Movements in Australian stock volatility: a disaggregated approach.

Abstract:

This paper applies a disaggregated approach to examine stock volatility at the firm, industry and market level in Australia. We employ the models advanced by Campbell, Lettau, Malkiel and Xu (2001) to carry out this disaggregation, and extend their methodology to incorporate: formal tests of changes in volatility as well as correlations; and the Hodrick-Prescott Filter to identify trends in the series. A trend of decreasing volatility is identified at all levels of aggregation, which is further supported by robust OLS analysis. Results also provide strong support for an increase in correlations between industries over the past 30 years. Coinciding spikes in the volatility and correlation series during periods of market stress has significant implications for portfolio diversification. No support is found for a month-of-the-year effect on volatility or correlations.

Keywords:

VOLATILITY; DISAGGREGATION OF VOLATILITY; CORRELATION; TIME-SERIES TRENDS; DIVERSIFICATION BENEFITS.

1. Introduction

Portfolio theory is a central tenet of modern finance theory. Any cursory examination of the portfolio variance formula reveals that individual stock volatility and inter-stock correlation is the key to reducing portfolio volatility. This paper revisits portfolio theory by re-examining stock volatility, as well as the correlation between individual stocks and industries.

Markowitz (1952) demonstrates the ability of investors to construct mean-variance efficient portfolios by increasing the number of constituent stocks in their portfolios. Indeed, as the number of assets within a portfolio becomes very large, portfolio variance is approximated by average covariance. Yet, reducing portfolio risk is not only restricted to increasing the number of stocks. King (1966) argues that any discussion of diversification and stock-price behaviour must consider firm, industry and market components. Evidence of this is seen by firms in the same industry, who are likely to have highly correlated returns. As such, diversification is optimal only if investment occurs over a range of stocks in different industries. Therefore, it is vital to be able to determine the break-up of an individual stock's risk into firm, industry and market components.

It is important to note that firm, industry and market factors influence the volatility of an average firm. As such, we argue the need to decompose average stock volatility. This stratification is informative, providing insight into the relative influence of firm, industry and country components of an average stock's volatility. For example, if volatility is only minimal at the industry level, then diversifying across industries may be less important.

The extant literature fails to consider the issue of disaggregated volatility in the Australian market. Australian studies mainly focus on volatility at the market level (see Brailsford & Faff 1993; Keams & Pagan 1993; Nicholls & Tonuri 1995), and attempt to model the time-variation in volatility. Specifically, Nicholls and Tonuri (1995) find that ARCH models provide a reasonable fit to account for the time-variation in volatility. Keams and Pagan (1993) and Brailsford (1994) identify an increase in market-level volatility within Australia since 1970. However, no study attempts to disaggregate Australian volatility into firm, industry and market components.

Research mainly addresses market-level volatility in accordance with the paradigm of diversification (see Officer 1973; Poterba & Summers 1986; Brailsford & Faff 1993; Whitelaw 1994; Hentschel 1995; Aggarwal, Inclan & Leal 1999). In general, we assume investors hold well diversified portfolios, so that idiosyncratic risk is minimised, and only systematic risk is priced. However, the focus on market-level volatility is criticised in recent studies. Duffee (1995) stresses the importance of considering firm-level volatility, while Malkiel and Xu (1999) and Campbell et al. (2001) argue for a complete disaggregation into firm; industry- and market-level volatility.

Xu and Malkiel (2003, p. 614) state, 'because of wealth constraints or by choice, many investors do not hold diversified portfolios.' In this case, it is crucial to identify the firm-specific risk of the securities to determine the investors' return. This is supported by Campbell et al. (2001, p. 1), who argue that 'the aggregate market return is only one component of the return to an individual stock.' They posit three additional reasons for the inclusion of disaggregation in any comprehensive analysis of volatility. First, 'day traders' and other arbitrageurs derive profits from the idiosyncratic risk of the securities they trade. Simply, stocks with higher volatility present an opportunity for increased profits (see Ingersoll 1987, ch 7; Shleifer & Vishney 1997). Second, firm-, industry- and market-level volatility are vital components of asset pricing models such as the Black-Scholes Model. Under the model, the price of an option is related to the total volatility (firm-, industry- and market-level) of the stock return, not just the market-level volatility (see Black & Scholes 1973). Third, to calculate abnormal returns in event study methodology, it is necessary to compare a stock's volatility with the industry and/or market-level volatility (Campbell, Lo & MacKinlay 1997, ch. 4). As such, we argue that for a complete analysis of volatility, all levels of disaggregation should be included.

