var calculation

What is VaR?

Value at Risk (VaR) is a risk metric used to estimate how much a portfolio could lose over a specific period at a given confidence level. For example, if your 1-day 95% VaR is $2,000, that means your model says there is a 95% chance losses will be less than $2,000 over one day, and a 5% chance losses could be larger.

VaR is popular because it expresses risk in a single number that investors, analysts, and executives can quickly understand. It is commonly used in asset management, treasury functions, hedge funds, and banking risk management.

The Formula Used in This Calculator

This page uses the parametric VaR approach with normally distributed returns:

• z = z-score for your confidence level (e.g., 1.645 for 95%).
• σ = daily volatility (as a decimal).
• μ = average daily return (as a decimal).
• t = time horizon in days.

If the calculated VaR% is negative (which can happen with very high positive expected returns), this tool floors VaR at zero because risk of loss cannot be negative.

Step-by-Step Example

Suppose you enter:

• Portfolio value = $100,000
• Confidence level = 95%
• Time horizon = 1 day
• Average daily return = 0.03%
• Daily volatility = 1.5%

The calculator converts percentage inputs to decimals, computes the z-score, scales volatility by the square root of time, and then estimates your VaR. The result gives both a dollar amount and a percentage of your portfolio.

How to Choose Better Inputs

1) Portfolio Value

Use current market value of all positions included in your risk scope. If you only want equity exposure, exclude cash and bonds; if you want total account risk, include everything.

2) Confidence Level

Common choices are 90%, 95%, and 99%. Higher confidence means a larger VaR estimate because you are looking deeper into the loss tail.

3) Time Horizon

Match horizon to your decision cycle. A trader might use 1-day VaR; a long-term allocator may watch weekly or monthly risk.

4) Mean Return and Volatility

These are usually estimated from historical returns. Volatility can change quickly in stressed markets, so a rolling estimate is often better than a fixed long-run average.

VaR Methods Compared

There are three common ways to calculate VaR:

• Parametric (this tool): Fast and simple, but assumes return distribution shape.
• Historical VaR: Uses real past returns and fewer distribution assumptions.
• Monte Carlo VaR: Simulates many future paths and can model complex portfolios.

For plain portfolios, parametric VaR is often enough for a first pass. For options, nonlinear payoffs, or high-stress planning, historical or Monte Carlo methods are usually preferred.

How to Interpret the Result Correctly

A VaR output is not a worst-case number. It is a threshold number.

• It tells you the loss level not exceeded with the selected confidence.
• It does not tell you how large losses can become beyond that threshold.
• It does not guarantee outcomes; it is a model-based estimate.

Key Limitations of VaR

• Tail blindness: VaR ignores how severe losses are past the confidence cutoff.
• Model risk: Wrong assumptions (normality, stable volatility, stable correlations) produce misleading outputs.
• Regime shifts: Calm-period data can underestimate crisis-period risk.
• Liquidity effects: VaR may not capture widening spreads and forced selling costs.

What to Use Alongside VaR

For practical risk management, combine VaR with:

1. Expected Shortfall (CVaR): average loss in the tail beyond VaR.
2. Stress Tests: scenario shocks such as rate spikes, crashes, and volatility jumps.
3. Max Drawdown: peak-to-trough loss over a period.
4. Position Limits: controls by sector, factor, and concentration.

A Practical Workflow

1. Calculate daily VaR for the total portfolio.
2. Break risk down by strategy, sector, or asset class.
3. Track VaR trends over time (not just one reading).
4. Compare model forecasts against realized outcomes.
5. Update assumptions and methods when market conditions shift.

Final Thoughts

VaR calculation is best viewed as a dashboard indicator, not a crystal ball. It is useful, fast, and widely adopted, but strongest when paired with scenario analysis and disciplined position management. Use this calculator as a starting point for understanding risk, then layer on deeper tools for decisions that matter.