β οΈ Value at Risk Calculator
Your worst day, quantified.
Daily VaR (95%)
Estimates for planning only, not financial advice.
A $1,000,000 portfolio with 1.5 percent daily volatility has a one-day 95 percent VaR of $24,675. Plain English: on 95 out of 100 days, losses stay under $24,675; on about 1 day in 20, they exceed it. The 99 percent VaR is $34,890. VaR does not say how bad that 1-in-20 day gets, only where it starts.
How to Use This Calculator
Enter portfolio value, daily volatility (standard deviation of daily returns), expected daily return, and confidence level. The calculator returns daily VaR plus square-root-of-time scaled 10-day, monthly, and annual figures.
Enter portfolio value and daily volatility. Estimate vol from recent daily returns or use VIX-implied figures.
Pick 95% (risk management standard) or 99% (regulatory standard).
Read multi-day VaR for position sizing: scale by the square root of days.
The Formula (Parametric VaR)
Parametric VaR assumes returns are normally distributed, which they are not: real markets have fat tails, so true 1-in-20 losses exceed the model's. The square-root scaling assumes independent daily returns. Both assumptions make this a useful risk ruler, not a prophecy.
Worked Example
$1,000,000, 1.5 percent daily vol, zero expected return, 95 percent. VaR: 1,000,000 x (1.645 x 0.015 - 0) = $24,675, or 2.47 percent of the portfolio. Ten-day: 24,675 x sqrt(10) = $78,028. Twenty-one-day (monthly): $113,091. Annual: $391,755. At 99 percent the daily figure rises to $34,890: the extra confidence costs about 41 percent more VaR.
What VaR Does Not Tell You
| VaR says | VaR does not say |
|---|---|
| Loss threshold exceeded 5% of days | How far beyond it losses go |
| Normal-market risk | Crash / tail risk |
| Single-number summary | Which positions drive the risk |
The classic critique: VaR tells you the minimum you lose on a bad day, not the maximum. Expected shortfall (average loss beyond VaR) answers the follow-up question and is the coherent risk measure regulators now prefer for trading books. Use VaR for limits and reporting, expected shortfall for "how bad can it really get," and stress tests for the scenarios models miss.
Practical Uses
Position sizing is the retail use: size positions so that a 2x VaR move does not impair the portfolio. Risk managers set VaR limits per desk and backtest them (expect about 5 percent exceedances at 95 percent; many more means the model is broken). And remember procyclicality: volatility estimated in calm markets understates VaR just when you need it. For return-per-risk on the same portfolio, our Treynor ratio calculator and Sortino calculator complement this risk view.
Backtesting and the Limits of VaR
A VaR number is only as good as its backtest. Regulators expect a 99 percent daily VaR to be breached roughly 2 to 3 times a year; consistently more breaches means the model understates risk, and consistently zero means it overstates it and wastes capital. Banks backtest VaR daily and face capital penalties for failures, which is why their models are elaborate. Your spreadsheet version deserves at least a casual backtest: run it over the last two years of your portfolio and count the breaches.
The deeper problem is what VaR ignores: the shape of the tail beyond the threshold. Two portfolios can share a 95 percent VaR of $10,000 while one loses $11,000 in its worst case and the other loses $500,000. Expected shortfall (the average loss when VaR is breached) fixes this blind spot and is why regulators now prefer it for trading books. The 2008 crisis was VaR's public humiliation: models calibrated on calm years said triple-A tranches were safe, then correlations went to one and losses blew past every VaR estimate simultaneously.
Use VaR for what it is: a standardized risk thermometer, useful for sizing positions, setting stop discipline, and comparing portfolios on one scale. Never use it as a worst case; the question "what is the most I can lose" has a different answer (usually everything, for levered or concentrated positions). Pair every VaR with a stress test: what happens if 2008, March 2020, or your sector's nightmare repeats? The stress test is where the real risk management lives.
A Thermometer, Not a Forecast
Value at Risk compresses portfolio risk into one number: the loss you should exceed only 5 percent of the time. Use it to size positions and compare strategies, backtest it honestly, and always pair it with expected shortfall and stress tests for the tail it cannot see. Risk you can measure is risk you can manage; risk you ignore because the model looked calm is how accounts blow up.