To create variance-efficient portfolios, it is crucial to consider both the correlation between firms and industries, and the components of stock volatility. If industry-level volatility is the largest component of an average stock's risk, then assessing the correlation between industries is essential. High levels of industry volatility would necessitate low correlations between industries to maintain the same diversification benefit. Should there be high levels of both industry volatility and industry correlations, then diversification would have to occur over a larger number of industries.

The extant literature also documents that volatility and correlations are not constant over time (see Shwert 1989; Brailsford 1995), which has important ramifications for diversification. An increase in volatility or correlations may require an increase in the number of stocks to achieve the same level of diversification. This paper thus provides rigorous tests for changes in disaggregated volatility. Further, by applying these tests to both firm and industry correlations, we are able to provide a comprehensive analysis of portfolio diversification.

This study provides the first disaggregated analysis of historical movements in volatility and correlations in the Australian market. In performing this disaggregation, we utilise the methodology of Campbell et al. (2001). Their methodology provides a simple summary of historical movements in market-, industry- and firm-level volatility, without requiring the estimation of covariances or betas for industries and firms. They find that market- and industry-level volatility in the USA has remained fairly stable from 1962 to 1997. However, firm-level volatility has almost doubled since 1962. Despite this increase in firm-level volatility, they observe that declining correlations between stocks allows the volatility of the market portfolio to remain unchanged.

We extend the analysis of Campbell et al. (2001) with the inclusion of three innovations. First, we provide formal tests for changes in Australian firm, industry and market-level volatility by employing OLS analysis with HAC consistent standard errors. Second, the application of the Hodrick-Prescott (H-P) Filter attempts to identify trends in the volatility series. Last, in an attempt to examine changing patterns in diversification benefits, we adopt the OLS analysis and H-P Filter on both firm- and industry-level correlation series.

The remainder of the paper is organised as follows. Section 2 details the methodological approach adopted, while section 3 describes the data employed. Section 4 presents the results of the study, with section 5 providing some concluding remarks.

2. Model Specification

2.1 Calculation of the Volatility Measures

Section 1 identifies the importance of using a disaggregated approach when investigating volatility. As Campbell et al. (2001, p. 4) argue, the 'goal is to define volatility measures that sum to the total return volatility of a typical firm, without having to keep track of covariances and without having to estimate betas for firms or industries.' We adopt Campbell et al.'s (2001) methodology to decompose Australian stock returns into a market-wide return, as well as industry-specific and firm-specific residuals. These components are used to construct the time-series volatility measures.

2.1.1 Return Decomposition In order to perform the return decomposition, we create the market and industry-level indices. Returns are calculated on a time interval of one trading day, denoted by the subscript s. All industry indices and the market index are value weighted by market capitalisation. (1) To determine the weight at time s, we use the market capitalisation of a firm at time [s.sub.-1]. The market and industry return indices are formally stated as:

[R.sub.is] = [summation over (j [member of] i)] [w.sub.is] [R.sub.is] (1)

[R.sub.ms] = [summation over (i)] [w.sub.is] [R.sub.is] (2)

where: [R.sub.is] = the return of industry i at time s; [w.sub.jis] = the weight of firm j in industry i at time s; [R.sub.jis] = the return of firm j in industry i at time s; [R.sub.ms] = the return on the market at time s; and [w.sub.is] = the weight of industry i in the market at time s.

The first step in the disaggregation of volatility is the decomposition of stock returns into market, industry and firm-specific components. The following equations detail the industry and firm return decompositions:

[R.sub.is] = [R.sub.ms] + [[epsilon].sub.is] (3)

[R.sub.jis] = [R.sub.is] + [[eta].sub.jis] (4)

where: [R.sub.is] = the return of industry i at time s; [R.sub.ms] = the market return at time s; and [R.sub.jis] = the return of firm j that belongs to industry i at time s.

