Podcast: Matthew Dixon on decomposition of portfolio risk

Decomposing the value-at-risk of a portfolio into its contributing components is important for identifying sources of risk, either by fund manager or factor.

Over the years, several approaches have been proposed, though each has at least one desirable feature missing.

In this episode of Quantcast, Matthew Dixon, assistant professor of applied mathematics at the Illinois Institute of Technology in Chicago, explains the methodology he developed with James Goldcamp, director at HedgeFacts, a financial software house.

“It is suitable for portfolios that hold derivatives, where there are nonlinear dependencies to market risk factors, and moreover is a fast analytic approximation that does not require Monte Carlo simulation,” says Dixon.

They refer to their model as the delta-gamma component VAR, because it is built on the delta-gamma approach in which the second-order effects – namely, those linked to the presence of non-linear factors – are also considered.

Their component VAR is designed to capture the correlation between assets in different sub-portfolios. The resulting VAR scores are additive, meaning the VAR of sub-portfolios sum to the portfolio VAR.

Other commonly used VAR decomposition methods do not have these properties. The marginal VAR of a sub-portfolio, for example, calculated on the difference between the portfolio with and without that sub-portfolio, does not fully capture the assets’ correlation. Incremental VAR, which depends on the weight of sub-portfolio, suffers similar drawbacks. “Incremental VAR entirely neglects correlations,” says Dixon. “When you rely on it you might get completely misleading results on sub-portfolio contributions to risk.” These two measures end up either overestimating or underestimating the contribution to total VAR.

Dixon and Goldcamp’s methodology can be seen as an extension of the classic approach by Philippe Jorion. Jorion’s component VAR, however, is only applicable to linear portfolios, therefore excluding portfolios holding derivatives.

Dixon is keen on developing a similarly rigorous method for expected shortfall. “We just consider VAR here, and that is rather limited. Expected shortfall is more widely respected, it’s more robust and it’s a coherent risk measure so one area we are working on is extending the methodology to expected shortfall.”

Index

00:00 Introduction to the decomposition of value-at-risk

07:42 What makes it difficult for nonlinear factors, such as derivatives?

11:02 Delta-gamma-theta approximation

14:15 Comparison to Jorion’s linear decomposition method

17:18 Cornish-Fisher expansion

20:43 Comparison with other common methods and results

29:20 Industry applications

32:30 Extension to expected shortfall

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