What is the difference between Historical, Parametric and Monte Carlo VaR?

Historical VaR uses the empirical distribution of past returns, Parametric (Variance–Covariance) VaR assumes returns are normally distributed and uses mean and standard deviation, while Monte Carlo VaR simulates many random return paths from an assumed distribution. Historical is simple and model-free, Parametric is fast but sensitive to normality assumptions, and Monte Carlo is flexible but computationally heavier.

Is VaR the worst-case loss I can experience?

No. VaR is not a worst-case loss; it is a quantile of the loss distribution. Losses worse than VaR are possible and can be substantial. For that reason, many risk managers also look at Expected Shortfall (also called Conditional VaR or CVaR), which measures the average loss beyond the VaR threshold.

How much historical data should I use for VaR?

There is no single correct answer, but a common practice is to use at least 1–3 years of daily data (250–750 observations). More data gives more stable estimates but may mix different market regimes. For very short-term trading strategies, a shorter but more recent window may be more relevant.

Can I use this VaR calculator for a single stock or crypto asset?

Yes. You can use this calculator for a single position or an entire portfolio. For a single asset, provide its historical returns or prices and your position size. For a portfolio, you can use portfolio-level returns or approximate by using a representative index or ETF.

Value at Risk (VaR) Calculator

Q: What is Value at Risk (VaR)?

Value at Risk (VaR) is a risk metric that estimates the maximum expected loss of a portfolio over a given time horizon at a specified confidence level. For example, a 1-day 99% VaR of $1,000 means that on 99% of days you expect to lose less than $1,000; on 1% of days you may lose more.

Estimate portfolio Value at Risk (VaR) using historical, parametric (variance–covariance) and Monte Carlo methods, with configurable confidence level and horizon.

VaR Calculator

Portfolio value

Total market value of the position or portfolio.

Confidence level

Higher confidence → larger VaR (more conservative).

Time horizon (days)

VaR is scaled from 1-day to this horizon using the square-root-of-time rule.

Method

Choose how VaR is estimated from your data.

Historical data (optional)

| Mode: returns

Paste a column of daily returns in % or prices. The calculator automatically detects separators (comma, semicolon, space, newline).

Results

Value at Risk

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Expected Shortfall (CVaR)

Average loss beyond VaR threshold (same horizon & confidence).

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What is Value at Risk (VaR)?

Value at Risk (VaR) is a widely used risk measure that answers the question: “What is the maximum loss I can expect over a given time horizon, with a given confidence level?”

Example: a 1‑day 99% VaR of $10,000 means that, based on your model and data, you expect to lose no more than $10,000 on 99% of days. On the remaining 1% of days, losses may be larger.

VaR methods supported by this calculator

1. Historical VaR

Historical VaR uses the empirical distribution of past returns. It makes no parametric assumption about the shape of returns (no normality assumption).

Collect a series of historical daily returns $ r_1, r_2, \dots, r_n $.
Sort them from worst to best.
Pick the appropriate quantile for your confidence level.

For a confidence level $ \alpha $ (e.g. 0.99) and loss $ L = -r \cdot V $:
$ \text{VaR}_\alpha = \text{quantile}_{1-\alpha}(L) $

This calculator converts your returns or prices into daily returns, then takes the empirical quantile corresponding to $ 1 - \alpha $.

2. Parametric (Variance–Covariance) VaR

Parametric VaR assumes returns are normally distributed with mean $ \mu $ and standard deviation $ \sigma $. For a 1‑day horizon:

$ \text{VaR}_{\alpha,1\text{d}} = \big( z_\alpha \sigma - \mu \big) \times V $
where $ z_\alpha $ is the standard normal quantile (e.g. 2.33 for 99%).

For a horizon of $ T $ days, we apply the square‑root‑of‑time rule:

$ \sigma_T \approx \sigma \sqrt{T}, \quad \mu_T \approx \mu T $
$ \Rightarrow \text{VaR}_{\alpha,T} = \big( z_\alpha \sigma \sqrt{T} - \mu T \big) \times V $

3. Monte Carlo VaR

Monte Carlo VaR simulates many random return scenarios from an assumed distribution (here, normal with mean $ \mu $ and volatility $ \sigma $), then computes the empirical loss quantile.

Choose $ \mu $, $ \sigma $ (or estimate them from data).
Simulate many daily returns for the chosen horizon.
Compute simulated losses and take the $ 1-\alpha $ quantile.

This method is flexible (you can extend it to non‑normal distributions or path‑dependent products), but more computationally intensive.

How this VaR calculator works

Input mode: you can paste either daily returns (in %) or prices.
Automatic parsing: the tool accepts commas, semicolons, spaces, and newlines.
Scaling: VaR is reported for your chosen horizon using the square‑root‑of‑time rule.
Expected Shortfall (CVaR): we also estimate the average loss beyond the VaR threshold.

Interpreting the output

VaR (currency): maximum expected loss in money terms.
VaR (%): same loss as a percentage of portfolio value.
CVaR: average loss in the worst $ (1-\alpha) $ fraction of cases.
Data summary: number of observations, mean, volatility, min/max, skewness.

Limitations and good practices

VaR is not a worst‑case loss; extreme events can be much worse.
Historical VaR assumes the past is representative of the future.
Parametric VaR is sensitive to the normality assumption and underestimates fat tails.
Always complement VaR with stress tests, scenario analysis, and Expected Shortfall.

FAQ

Is a higher VaR always bad?

Not necessarily. Higher VaR usually reflects higher risk, but it may be acceptable if it is compensated by higher expected return and fits your risk appetite and capital constraints.

What confidence level should I use?

Common choices are 95% and 99%. Trading desks and regulators often use 99% 1‑day VaR; asset managers may look at 95% weekly or monthly VaR. Higher confidence levels focus on rarer, more extreme losses.

Can I use this for intraday VaR?

The calculator is built around daily data and the square‑root‑of‑time rule. For intraday VaR, you would need high‑frequency data and a model that accounts for intraday volatility patterns.