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On the Validity of Risk Measures over Time: Value-at-Risk Conditional Tail Expectations and the Bodi
Company: Boston University
Year Of Publication: 2005
Month Of Publication: August
Pages: 37
Download Count: 341
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Comment Num: 0
Language: EN
Who Can Read: Free
Date: 8-12-2007
Publisher: Administrator
Over the past decade, risk measurement has received a much needed amount of attention from the financial community. Risk measures based on fixed quantiles under the actual probability distribution, especially Value-at-Risk and its refinement the Conditional Tail Expectation, were instrumental in capturing the attention of financial decision-makers. However, these were developed in a way that is inconsistent with economic theory. Consequently, these instruments possess characteristics that make them invalid risk measures for the purposes they intend to serve, be it informing life-cycle investors or guaranteeing the firm's capital adequacy through regulation. In particular, in addition to failing to guarantee the intregity of financial firms when used for capital adequacy, these measures can eventually decrease with the investment horizon. Risk-neutral fixed-quantile measures are valid for framing life-cycle decisions because of their economic content. When endowed with a dynamic replication technology, Q- measure fixed-quantile risk measures become least-cost insurance contracts that may be used for capital adequacy considerations. However, no single quantile of the risk-neutral distribution can be used for the procurement of risk capital at all horizons. A risk-neutral varying-quantile instrument is needed. This unique instrument is a put option proposed by Merton-Perold (1993) and Bodie (1995). The Bodie-Merton-Perold Put is universally valid for both risk disclosure to investors and for the regulatory provision of risk capital at all horizons. It is a natural candidate for an industry standard in risk measurement.
Treussard, Jonathan Sign in to follow this author
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