# Attributing Portfolio Value at Risk: Relations with Component VaR, Marginal VaR, and Incremental VaR

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Consider a simple portfolio worth , consisting of two assets. Its value at risk, , depends on the initial position size of one of the assets (blue arrow). A hypothetical change in the position size of this asset will trace out a new hypothetical portfolio, plotted as the blue curve.

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Contributed by: Pichet Thiansathaporn (July 2012)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: , as a measure of VaR's sensitivity to small changes in portfolio holdings, is less reliable where VaR is nonlinear, seen as a large divergence between the blue portfolio VaR curve and its linear interpolation (slope of gray triangle)

Snapshot 2: portfolio has no diversification benefit (vanishing ) when assets are perfectly correlated (), in which case attains its maximum value

Snapshot 3: diversification benefit is maximized (largest ) when assets are perfectly contrarian (), in which case attains a minimum value

Reference

[1] P. Jorion, *Value at Risk:* *The New Benchmark for Managing Financial Risk*,* *2nd ed., New York: McGraw-Hill, 2001 pp. 153–163.