MODELLING THE EQUITY BETA RISK OF AUSTRALIAN

FINANCIAL SECTOR COMPANIES

FRIDA LIE, ROBERT BROOKS and ROBERT FAFF

RMIT University

In this paper we apply the generalised auto-regressive conditional heteroskedasticity (GARCH) and

Kalman Filter approaches to modelling the equity beta risk of a sample of ®fteen Australian

®nancial sector companies. A de-regulated environment in which strong competitive forces are at

play typi®es the period of investigation. Consistent with the existing literature, we ®nd that these

modelling techniques perform well and, in particular, that the Kalman Filter approach is preferred.

Further, we ®nd that considerable variability of risk occurs throughout the sample period. Thus,

extending the evidence of Harper and Scheit (1992); Brooks and Faff (1995) and Brooks, Faff and

McKenzie (1997), we ®nd evidence consistent with the hypothesis that deregulation has impacted

the risk of banking sector stocks.

I. In t ro duc t i o n

The issue of testing and modelling bank risk instability has attracted increasing attention

in recent times [in the case of recent US work see for example, Alexander and Spivey

(1994); Dickens and Philippatos (1994); Shiers (1994); Song (1994); Brooks, Faff, Ho and

McKenzie (2000) and McKenzie, Brooks, Faff and Ho (1999)]. This interest has been

heightened given the pace with which the world's major economies and capital markets have

moved toward de-regulation, since in the context of the associated increase in globalisation

and integration of markets, banks have experienced greatly increased competition. The

Australian situation is a case in point which is underlined by the release of the report of the

Wallis inquiry `The Wallis Report' [Financial System Inquiry Final Report (1997)].

The existing Australian literature in this area comprises Harper and Scheit (1992);

Brooks and Faff (1995) and Brooks, Faff and McKenzie (1997). Harper and Scheit (1992)

found that there was little evidence of risk instability for the three main Australian banks.

Brooks and Faff (1995) applying a different testing methodology to a similar dataset, largely

con®rm their ®nding. However, Brooks, Faff and McKenzie (1997) apply a testing and

modelling strategy which suggests that bank risk has varied over time in a manner that may

well be related to deregulatory changes.

# Blackwell Publishers Ltd, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden

MA 02148, USA and the University of Adelaide and Flinders University of South Australia 2000.

The authors are grateful for the helpful comments provided by an anonymous referee.

Correspondence to: Robert Brooks, School of Economics and Finance, RMIT, GPO Box 2476V,

Melbourne, Victoria 3001, Australia. Phone: ‡ 61-3-9925 5864, Fax: ‡ 61-3-9925 5986, Email:

robert.brooks@ rmit.edu.au

The basic methodology used by Brooks, Faff and McKenzie (1997) is the generalised

auto-regressive conditional heteroskedasticity (GARCH) approach. This methodology is a

popular statistical technique for modelling time varying betas. Indeed, these models have

been applied to determine time varying betas for US industry portfolios by Braun, Nelson

and Sunier (1995), for national stock market indices by Giannopolous (1995), for US mining

stocks by McClain, Humphreys and Boscan (1996), for US computer industry stocks by

Gonzales-Rivera (1996), for Australian industry portfolios by Brooks, Faff and McKenzie

(1998) and for US banking industry stocks by Brooks, Faff, Ho and McKenzie (2000) and

McKenzie, Brooks, Faff and Ho (1999).

The main purpose of the present paper is to extend the analysis of Brooks, Faff and

McKenzie (1997) (a) to a wider range of Australian banking sector stocks; (b) over a more

recent time period; (c) using daily (as opposed to monthly) data; and (d) to include a

comparison of GARCH generated betas to a set of Kalman Filter [for example, see Wells

(1994)] counterparts. In this context, Brooks, Faff and McKenzie (1998) found that the

Kalman Filter produced superior time-varying beta estimates to the GARCH technique for

Australian industry portfolios. Brooks, Faff and McKenzie (1997) only investigated a sample

of three major banks, over a sample period ending in 1992 using monthly data. The current

paper extends this investigation to a daily dataset comprising of ®fteen ®nancial sector

stocks and conducts a comparison of modelling techniques, with a sample period extending

through to September 1998.

