ratio and equal-risk-contribution weights each come from a paper or document that defines them, which is why their formulas do not vary between providers the way a chart indicator's can. They also share a dependence on the return history and covariance matrix used, which is estimated from a sample and will differ from what the next period delivers.

How do you choose a Portfolio & Risk indicator?

• For sizing, read gross and net exposure first and beta-adjusted exposure second; a long-short book that is dollar-neutral is rarely beta-neutral
• For diversification, prefer the effective number of bets or the diversification ratio over the position count, since ten stocks in one sector are closer to one bet than to ten
• For loss, use drawdown and recovery time for what has happened and VaR for what the model expects, and read component VaR to find which position carries the tail
• For judging a manager or a strategy, pair alpha with tracking error and active share; a high alpha with low active share is usually a benchmark mismatch
• Use the Kelly fraction as a ceiling rather than a target, since it assumes the edge is known exactly and the full fraction has drawdowns most investors will not hold through

Portfolio & Risk indicators at a glance

Indicator	What it measures	How it is read
Sterling Ratio	The Sterling ratio compares annualized return with a drawdown measure.	Higher values mean more return per unit of drawdown.
Burke Ratio	The Burke ratio divides a portfolio's excess return by the square root of the sum of its squared drawdowns, so repeated or deep drawdowns are penalized more than a single one.	Higher is better: more excess return per unit of drawdown pain.
Martin Ratio	The Martin ratio divides a portfolio's excess return by the Ulcer Index, which measures the depth and duration of drawdowns.	Higher means more excess return per unit of drawdown stress.
Ulcer Performance Index	The Ulcer Performance Index divides excess return by the Ulcer Index, a measure of the depth and duration of percentage drawdowns from the running peak.	Higher is better.
Current Drawdown	Current drawdown is the percentage decline of the portfolio's present value from its highest previous value (its running peak).	It shows how far the portfolio is below its high right now.
Drawdown Duration	Drawdown duration is the length of time a portfolio spends below a previous equity peak, measured from the peak to the date the peak is regained (or to the latest date if it has not been regained).	Longer durations mean a longer wait to get back to the prior high.
Recovery Time	Recovery time is how long it takes a portfolio to climb back to its prior peak after reaching the bottom of a drawdown, measured from the trough date to the date the earlier high is regained.	Longer recovery times mean a longer period before earlier losses were repaid.
Downside Deviation	Downside deviation is the root mean square of returns that fall below a minimum acceptable return (MAR), counting returns at or above the MAR as zero.	A lower number means smaller or fewer shortfalls below the target.
Upside Capture Ratio	The upside capture ratio compares a portfolio's performance with its benchmark's only during periods when the benchmark rose.	Above 100% means the portfolio participated more than fully in rising markets.
Downside Capture Ratio	The downside capture ratio compares a portfolio's performance with its benchmark's only during periods when the benchmark fell.	Below 100% means the portfolio fell less than the benchmark in down markets, above 100% means it fell more.
Tracking Error	Tracking error is the standard deviation of the difference between a portfolio's returns and its benchmark's returns, the active returns.	A low tracking error means returns stay close to the benchmark; a high one means they diverge, up or down.
Active Share	Active share is the fraction of a portfolio that differs from its benchmark: half the sum of the absolute differences between portfolio weights and benchmark weights across every holding in either one.	It runs from 0% (the portfolio holds exactly the benchmark weights) to 100% (no overlap with the benchmark).
Portfolio Alpha	Portfolio alpha is the part of a portfolio's return not explained by its exposure to market or factor returns.	Positive alpha means return beyond what the chosen factors explain.
Jensen Alpha	Jensen's alpha is the portfolio's average return in excess of what the capital asset pricing model predicts from its beta, the risk-free rate and the market return.	Positive alpha means the portfolio earned more than its market exposure would explain; negative means less.
Parametric VaR	Parametric (variance-covariance) VaR assumes portfolio returns follow a known distribution, usually normal, and computes the loss threshold from the portfolio's volatility and a z-score for the confidence level.	It is the loss that the model says will be exceeded with probability 1 minus the confidence level over the horizon.
Historical VaR	Historical Value at Risk estimates a loss threshold directly from the empirical distribution of past portfolio returns, as the percentile of that history that corresponds to the chosen confidence level, with no distribution assumed.	A 1-day 95% VaR of 2% means that in the sampled history the portfolio lost more than 2% on about 5% of days.
Monte Carlo VaR	Monte Carlo VaR estimates Value at Risk by simulating many possible future return scenarios from an assumed model, revaluing the portfolio in each, and reading the loss at the chosen percentile of the simulated profit and loss.	Read it as the loss exceeded in only the stated fraction of simulated outcomes.
Marginal VaR	Marginal VaR is the rate of change of portfolio Value at Risk with respect to a small increase in one position's size.	A larger marginal VaR means a bit more of that position raises tail risk faster.
Component VaR	Component VaR is the part of a portfolio's total Value at Risk attributable to one position: the position's weight times its marginal VaR.	A large component VaR flags a position that dominates the tail risk.
Incremental VaR	Incremental VaR is the change in portfolio Value at Risk caused by adding a position, removing one, or resizing a trade, found by recomputing VaR with and without the change.	A positive value means the trade adds to tail risk, a negative value means it hedges the existing book.
Beta-Adjusted Exposure	Beta-adjusted exposure scales each position's market value by its beta to a chosen market index, then sums and divides by equity, showing how much market sensitivity the book carries rather than just how much capital is deployed.	A value of 1.0 means the book moves about as much as the index for a given index move; above 1.0 it is leveraged to the market, near 0 it is roughly market-neutral, and negative means net short market sensitivity.
Gross Exposure	Gross exposure is the total market value of long and short positions combined, expressed as a share of account equity.	100% means deployed capital equals equity; above 100% means the account uses leverage or shorts.
Net Exposure	Net exposure is long market value minus short market value, expressed as a share of account equity.	Positive means net long, negative net short, near zero roughly dollar-neutral.
Factor Exposure	Factor exposure is a portfolio's sensitivity (loading) to a return factor such as the market, size or value.	An exposure of 1.0 means the portfolio is expected to move one-for-one with the factor, 0 means no sensitivity, and negative means it moves opposite.
Factor Contribution to Risk	Factor contribution to risk splits portfolio variance into the part driven by each common factor (market, size, value and so on) and a residual part, using the portfolio's factor exposures and the factor covariance matrix.	Large shares show which factors dominate risk; the residual share shows how much risk is stock-specific.
Risk Contribution	Risk contribution shows what share of total portfolio risk comes from each holding, taking correlations into account.	Compare each share with the position's weight: a 10% holding contributing 30% of risk is a concentrated source of risk.
Marginal Contribution to Risk	Marginal contribution to risk (MCTR) is how much portfolio volatility changes for a small increase in one asset's weight.	It is a per-unit-weight rate: assets with a high MCTR add the most volatility at the margin, assets with a low or negative MCTR dilute it.
Diversification Ratio	The diversification ratio compares the weighted average of the individual asset volatilities with the volatility of the portfolio.	A ratio of 1 means no diversification benefit (all assets perfectly correlated); higher values mean more of the stand-alone risk is cancelled by combining the assets.
Effective Number of Bets	Effective number of bets counts how many independent sources of risk a portfolio really holds.	It ranges from 1 (all risk in one bet) to the number of factors (risk spread equally).
Herfindahl Concentration Index	The Herfindahl concentration index is the sum of the squared portfolio weights.	It ranges from 1/n (equal weights) to 1 (one holding).
Portfolio Turnover	Portfolio turnover measures how much of a portfolio is traded over a period.	A turnover of 100% means the equivalent of the whole portfolio was replaced once during the period.
Correlation Concentration	Correlation concentration describes how much of a portfolio's risk is driven by holdings that move together.	Values near 1 mean the holdings behave like one position and diversification is weak; values near 0 mean returns are largely independent.
Volatility Contribution	Volatility contribution is the portion of portfolio volatility, in volatility units, attributable to one position through the Euler decomposition.	It answers how many percentage points of the portfolio's volatility each holding supplies.
Drawdown Contribution	Drawdown contribution attributes a portfolio's peak-to-trough loss to its individual positions or sleeves, showing which holdings caused the decline.	Large negative contributions identify where the loss came from; positive ones identify positions that cushioned it.
Risk Parity Weight	Risk parity weights size each asset so that all contribute equally to portfolio risk, rather than holding equal capital.	Weights shift toward calmer assets so no single asset dominates risk.
Kelly Fraction	The Kelly fraction is the share of capital that maximizes the long-run expected logarithmic growth of capital for a repeated bet with known odds.	It is a theoretical growth-optimal size; a result of zero or below means no bet has positive edge.
Maximum Diversification Weight	Maximum diversification weights are the portfolio weights that maximize the diversification ratio, the weighted average asset volatility divided by portfolio volatility, subject to constraints such as being fully invested and long-only.	The resulting weights tilt toward assets with low correlation to the rest and away from assets that are highly correlated with many others.
Risk-Adjusted Return	Risk-adjusted return expresses return per unit of risk taken.	Higher values mean more return per unit of risk, which allows comparing strategies with different volatility.
Gain-to-Pain Ratio	The gain-to-pain ratio divides the sum of all periodic returns by the absolute value of the sum of the negative returns.	Values above 1 mean total gains exceeded the total of the losses; common rules of thumb treat higher as better, but there is no universal threshold.

