Model daily returns, weights, volatility, and correlation easily. Choose confidence levels and horizons for decisions. Get VaR and ES in percent and currency instantly.
Use parametric or Monte Carlo when you have weights, mean returns, and volatility. Use historical when you have a return series.
This sample matches the default inputs. Replace with your portfolio values.
| Asset | Weight | Mean (daily %) | Volatility (daily %) |
|---|---|---|---|
| Asset A | 0.50 | 0.03 | 1.20 |
| Asset B | 0.30 | 0.02 | 0.90 |
| Asset C | 0.20 | 0.01 | 0.60 |
Portfolio return: rp = \(\sum_i w_i r_i\). Mean: \(\mu_p = \sum_i w_i \mu_i\).
Covariance: \(\Sigma_{ij} = \sigma_i\sigma_j\rho_{ij}\). Portfolio variance: \(\sigma_p^2 = w^T\Sigma w\).
Parametric VaR: with tail probability \(\alpha = 1-c\), \(\text{VaR} = \max(0, - (\mu_h + \sigma_h z_\alpha))\), where \(z_\alpha\) is the normal quantile.
Expected Shortfall: \(\text{ES} = \max(0, -\mu_h + \sigma_h \phi(z_\alpha)/\alpha)\), with \(\phi\) the normal density.
Historical VaR: \(\text{VaR} = \max(0, -q_\alpha)\), where \(q_\alpha\) is the empirical \(\alpha\)-quantile of returns.
Value at Risk estimates a loss threshold that should not be exceeded with the selected confidence. If 1‑day VaR is 1.8%, a 1,000,000 portfolio implies 18,000 potential loss on most days. Compare VaR (%) to trading limits and VaR (currency) to cash buffers. Expected Shortfall complements VaR by averaging tail losses beyond the threshold, highlighting how severe losses may be during stress. Track both metrics when volatility changes quickly. For intraday desks, recalc after large moves, review positions, and adjust limits accordingly.
Confidence controls the tail probability α = 1 − c. A move from 95% to 99% typically increases VaR because the quantile shifts deeper into the loss tail. Horizon assumptions matter: this calculator scales mean linearly and volatility by √h in parametric and Monte Carlo, and optionally scales historical VaR the same way. Use multi‑day horizons for liquidity planning, but verify scaling against actual holding periods, rebalancing frequency, and market closure risk.
Portfolio volatility depends on covariance, not just individual asset risk. Entering a full correlation matrix allows realistic diversification and concentration effects. High positive correlations push σp upward, raising VaR and ES, while low or negative correlations reduce them. Use normalization so weights sum to one, then test sensitivity by varying ρ. When correlations are unstable, apply conservative floors, stress correlations toward 1, and compare results to understand diversification fragility.
Historical simulation relies on the return series you paste. More observations reduce estimation noise; 250–1,000 daily points is common for baseline monitoring. Clean the series by removing obvious data errors, aligning calendars, and using consistent return definitions. Monte Carlo results depend on simulation count and distributional assumptions; increase simulations for stable percentiles, set a seed for reproducibility, and document parameter sources for μ and σ.
VaR is not a worst‑case loss and will be breached roughly α of the time under model assumptions. Backtest by counting exceedances over a rolling window and investigate clusters. Establish escalation thresholds, such as repeated breaches or large ES jumps. Use exports for audit trails, include method selection rationale, and review inputs during regime shifts. Combine VaR with stress tests, scenario analysis, and liquidity metrics for a more resilient risk framework.
VaR is a loss threshold at a chosen confidence, such as the 95% quantile. Expected Shortfall averages losses beyond that threshold, so it is more sensitive to extreme tail events and usually larger than VaR.
Use parametric when returns are roughly normal and you have weights, mean, volatility, and correlation. Use historical when you trust an empirical return series. Use Monte Carlo to reduce quantile noise and run sensitivity, but note its distribution assumptions.
VaR scales with portfolio exposure. If weights do not sum to one, you may be implicitly levered or under-invested, changing variance and loss size. Normalization forces weights to sum to one so results reflect the intended allocation mix.
Five points is a minimum, but it is not robust. For daily monitoring, 250 points (about one trading year) is a common baseline. For more stable tail estimates, use 500–1,000 points and review outliers and data gaps.
Yes, but keep units consistent. If you paste weekly or monthly returns, set horizon days to match that period and avoid sqrt-time scaling unless you have validated it for your frequency. Interpret μ and σ inputs with the same frequency.
Portfolio risk depends on covariances across assets. When correlations rise during stress, diversification shrinks and VaR can jump even if single-asset volatility is unchanged. Testing different correlation assumptions helps reveal concentration and contagion risk.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.