The residuals ([[epsilon].sub.is] and [[eta].sub.jis]) obtained from equations (3) and (4) are used to construct our estimates of industry and firm-level volatility.

2.1.2 Volatility Calculation The three volatility measures of the disaggregated approach are outlined below. First, the monthly market volatility (MK[T.sub.t]) measure is presented in equation (5):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

where: [[??].sub.mt] = market volatility in period t; [R.sub.ms] = the market return at time s; and, [[mu].sub.m] = the mean market return for the month in question.

It is important to note that all volatility measures are based on the summation of daily observations, and are calculated at a time interval of one calendar month, denoted by the subscript t.

Second, the volatility of industry i is calculated in two parts. The daily industry-specific residuals obtained in equation (3) are averaged over industries via equation (6). Subsequently, the monthly measure of industry volatility ([IND.sub.t]) is determined by summing the daily volatility estimates over the month t. The equations for industry volatility are presented below:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7)

where: [summation over (i)][w.sub.is][[epsilon].sup.2.sub.is] = the daily squared residuals weighted for that particular industry's weight in the market at time s; and

[summation over (s [member of] t)][[??].sup.2].sub.[epsilon]is] = the monthly industry volatility measure calculated by summing the weighted daily squared residuals.

Finally, we utilise a similar approach to calculate firm-specific volatility, using residuals acquired from equation (4). The weighted average of the firm-specific residual ([[??].sup.2.sub.[eta]is]) within an industry is averaged over that particular industry's weight in the market ([[??].sup.2.sub.[eta]s]). Monthly firm-level volatility ([FIRM.sub.t]) is derived from the summation of these daily observations:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (10)

where: [summation over (j[epsilon]i)] [w.sub.jis][[eta].sup.2.sub.jis] = the daily squared firm residuals weighted by industry membership;

[summation over (i)] [w.sub.is] [[??].sup.2.sub.[eta]is] = the weighted average of daily firm-specific volatilities; and

[summation over (s[epsilon]t)][[??].sup.2.sub.[eta]s] = the monthly firm volatility measure.

The above industry and firm volatility series represent volatility for an average industry and firm respectively. We would expect to observe this level of volatility if a firm or industry was selected at random.

2.2 Graphical Analysis

In analysing volatility over time in Australia, we are interested in the identification of trends. We apply the H-P [Filter.sup.2] to ascertain the existence of such trends in the three volatility series. The H-P Filter is a smoothing method used to estimate the long-term trend component of a series. It is a two-sided linear filter that computes the smoothed series s of y by minimising the variance of y around s. This is subject to a penalty that constrains the second difference of s. The filter is formally presented in equation (11):

[T.summation over (t=1)][([y.sub.t] - [s.sub.t]).sup.2] + [lambda] [T-1.summation over (t=2)] [(([s.sub.t+1] - [s.sub.t]) - ([s.sub.t] - [s.sub.t-1])).sup.2] (11)

The penalty parameter A controls the smoothness of the series. Consistent with Hodrick and Prescott (1997), we employ a smoothing parameter of 14,400, as required for monthly data.

2.3 OLS Analysis

2.3.1 Trend Analysis Further examination of any trends identified by the H-P Filter analysis is investigated using ordinary least squares (OLS) regressions. These regressions attempt to ascertain whether there has been a change in the mean level of volatility. Specifically, this study examines Australian volatility from 1973 to 2003, which we split into six time periods. Each period is five years in length, except for the last period which contains six years of monthly volatility estimates. This allotment allows us to determine whether there has been a change in the mean level of volatility over the entire sample period. The volatility series are regressed against dummy variables representing each time period. This model is formally presented below:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (12)

where: [Vol.sub.kt] = the particular disaggregated volatility series at time t (firm, industry or market-level);

[[beta].sub.0] = the mean level of volatility from 1973-1977 at time t; and

[[beta].sub.1-5] = the difference in mean level volatility from 1973-1977 to the period under study at time t.