Each row is the opening sentence of that indicator's own definition and reading, so the table says exactly what the profile says.

What limits do Portfolio & Risk indicators share?

Every measure here is estimated from a sample of returns or a covariance matrix that the next period will not reproduce exactly: VaR says nothing about the size of losses beyond its threshold and was computed to within its stated confidence during 2008 while the losses that mattered sat outside it, correlations rise in a crash so the diversification ratio measured in calm markets overstates the protection, and alpha against the wrong benchmark measures the benchmark error rather than skill. Drawdown is path-dependent and a single history, so a strategy's worst drawdown is a lower bound on its worst possible one.

Frequently Asked Questions

What is value at risk?

Value at risk is the loss that a portfolio is not expected to exceed over a stated horizon at a stated confidence, such as a one-day loss not exceeded 95 percent of the time. Historical VaR reads it from past returns, parametric VaR assumes a normal distribution with the portfolio's volatility, and Monte Carlo VaR simulates it from a model. It says nothing about how large the loss is on the days it is exceeded.

What is the difference between tracking error and active share?

Tracking error is the standard deviation of the difference between a portfolio's return and its benchmark's, measured over time. Active share is the share of the portfolio's holdings that differ from the benchmark's, measured at a point in time. A fund can have low tracking error with high active share if its deviations offset, and Cremers and Petajisto found that high active share predicted outperformance where tracking error alone did not.

What is risk contribution?

Risk contribution is the share of a portfolio's total volatility attributable to one position, computed from its weight, its volatility and its correlation with the rest. Because it includes correlation, a position's risk contribution can be far larger than its weight, and a risk-parity portfolio is one whose positions are sized so that each contributes the same amount.

What is the Kelly fraction?

The Kelly fraction is the share of capital that maximizes the long-run growth rate of wealth for a bet with a known edge and odds, derived by John Kelly in 1956. For investments it is the expected excess return divided by the variance. It assumes the edge is known exactly and produces large drawdowns, which is why practitioners who use it size at a half or a quarter of the computed fraction.