Multi-Currency Portfolio Risk Calculator
Estimate the total volatility-adjusted risk of a multi-currency portfolio holding USD, EUR, and GBP positions. Use it to understand how correlations between currencies reduce or amplify overall portfolio risk.
About this calculator
Portfolio risk across multiple currency positions is not simply the sum of individual risks — correlations between currencies partially offset each other. For three positions the portfolio volatility formula is: σ_p = √[ (w₁σ₁)² + (w₂σ₂)² + (w₃σ₃)² + 2ρ(w₁σ₁)(w₂σ₂) + 2ρ(w₁σ₁)(w₃σ₃) + 2ρ(w₂σ₂)(w₃σ₃) ], where w₁, w₂, w₃ are the dollar-value positions, σ₁, σ₂, σ₃ are the annualised volatilities of each currency, and ρ is the average pairwise correlation. The result is expressed in dollars of annualised risk. A correlation of 0 means currencies move independently; a correlation of 1 means they move together, producing no diversification benefit. Negative correlations can reduce total risk below any single position's risk in isolation. This measure is analogous to the portfolio standard deviation used in equity risk management.
How to use
Suppose USD position = $100,000 (σ = 5%), EUR = $80,000 (σ = 7%), GBP = $60,000 (σ = 6%), average correlation ρ = 0.4. Compute each weighted volatility: USD term = 100,000 × 0.05 = $5,000; EUR = 80,000 × 0.07 = $5,600; GBP = 60,000 × 0.06 = $3,600. Variance = 5000² + 5600² + 3600² + 2(0.4)(5000)(5600) + 2(0.4)(5000)(3600) + 2(0.4)(5600)(3600) = 25,000,000 + 31,360,000 + 12,960,000 + 22,400,000 + 14,400,000 + 16,128,000 = 122,248,000. Portfolio risk = √122,248,000 ≈ $11,057 annualised.
Frequently asked questions
How does currency correlation affect the total risk of a multi-currency portfolio?
When currency pairs are positively correlated — meaning they tend to move in the same direction — losses on one position are often accompanied by losses on others, increasing total portfolio risk. Conversely, low or negative correlations provide diversification, so a loss in one currency may be offset by a gain in another. The cross-product terms (2ρσᵢσⱼwᵢwⱼ) in the variance formula capture this relationship mathematically. A portfolio manager who ignores correlations and simply sums individual risks will overestimate risk when correlations are negative and dangerously underestimate it when correlations spike toward 1 during market stress.
What is the difference between currency volatility and currency portfolio risk?
Currency volatility refers to the price variability of a single currency pair, typically expressed as an annualised standard deviation of returns. Portfolio risk, by contrast, accounts for the combined effect of all positions simultaneously, incorporating both their individual volatilities and the correlations between them. A large position in a low-volatility currency can contribute more risk than a small position in a high-volatility currency, depending on correlations with the rest of the portfolio. Portfolio risk is always less than or equal to the weighted sum of individual volatilities (unless all correlations equal 1), reflecting the diversification benefit of holding multiple positions.
How should a risk manager use annualised portfolio currency risk to set trading limits?
Annualised portfolio risk in dollar terms can be scaled to any horizon using the square-root-of-time rule: daily risk ≈ annualised risk / √252, weekly ≈ annualised / √52. This daily figure feeds directly into Value-at-Risk (VaR) calculations — for example, a 1-day 99% VaR ≈ 2.33 × daily risk. Risk managers set position limits so that VaR stays within board-approved thresholds. When correlations rise during crises, recalculating the portfolio risk with updated inputs quickly shows whether limits are being breached. Stress-testing with correlation = 1 gives a worst-case undiversified risk figure that complements the base-case calculation.