Why VAR Fails: Long Memory and Extreme Events in Financial Markets

Los, Cornelis A.

doi:10.2139/ssrn.630668

Cited by 10 publications

(14 citation statements)

References 29 publications

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“…Such estimation relies on a revised and adjusted version of the classic rescaled range analysis methodology (R/S) first introduced by Hurst (1951), and subsequently enhanced by Wallis (1969a and1969b). Similar to Hurst's results in Geophysics and to financial literature (Malevergne and Sornette, 2006;Los, 2005;Daníelsson and Zigrand, 2005), results confirm that numerous individual risk factors exhibit significant long-term dependence, thus invalidating the square-root-of-time rule. Interestingly, most previous findings related to long-term dependence in financial time-series are still supported, even after the most recent period of market crisis.…”

Section: Figuresupporting

confidence: 84%

“…Despite considering comparative results of both R/S and mR/S as inconclusive, Los (2003) states that evidence documented by Peters (1994) shifts the balance of proof in direction of the existence of the long-term dependence in financial assets' time-series. Peters' (1994) works on long-term dependence in capital markets discarded autoregressive processes (AR), moving average (MA) and autoregressive moving average (ARMA) as sources of the persistence effect or long-term memory that is captured by the R/S, whilst GARCH processes showed a marginal persistence effect.…”

Section: Shortcomings Ofmentioning

confidence: 91%

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Portfolio optimization and long-term dependence

León¹,

Reveíz²

2010

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Whilst emphasis has been given to short-term dependence of financial returns, longterm dependence remains overlooked. Despite financial literature provides evidence of long-term's memory existence, serial-independence assumption prevails.This document's long-term dependence assessment relies on rescaled range analysis (R/S), a popular and robust methodology designed for Geophysics but extensively used in financial literature. Results correspond to most of the previous evidence of significant long-term dependence, particularly for small and illiquid markets, where persistence is its most common kind. Persistence conveys that the range of possible future values of the variable will be wider than the range of purely random and independent variables.Ahead of R/S financial literature, authors estimate an adjusted Hurst exponent in order to properly estimate the covariance matrix at higher investment horizons, avoiding the traditional -independence reliant-square-root-of-time rule.Ignoring long-term dependence within the mean-variance portfolio optimization results in concealed risk taking; conversely, by adjusting for long-term dependence the weight of high (low) persistence risk factors decreases (increases) as the investment horizon widens. This alleviates some well-known shortcomings of conventional portfolio optimization for long-term investors (e.g. central banks, pension funds and sovereign wealth managers), such as excessive risk taking in long-term portfolios, extreme weights, home bias, and reluctance to hold foreign currency-denominated assets.Keywords: Portfolio optimization, Hurst exponent, long-term dependence, biased random walk, rescaled range analysis. JEL Classification: G11, G32, G20, C14. † We are grateful to Marco Ruíz, Jack Bohn and Daniel Vela, who provided valuable comments and suggestions. Research assistance, comments and suggestions from Karen Leiton and Francisco Vivas are acknowledged and appreciated. As usual, the opinions and statements are the sole responsibility of the authors.

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Section: Figuresupporting

confidence: 84%

Section: Shortcomings Ofmentioning

confidence: 91%

Portfolio optimization and long-term dependence

León¹,

Reveíz²

2010

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“…Once again, this confirms frequency distributions and their moments failing to capture other type of structures in timeseries, such as serial dependence. This is rather relevant since it is well-documented that focusing on the frequency of returns ignores the importance of their sequence, which could be the main reason why Value at Risk, Expected Shortfall or Extreme Value Theory tend to underestimate risk (Malevergne and Sornette, 2006;Los, 2005;Sornettte, 2003), whilst customary use of GARCH models is insufficient to account for observed volatility. 7 4 degrees of freedom, is unable to account for the dependencies observed in real DJIA data.…”

Section: Source: Authors' Calculationsmentioning

confidence: 99%

Monte Carlo Simulation of Long-Term Dependent Processes: A Primer

León¹,

Reveíz²

2012

Wilmott

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“…Respecto de los resultados de ambas metodologías, Los (2003) afirma que la evidencia empírica documentada por Peters (1994) para el caso de series de precios tiende a favorecer las conclusiones de Mandelbrot y Wallis (1969a y 1969b) y Mandelbrot (1972Mandelbrot ( y 1965) -no las de Lo (1991)-sobre la presencia de dependencia de largo plazo, aunque reconoce que todavía es prematuro concluir de manera definitiva sobre el tema.…”

Section: Gráficounclassified

Dependencia de largo plazo y la regla de la raiz del tiempo para escalar la volatilidad en el mercado colombiano

León-Rincón¹,

Vivas²,

León³

2010

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Dependencia de largo plazo y la regla de la raíz del tiempo para escalar la volatilidad en el mercado colombiano Por: Carlos León Francisco Vivas Núm. 603 2010 Dependencia de largo plazo y la regla de la raíz del tiempo para escalar la volatilidad en el mercado colombiano 1 Carlos León Francisco Vivas Banco de la República Colombia Dependencia de largo plazo y la regla de la raíz del tiempo para escalar la volatilidad en el mercado colombiano † Carlos León ♠ Francisco Vivas ♣ ♣ ♣ ♣ Banco de la República ColombiaResumen Es una práctica muy difundida el multiplicar la desviación estándar por la raíz del tiempo para escalarla a otros plazos. Así, con base en la estimación de la desviación estándar o del VaR (Value at Risk) diario, es usual obtener la desviación estándar o el VaR para un periodo de diez días como el producto de la primera y la raíz de diez.Esta práctica, basada en la hipótesis de los mercados eficientes, supone que los cambios de los precios son independientes entre sí; es decir, que las series de tiempo no presentan memoria.El presente documento se ocupa de estimar la presencia de memoria de largo plazo en los mercados cambiario, accionario y de renta fija colombianos, para lo cual se utiliza la metodología de rango reescalado clásico (R/S) y modificado (mR/S).Además de encontrar persistencia significativa para el mercado accionario y de renta fija, se estima el exponente de Hurst ajustado, el cual sirve para cuantificar el error derivado de algunas prácticas basadas en el supuesto de independencia.De acuerdo con los resultados obtenidos para dichos mercados, (i) el supuesto según el cual los precios reflejan toda la información disponible es errado; (ii) algunas prácticas en la optimización de portafolios y la valoración de activos son cuestionables, y (iii) tal como se infiere de la revisión hecha en 2009 por el Comité de Basilea a los estándares cuantitativos para el cálculo del riesgo de mercado, la regla de la raíz del tiempo subestima significativamente el riesgo.

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Why VAR Fails: Long Memory and Extreme Events in Financial Markets

Cited by 10 publications

References 29 publications

Portfolio optimization and long-term dependence

Portfolio optimization and long-term dependence

Monte Carlo Simulation of Long-Term Dependent Processes: A Primer

Dependencia de largo plazo y la regla de la raiz del tiempo para escalar la volatilidad en el mercado colombiano

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