2.3.2 Month of the Year Effect Research into return data examines the existence of monthly seasonality. Rozeff and Kinney (1976) examine share return seasonality in the USA and find abnormally high share returns in the month of January. Brown, Klein, Kleidon and Marsh (1983) and Brailsford and Easton (1991) examine monthly seasonality in Australia and find large returns in January and April. We assert that abnormal returns during some months may correspond to abnormal levels of volatility. As such, we employ the following model to assess whether there is a month of the year effect in any of the volatility series:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (13)

where: [Vol.sub.kt] = the particular disaggregated volatility series at time t (firm, industry or market-level);

[[beta].sub.0] = the mean level of volatility during the month of January at time t; and

[[beta].sub.1-11] = the difference in mean level volatility from January to each of the other months, at time t.

2.4 Correlation Analysis

While Campbell et al. (2001) study correlations at a firm-level, we extend their analysis by also considering trends in correlations at an industry-level. This analysis provides an insight into any change in diversification benefits in the Australian market over the past 30 years. In order to construct a monthly firm correlation series, we calculate all pairwise correlations between firm returns using daily observations within each month. We then calculate an equally weighted average of these pairwise correlations. This process is also applied to calculate an industry correlation series. To determine if any trends are evident in the correlation series we then employ both the H-P Filter and OLS regressions outlined in sections 2.2 and 2.3.

3. Data

To calculate firm returns we use daily data from DataStream International, spanning from 1 January 1973 to 31 December 2003. We collect total return data (which incorporates price, dividends and capitalisation changes) and market capitalisation data for the firm-level constituents of the ASX All Ordinaries Index.

Further, to aggregate these firms into industries, (3) we also collect their three digit DataStream International Sub Sector classification codes. The total number of firms covered in our data set range from 43 in January 1973 to 481 in December 2003.

To ensure the volatility estimates are accurate representations of the volatility faced by an investor, we remove public holidays and non-trading days from the initial sample. The resulting sample size comprises 7,869 daily observations, with 372 months of volatility estimates. Results and analysis are presented for the three volatility series (firm, industry and market-level volatility) and two correlation series (firm and industry-level correlations).

Summary statistics for the three volatility series are presented in table 1 below. Examination of the table reveals that all three series suffer from autocorrelation. The Q (10) statistic is the Box-Ljung portmanteau test for first to tenth-order autocorrelation, and is distributed [x.sup.2]. At all levels of disaggregation, there is significant autocorrelation at the 5% level. In order to account for this autocorrelation, all standard errors of the estimated regression coefficients in equations (12) and (13) are heteroscedasticity and autocorrelation (HAC) consistent. The HAC standard errors are calculated using the Newey and West (1987) adjustment. Further examination of the table reveals that all series are stationary with ADF test-statistics all significant at the 1% level. It is interesting to note that the mean firm-level volatility (0.0046) is much higher than both the mean market-level volatility (0.0023), and mean industry-level volatility (0.0012). This is consistent with Campbell et al. (2001) who find that firm volatility is on average much higher than market-level volatility in the USA.

4. Results

4.1 Graphical Analysis of Volatility Series

Figure 1 presents the time series plots of the disaggregated Australian volatility series. First, it is apparent that after an initial high period from 1973-1976, market-level volatility remains fairly constant at 0.003. We note, however, that a spike in volatility occurs during the stock market crash of October 1987 (with a volatility measure of 0.10). Application of the H-P Filter (illustrated in fig. 2a) identifies an overall downward trend in market-level volatility, with a spike during the 1987 crash. Campbell et al. (2001) and Schwert (1989) note that during periods of recession there are temporary increases in volatility. These changes in volatility are not persistent over time and also occur in periods of market stress, such as the 1987 crash. We find support for this argument with high levels of volatility during the 1974, 1976 and 1981 recessions. Conversely, volatility is relatively low during the 1991 recession.

