Value at Risk & Expected Shortfall Calculator

About the Value at Risk & Expected Shortfall Calculator

Value at risk (VaR) is the loss a portfolio would not exceed on, say, 95 or 99 days out of 100, judging by how its holdings moved in the past; expected shortfall (ES, or CVaR) is the average loss on the days beyond it. This calculator works out both for your own holdings from your own price history, three ways: historical (the losses your holdings would have had on each past day), parametric (a normal distribution with the volatility and correlations of your data) and Cornish–Fisher (the normal one corrected for skew and fat tails).

It also shows which holding adds most to the risk (component VaR), the worst stretch of days in your data, your own stress scenarios — a fall you choose for each holding — and a histogram of the daily gains and losses with the VaR and ES marked. Load prices for each holding (or try the sample), enter what each holding is worth now, and choose the confidence and the number of days.

It works for any market and currency. Your files are read in your browser and never uploaded.

Common uses

• Put a figure on how much a portfolio could lose in a day or a week before deciding how much risk to carry.
• See which holding drives most of the risk, and how a hedge or a short position changes it.
• Test your portfolio against a scenario of your own: a 20% fall in shares, a jump in rates, a currency move.
• Compare historical, normal and fat-tailed estimates of the same risk.

The formulas

• Parametric VaR = z_α × σ_P × √(days), where σ_P is the daily standard deviation of the portfolio’s value, worked out from the variances and correlations of your holdings’ returns, and z_α the normal quantile (1.645 at 95%, 2.326 at 99%) — the method of the RiskMetrics Technical Document. Normal ES = σ_P × φ(z_α) ÷ (1 − α) × √(days).
• Historical VaR = minus the (1 − α) percentile of the portfolio’s daily gains and losses (with today’s holdings on each past day); historical ES = minus the mean of the days at or beyond it.
• Cornish–Fisher VaR replaces z_α with z + (z² − 1)S/6 + (z³ − 3z)K/24 − (2z³ − 5z)S²/36, using the skewness S and excess kurtosis K of your data.
• Component VaR of a holding = its value × (Σv)ᵢ ÷ σ_P × z_α × √(days) (less its value × its average daily return × days, when you subtract the average): the components add up to the portfolio’s parametric VaR, and a hedge has a negative one. Component ES splits the historical ES the same way: each holding’s average loss on the days beyond the VaR.
• Expected shortfall at 97.5% is the level the Basel market-risk standard asks banks to use.

Reading the results

• A one-day 95% VaR of 20,000 means that on about 1 day in 20 of your data’s kind, the loss was larger than 20,000; it says nothing about how much larger. The expected shortfall says that: the average loss on those days.
• The days worse than the VaR compare your data with the level: at 95%, about 5 in 100 days are expected beyond it.
• Component VaR shows where the risk comes from: a holding can be a small share of the money and a large share of the risk.
• The worst stretch and your scenarios describe losses beyond the statistics: a VaR is not the largest possible loss.

What it leaves out

Everything not in your price history: events that did not happen in it, gaps between trading days, the cost of selling in a falling market and changes in your holdings. Several-day figures scale one-day ones by the square root of time, which assumes independent days with the same spread. Holdings in other currencies should be entered at their value in one currency; their exchange-rate risk counts only if your price files are in that currency.

Limitations

• It needs a price history of each holding on common dates; the longer the history, the steadier the historical figures.
• One currency: enter every holding at its value in the same currency.
• Linear holdings only: options and other non-linear positions need their own model.
• Hypothetical estimates from past data: not a forecast and not a limit on losses.

Privacy

Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.