The plan of this paper is as follows. In Section II we outline the bivariate GARCH and

Kalman Filter models that is used to estimate the time varying betas. Section III details the

data to be analysed and presents our empirical results. Section IV contains some concluding

remarks.

II. Mo d e l Sp e c i f icat i o n

The market model is one of the most commonly used techniques by which ®nance

researchers estimate systematic risk and may be summarised as

R

it

ˆ á

i

‡ â

i

R

Mt

‡ å

it

(1)

where R

it

is the return for an individual stock, R

Mt

is the return to the market most commonly

proxied by the return to a representative index, å

it

is a stochastic error term assumed to be

distributed IN (0, ó

2

i

), á

i

and â

i

are ®rm speci®c point estimates which are assumed

constant over time, where beta represents the systematic risk for asset i. This model of

constant risk can be relaxed in a variety of ways ± two such cases are outlined in the

following sections.

GARCH±based approach to modeling time-varying beta

First we will estimate the time varying conditional beta (â

it

) using a M-GARCH model

introduced by Bollerslev (1990).

1

A bivariate version of this model is to be used in the

1

Several other techniques can be used to model conditional betas, including, the Schwert and Seguin

(1990) approach and the economic variable market model (EVMM) approach [see for example, Abell

and Krueger (1989)]. These approaches will not be explored in the current paper as they have generally

found to be inferior to both the GARCH and Kalman Filter approaches [see for example, Brooks, Faff

and McKenzie (1998)].

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current paper and may be summarised as follows. We begin by specifying the functional

form of the conditional mean as

R

it

ˆ å

it

i ˆ 1, 2

(2)

where R

it

is the column vector of determinant variables and å

it

is the column vector of error

terms which may be described as å

it

jØ

tÿ1

N(0, H

t

) ie. å

it

is conditioned by the complete

information set Ø

tÿ1

and is normally distributed with zero mean and a conditional

covariance matrix H

t

. Explicitly, H

t

is of the form

H

t

ˆ h

11,t

h

12,t

h

21,t

h

22,t

(3)

A functional form must be speci®ed for this conditional variance matrix H

t

and in this

paper, a GARCH(1,1) model has been chosen. Thus, the conditional variance equations may

be compactly written in vector form as

h

11,t

h

12,t

h

22,t

2
6

6

6

4

3
7

7

7

5

ˆ

c

11

c

12

c

22

2
6

6

6

4

3
7

7

7

5

‡

a

11

a

12

a

13

a

21

a

22

a

23

a

31

a

32

a

33

2
6

6

6

4

3
7

7

7

5

3

å

2

1,tÿ1

(å

1,tÿ1

)(å

2,tÿ1

)

å

2

2,tÿ1

2
6

6

6

4

3
7

7

7

5

‡

b

11

b

12

b

13

b

21

b

22

b

23

b

31

b

32

b

33

2
6

6

6

4

3
7

7

7

5

3

h

11,tÿ1

h

12,tÿ1

h

22,tÿ1

2
6

6

6

4

3
7

7

7

5

(4)

or:

(vech)H

t

ˆ C ‡ Aå ‡ BH

tÿ1

(5)

where H

t

, C, A, å, and B represent their respective matrices in the above equation. In this

simple GARCH(1,1) parameterisation, there are 21 individual coef®cients and as the order

of the GARCH model increases so too does the number of parameters and at an exponential

rate. Pagan (1996 p. 79) argues that most applications have concentrated upon ways of

restricting Equation (5) to reduce the number of unknown parameters. Bollerslev (1990)

proposes setting the off-diagonals in the coef®cient matrices (i.e. matrices A and B) equal to

zero. Thus, the conditional variance of each equation may be speci®ed as

h

11,t

ˆ c

11

‡ a

11

å

2

1,tÿ1

‡ b

11

h

11,tÿ1

(6)

h

22,t

ˆ c

22

‡ a

33

å

2

2,tÿ1

‡ b

33

h

22,tÿ1

(7)