[FIGURES 1-2 OMITTED]

Consistent with Campbell et al. (2001), average industry volatility (0.0012) is considerably lower than market-level volatility (0.0023). However, in examining industry series trends, our results differ from the findings of Campbell et al. (2001), who fail to identify a trend in industry volatility in the USA. A downward trend in industry volatility is evident in figure 2b. Industry-level volatility is high from 1973-1977, corresponding with the 1974 and 1976 recessions. Falling for the following ten years (with the exception of a spike in 1987), industry-level volatility drops to its lowest point in 1990, where it remains stable until 1996. A rapid increase is evident from 1997-2001, which we attribute to the technology-sector boom and bust period. These trends are further examined in section 4.2 employing OLS regression analysis.

Figure 1c captures an overall decrease in firm-level volatility punctured with spikes in 1978, 1987 and 1999-2000. These results are supported by the H-P Filter in Figure 2c, with a clearly evident downward trend in firm-level volatility in Australia. This contradicts with Campbell et al.'s (2001) findings of an increase in firm-level volatility in the USA.

4.2 OLS Analysis of Volatility Series

We extend the graphical analysis of Campbell et al. (2001) in table 2 by employing OLS methodology with HAC-consistent standard errors. This analysis attempts to identify significant differences in the mean level of volatility, comparing 1973-1977 with each of the subsequent time periods. The OLS results at a market-level support the analysis in section 4.2, with the mean market-level volatility significantly lower during 1988 to 2003. These results are consistent with the graphical analysis (fig. 1a and 2a) highlighted in section 4.1.

At an industry and firm level, results reveal that the mean level of volatility significantly trends downwards from 1973 to 2003. Again, this is consistent with the findings in section 4.1. One exception is 1998-2003, where there is no significant change in the mean level of industry volatility. We suggest this is due to the high level of volatility experienced in both time periods. Specifically, the first time period incorporates the 1974 and 1976 recessions, while the last period (1998-2003) contains the technology-sector boom and bust.

We consider whether a month-of-the-year effect exists within our disaggregated volatility series in table 3. Our results suggest that no such effect exists at any level of volatility. As such, we surmise that the month of year is not influential upon volatility levels.

4.3 Graphical Analysis of Correlation Series

We use daily pairwise correlations to document any trends in correlations over time. (4) Figure 3 reveals clear trends in both the industry- and firm-level correlation series. At an industry level, correlations increase markedly from 17% in 1980 to 38% in 1987, and remain fairly constant thereafter. This is evidenced in both the raw correlation series (fig. 3a) and the H-P Filter plots (fig. 3c). Spikes in industry-level correlation during 1987 and 1999 are clearly evidenced in figure 3a, and correspond to the spikes identified in figure 1b for the industry-level volatility series. Lin, Engle and Ito (1994) and Erb, Harvey and Viskanta (1994) find that correlations tend to increase during periods of high volatility. As such, we argue that the high levels of volatility experienced during the stock market crash of 1987 and the technology-sector boom and bust period of 1999-2001 may lead to the corresponding increases in correlations.

Firm-level correlations (fig. 3b and 3d) reveal a sharp increase in correlations from 4% in 1980 to 9% in 1985, before trending back to 4% from 1990 onwards. These results differ from those of Campbell et al. (2001) who identify a decrease in firm-level correlations in the USA, throughout their sample. Consistent with the results for the industry series, periods of increased firm-level correlations (1987 and 1999-2000) correspond to periods of high firm-level volatility.

We find a trend of decreasing volatility at all levels of aggregation, which is further supported by robust OLS analysis. The implication of decreasing industry-level volatility for portfolio risk is that diversification over a range of industries is less important. However, our examination of industry-level correlations reveals an increase in average industry correlations over the past 30 years. This implies that diversification should at least be maintained or increased to achieve the same level of portfolio risk. While there is no significant trend of increasing or decreasing correlations between firms, we do find that spikes in firm-level volatility (such as the 1987 crash and 1999-2001 technology-sector boom and bust) coincide with spikes in correlations between firms. Due to the fact that there is a coinciding spike in both volatility and correlations, portfolio variance must increase. As a result, investors may not be able to gain the benefits of diversification when they need them most.

