Portfolio Value at Risk (VaR

Quantitative Finance & Market Risk Management: VaR vs. Expected Shortfall (CVaR)

Value at Risk (VaR), originally popularized by J.P. Morgan's RiskMetrics in 1994, is the standard industry metric for quantifying downside portfolio market risk:

• Understanding the VaR Statement: "We are 95% confident that the portfolio will not lose more than 49,248 over the next 10 trading days."

• The Fat-Tail Limitation of VaR: VaR tells you nothing about what happens during the worst 5% of trading days (the tail beyond the cutoff).

• Expected Shortfall: Recommended under Basel III / FRTB regulations, Conditional VaR measures the average loss conditional on the fact that VaR has already been breached (sub-additive and coherent risk measure).

How to Use This Calculator

Enter your Total Portfolio Investment Capital () (e.g. 1,000,000), Statistical Confidence Level — choose from options such as 90% Confidence (Z = 1.2816 | α = 10%), 95% Confidence (Z = 1.6449 | α = 5% [RiskMetrics Standard]), 97.5% Confidence (Z = 1.9600 | α = 2.5% [FRTB Basel III]), Holding Period Horizon (Trading Days) (e.g. 10 (1-Day, 5-Day Week, 10-Day Basel III, or 21-Day Month)), Expected Annual Portfolio Return (%) (e.g. 8.0 (8% expected annual return)), and Annualized Volatility / Standard Deviation (σ %) (e.g. 16 (16% annualized portfolio volatility)). Results update instantly as you type — no submit button or page reload required. Adjust any value to compare scenarios side by side.

The Formula

Quantitative Portfolio Risk Management \& Basel III VaR equations:

Daily Volatility: σ_daily = σ_annual√(252), Daily Mean: μ_daily = μ_annual252

Horizon Scaled Parameters: σ_t = σ_daily × √(t), μ_t = μ_daily × t

Parametric Value at Risk (VaR_1-α) = V_0 × (Z_α · σ_t - μ_t)

Conditional VaR (Expected Shortfall CVaR) = V_0 × (φ(Z_α)α · σ_t - μ_t)

Basel III Regulatory Scaling: VaR_10-day = VaR_1-day × √(10)

Worked Example

For example, evaluating a \1,000,000.00 investment portfolio with 16.0\% annual volatility (1.008\% daily vol), 8.0\% expected annual return, at \ over a 10-day Basel horizon): Scaled 10-day volatility is 3.187\%. The 10-Day 95% Parametric VaR is \49,248.00 (4.92\% of portfolio). Conditional VaR (Expected Shortfall) is \62,561.00 (6.26\%), and the 1-Day 99% Regulatory VaR is \23,137.00.

Understanding Your Result

Evaluate your result against the specific financial decision driving this calculation. Small input differences can create large output swings — run two or three scenarios (conservative, base, optimistic) to understand the range of outcomes. For decisions involving more than a month's income, validate your result against a second source or consult a certified financial planner (CFP) or CPA depending on the tax implications.