Value at Risk Methods and Portfolio Risk Contributions

Summary

The article explains Value at Risk (VaR) as a loss threshold for a portfolio over a specified horizon and confidence level. It distinguishes losses measured relative to the expected value from absolute losses, then describes historical or non-parametric estimation from past returns, parametric estimation under an assumed return distribution, and Monte Carlo simulation. Its examples use daily return observations and compare historical and normal-model estimates, illustrating how the chosen method and definition affect the reported VaR.

For portfolios, the article relates risk to asset weights, volatilities, and covariances. It introduces marginal VaR as sensitivity to a position change, incremental VaR as the effect of a set of changes, and component VaR as an allocation of total risk across holdings. The treatment is partly incomplete in the supplied text, and the examples rely on distributional assumptions or historical observations. VaR is a threshold, not a maximum possible loss; losses can exceed it, and the article points readers toward expected shortfall for further tail-risk analysis.

Key ideas

• VaR estimates a loss threshold for a chosen confidence level and time horizon, rather than the worst possible loss.
• Historical VaR reads a loss quantile from observed returns without assuming a distribution.
• Parametric VaR uses a return-distribution assumption and scales risk using portfolio volatility and the time horizon.
• Monte Carlo VaR estimates the loss threshold from simulated scenarios.
• Marginal, incremental, and component VaR describe sensitivity, portfolio changes, and asset-level contributions to total risk.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.