Estimation of tail‐related risk measures in the Indian stock market: An extreme value approach

• Author: Madhusudan Karmakar
• DOI: http://doi.org/10.1016/j.rfe.2013.05.001
• Published date: 01 September 2013
• Date: 01 September 2013

Estimation of tail-related risk measures in the Indian stock market: An

extreme value approach

Madhusudan Karmakar

Indian Institute of Management, Prabandh Nagar, Off Sitapur Road, Lucknow, 226 013 UP, India

abstractarticle info

Article history:

Received 21 July 2011

Received in revised form 21 June 2012

Accepted 9 September 2012

Available online 3 May 2013

JEL classification:

C15

G1

Keywords:

Extreme value theory

Peak over threshold method

GARCH

Value at Risk

Expected shortfall

The purpose of the study is to estimate tail-related risk measures using extreme value theory (EVT) in the

Indian stock market. The study employs a two stage approach of conditional EVT originally proposed by

McNeil and Frey (2000) to estimate dynamic Value at Risk (VaR) and expected shortfall (ES). The dynamic

risk measures have been estimated for different percentiles for negative and positive returns. The estimates

of risk measures computed under different quantile levels exhibit strong stability across a range of the selected

thresholds, implying the accuracy and reliability of the estimated quantile based risk measures.

© 2013 Elsevier Inc. All rights reserved.

1. Introduction

Over the last two and half decades, the financial world has witnessed

the bankruptcy or near bankruptcy of several institutions that incurred

huge losses due to their exposures to unforeseen market moves. In the

wake of these financial disasters, it hasbecome clear to both riskman-

agers andpolicy makers that the development ofstandard measures of

the market risk is of paramount importance to the financial industry.

The Value at Risk (VaR) model has emerged as a popular measure of

market risk (see, e.g., Jorion, 2000) whose origin dates back to the late

1980s at J.P. Morgan. VaR answers the question of how much we can

lose,withagivenprobability,overacertainhorizon.Fromamathemat-

ical viewpoint VaR is simply a qua ntile of the Profit & Loss (P&L)distri-

bution of a given portfolio over a prescribed holding period.

The VaR technique has undergone significant refinement since it

originally appeared more than two decades ago and now the existing

approaches for estimating VaR can be divided into three groups: the

non-parametric historical simulation (HS) method; fully parametric

methods based on an econometric model for volatility dynamics and

the assumptionof conditional normality(e.g., J.P. Morgan'srisk metrics

and most models from the ARCH/GARCHfamily); and finally methods

based on extremevalue theory (EVT).

In the HS-approach the estimated P&L distribution of a portfolio is

simply given by the empirical distribution of past gains and losses on

this portfolio. The method is therefore easy to implement and avoids

“ad-hoc-assumptions”on the form of the P&L distribution. However,

the method suffers from some serious drawbacks. Extreme quantiles

are notoriouslydifficultto estimate, as extrapolationbeyond past obser-

vations is impossible and extreme quantile estimates within sample

tend to be very inefficient —the estimatoris subject to a high variance.

Econometricmodels of volatility dynamics that assumeconditional

volatility,such as GARCH-models do yield VaR estimateswhich reflect

the current volatility background.The main weakness of thisapproach

is that the assumptionof conditional normality does not seemto hold

for financialtime series data.

1

Theestimationofreturndistributionoffinancial time series via

EVTisatopicalissuewhichhasgivenrisetosomework(Bali, 2003,

2007; Danielsson & de Vries, 1997a,b,c; Danielsson, Hartmann, & de

Vries, 1998; Embrechts, Resnick, & Samorodnitsky, 1998, 1999; Longin,

1997; McNeil, 1997, 1998). In most of these papers the focus is on es-

timating the unconditional (stationary) distribution of asset returns.

Longin (2000) andMcNeil (1998) use estimation techniques based on

Review of Financial Economics 22 (2013) 79–85

E-mail address: madhu@iiml.ac.in.

1

To overcome the drawbacks of normal distribution, Bali and Theodossiou (2007)

and Bali, Mo, and Tang (2008) use GARCH models with skewed fat-tailed distributions

to estimate VaR and expected shortfall.

1058-3300/$ –see front matter © 2013 Elsevier Inc. All rights reserved.

http://dx.doi.org/10.1016/j.rfe.2013.05.001

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