Forecasting the Daily Time‐Varying Beta of European Banks During the Crisis Period: Comparison Between GARCH Models and the Kalman Filter

• Author: Taufiq Choudhry,Yuanyuan Zhang
• Published date: 01 December 2017
• Date: 01 December 2017
• DOI: http://doi.org/10.1002/for.2442

Forecasting the Daily Time-Varying Beta of European Banks During

the Crisis Period: Comparison Between GARCH Models and the

Kalman Filter

YUANYUAN ZHANG

1

AND TAUFIQ CHOUDHRY

2

*

1

School of Securities and Futures, Southwestern University of Finance and Economics, People's

Republic of China

2

School of Business, University of Southampton, UK

ABSTRACT

This intention of this paper is to empirically forecast the daily betas of a few European banks by means of four

generalized autoregressive conditional heteroscedasticity (GARCH) models and the Kalman filter method during the

pre-global financial crisis period and the crisis period. The four GARCH models employed are BEKK GARCH,

DCC GARCH, DCC-MIDAS GARCH and Gaussian-copula GARCH. The data consist of daily stock prices from

2001 to 2013 from two large banks each from Austria, Belgium, Greece, Holland, Ireland, Italy, Portugal and

Spain. We apply the rolling forecasting method and the model confidence sets (MCS) to compare the daily forecasting

ability of the five models during one month of the pre-crisis (January 2007) and the crisis (January 2013) periods.

Based on the MCS results, the BEKK proves the best model in the January 2007 period, and the Kalman filter overly

outperforms the other models during the January 2013 period. Results have implications regarding the choice of model

during different periods by practitioners and academics. Copyright © 2016 John Wiley & Sons, Ltd.

key words forecasting; Kalman filter; GARCH; time-varying beta; financial crisis; volatility

INTRODUCTION

One of the major changes to the standard capital asset pricing model (CAPM) is the replacement of the constant beta

by a time-varying beta (Fabozzi and Francis, 1978).

1

Over the years several different econometric methods have been

applied to estimate time-varying betas of different countries and firms (Brooks et al., 1998).

2

Along with other

methods, different versions of the generalized autoregressive conditional heteroscedasticity (GARCH) model and

the Kalman filter (KF) have been employed in previous studies to estimate the time-varying beta.

3

The GARCH

models apply the conditional variance information to construct the conditional beta series, while the Kalman ap-

proach recursively estimates the beta series from an initial set of priors, generating a series of conditional alphas

and betas in the market model.

By employing four GARCH models and the KF method, this paper empirically estimates and attempts to forecast

the daily betas of 16 banks from eight small European Union (EU) countries during the pre-global financial crisis and

the crisis period. The rolling forecast procedure is applied to forecast the time-varying beta, and the model confidence

set (MCS) is applied to provide a comparison of the forecasting ability of the different models.

4

This paper thus draws

a comparison between the forecasting ability of the five models during the non-volatile pre-crisis and the volatile cri-

sis periods.

5

The four GARCH models employed are the BEKK GARCH, DCC GARCH, DCC-MIDAS GARCH

and Gaussian-copula GARCH. We investigate these GARCH models because of their high-quality forecasting ability

as recorded in the literature. The BEKK GARCH model has high forecasting performance in predicting out-of-sam-

ple volatility and hedge ratio (Huang et al., 2010; Zhang and Choudhry, 2013). Peters (2008) found that the DCC

model forecasts the covariance matrix better than the naïve model over a short period of time, given high persistence.

The DCC is often the most accurate forecasting model, depending on the forecasting criteria (Engle, 2002). Patton

(2006) suggests that copula has high potential for measuring value-at-risk, multivariate estimations and forecasting

for economists, practitioners and academics. The Gaussian-copula GARCH is the simplest copula family model,

and Hsu et al. (2008) find that it effectively reduces the variance of returns of hedged portfolios in both the in-sample

*Correspondence to: Taufiq Choudhry, School of Business, University of Southampton, UK.

E-mail: t.choudhry@soton.ac.uk

1

According to Bos and Newbold (1984), the variation in the stock's beta may be due to the influence of microeconomic factors and/or

macroeconomic factors. A detailed discussion of these factors is provided by Rosenberg and Guy (1976a, 1976b).

2

Brooks et al. (1998) cite several papers that apply these different methods to estimate the time-varying beta.

3

A variety of GARCH models have been employed to model time-varying betas for different stock markets (see Bollerslev et al., 1988; Engle and

Rodrigues, 1989; Bodurtha and Mark, 1991; Ng, 1991; Koutmos et al., 1994; Braun et al., 1995; Giannopoulos, 1995; Gonzales-Rivera, 1996;

Brooks et al., 1998; Yun, 2002; Choudhry and Wu, 2008). Similarly, the KF technique has also been used by some studies to estimate the time-

varying beta (see Black et al., 1992; Well, 1994; Choudhry and Wu, 2008).

4

Wilhelmsson (2013) applies the MCS procedure in the S&P 500 returns in out-of-sample density forecast.

5

Poon and Granger (2003) provide an excellent survey of GARCH and other models’forecasting ability.

