Value at Risk (VaR): Measure Investment Risk Simply

Value at Risk (VaR) answers the most practical question in risk management: "How much could I lose?" More precisely, the VaR of a portfolio at confidence level c over a horizon T is the loss threshold that will not be exceeded with probability c. A 1-day 95% VaR of ₹20,000 means losses should stay below ₹20,000 on 95 out of 100 days.

This matters because VaR compresses an entire portfolio's market risk into a single rupee number that managers, regulators, and boards can act on. It sets trading limits, determines bank capital under the Basel accords, and appears in every fund risk report.

Key Concepts

• Confidence level: typically 95% or 99%; higher confidence means a larger VaR number and fewer expected breaches.
• Horizon: the period the VaR covers, usually 1 day for trading or longer for strategic risk; risk scales with the square root of time.
• Parametric VaR: assumes returns follow a known distribution (often normal) and computes VaR from volatility; fast but assumption-heavy.
• Historical VaR: reads the loss threshold directly from past returns; no distribution assumed, but history may not repeat.
• Expected shortfall: the average loss beyond the VaR threshold; the coherent complement that VaR itself omits.

Formulas

Parametric one-period VaR under normal returns: VaR_c = z_c × σ × V, where z_c is the standard normal quantile (1.645 for 95%, 2.326 for 99%), σ is the return volatility over the horizon, and V is the portfolio value. Time scaling: σ_T = σ_daily × √T, so a 10-day VaR is √10 ≈ 3.16 times the 1-day VaR. Assumes normally distributed returns and stable volatility over the horizon.

Worked Example

A ₹10,00,000 equity portfolio has daily return volatility σ = 1.2%. The 1-day 95% VaR is 1.645 × 0.012 × 10,00,000 = ₹19,740. Interpretation: we are 95% confident the portfolio will not lose more than ₹19,740 tomorrow; equivalently, we expect to breach this threshold roughly 1 day in 20, about 12 to 13 trading days per year. The 1-day 99% VaR is 2.326 × 0.012 × 10,00,000 = ₹27,912, larger because higher confidence demands a wider safety band. Scaling to a 10-day horizon: 19,740 × √10 = 19,740 × 3.16228 = ₹62,423.40. Note what VaR does not say: on the 5% of days when losses exceed ₹19,740, they could exceed it by any amount, which is why expected shortfall and stress tests accompany VaR in practice.

Common Misconceptions

• VaR is the maximum possible loss. It is a threshold with a stated exceedance probability; the tail beyond it is unmeasured, and real crises have produced losses many multiples of VaR.
• VaRs add up across desks. Portfolio VaR is generally less than the sum of standalone VaRs because of diversification; simple addition overstates risk when positions offset each other.
• A VaR that backtests well means the portfolio is safe. Backtesting checks the model's calibration, not the future; VaR models famously failed in 2008 because volatility and correlations spiked together.

Real-World Applications

VaR sets trader position limits, computes regulatory market-risk capital for banks under Basel rules, sizes hedge-fund risk budgets, and anchors the risk sections of fund prospectuses and annual reports.

Value at Risk turns "how much could I lose" into one number tied to a confidence level and a horizon, but it must be paired with tail measures like expected shortfall, because VaR is silent about how bad the bad days get.