--- title: "Parametric VaR: Formula, Meaning" description: "Parametric (variance-covariance) VaR assumes portfolio returns follow a known distribution, usually normal, and computes the loss threshold from the..." canonical: https://www.getswoopr.com/indicators/portfolio-and-risk/parametric-var/ source: "Swoopr Investment: https://www.getswoopr.com" --- ## Direct Answer > 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. Real returns have fatter tails than the normal distribution, so it tends to understate extreme losses, and it handles options and other non-linear positions poorly. # Parametric VaR: Formula, Meaning, Signals, Examples and How to Use It ## How Is Parametric VaR Calculated? 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. **Formula:** `VaR = V x (z x sigma_p - mu_p); with zero mean, VaR = V x z x sigma_p` **Inputs:** - Portfolio value V - Portfolio volatility over the horizon - Expected return over the horizon (often set to zero) - Z-score (1.645 at 95%, 2.326 at 99%) **Worked example.** A 1,000,000 portfolio with 1.2% daily volatility has a one-day 95% parametric VaR of $19740.00 under a normal, zero-mean assumption. The inputs are illustrative numbers, not market data. **Reading it.** It is the loss that the model says will be exceeded with probability 1 minus the confidence level over the horizon. A longer horizon is often approximated by multiplying by the square root of the number of days. **Limits.** Real returns have fatter tails than the normal distribution, so it tends to understate extreme losses, and it handles options and other non-linear positions poorly. ## What is 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. ## How to use Parametric VaR It is the loss that the model says will be exceeded with probability 1 minus the confidence level over the horizon. A longer horizon is often approximated by multiplying by the square root of the number of days. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime. ## Strengths - A closed form from portfolio volatility and a z-score means it can be computed instantly from a covariance matrix. - Horizon and confidence enter as multipliers on one volatility figure, so changing either is only a change of multiplier. - Reproducible when the formula and data convention are fixed. ## Weaknesses and limitations - It treats volatility as constant across the lookback, so it responds slowly when markets move from calm to turbulent. - Setting the mean to zero ignores expected drift, which matters little for a day but more for monthly or longer horizons. - Correlated indicators can create false confidence by repeating the same underlying information. ## Editorial and risk note This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance. ## Frequently Asked Questions Is Parametric VaR a buy or sell signal? No. It is the loss that the model says will be exceeded with probability 1 minus the confidence level over the horizon. Real returns have fatter tails than the normal distribution, so it tends to understate extreme losses, and it handles options and other non-linear positions poorly. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions. What is the best setting for Parametric VaR? Parametric VaR is computed from portfolio value V; portfolio volatility over the horizon; expected return over the horizon (often set to zero), so the choices that matter are the data convention and the window it is read over. Test those across instruments, regimes and out-of-sample periods instead of fitting one historical winner. Can Parametric VaR be used by itself? Real returns have fatter tails than the normal distribution, so it tends to understate extreme losses, and it handles options and other non-linear positions poorly. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone. Does Parametric VaR work on every timeframe? The calculation (VaR = V x (z x sigma_p - mu_p); with zero mean, VaR = V x z x sigma_p) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it. Why does Parametric VaR give false signals? It treats volatility as constant across the lookback, so it responds slowly when markets move from calm to turbulent. Setting the mean to zero ignores expected drift, which matters little for a day but more for monthly or longer horizons. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated. How should Parametric VaR be backtested? Rebuild Parametric VaR from portfolio value V using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline. ## References - [J.P. Morgan/Reuters, hosted by MSCI: RiskMetrics Technical Document, Fourth Edition (1996)](https://www.msci.com/documents/10199/5915b101-4206-4ba0-aee2-3449d5c7e95a) S Swoopr Editorial Team The Swoopr Editorial Team produces independent investment education, research, and tools for understanding markets, evaluating opportunities, and managing risk. All content is educational only and does not constitute personalized investment advice. See our [editorial policy](https://www.getswoopr.com/legal/editorial-policy/) and [corrections policy](https://www.getswoopr.com/legal/corrections-policy/).