The Quantitative Finance Library

Risk Horizon and Rebalancing Horizon in Portfolio Risk Measurement This paper analyzes portfolio risk and volatility in the presence of constraints on portfolio rebalancing frequency. This investigation is motivated by the incremental risk charge (IRC) introduced by the Basel Committee on Banking Supervision. In contrast to the standard market risk measure based on a ten-day value-at-risk calculated at 99% confidence, the IRC considers more extreme losses and is measured over a one-year horizon. More importantly, whereas ten-day VaR is ordinarily calculated with a portfolio’s holdings held fixed, the IRC assumes a portfolio is managed dynamically to a target level of risk, with constraints on rebalancing frequency. The IRC uses discrete rebalancing intervals (e.g., monthly or quarterly) as a rough measure of potential illiquidity in underlying assets. We analyze the effect of these rebalancing intervals on the portfolio’s profit and loss distribution over a risk-measurement horizon. We derive limiting results, as the rebalancing frequency increases, for the difference between discretely and continuously rebalanced portfolios; we use these to approximate the loss distribution for the discretely rebalanced portfolio relative to the continuously rebalanced portfolio. Our analysis leads to explicit measures of the impact of discrete rebalancing under a simple model of asset dynamics. , P.Glasserman (2009)

Variance Risk Premia , P.Carr, L.Wu (2007)

The Use of GARCH Models in VaR Estimation , T. Angelidis, A. Benos, S. Degiannakis (2003)

Dynamic Value-at-Risk , A.Rogachev (2002)

Valuation and Risk Metrics , Comm of CROs (2002)

An Empirical Evaluation of Value at Risk by Scenario Simulation , P.Abken (2000)

Efficient Monte Carlo Methods for Value-at-Risk , P.Glasserman, P.Heidelberger, P.Shahabuddin (2000)

Coherent measures of risk , P. Artzner & F. Delbaen & J. Eber & D. Heath (1998)

Incorporating Volatility Updating into The Historical Simulation Method for Value At Risk , J. Hull, A. White (1998)

Value At Risk when Daily Changes in Market Variables are not Normally Distributed , J. Hull, A. White (1997)

Risk Horizon and Rebalancing Horizon in Portfolio Risk Measurement This paper analyzes portfolio risk and volatility in the presence of constraints on portfolio rebalancing frequency. This investigation is motivated by the incremental risk charge (IRC) introduced by the Basel Committee on Banking Supervision. In contrast to the standard market risk measure based on a ten-day value-at-risk calculated at 99% confidence, the IRC considers more extreme losses and is measured over a one-year horizon. More importantly, whereas ten-day VaR is ordinarily calculated with a portfolio?s holdings held fixed, the IRC assumes a portfolio is managed dynamically to a target level of risk, with constraints on rebalancing frequency. The IRC uses discrete rebalancing intervals (e.g., monthly or quarterly) as a rough measure of potential illiquidity in underlying assets. We analyze the effect of these rebalancing intervals on the portfolio?s profit and loss distribution over a risk-measurement horizon. We derive limiting results, as the rebalancing frequency increases, for the difference between discretely and continuously rebalanced portfolios; we use these to approximate the loss distribution for the discretely rebalanced portfolio relative to the continuously rebalanced portfolio. Our analysis leads to explicit measures of the impact of discrete rebalancing under a simple model of asset dynamics. , P.Glasserman (2009)

The StressVaR: A New Risk Concept for Superior Fund Allocation In this paper we introduce a novel approach to risk estimation based on nonlinear factor models - the "StressVaR" (SVaR). Developed to evaluate the risk of hedge funds, the SVaR appears to be applicable to a wide range of investments. Its principle is to use the fairly short and sparse history of the hedge fund returns to identify relevant risk factors among a very broad set of possible risk sources. This risk profile is obtained by calibrating a collection of nonlinear single-factor models as opposed to a single multi-factor model. We then use the risk profile and the very long and rich history of the factors to asses the possible impact of known past crises on the funds, unveiling their hidden risks and so called "black swans". In backtests using data of 1060 hedge funds we demonstrate that the SVaR has better or comparable properties than several common VaR measures - shows less VaR exceptions and, perhaps even more importantly, in case of an exception, by smaller amounts. The ultimate test of the StressVaR however, is in its usage as a fund allocating tool. By simulating a realistic investment in a portfolio of hedge funds, we show that the portfolio constructed using the StressVaR on average outperforms both the market and the portfolios constructed using common VaR measures. For the period from Feb. 2003 to June 2009, the StressVaR constructed portfolio outperforms the market by about 6% annually, and on average the competing VaR measures by around 3%. The performance numbers from Aug. 2007 to June 2009 are even more impressive. The SVaR portfolio outperforms the market by 20%, and the best competing measure by 4%. , C.Coste, R.Douady, I.I.Zovko (2009)