Coherent Measurement of Factor Risks

53 Pages Posted: 30 May 2006

See all articles by Alexander S. Cherny

Alexander S. Cherny

Moscow State University

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Date Written: May 2, 2006


We propose a new procedure for the risk measurement of large portfolios.

It employs the following objects as the building blocks:

- coherent risk measures introduced by Artzner, Delbaen, Eber, and Heath;

- factor risk measures introduced in this paper, which assess the risks driven by particular factors like the price of oil, S&P500 index, or the credit spread;

- risk contributions factor risk contributions, which provide a coherent alternative to the sensitivity coefficients.

We also propose two particular classes of coherent risk measures called Alpha VAR and Beta VAR, for which all the objects described above admit an extremely simple empirical estimation procedure. This procedure uses no model assumptions on the structure of the price evolution.

Moreover, we consider the problem of the risk management on a firm's level. It is shown that if the risk limits are imposed on the risk contributions of the desks to the overall risk of the firm (rather than on their outstanding risks) and the desks are allowed to trade these limits within a firm, then the desks automatically find the globally optimal portfolio.

Keywords: Alpha VAR, Beta VAR, capital allocation, coherent risk measure, extreme measure, factor risk, risk contribution, risk trading, tail correlation, Tail VAR, Weighted VAR

JEL Classification: C15, G32

Suggested Citation

Cherny, Alexander S. and Madan, Dilip B., Coherent Measurement of Factor Risks (May 2, 2006). Available at SSRN: or

Alexander S. Cherny (Contact Author)

Moscow State University ( email )

Faculty of Mechanics and Mathematics
Department of Probability Theory
Moscow, 119992
007 095 939 14 03 (Phone)
007 095 939 14 03 (Fax)


Dilip B. Madan

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

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