To derive the conditional covariance equation h

12,t

, the correlation between the return

series is assumed by Bollerslev to be constant. Accordingly, the conditional covariance may

be estimated as

h

12,t

ˆ r 3 (h

11,t

3 h

22,t

)

1=2

(8)

Thus, by making the simplifying assumptions above we are left with just seven (a

11

a

33

b

11

b

33

c

11

c

22

and r) from the original 21 parameters. Where the `a' and `b' coef®cients are

non-negative and the c coef®cients are positive, then the positive de®niteness of H

t

can be

guaranteed (see Engle and Kroner (1995)).

This bivariate GARCH model provides the elements necessary to construct the time series

MODELLING THE EQUITY BETA RISK

2000

303

# Blackwell Publishers Ltd/University of Adelaide and Flinders University of South Australia 2000.

â

it

. Recall â

it

ˆ cov

t

(R

it

, R

Mt

)=var

t

(R

Mt

) where â

it

is the conditional beta for the individual

stock i. The econometric speci®cation of the M-GARCH model provides direct estimates of

cov

t

(R

it

, R

Mt

) and var

t

(R

Mt

) where the model is ®tted to the return of an individual stock as

well as a market index. In this case, an estimate of cov

t

(R

it

, R

Mt

) is provided in the form of

h

12,t

and the var

t

(R

Mt

) in the form of h

22,t

. Hence, full time series of â

it

may be generated

for the series R

i

where a multivariate GARCH model is ®tted to R

i

and R

M

.

Kalman Filter±based approach to modelling time-varying beta

The second approach to modelling beta considered in this paper is a state-space rep-

resentation using the Kalman Filter.

2

This technique estimates a time-varying beta by

specifying a measurement equation

R

it

ˆ á

t

‡ â

K

it

R

Mt

‡ å

t

å

t

N(0, Ù)

(9)

where the process that de®nes the time varying beta is given by the transition equation

â

K

it

ˆ Tâ

K

itÿ1

‡ ç

t

ç

t

N(0, Q)

(10)

In our case we set T ˆ 1 and hence choose to model the time varying process as a random

walk.

Both the GARCH and Kalman Filter approaches generatea conditional beta series for

each bank. Following Brooks, Faff and McKenzie (1998), we assess the relative dominance

of one technique over the other using the Mean Absolute Error (MAE) and the Mean

Squared Errorr (MSE) metrics.

3

III. E m p i r ica l R e s u lt s

Data and preliminaries

We obtained daily price data on ®fteen Australian banking and ®nancial institution stocks

from the Datastream database. The ®fteen stocks are listed in Table I. All data were gathered

from the ®rst available observation to 10 September 1998. We note that the market index,

which is measured by the All Ordinaries Accumulation Index, was available from 1 January

1980. Thus, the start of the sample period varies across the stocks analysed. As shown in

Table I they vary from the earliest of 1 January 1980 for National Australia Bank and

Westpac Banking Corporation to the latest of 5 August 1996 for Hartley Poynton. All of our

price data were converted to returns by assuming continuous compounding.

The ®rst step in our analysis was to apply the standard market model to obtain OLS point

estimates of beta and they are also reported in Table I. All ®fteen stocks have betas which

are signi®cantly different from zero. For twelve of the stocks the betas are also signi®cantly

different from unity. The three exceptions are ANZ Bank, Macquarie Bank and the Westpac

Banking Corporation. The lowest beta is 0.2076 for Rock the Building Society. The highest

beta is 1.3282 for ANZ Bank. There is only one other stock with an estimated beta which

exceeds unity ± namely, 1.2447 for Macquarie Bank. Generally, the outcome of these point

2

The Kalman Filter is a popular approach applied in several similar situations in the literature. For

example, see Burmeister, Wall and Hamilton (1986), Cheung (1993) and Faff and Heaney (1999) who

have applied it to the task of extracting a time-varying expected in¯ation series.

