Value at Risk Calculator - Parametric Portfolio Loss Estimate
Use this Value at Risk calculator with parametric VaR, z-score, and time horizon to estimate portfolio loss at a chosen confidence level.
Value at Risk Calculator
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What Is Value at Risk Calculator?
A Value at Risk calculator turns a portfolio value, an expected return, a daily standard deviation, and a chosen confidence level into a single dollar loss estimate, so traders, risk managers, and individual investors can size a position against a defensible downside figure.
- • Single-day trading risk limit: Estimate the one-day VaR so the trading desk can cap notional exposure.
- • Multi-week capital allocation: Run a 21-day or half-year VaR to compare new allocations.
- • Compare strategies on the same scale: Compute VaR for a passive index and a tactical sleeve, then look at the VaR-to-return ratio.
- • Document a stress test: Show the parametric VaR alongside the z-score and time horizon so the committee can see which assumption drove the loss.
Value at Risk is the workhorse market-risk metric in finance. The parametric approach used here is the simplest of the three main VaR families (historical, parametric, and Monte Carlo).
How Value at Risk Calculator Works
The parametric VaR formula multiplies the portfolio value by the difference between a volatility shock and the expected return. The volatility shock is the chosen one-tailed z-score times the square root of the time horizon in days times the daily standard deviation. When the expected return exceeds the shock, the calculator floors the loss at zero.
- PV — Portfolio value: Current market value of the portfolio, in your reporting currency. The dollar loss scales linearly with this input.
- ER — Expected return: Expected return over the time horizon, as a percent. Ten means 10% over the horizon, not 10% per day.
- SD — Daily standard deviation: Daily standard deviation of portfolio returns, as a percent. Equity portfolios typically fall in the 0.5% to 2% range.
- Days — Time horizon: Time horizon in days. The formula scales daily volatility by the square root of this number, so 252 days is one trading year.
- Z-score — Confidence multiplier: One-tailed z-score for the chosen confidence level. 1.6449 for 95%, 2.3263 for 99%, 1.2816 for 90%, drawn from the standard normal table.
The z-score is the bridge between the confidence level and the parametric distribution. At 95% the one-tailed z-score is 1.6449; at 99% it rises to 2.3263. The square root of days scaling is the convention used by J.P. Morgan's RiskMetrics Technical Document.
Fund Alpha half-year VaR: $1,000,000 portfolio, 10% expected return, 0.6% daily SD, 182.5 days, 95% confidence
PV = $1,000,000, ER = 10%, SD = 0.6%, days = 182.5, confidence = 95%
Z = 1.6449, sqrt(182.5) = 13.5093, shock = 1.6449 x 13.5093 x 0.6% = 13.33%, loss decimal = 13.33% - 10% = 3.33%, VaR = 3.33% x $1,000,000 = $33,324.49.
Value at Risk = $33,324.49 (3.33% of portfolio), z-score = 1.6449, time factor = 13.5093, volatility shock = 13.33%.
According to Omni Calculator.
Once the VaR figure is set, pair it with the Sharpe Ratio Calculator to see how much excess return the portfolio earns per unit of total volatility on the same horizon.
Key Concepts Explained
Four ideas make the parametric VaR number easier to interpret, especially when you compare it with other risk metrics or feed it into a downstream capital decision.
One-tailed z-score and the confidence level
VaR uses the one-tailed z-score, not the two-tailed. At 95% confidence the one-tailed z is 1.6449; the two-tailed 95% z would be 1.96 and would overstate the loss. The standard normal table is the canonical source.
Square-root-of-time scaling
Daily standard deviation is scaled by the square root of the time horizon in days. Twenty-one days gives 4.58, 252 days gives 15.87, and 182.5 days gives 13.51. The scaling assumes returns are roughly independent.
Parametric VaR assumes a normal distribution
The formula is parametric because it assumes returns are normally distributed around the expected return. Real portfolios have fat tails and skewness, so parametric VaR understates extreme losses. Conditional VaR is the standard follow-up.
Loss regime: real loss versus covered loss
When the volatility shock exceeds the expected return, VaR is a real dollar loss. When the expected return covers the shock, the formula returns a negative number and the calculator floors VaR at zero.
When the goal is to focus on the loss tail rather than total volatility, the Sortino Ratio Calculator uses downside deviation in the denominator.
How to Use This Calculator
Run this Value at Risk calculator with the same units and time convention as the rest of your risk report, and treat the dollar figure as one input to a larger position-sizing decision.
- 1 Enter the portfolio value: The dollar loss scales linearly with this input, so $10 million produces a 10x larger VaR than $1 million.
- 2 Enter the expected return over the horizon: Type the return as a percent. If using an annualized return, multiply by the fraction of the year the horizon covers.
