Currency Volatility Risk Calculator
Computes the Value at Risk (VaR) for a foreign currency position given its annual volatility, confidence level, and holding period. Use it to quantify worst-case FX losses for risk management or regulatory reporting.
About this calculator
Value at Risk (VaR) estimates the maximum loss a portfolio is unlikely to exceed over a given time horizon at a specified confidence level. For a currency position under the parametric (variance-covariance) method, the formula is: VaR = Position Size × (Annual Volatility / 100) × Z × √(Time Horizon / 365), where Z is the standard normal z-score corresponding to the chosen confidence level (e.g., Z = 1.645 for 95%, Z = 1.96 for 97.5%, Z = 2.326 for 99%). The square-root-of-time rule scales annual volatility down to the desired holding period, assuming daily returns are independent and normally distributed. A VaR of $50,000 at 99% confidence over 10 days means there is only a 1% chance of losing more than $50,000 in that period.
How to use
You hold a $500,000 EUR/USD position. Annual volatility is 8%, confidence level z-score is 1.96 (97.5%), and the time horizon is 10 days. Step 1: Scale volatility to horizon: 0.08 × √(10/365) = 0.08 × 0.16529 = 0.013223. Step 2: VaR = $500,000 × 0.013223 × 1.96 = $500,000 × 0.025917 ≈ $12,958. At 97.5% confidence, you should not lose more than approximately $12,958 on this position over the next 10 days under normal market conditions.
Frequently asked questions
What does a 99% confidence level mean in currency VaR calculations?
A 99% confidence level means the model predicts that losses will not exceed the calculated VaR value on 99 out of every 100 trading days — or equivalently, there is a 1% probability of losses exceeding VaR on any given day. The corresponding z-score used in the formula is approximately 2.326. It is important to understand that VaR says nothing about the size of losses beyond the threshold — the remaining 1% of outcomes (tail risk) can be far larger than the VaR figure itself. This limitation is why institutions often complement VaR with stress testing and Expected Shortfall (CVaR) measures.
How does annual volatility affect the currency Value at Risk estimate?
Annual volatility is the primary driver of VaR — it enters the formula linearly, so doubling volatility doubles the VaR estimate. Currency volatility is typically measured as the annualized standard deviation of daily log-returns, derived from historical price data or implied from options markets. Major currency pairs like EUR/USD might have annual volatility of 6–10%, while emerging-market pairs can exceed 15–20%. During market stress events, realized volatility can spike dramatically above historical averages, meaning historical VaR models may significantly understate actual risk. Traders should update volatility inputs frequently and consider using stressed VaR scenarios.
Why does the square root of time appear in the VaR formula for currency risk?
The square-root-of-time rule comes from statistics: if daily price changes are independent and identically distributed, the standard deviation of returns over T days equals the daily standard deviation multiplied by √T. Since annual volatility represents roughly 252 trading days of compounded risk, scaling it to a shorter horizon requires dividing by √252 (or equivalently multiplying by √(T/365) for calendar days). This rule is a simplifying assumption — in reality, currency returns exhibit autocorrelation, fat tails, and volatility clustering, which can make the square-root rule inaccurate over longer horizons. Despite its limitations, it remains the standard approximation used in Basel regulatory frameworks.