Ebook Risk Horizon and Rebalancing Horizon in Portfolio Risk Measurement
In 2007, the Basel Committee on Banking Supervision proposed a new measure of market risk known as the incremental risk charge, or IRC; the proposal was updated in January 2009 and is expected to take effect in 2010. The IRC is incremental to the current Basel standard for market risk, which is based on a 99% value-at-risk (VaR) measured over a ten-day horizon. The standard VaR measure was designed to capture the risk in short-term fluctuations of highly liquid securities; but, over time, banks have come to include less liquid assets in their trading books.
The IRC arose in response to this changing composition of bank portfolios and as part of a broader attempt to equalize capital charges for similar risks held in banking and trading books. The proposal is detailed in reports of the Basel Committee ([4, 5]); for perspectives from the industry, see Duncan et al. [16], Sebton et al. [31], and Smillie and Epperlein [32]. For general background on risk capital, see, e.g., Crouhy, Galai, and Mark [11] and McNeil, Frey, and Embrechts [28].
The Basel principles for calculating the IRC include the following key elements:
- a 99.9% VaR,
- measured over a one-year time horizon,
- assuming the portfolio is managed to a target level or risk,
- incorporating “liquidity horizons” for less liquid assets.
The first two features are stringent but otherwise straightforward extensions of the traditional ten day 99% VaR; the last two features are novel. A standard ten-day VaR calculation uses a “buy and hold” assumption under which a portfolio is held fixed throughout the VaR horizon while market prices change. The IRC recognizes the implausibility of this assumption over a one-year horizon and allows the portfolio composition to change within the VaR interval. The notion of a target level of risk precludes a calculation in which a portfolio is artificially assumed to move to safe assets following losses; instead, the portfolio must be rebalanced to reflect a level of risk representative of the bank’s trading. The last feature of the IRC limits the frequency of rebalancing to capture potential illiquidity in the underlying assets. A typical rebalancing frequency is monthly or quarterly.
The purpose of this article is to analyze these features of the proposed risk measure, with particular emphasis on the impact of the liquidity intervals nested within the longer risk horizon. The IRC provides the motivation for this investigation, but we see these features of the IRC as having broader applicability — any prescription for measuring portfolio risk over a moderately long horizon must address the question of how the portfolio evolves over the horizon; a target level of risk with constraints on rebalancing frequency provides a natural framework. Moreover, guidelines put forward by the Basel Committee often influence risk measurement and risk management even beyond the domain of bank supervision.
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