Published in Wilmott Magazine, May 2006

Visitor no. 6229 as of February 20, 2006

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A VaR-based Model for the Yield Curve

Ruben D. Cohen (ruben.cohen@citigroup.com)

Abstract

An intuitive model for the yield curve, based on the notion of value-at-risk, is presented. It leads to interest rates that hedge against potential losses incurred from holding an underlying risky security until maturity. This result is also shown to tie in directly with the Capital Asset Pricing Model via the Sharpe Ratio. The conclusion here is that the normal yield curve can be characterised by a constant Sharpe Ratio, non-dimensionalised with respect toÖT, where T is the bond maturity.

Among other features of the model are that it is able to explain, qualitatively if not quantitatively, the existence of (1) a normal yield curve at times of “normal economic growth”, (2) an inverted curve during periods of “high uncertainty”, “high interest rates” or “low economic growth”, (3) a flat yield curve in more certain times and (4) a liquidity trap when economic growth is expected to be negative.