Nonparametric Factor Analytic Risk Measurement in Common Stocks in Financial Firms: Evidence from Korean Firms

• Author: Seung Y. Cha,Seungho Baek,Joseph D. Cursio
• DOI: http://doi.org/10.1111/ajfs.12098
• Published date: 01 August 2015
• Date: 01 August 2015

Nonparametric Factor Analytic Risk

Measurement in Common Stocks in Financial

Firms: Evidence from Korean Firms*

Seungho Baek

Murray Koppelman School of Business, City University of New York

Joseph D. Cursio

Stuart School of Business, Illinois Institute of Technology

Seung Y. Cha**

College of Business, Seoul National University

Received 24 June 2014; Accepted 22 January 2015

Abstract

This research examines the efficiency of nonparametric factor analytic approaches in measur-

ing risk in common stocks of Korean financial firms from the risk-management perspective.

This paper shows that using only one risk factor extracted from principal component analy-

sis, the parallel shift or market movement factor, has sufficient accuracy for downside risk

measures. We assess accuracy by applying Monte Carlo simulation to obtain VaR and ES for

the Korean financial sector and industries within the financial sector (banks, insurance com-

panies, and investment andsecurity trading companies), and further estimate the risk conta-

gious effect on financial firms.

Keywords Risk management; Monte Carlo simulation; Value at risk; Expected shortfall; Sys-

temic risk; Principal component analysis

JEL Classification: G11, G17, G21

*We would like to thank the editors, Bong-soo Lee and Hee-Joon Ahn, and anonymous ref-

erees for their valuable comments. We also gratefully acknowledge the comments received

from John Bilson, Rick Cooper, Michael Ong, Kihoon Hong, Tolga Cenesizoglu, and seminar

participants at the 2013 Financial Management Association Meetings. This research was par-

tially supported by the Institute of Finance and Banking in the College of Business Adminis-

tration at Seoul National University.

**Corresponding author: Seung Y. Cha, College of Business Administration, Seoul National

University, San 56-1, Shillim-dong, Kwanak-gu Seoul 151-742, Korea. Tel: 82-2-880-6900,

Fax: 82-2-880-8411, email: sycha77@snu.ac.kr.

Asia-Pacific Journal of Financial Studies (2015) 44, 497–536 doi:10.1111/ajfs.12098

©2015 Korean Securities Association 497

1. Introduction

Financial institutions are regarded as the most important monetary resources in

each country’s economy. Sullivan and Sheffrin (2003) define the financial sector as

the system that allows the transfer of money between investors and borrowers. The

financial system has complex interconnections composed of financial interme diates,

financial products, investors and markets. The financial sector is highly regulated

and monitored by governments and evaluated by credit rating agencies such as the

Fitch Group, Standard and Poor’s, and Moody’s. Despite regulatory efforts, critical

disasters have originated from the financial industry. In particular, the 2007 world-

wide financial meltdown was triggered by United States financial institutions reli-

ance on their speculative investment strategy strategies and the improper risk

management of fixed income products, including subprime mortgages. Large finan-

cial institutions such Lehman Brothers, Wachovia, Merrill Lynch, Washington

Mutual, Bank of America, J.P. Morgan, Citigroup, and AIG held sizable toxic assets,

which they were unable to liquidate, and thus faced critical liquidity issues. Some

banks survived only because of government intervention, at substantial cost to tax-

payers, while other banks such as Lehman Brothers declared bankruptcy. As a

result, the United States and global markets entered into a severe economic down-

turn, a collapse from which the global economy is still suffering. The recent 2007

financial crisis demonstrates how risk management failure or the insolvency of an

individual financial firm can result in the failure of the entire economic system.

Because of this spillover effect of shocks from one institution to another (see

Kaufman, 1994), the measurement of an individual firm’s risk and the systemic risk

over the entire financial system is critical in risk management.