3

See Brooks, Faff and McKenzie (1998) for details.

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estimates of beta risk indicate that the sample of banking and ®nance stocks is less risky than

the average across the market.

GARCH time-varying betas

GARCH models were estimated for each of the ®fteen banking stocks and the market

portfolio. Given the widespread popularity of the GARCH (1,1) model in the literature [see

Bollerslev, Chou and Kroner (1992)] this speci®cation is utilised. This choice can also be

justi®ed on the grounds of parsimony. The results of this GARCH (1,1) estimation are

reported in Table II. In all cases we ®nd that the á and â coef®cients in the conditional

variance equation of the GARCH (1,1) model are signi®cantly different from zero. The most

persistent of the GARCH models is for First Australian Building Society (á

1

‡

â

1

ˆ 0:9918), while the least persistent of the GARCH models is for the Bank of Queens-

land (á

1

‡ â

1

ˆ 0:6543). Thus, all of our ®tted GARCH models are stationary in that the

sum of the parameters is less than unity.

The other element we require for using the Bollerslev (1990) restricted version of the

bivariate GARCH model is the correlation between individual stock returns and the market

return. These correlations are reported in the ®nal column of Table II. They range from

0.1162 in the case of Rock the Building Society to 0.6828 in the case of the ANZ Bank.

The next step in our analysis is to calculate time varying betas for each of the ®fteen

stocks following the process outlined in Section II. As mentioned earlier, we will be

comparing the time varying beta generated by GARCH approach to those generated by

Kalman Filter approach. It turns out (not unexpectedly) that the Kalman approach tends to

produce very large (and in some cases negative) outliers in the initial stages of estimation

due to a `start-up' values problem. Thus, to avoid an unfair bias against this technique due to

this problem, the ®rst 50 observations are excluded from the analysis that goes on to generate

time-varying betas.

Table I OLS Beta Estimates for Australian Banking and Financial Institutions Stocks

Company Name

Sample Period Start Date

Point Estimate Beta (â

i

)

Adelaide Bank

24 December 1993

0.7359

ab

ANZ Bank

10 February 1992

1.3282

a

Bendigo Bank

2 April 1993

0.5262

ab

Bank of Queensland

28 June 1988

0.2817

ab

BT Australia

3 August 1989

0.5820

ab

Bank of Western Australia

1 February 1996

0.7233

ab

Commonwealth Bank

13 September 1991

0.8419

ab

First Australian Building

6 October 1993

0.2785

ab

Hartley Poynton

5 August 1996

0.3565

ab

Macquarie Bank Ltd

29 July 1996

1.2446

a

National Australia Bank

1 January 1980

0.8385

ab

Rock the Building Society

10 December 1992

0.2076

ab

Suncorp-Metway

18 May 1990

0.4935

ab

Wide Bay Capricorn

19 September 1994

0.28763

ab

Westpac Banking Corporation

1 January 1980

0.9609

a

This table lists the ®fteen banking sector stocks used in the study and reports the sample start date for

each stock. The table also reports the OLS point estimate of beta for each stock. Where the beta is

signi®cantly different from zero this is indicated by the superscript `a'. Where the beta is signi®cantly

different from unity this is indicated by the superscript `b'.

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# Blackwell Publishers Ltd/University of Adelaide and Flinders University of South Australia 2000.