4.4 OLS Analysis of Correlation Series

Table 4 findings support the graphical analysis presented in figure 3. The mean level of correlations is significantly higher from 1983 to 2003 at an industry-level, while mean firm-level correlations are significantly higher from 1983-1987, and significantly lower from 1998 2003.

Lastly, table 5 reveals that there is no month of the year effect identified in any of the correlation series. This is consistent with the volatility findings in table 3.

5. Conclusion

This study provides the first disaggregated analysis of historical movements in volatility and correlations in the Australian market. While this paper utilises the methodology of Campbell et al. (2001), we extend their analysis with the inclusion of three innovations. First, we provide formal tests for changes in firm, industry and market-level volatility by employing OLS analysis with HAC-consistent standard errors. Second, the application of the H-P Filter attempts to identify trends in the series. Lastly, we apply the OLS analysis and H-P Filter on both firm- and industry-level correlation series to identify changing patterns in diversification benefits.

These innovations provide evidence of a decrease in volatility at a firm-, industry-and market-level. This is of interest to arbitrageurs who derive profits from the volatility of the individual stocks they hold. Further, our results show an increase in industry-level correlations, and high levels of firm-level correlations during periods of high volatility. This increase has important ramifications for portfolio construction. Investors and portfolio managers rely upon the benefits of holding a well diversified portfolio during periods of market stress. However, as correlations increase, the number of stocks required to achieve the same level of diversification benefit also increases. Therefore, to ensure their portfolios are adequately diversified, both individual investors and portfolio managers should be aware of the changing levels of correlations.

The author gratefully acknowledges the helpful suggestions made by Michael Martin and Tom Smith.

(Date of receipt of final transcript: February 1, 2005. Accepted by Garry Twite, Area Editor.)

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(1.) The indices are comprised of all constituent firms at time s.

(2.) Hodrick and Prescott (1997) develop the filter to identify trends in post-war USA business cycles.

(3.) The ten DataStream industry classifications for Australia include: basic industries; cyclical consumer goods; cyclical services; financials; general industries; non-cyclical consumer goods; non-cyclical services; resources; utilities; and, information technology.

(4.) The number of stocks in the firm correlation calculation range from 43 in January 1973 to 481 in December 2003. Thus, the number of pairwise correlations each day range from 903 to 115,430. At an industry-level, there are ten industries corresponding to 45 pairwise industry correlations per day.

Stephen Sault, School of Finance and Applied Statistics, Australian National University, Canberra, ACT, 0200. Email: [e-mail]

Table 1
Summary Statistics: Firm, Industry and Market-Level Volatility
Series

The notation used in the table below is defined as follows: Market
is the volatility measure for the Australian market. Industry is the
volatility measure for an average industry in Australia. Firm is the
volatility measure for an average firm in Australia.

Series      Mean    Standard      Min       25th      Median
                    Deviation            Percentile

Market     0.0023    0.0056     0.0002     0.0009     0.0014
Industry   0.0012    0.0009     0.0003     0.0007     0.0010
Firm       0.0046    0.0035     0.0016     0.0029     0.0038

Series        75th        Max      Q (10)        ADF
           Percentile                         Test- Stat

Market       0.0023     0.1010    22.01        -7.36 ***
                                  (0.02) **
Industry     0.0014     0.0090   292.66        -5.55 ***
                                  (0) ***
Firm         0.0052     0.0452   108.62        -5.91 ***
                                  (0) ***

Note: * significant at the 10% level;

** significant at the 5% level; and


*** significant at the 1% level.

Table 2
Results of the Trend Analysis for Volatility

The table below presents results for equation (12) using volatility
data. Market is the volatility measure for the Australian market.
Industry is the volatility measure for an average industry in
Australia. Firm is the volatility measure for an average firm in
Australia. The intercept measures the mean level of volatility in
the years 1973-1977. Each of the other time periods measures the
difference in mean level volatility from the intercept.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where: [Vol.sub.kt] = the particular disaggregated volatility series
at time t (firm, industry, or market-level);

[[beta].sub.0] = the mean level of volatility from 1973-1977 at time t;

[[beta].sub.1] - [[beta].sub.5] = the difference in mean level
volatility from 1973-1977 to the period under study at time t; and,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = dummy variable
equal to 1 when the volatility lies within the time period (XX-YY)
at time t, or otherwise zero.

