Portfolio Risk 6 min read Updated July 2026

Portfolio VaR Explained: Value at Risk with Real Covariance Data

Understand how Value at Risk works, why flat volatility assumptions understate tail risk, and how ClaudeFinLab computes portfolio VaR using real historical covariance through Claude.

What is Value at Risk?

Value at Risk (VaR) estimates the maximum expected loss of a portfolio over a specific time horizon at a given confidence level. For example, a 1-day 95% VaR of $50,000 means: there is a 95% probability that the portfolio will not lose more than $50,000 in a single day.

VaR is used by banks, hedge funds, and asset managers to:

  • Set risk limits and capital buffers
  • Report market risk to regulators (Basel III/IV)
  • Monitor daily position risk against thresholds
  • Compare risk across strategies or portfolios

The Three VaR Methods

1. Parametric VaR (Variance-Covariance)

Assumes returns are normally distributed and uses a covariance matrix to compute portfolio variance. Fast but underestimates tail risk because real returns have fat tails.

Formula: VaR = Z × σ_portfolio × Portfolio Value, where Z is the z-score for the confidence level (1.645 for 95%, 2.326 for 99%).

2. Historical Simulation VaR

Replays actual historical returns against the current portfolio and reads the loss at the required percentile. No distribution assumption — but requires sufficient historical data and is backward-looking.

3. Monte Carlo VaR

Simulates thousands of return paths using a statistical model and reads the loss at the required percentile. Most flexible but computationally expensive.

ClaudeFinLab approach: The Portfolio VaR skill uses real historical covariance data sourced via yfinance — not flat single-asset volatility assumptions. This captures actual correlations between assets, giving a more accurate portfolio-level risk estimate.

Why Flat Volatility is Wrong

A common shortcut is to estimate portfolio VaR as a weighted average of individual asset volatilities. This ignores correlations between assets, which is the entire point of diversification.

Example: A portfolio of two assets, each with 20% annual vol, would have a portfolio vol of:

  • 20% if they are perfectly correlated (ρ = 1) — no diversification benefit
  • 14.1% if they are uncorrelated (ρ = 0) — significant diversification
  • 0% if they are perfectly negatively correlated (ρ = −1) — full hedge

Using the full covariance matrix captures all pairwise correlations. Flat volatility gives the worst-case answer regardless of how the portfolio is actually structured.

Computing VaR Through Claude

{
  "mcpServers": {
    "claudefinlab-portfolio": {
      "url": "https://claudefinancelab.com/portfolio/sse",
      "headers": { "Authorization": "Bearer YOUR_API_KEY" }
    }
  }
}

Then: "Compute 1-day 95% VaR for a portfolio: $500K in AAPL, $300K in MSFT, $200K in BND. Use 252 days of historical covariance."

The tool returns: portfolio VaR in dollars and percent, component VaR by position, marginal VaR for each asset, and the correlation matrix used.

VaR Limitations

  • VaR doesn't tell you what the loss will be beyond the confidence threshold — use CVaR (Expected Shortfall) for tail risk measurement
  • Historical VaR assumes the past predicts the future — it can miss unprecedented events
  • VaR is not subadditive in all cases — combining two portfolios can produce a VaR larger than the sum of parts
  • 1-day VaR assumes positions can be liquidated overnight — liquidity-adjusted VaR is needed for illiquid positions

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