Calculating Value At Risk

When To Use

Computing portfolio VaR at specified confidence levels (typically 95% or 99%) and holding periods (1-day, 10-day)
Comparing risk estimates across parametric (variance-covariance), historical simulation, and Monte Carlo approaches
Backtesting an existing VaR model against realized P&L to assess model adequacy
Supporting regulatory capital calculations under Basel framework internal models approach [VERIFY: Basel III/IV applicability for jurisdiction]
Producing risk reports for portfolio managers, risk committees, or regulators

Portfolio composition: Asset classes, positions, notional values, currency denominations
Market data: Historical returns series (minimum 1 year for historical simulation; 3-5 years preferred), closing prices, FX rates, yield curves
Parameters: Confidence level (e.g., 99% for regulatory, 95% for internal), holding period, lookback window length
Correlation/covariance data: Correlation matrix or raw return series for parametric method; decay factor if using exponentially weighted moving average (EWMA)
Distribution assumptions: Normal, Student-t, or empirical for parametric; number of simulations and random seed for Monte Carlo
Benchmark P&L: Realized daily P&L series for backtesting (minimum 250 trading days)

Collect and align time series to consistent trading calendar (handle holidays, missing data)
Compute log returns or arithmetic returns (state choice and rationale)
Check for stale prices, outliers, and corporate actions; flag gaps with [VERIFY]
Convert multi-currency positions to base currency using consistent FX rates

Parametric (Variance-Covariance): Best for linear portfolios (equities, FX). Compute portfolio variance as w'Σw. VaR = z_α × σ_p × √(holding period). Note: assumes normal returns — underestimates tail risk for fat-tailed distributions
Historical Simulation: Rank historical portfolio P&L; VaR = the (1-α) percentile loss. No distributional assumption required. Sensitive to lookback window choice — shorter windows react faster to regime changes
Monte Carlo: Fit stochastic model to risk factors, simulate N paths (10,000+ recommended), revalue portfolio on each path, extract percentile. Required for portfolios with options or path-dependent instruments. Specify random number generator and variance reduction technique (antithetic variates, importance sampling)

Run selected method(s); compute VaR at each requested confidence level and holding period
For 10-day VaR from 1-day: use square-root-of-time scaling only if returns are i.i.d. [VERIFY: whether autocorrelation or volatility clustering invalidates scaling rule]
Calculate Component VaR and Marginal VaR to attribute risk to individual positions or asset classes
If running multiple methods, present side-by-side comparison table

Compare realized P&L breaches against VaR predictions over the test window
Kupiec POF test: Binomial test on number of exceptions vs. expected count — report p-value
Christoffersen test: Check for independence of exceptions (clustered breaches indicate model failure)
Classify model in Basel traffic-light zones: Green (0-4 exceptions at 99%/250 days), Yellow (5-9), Red (10+) [VERIFY: current regulatory thresholds for applicable regime]
Document exception dates and magnitudes; investigate any breach exceeding 2× VaR

Compute Conditional VaR (Expected Shortfall / CVaR) as the average loss beyond VaR threshold
Run sensitivity on key parameters: vary lookback window (250, 500, 750 days), confidence level, and decay factor
Report how VaR changes under stressed correlation assumptions (e.g., correlations → 1 in crisis)

Produce a VaR Calculation Worksheet containing:

Summary table: VaR figures by method, confidence level, and holding period
Component VaR breakdown: Top 10 risk contributors by position or asset class
Backtest results: Exception count, Kupiec p-value, Christoffersen p-value, traffic-light classification
CVaR / Expected Shortfall: For each method and confidence level
Sensitivity table: VaR under alternative parameter choices
Assumptions log: Every distributional, data, and modeling assumption stated explicitly
Methodology narrative: Plain-language explanation of approach suitable for risk committee review

VaR at 99% must exceed VaR at 95% for the same method and holding period — flag if violated
Component VaR values should sum approximately to diversified portfolio VaR (exact for parametric; approximate for simulation methods)
Monte Carlo VaR should converge as simulation count increases — run at 10K and 50K and confirm difference < 5%
Backtest exception rate should fall within 2 standard deviations of expected rate — otherwise flag model inadequacy
Confirm holding-period scaling is appropriate: if significant autocorrelation exists in returns, do not apply square-root-of-time rule without adjustment
Cross-check: historical simulation VaR should be broadly consistent with parametric VaR for linear portfolios with near-normal returns; large divergence signals fat tails or non-linearity
All market data sources and observation dates must be cited; any interpolated or proxy data marked [VERIFY]