In the ®rst two columns of Table III we report the average GARCH-based time varying

beta for each of the stocks, as well as the range (high±low) of observations on the time

varying beta. The ®rst thing of note is the fact that the average of the time varying betas are

remarkably similar to the OLS point estimates of beta for the ®fteen stocks (reported in

Table I). Indeed, the cross sectional correlation between these two series is 0.992. In only

one case is the difference between the point estimate and the average conditional beta greater

than 0.1. This case is Westpac Banking Corporation where the difference is 0.1342 (for

National Australia Bank the difference is 0.0942). Interestingly, these two banks represent

the longest data series in our sample.

These small differences however mask the power of the GARCH approach to the

estimation of time varying betas. This is ®rst illustrated by considering the range of beta

estimates produced. These results are reported in the second column of Table III. The widest

range is 4.475 for the Westpac Banking Corporation in which beta varies from a low of

0.3077 to a high of 4.7823. There are four other stocks where the range is around 2 or

Table II GARCH Models for Australian Banking and Financial Institutions Stocks

Company Name

á

0

á

1

â

1

r

Rt,Rm

Adelaide Bank

0.00008

(6.165)

0.1865

(6.515)

0.4808

(6.931)

0.3990

ANZ Bank

0.00001

(4.843)

0.1226

(8.115)

0.8233

(39.297)

0.6828

Bendigo Bank

0.00004

(5.557)

0.1453

(7.640)

0.6702

(15.157)

0.2833

Bank of Queensland

0.00006

(16.858)

0.1795

(15.971)

0.4749

(17.833)

0.1728

BT Australia

0.00007

(4.859)

0.0734

(5.144)

0.7337

(15.658)

0.2425

Bank of Western Australia

0.00002

(2.107)

0.0596

(2.699)

0.8275

(11.949)

0.4549

Commonwealth Bank

0.00001

(5.617)

0.1236

(6.472)

0.7204

(17.439)

0.6036

First Australian Building

0.00001

(9.001)

0.0312

(7.577)

0.9606

(232.72)

0.1381

Hartley Poynton

0.00007

(3.492)

0.1301

(5.096)

0.7087

(11.908)

0.1541

Macquarie Bank Ltd

0.00008

(5.795)

0.3452

(8.933)

0.3502

(4.540)

0.6258

National Australia Bank

0.00002

(17.048)

0.1489

(24.986)

0.7106

(53.449)

0.5682

Rock the Building Society

0.00001

(5.957)

0.0394

(7.555)

0.9223

(104.772)

0.1162

Suncorp-Metway

0.00006

(12.950)

0.3048

(13.399)

0.3824

(10.232)

0.2849

Wide Bay Capricorn

0.00002

(6.264)

0.1184

(9.566)

0.7836

(34.036)

0.1658

Westpac Banking Corporation

0.00003

(13.255)

0.1450

(32.906)

0.7221

(59.953)

0.6252

Market Portfolio

0.00001

(13.266)

0.2719

(62.187)

0.5763

(33.776)

1.0000

This table reports the parameter estimates for the GARCH (1,1) model for the ®fteen banking sector

stocks, as well as for the market portfolio. The t-tests for the hypothesis that the coef®cients equal

zero are reported in parenthesis. The table also reports correlations between individual stock returns

and the market return.

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greater. These cases are the National Australia Bank (0.2721 to 4.0901), Macquarie Bank

Ltd (0.5559 to 2.8421), the Bank of Queensland (0.0865 to 2.1762) and the ANZ Bank

(0.7513 to 2.7453). The smallest range is 0.3275 for Rock the Building Society (0.0680 to

0.3855).

Kalman Filter time-varying betas

The mean and high/low values of Kalman-Filter time-varying beta of the 15 banking

stocks is presented in the ®nal two columns of Table III. A number of key features are

evident. The ®rst and most notable ®nding is that the Kalman approach generates a range of

observations which are generally larger than those generated by the GARCH technique. This

is contrary to the ®ndings of Brooks, Faff and McKenzie (1998) in that they found a

narrower range for the Kalman approach. The different ®nding is very likely due to the use

Table III Time Varying Beta Estimates for Australian Banking and Financial Institution Stocks