                                     Volatility Series
                         Market          Industry            Firm

[[beta].sub.0]         0.0033            0.0017            0.0069
                      (4.4739 ***)      (9.9009 ***)      (7.2114 ***)
[[beta].sub.1]        -0.0010           -0.0004           -0.0021
                     (-1.2583)         (-1.7150 *)       (-2.0817 **)
[[beta].sub.2]         0.0006            0.0004           -0.0022
                      (0.3045)         (-1.7523 *)       (-1.7927 *)
[[beta].sub.3]        -0.0016           -0.0010           -0.0037
                     (-2.0446 **)      (-5.5661 ***)     (-3.7154 ***)
[[beta].sub.4]        -0.0020           -0.0010           -0.0038
                     (-2.6682 ***)     (-5.3348 ***)     (-3.8142 ***)
[[beta].sub.5]        -0.0019           -0.0001           -0.0018
                     (-2.6018 ***)     (-0.4864)         (-1.822 *)
F-stat                 2.394 **         15.26 ***         10.67 ***
Multiple [R.sup.2]     0.0317            0.1725            0.1272
Adjusted [R.sup.2]     0.01844           0.1612            0.1153

Note: * significant at the 10% level;

** significant at the 5% level; and

*** significant at the 1% level.

Table 3
Results of the Month of the Year Analysis for Volatility

The table below presents results for equation (13) using volatility
data. Market is the volatility measure for the Australian market.
Industry is the volatility measure for an average industry in
Australia. Firm is the volatility measure for an average firm in
Australia. The intercept measures the mean level of volatility
during the month of January. Each of the other months measures the
difference in mean level volatility from the intercept.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (13)

where: [Vol.sub.kt] = the particular disaggregated volatility series
at time t (firm, industry or market-level);

[[beta].sub.0] = the mean level of volatility during the month of
January at time t;

[[beta].sub.1] - [[beta].sub.11] = the difference in mean level
volatility from January to each of the other months, at time t; and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] = dummy variable
equal to 1 when the volatility lies within that month at time t, or
otherwise zero.

                                     Volatility Series
                         Market          Industry            Firm

[[beta].sub.0]         0.002            0.001              0.004
                      (6.3629 ***)     (7.0711 ***)       (8.8429 ***)
[[beta].sub.1]         0.000            4.46E-05           0.0003
                      (0.4816)         (0.3485)           (0.8445)
[[beta].sub.2]        -4.85E-05         0.000              5.91E-05
                      (0.1498)        (-0.5590)           (0.1352)
[[beta].sub.3]        -0.0003          -0.0002            -0.0003
                     (-0.9782)        (-0.8789)          (-0.6053)
[[beta].sub.4]        -0.0002          -4.90E-05           1.03E-05
                     (-0.7004)        (-0.2440)           (0.0196)
[[beta].sub.5]        -0.0004          -0.0002            -0.0001
                     (-1.0965)        (-0.9438)          (-0.1983)
[[beta].sub.6]        -0.0004          -0.0001            -0.0005
                     (-1.0828)        (-0.6742)          (-0.8705)
[[beta].sub.7]         8.18E-05        -0.0002            -6.22E-05
                      (0.1769)        (-0.9659)          (-0.0987)
[[beta].sub.8]         0.0006          -6.74E-06           0.0007
                      (0.8812)        (-0.2810)           (0.9921)
[[beta].sub.9]         0.0042           0. 0005            0.0021
                      (1.3126)         (1.3236)           (1.8725 *)
[[beta].sub.10]        0.0010           5.28E-05           0.0008
                      (1.3183)         (0.2544)           (1.2323)
[[beta].sub.11]       -0.0003          -0.0002             0.0008
                     (-1.5923)        (-1.1387)           (0.5993)
F-stat                 1.571            1.318              1.301
Multiple [R.sup.2]     0.0479           0.0387             0.0382
Adjusted [R.sup.2]     0.0189           0.0093             0.0088

Note: * significant at the 10% level;
** significant at the 5% level; and
*** significant at the 1% level.