To measure the level of risk, value at risk (VaR) has emerged as the standard

benchmark for quantifying downside risk. VaR estimates the potential loss amount

of a firm’s assets over a given period. Many banks and financial institutions have

disclosed VaR information in their quarterly and annual financial reports not only

to satisfy regulation policy but also to show their competitiveness of asset manage-

ment strategy. With VaR reports, risk managers in financial firms and government

financial supervisors monitor individual firm and sector-wide risk exposure and

identify the level of capital adequacy for their business and for the entire financial

industry. The results of Jorion’s (2002) study of the relation between the trading

VaR disclosure of United States commercial banks and the variability of trading

revenue suggests that VaR disclosures are informative.

Generally, there are two major approaches to VaR analysis, local valuation and

full valuation methods. The local valuation method is an analytical procedure that

assumes that the distribution of returns is known. In other words, provided with a

parametric probability density function (e.g. normal density), this method values

portfolio risk using a linear combination of parameters such as mean and standard

deviation. The full valuation method is a simulation, or scenario-based, approach.

There are two prominent empirical techniques in the full valuation method:

S. Baek et al.

498 ©2015 Korean Securities Association

historical simulation and Monte Carlo (MC) simulation. Both historical and MC

simulations are more useful than the local valuation method in that they (i) better

reflect extreme events, (ii) allow for non-constant correlation between underlying

assets, and (iii) allow for leptokurtosis (“fat-tails”) for measuring risk. Unlike the

local valuation method, the full valuation method is not a linear approach but

instead computes VaR using the ranking of percentage and does not assume the

shape of the distribution of asset returns. Because this approach is not dependent on

parameters, this is also referred to as nonparametric VaR. As long as information of

underlying assets is properly contained, this method is efficient. However, the main

disadvantage of the full valuation method is that it does not consider any future

volatility higher than the peak historical volatility, because historical simulation

depends on the historical events over a specified time frame. On the other hand, MC

simulation is more flexible than historical simulation because it considers extreme

events and fat-tail issues when applying stochastic process regardless of sample size.

When applying the MC method to generate various scenarios of asset prices at

t+1, both Cholesky decomposition and eigenvalue decomposition (EVD) have been

used. Note that, EVD is a part of principal component analysis (PCA) and thus PCA

can be applicable as a decomposition technique, which reduces the number of risk

factors that affect the movement of portfolio values. Thus, we can identify how indi-

vidual variables affect a portfolio movement because with a few principal compo-

nents we can reproduce the covariance structure of asset price along with individual

variable effect. Identification of these risk factors can aid in constructing scenario

analyses and stress tests for risk management. For example Litterman and Scheink-

man (1991) used PCA to decompose the returns of fixed income securities into level,

steepness and curvature components. Frye (1997) creates VaR scenarios from these

three components and describes these scenarios as “useful and easily understood.”

Holton (2003) points that PCA can be used even if the variance–covariance matrix is

not positive definite, typically a result of multicolinearity or a lack of sufficient his-

torical data causing one or more eigenvalues to be negative.

Principal component analysis can usually be performed by eigenvalue decompo-

sition (EVD) and singular value decomposition (SVD). By applying EVD-based

PCA Jamshidian and Zhu (1997) first compute the VaR of multivariate currencies

and interest rate assets employing the MC method while Frye (1997) and Loretan

(1997) study PCA applicability in the context of parametric based VaR. Under the

nonparametric framework, we will consider SVD, first suggested by Stewart (1993),

as well as eigenvalue decomposition. SVD has been widely used in digital imaging

processing in engineering and signal processing, but today many investment banks

and hedge funds employ this method to derive the asset price of financial deriva-

tives and to extract invisible risk factors in interest rate modeling. Although the

eigenvalue approach and SVD theoretically return the exact same values, from a

numerical analysis point of view the eigenvalue approach is widely regarded as

not as stable. We therefore use both decomposition methods to test for numerical

stability in practice.

Nonparametric Factor Analytic Risk Measurement in Common Stocks

©2015 Korean Securities Association 499