Garch Conditional Beta

Kalman Filter conditional Beta

Company Name

Average Time-

Varying Beta

High

(Low)

Average Time-

Varying Beta

High

(Low)

Adelaide Bank

0.7787

1.7530

(0.3946)

0.6454

2.2186

(ÿ0.6899)

ANZ Bank

1.3687

2.7453

(0.7513)

1.3280

2.7208

(0.4264)

Bendigo Bank

0.5426

1.1565

(0.2991)

0.3634

1.3062

(ÿ0.2801)

Bank of Queensland

0.2971

2.1762

(0.0865)

0.2279

2.4602

(ÿ1.8204)

BT Australia

0.6094

0.9894

(0.1751)

0.5123

1.6548

(ÿ0.4184)

Bank of Western Australia

0.8080

1.1559

(0.2359)

0.6360

2.0837

(ÿ0.6883)

Commonwealth Bank

0.8731

2.2368

(0.4188)

0.8190

2.2684

(ÿ1.5351)

First Australian Building

0.2853

0.5724

(0.0310)

0.1946

3.3290

(ÿ1.4644)

Hartley Poynton

0.3990

0.8798

(0.1221)

0.3776

2.7729

(ÿ1.3543)

Macquarie Bank Ltd

1.1768

2.8421

(0.5559)

0.7498

2.4918

(ÿ0.8156)

National Australia Bank

0.9327

4.0901

(0.2721)

0.8792

4.9202

(ÿ5.1527)

Rock the Building

0.2183

0.3855

(0.0680)

0.1122

1.2046

(ÿ0.9497)

Suncorp-Metway

0.5125

2.1492

(0.1995)

0.4664

3.9367

(ÿ3.3940)

Wide Bay Capricorn

0.3022

0.6654

(0.1112)

0.1697

1.6786

(ÿ1.8488)

Westpac Banking Corporation

1.0951

4.7823

(0.3077)

1.0367

3.8029

(ÿ3.4626)

This table presents the average time-varying beta estimated using the GARCH and Kalman Filter

approaches for each of the ®fteen banking sector stocks. The high and low values (in parentheses) for

the time varying beta estimates produced by each approach are presented in columns 2 and 4,

respectively.

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# Blackwell Publishers Ltd/University of Adelaide and Flinders University of South Australia 2000.

of daily data for individual stocks here, rather than monthly data for industry portfolios in

Brooks, Faff and McKenzie (1998). Second, in the case of the Kalman method, the largest

range of betas occurred for National Australia Bank while Bendigo Bank produced the

smallest range of observations.

Third, it is noted that in several cases the Kalman betas achieved negative values ± indeed,

only ANZ avoided such a situation. While the ®nding of some negative betas when using

daily data is of no surprise, the high incidence of this leads us to be a little suspicious of the

Kalman betas. Fourth, like the GARCH time varying betas, the Kalman counterparts take on

average values quite similar to the OLS point estimates. However, it is true to say that the

Kalman averages diverge a little more. For example, in the case of Macquarie Bank the

average Kalman beta is only 0.7498 compared to an OLS point estimate of 1.2825. Despite

this difference, the correlation between the OLS beta estimate and the mean Kalman beta

across the 15 stocks is 0.93.

We have also generated the correlation coef®cient between the GARCH and Kalman

conditional beta of each stock. Typically, these correlation coef®cients were considerably

less than unity. The average correlation coef®cient (high/low range) across all ®fteen stocks

between the GARCH and Kalman conditional beta was 0.1334 (0.703 for the ANZ Bank and

ÿ0.1246 for Rock the Building Society). To provide a visual appreciation of the differences

between the two time-varying beta series, plots for ANZ and Adelaide Bank are shown in

Figures 1 and 2, respectively. In both cases the plots provide a comparative picture of the

two beta series over the ®nal two years of the sample. The plot of the ANZ betas con®rms

the close relationship between the beta series, whereas the plot for the Adelaide Bank reveals

considerable divergence between the beta series.