Use It, Then Look Past It
VaR earns its place in every risk toolkit: one number, comparable across portfolios, backtestable against history. Just never let it be the only number. Pair it with expected shortfall for the tail, stress tests for the regime breaks, and position limits for the days models fail. The investors who survived 2008 were not the ones with the best VaR models; they were the ones who asked what happened if the model was wrong.
Estimates for planning only, not financial advice.
Frequently Asked Questions
What is Value at Risk (VaR)?
The maximum expected loss over a period at a given confidence level. A $24,675 one-day 95% VaR means losses should exceed $24,675 on only about 1 day in 20. It quantifies normal-market risk in one number. Think of it as a weather forecast for your portfolio: not the worst possible storm, but the loss level that should hold on 19 out of 20 trading days.
How do you calculate parametric VaR?
VaR = portfolio value x (z-score x volatility - expected return), with z = 1.645 at 95% or 2.326 at 99%. For $1M at 1.5% daily vol: $1M x 1.645 x 0.015 = $24,675/day. The z-score comes from the normal distribution: 1.645 standard deviations covers 95% of outcomes. Expected return is often set to zero for short horizons, a conservative simplification.
What is the difference between 95% and 99% VaR?
The confidence level: 95% VaR is exceeded ~1 day in 20; 99% ~1 day in 100. The 99% figure is larger (here $34,890 vs $24,675). Risk managers use 95%; bank regulators typically require 99%. Higher confidence means a bigger number and fewer expected breaches: choose 99% when the cost of being wrong is severe, 95% for everyday risk monitoring.
How do you scale VaR to multiple days?
Multiply by the square root of days (assuming independent returns): 10-day VaR = daily x sqrt(10). A $24,675 daily VaR becomes ~$78,028 over 10 days. This understates risk if losses cluster, as they do in crises. The square-root rule assumes each day's return is independent; during selloffs, down days follow down days, and actual multi-day losses exceed the scaled figure.
What are the limitations of VaR?
It assumes normal returns (understating fat tails), says nothing about losses beyond the threshold, and can be gamed by tail-risk-heavy strategies. It failed famously in 2008. Pair it with expected shortfall and stress tests. A strategy that loses $1 more than VaR every breach looks identical to one that loses $1 million more; VaR cannot tell them apart, which is exactly its danger.
What is expected shortfall?
The average loss on days when VaR is exceeded: 'when it is bad, how bad is it on average.' It is a coherent risk measure (unlike VaR) and the Basel standard for trading-book capital. Always ask for it alongside VaR.
How is volatility estimated for VaR?
From historical daily returns (e.g., one year of data), exponentially-weighted schemes like RiskMetrics, or implied volatility from options. Each gives different VaR; calm-period estimates understate risk systematically. RiskMetrics weights recent days more heavily, reacting faster to regime changes; plain historical volatility treats last year equally. Implied volatility reflects what options traders expect, not what happened.
What is VaR backtesting?
Counting actual exceedances: at 95% VaR expect ~5% of days to breach. Persistently more breaches means the model underestimates risk. Regulators use traffic-light systems with capital penalties for failing models. Over 250 trading days, expect about 12 to 13 breaches at 95%; green zone is under 5, yellow 5 to 9, red 10+, with real capital consequences for banks in the red.
Can individuals use VaR?
Yes, for position sizing and sleep-at-night checks: size any speculative position so its VaR is money you can lose. Retail brokerages rarely show it, so this calculator fills the gap for concentrated portfolios. A practical rule: no single position's 99% VaR should exceed 2% of your net worth unless you genuinely understand and accept the tail risk.
Does diversification reduce VaR?
Yes, when assets are not perfectly correlated: portfolio VaR is less than the sum of position VaRs. The difference is the diversification benefit. In crashes correlations spike toward 1 and the benefit evaporates, which VaR models often miss. This is why diversified portfolios still crashed in 2008: the diversification VaR assumed was a fair-weather phenomenon.