Table 4
Results of the Trend Analysis for Correlations

The table below presents results for equation (12) using correlation
data. Industry is the measure of the average pairwise correlations
between all industries. Firm is the measure of the average pairwise
correlations between all firms. The intercept measures the mean
correlation during the years 1973-1977. Each of the other time periods
measures the difference in the mean level of correlations from the
intercept.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (12)

where: [Cor.sub.kt] = the particular average correlation series at
time t (firm or industry);

[[beta].sub.0] = the mean level of average correlation from 1973-1977
at time t;

[[beta].sub.1] - [[beta].sub.s] = the difference in mean level average
correlation from 1973-1977 to the period under study at time t; and,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] = dummy variable
equal to 1 when the correlation lies within the time period (XX-YY) at
time t, or otherwise zero.

                            Correlation Series

                        Industry         Firm

[[beta].sub.0]         0.2411          0.058
                      (8.5603 ***)    (7.9790 ***)
[[beta].sub.1]        -0.0349         -0.0096
                     (-1.0751)       (-1.1383)
[[beta].sub.2]         0.1067          0.0269
                      (2.9572 ***)    (2.4984 **)
[[beta].sub.3]         0.1254         -0.0150
                      (3.9654 ***)   (-1.6531 *)
[[beta].sub.4]         0.1044         -0.0085
                      (3.003 ***)    (-0.8674)
[[beta].sub.5]         0.0922         -0.0222
                      (2.7618 ***)   (-2.7766 ***)
F-stat                15.58 ***       11.32 ***
Multiple [R.sup.2]     0.1755          0.1339
Adjusted [R.sup.2]     0.1642          0.1221

Note: * significant at the 10% level;
** significant at the 5% level; and
*** significant at the 1% level.

Table 5
Results of the Month of the Year Analysis for Correlations

The table below presents results for equation (13) using correlation
data. Industry is the measure of the average pairwise correlations
between all industries. Firm is the measure of the average pairwise
correlations between all firms. The intercept measures the mean
between all industries. Firm is the measure of the average pairwise
Each of the other months measures the difference in mean level
correlation from the intercept.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (13)

where: [Cor.sub.kt] = the particular average correlation series at
time t (firm or industry);

[[beta].sub.0] = the mean level of average correlation from 1973-1977
at time t;

[[beta].sub.1] - [[beta].sub.s] = the difference in mean level average
correlation from 1973-1977 to the period under study at time t; and,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] = dummy variable
equal to 1 when the correlation lies within the time period (XX-YY) at
time t, or otherwise zero.

                         Correlation Series

                       Industry          Firm

[[beta].sub.0]         0.3228          0.0525
                     (17.2482 ***)    (9.5190 ***)
[[beta].sub.1]        -0.0228         -0.0043
                     (-0.9372)       (-0.6868)
[[beta].sub.2]        -0.0095         -0.0027
                     (-0.3161)       (-0.3190)
[[beta].sub.3]        -0.0081          0.0018
                     (-0.2848)        (0.2236)
[[beta].sub.4]        -0.0576         -0.0032
                     (-1.0210)       (-0.3932)
[[beta].sub.5]        -0.0861         -0.0092
                      (1.3466)       (-1.1596)
[[beta].sub.6]        -0.0364         -0.0048
                     (-0.9989)       (-0.5541)
[[beta].sub.7]        -0.0014         -0.0039
                     (-0.0423)       (-0.5075)
[[beta].sub.8]         0.0260          0.0022
                      (0.9151)        (0.2639)
[[beta].sub.9]         0.0474          0.0261
                      (1.5476)        (1.1285)
[[beta].sub.10]       -0.0058          0.0085
                     (-0.2159)        (1.0817)
[[beta].sub.11]       -0.0281         -0.0074
                     (-1.0400)       (-1.1139)
F-Stat                 1.498           1.507
Multiple [R.sup.2]     0.0565          0.0440
Adjusted [R.sup.2]     0.0276          0.0148

Note: * significant at the 10% level;
** significant at the 5% level; and
*** significant at the 1% level.