This general ®nding of differences between the competing time-varying betas leads to the

obvious question of which method produces superior estimates? It is to this question that we

now turn.

Figure 1. Time-varying Beta Plot for the ANZ Bank

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Choosing the superior time-varying betas for banking stocks

As outlined earlier, the superiority of time-varying betas is assessed by forecasting each

stock return series in-sample and comparing the forecast error (MAE and MSE) produced by

each technique. The results of this procedure are presented in Table IV.

Figure 2. Time-varying Beta Plot for the Adelaide Bank

Table IV In-Sample Forecast Error Summary

MAE

MSE

Combpany Name

GARCH

Kalman

GARCH

Kalman

Adelaide Bank

0.01279

0.00035

4.37E-12

3.49E-23

ANZ Bank

0.00852

0.00013

0.00615

0.00007

Bendigo Bank

0.01021

0.00021

0.00953

0.00018

Bank of Queensland

0.00757

0.00017

0.00673

0.00014

BT Australia

0.01440

0.00037

0.01363

0.00034

Bank of Western Australia

0.01046

0.00020

1.08E-14

2.07E-28

Commonwealth Bank

0.00631

0.00008

9.02E-08

1.60E-14

First Australian Building

0.00908

0.00027

0.00812

0.00020

Hartley Poynton

0.01348

0.00043

5.30E-16

4.67E-33

Macquarie Bank Ltd

0.01173

0.00036

4.13E-12

3.30E-23

National Australia Bank

0.00785

0.00014

0.00509

0.00006

Rock the Building Society

0.00870

0.00020

0.00353

0.00003

Suncorp-Metway

0.00925

0.00018

0.00725

0.00012

Wide Bay Capricorn

0.00784

0.00018

5.50E-16

7.89E-30

Westpac Banking Corporation

0.00843

0.00014

0.00547

0.00006

This table reports the Mean Absolute Error (MAE) and Mean Squared Error (MSE) between the

observed banking stock returns series and the in-sample forecast series where forecasts were generated

using each of the GARCH and Kalman Filter methods of estimating conditional beta

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# Blackwell Publishers Ltd/University of Adelaide and Flinders University of South Australia 2000.

From Table IV, we can see that in every case the Kalman Filter approach produces the

smaller forecast error compared to the GARCH technique. The average MAE for GARCH

was 0.0097 while the average MAE for Kalman Filter approach was only 0.00437. To test

the robustness of this ®nding to the error measure chosen, Table IV also presents the MSE

and the same result is evident. The GARCH model produces a higher average MSE of

0.00023 compared to the average MSE for the Kalman Filter technique of only 0.00008.

This ®nding in favour of the Kalman technique con®rms the same ®nding reported by

Brooks, Faff and McKenzie (1998) for monthly data on Australian industry portfolios.

IV. C o nc lu s i o n

In this paper we apply the generalised auto-regressive conditional heteroskedasticity

(GARCH) and Kalman Filter approaches to modelling the equity beta risk of a sample of

®fteen Australian ®nancial sector companies. A de-regulated environment in which strong

competitive forces are at play typi®es the period of investigation, which in all cases extends

through to September 1998. Consistent with the existing literature, the results show that

there is much day to day variability in the betas, which is well captured by both models,

consistent with the hypothesis that deregulation has impacted the risk of banking sector

stocks. Thus, we extend the evidence of Harper and Scheit (1992); Brooks and Faff (1995)

and Brooks, Faff and McKenzie (1997). Further, we use some basic error metrics to compare

the in-sample performance of the two time-varying beta techniques to forecast returns. This

analysis clearly favours the Kalman method ± thus supporting the ®ndings of Brooks, Faff

and McKenzie (1998) who examined time varying betas for Australian industry portfolios

(using monthly data). Therefore, the superiority of the Kalman Filter in producing time-

varying beta estimates for Australian industry portfolios extends at least as far as ®nance

sector stocks.

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