- 3 Enter the daily standard deviation: Compute this from your return series. Equity portfolios typically land between 0.5% and 2% per day.
- 4 Enter the time horizon in days: Use 1 for a one-day VaR, 21 for one trading month, 252 for one trading year, or 182.5 for six calendar months.
- 5 Pick the confidence level: Choose 90%, 95%, or 99%. 95% is the most common for an internal risk report; 99% is the default for regulatory capital.
If the expected return is built from a market-risk model rather than a historical average, the CAPM Calculator keeps the risk-free rate, beta, and market premium assumptions consistent.
Benefits of Using This Calculator
A focused parametric Value at Risk calculator converts a handful of summary statistics into a single dollar loss that fits on one line of a risk report.
- • Single-figure downside: One dollar VaR number for a risk dashboard, with the confidence level and time horizon shown.
- • Auditable components: The z-score, time-scaling factor, and volatility shock are surfaced as separate outputs.
- • Multi-horizon support: Run a 1-day, 21-day, or 252-day VaR at 90%, 95%, or 99% confidence without rewriting the formula.
- • Honest edge cases: Zero standard deviation, 50% confidence, and negative expected return are all handled explicitly with a loss regime label.
- • Downstream comparisons: Pair the VaR figure with the Sharpe ratio to see return per unit of parametric downside risk.
To separate systematic market risk from the portfolio-specific risk in the VaR figure, the Portfolio Beta Calculator shows the same inputs from a beta-only angle.
Factors That Affect Your Results
Three modeling choices drive the Value at Risk figure more than any other input, and each one can move the dollar loss by an order of magnitude.
Daily standard deviation and the volatility input
The daily standard deviation is the single biggest driver of VaR. Doubling it roughly doubles the dollar VaR. Compute it from a long enough sample (at least 60 trading days).
Time horizon and the square-root-of-time assumption
VaR scales with the square root of the time horizon, so a 252-day VaR is sqrt(252/21) = 3.46 times larger than a 21-day VaR. J.P. Morgan's RiskMetrics Technical Document is the standard reference.
Confidence level and the z-score choice
The one-tailed z-score grows nonlinearly with the confidence level. Moving from 95% (z = 1.6449) to 99% (z = 2.3263) increases the volatility component by a factor of 1.41.
- • Parametric VaR assumes returns are normally distributed. Real portfolios have fat tails, so the metric can understate extreme losses.
- • The square-root-of-time scaling assumes independent daily returns, which is reasonable in calm markets but breaks down in stress events when correlations rise.
According to J.P. Morgan RiskMetrics. When the VaR number is presented alongside a risk-adjusted return for a well-diversified portfolio, the Treynor Ratio Calculator adds the per-unit-of-systematic-risk view.
Frequently Asked Questions
Q: What is Value at Risk (VaR) and what does it measure?
A: Value at Risk is a statistical measure that estimates the maximum loss a portfolio could suffer over a stated time horizon at a stated confidence level. A 95% one-month VaR of $50,000 means there is a 95% probability the portfolio will not lose more than $50,000 over the next month.
Q: How is Value at Risk calculated with the parametric formula?
A: The parametric formula is VaR = max(0, (z-score x sqrt(days) x SD - ER)) x portfolio value, floored at zero. The z-score comes from the standard normal table, the daily standard deviation comes from the portfolio's return history, and the time horizon in days sets the square-root-of-time scaling factor.
Q: What z-score is used for a 95% confidence VaR?
A: A one-tailed 95% confidence VaR uses a z-score of 1.6449. The one-tailed convention is important because VaR only cares about the loss tail. A two-tailed 95% z-score of 1.96 would overstate the loss by roughly 19%.
Q: How does the time horizon change the VaR estimate?
A: The daily standard deviation is scaled by the square root of the time horizon in days. A 21-day VaR uses a factor of 4.58, a 252-day VaR uses 15.87, and a 182.5-day VaR uses 13.51. The scaling assumes returns are roughly independent over the horizon, which is acceptable for diversified liquid portfolios but breaks down in stress events.
Q: What are the main limitations of the Value at Risk model?
A: Parametric VaR assumes returns are normally distributed, so it understates the size of extreme losses. It also assumes daily returns are independent, which fails in a market stress. And it tells you the threshold, not the average loss beyond it. Conditional VaR (Expected Shortfall) is the standard follow-up for tail-sensitive decisions.
Q: How is VaR different from Conditional VaR (Expected Shortfall)?
A: VaR is a threshold: the loss not expected to be exceeded at the chosen confidence level. Conditional VaR (also called Expected Shortfall) is the average loss given that the loss has already exceeded VaR. Conditional VaR is more sensitive to the tail and is the preferred risk measure for many regulators and for portfolios with fat-tailed return distributions.