Journal of Forecasting,J. Forecast. 36, 956–973 (2017)

Published online 14 September 2016 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/for.2442

Copyright © 2016 John Wiley & Sons, Ltd.

estimate and out-of-sample forecast. The DCC-MIDAS model reduces the persistence of the short-run correlation dy-

namics in the correlation prediction (Colacito et al., 2011). More recently, Baele and Londono (2013) study the dy-

namics and determinants of industry beta and support the advantage of DCC-MIDAS GARCH in reducing the

downside risk based on 30 US industry portfolios between 1970 and 2009.

6

We also apply the KF because of the

evidence in the literature of its superiority in forecasting ability over GARCH models (see Choudhry and Wu, 2008).

The data applied in this study consist of daily stock prices during 2001–2013 from two large banks each from

Austria, Belgium, Greece, Holland, Republic of Ireland, Italy, Portugal and Spain. Given the robust forecasting abil-

ity of these models and the dramatic effect of the financial crisis on banks across Europe, it is of interest to empirically

investigate the effect of the crisis on the betas of a few European banks and the ability of these models to forecast the

betas of these banks during the erratic crisis period. It is well documented that during periods of turmoil financial cri-

sis volatility of financial market tends to rise (Schwert, 2011), which directly affects the beta of firms. It is of empir-

ical interest to investigate which model provides the best forecast during volatile periods compared to non-volatile

periods. To the best of our knowledge, this is the first empirical attempt to forecast the beta of banks during the cur-

rent crisis period and compare this to the pre-crisis period forecast.

Forecasting time-varying beta is important for several reasons. Since the beta (systematic risk) is the only risk that

investors should be concerned about, prediction of the beta value makes it easier for them to make investment deci-

sions. The value of beta can also be used by market participants to measure the performance of fund managers

through the Treynor ratio. For corporate financial managers, forecasts of the conditional beta are beneficial in capital

structure decisions and investment appraisal. Accurate estimation of beta helps measure cost of capital and enhance

supervisions of systematic risk (Baele et al., 2015).

The current global financial crisis is considered to be the worst financial crisis since the Great Depression of

1929–33 (Guidolin and Tam, 2013). According to Guidolin and Tam (2013), the Great Depression involved runs

on banks by depositors, whereas the current crisis reflected panic in wholesale funding market s that left banks unable

to roll over short-term debt. The crisis started with the burst of the price bubble in the US real estate market in mid

2007. The crisis reached its peak by October 2008 when the Lehman Brothers defaulted (Bordo and Meissner, 2012;

Adcock et al., 2014). During the current crisis period we see an increase in the level of private debt in the EU. This is

particularly pronounced in Greece (217%), Ireland (101%), and Spain (75.2%). After the crisis there was a steep rise

in public debt, by a magnitude of five in Ireland and by a magnitude of three in Spain. The resulting necessary EU

financial assistance to a few of these countries was substantial. In July 2012, the Eurogroup agreed to provide Spain

with bailout financial assistance of EUR 100 billion. Two Greek economic adjustment programs were agreed in May

2010 and May 2012 and were worth more than EUR 150 billion. Assistance to Ireland and Portugal in 2011 summed

to a total amount of more than EUR 48 billion. Among the countries under study, Austria was least affected by the

crisis.

This paper contributes to the literature in two main ways. First, we forecast the time-varying betas of a few

European banks during the crisis. As discussed earlier, forecasting of the betas is important from an investor's

and a practitioner's point of view. This is even more crucial during the current atmosphere of the global financial

crisis. Second, as advocated by previous research papers (e.g. Brooks et al., 1998; Faff et al., 2000), we provide

an extended comparison between the forecasting ability of the GARCH models and the KF procedure. As stated

earlier, we apply the rolling forecast method and the MCS to compare the forecasting ability of the five models.

We provide a comparison of the forecasting results between the pre-crisis and the crisis periods. In this manner,

we can assess which model provides a better forecast during non-volatile and volatile periods. This is the unique

contribution of the paper to the literature—taking into consideration the use of MCS and the rolling method of

forecasting.

In summary of our results, during the pre-crisis period, the BEKK is the best model and the KF predominantly

outperforms other models during the crisis period. The performance of the KF is also robust during the pre-crisis pe-

riod. The ability of the KF procedure to estimate the beta directly may have given it the advantage of forecasting the

beta during the high-volatility financial crisis period. These results have implications for model selection during vol-

atile and non-volatile periods by practitioners and academics.

The remainder of this paper is structured as follows. A summary of previous studies is provided in the next

section. The third section briefly discusses the conditional CAPM model. The fourth and fifth sections discuss,

in depth, the four GARCH models and the KF method, respectively. The sixth section includes a brief discussion

of the rolling forecasting procedure, and the selected data are described in the seventh section. The MCS is

described and discussed in the eighth section. The ninth presents briefly the GARCH and KF results, and the

forecasted test results are presented in the 10th section. The conclusion and implications are presented in the

11th section.

6

More implications of the DCC-MIDAS model are provided in Turhan et al. (2014).

Forecasting the Daily Time-Varying Beta of European Banks 957

Copyright © 2016 John Wiley & Sons, Ltd. J. Forecast. 36, 956–973 (2017)