Equity market valuation: assessing the adequacy of value measures to predict index returns.

Abstract:

Following the work of Lee, Myers and Swaminathan (1999), we develop robust tests of their intrinsic value measure, along with other traditional measures of value, for the Australian Stock Market. Specifically, we apply the tests to a broadly matched version of the Australian Asia Pacific Extra Liquid Series (APELS), which was recently introduced to Australia. A primary motivation for the paper was to assess the suggestion implied in the US study of a violation of capital market efficiency, where the use of publicly available information, namely a fundamental valuation measure using consensus analysts forecasts, could be used to predict returns. Our results do not support the conclusions reached by Lee, Myers and Swaminathan (1999). Possible reasons for this are the differing Market structures, the use of a different Index or the use of alternative statistical tests.

Keywords:

ECONOMETRICS; MARKET EFFICIENCY; STOCK PRICES; VALUATION; SECURITIES MARKETS.

1. Introduction

The purpose of this study is to test and extend the study of Lee Myers and Swaminathan (1999) (1) on a portfolio of Australian Stocks. Specifically, we have attempted to apply a residual income valuation model as developed by Ohlson (1990) and extended by LMS (1999) to compute a measure of the intrinsic value for the Australian Portfolio.

The major motivation for the paper was to reassess claims made by recent studies including LMS (1999) of the ability of measures of a firm's value to predict future returns. Many of the results presented by LMS (1999) suggest that future returns on a portfolio of assets based on the Dow Jones Index could be predicted by an appropriately constructed measure of the portfolio's intrinsic value. Based on the LMS (1999) framework, it is possible that parity does not always strictly hold between market price and intrinsic value; instead the two are co-integrated and are convergent in the long run. That is to say, any divergence between prices and value in the short run should not be persistent (the deviation is non-stationary).

The criterion used in LMS (1999) for assessing the adequacy of a firm's value measure is based on the measure's relative ability to track price variation over time, and its ability to predict market returns over time. Their study concludes that intrinsic value measures, based on Ohlson's (1990) valuation model, outperform more traditional market measures currently used by practitioners. For the purposes of our study, we consider the following set of instruments in competition to the intrinsic value measure constructed in LMS (1999): book-to-market (B/P), Earnings yield (E/P) and Dividend yield (D/P) and consensus analysts earnings yields forecasts (FE/P). Having constructed the index for Australian stocks which broadly matches the APELS, the corresponding series of B/P, E/P and D/P for the index are also constructed and used in subsequent analysis.

The investigation proceeds in a number of steps. We firstly investigate the tracking ability of the various instruments considered by testing their stationarity properties. Using Australian data, we can investigate whether the constructed intrinsic value measure along with the other competing instruments actually satisfy the first key criterion by LMS (1999) as to a measure's adequacy. Results seem to suggest that all instruments including the value measure behave poorly with respect to their mean reversion properties.

The second set of analyses pertains to an instrument's ability to predict future returns over various horizons. This study seeks to determine whether the construction of `superior' measures, based on their apparent ability to better predict returns, are in fact the result of the statistical properties of the testing procedures used. The main tool adopted by many studies, such as Fama and French (1988a,b; 1989) along with LMS (1999) in assessing predictability, is regression analysis. Such a strategy reduces to regressing overlapping returns for various holding periods on a set of predetermined instruments or forecasting variables. LMS (1999) use both the R-squared values from the multiperiod regressions and the significance of estimated slope parameters as evidence supporting the idea that various measures have the ability to predict future returns.

In essence, the results implied by the US study conducted by LMS (1999) suggest a violation of capital market efficiency, whereby a composite measure constructed using publicly available information (the `intrinsic value' measure) can be used to predict future returns. This would suggest that traders could generate superior returns by adopting appropriately constructed trading strategies. However, as several authors have noted, among them Kirby (1997), Richardson and Smith (1991; 1994), Richardson and Stock (1989) and Hodrick (1992), the use of small sample sizes and overlapping observations induces serial correlation and conditional heteroskedasticity in the distribution of the estimators. Failure to adequately account for this can render the inferences drawn misleading. If this is indeed the case, then an appropriate set of tests must be designed to take into account the effects of overlapping observations and size effects of the test statistics adopted. In this study we derive test statistics for a joint system of regressions, and test both individually and jointly whether the slope coefficient estimates of a series of long-horizon regressions are significant. Furthermore, we explicitly incorporate size effects of the tests by incorporating the null hypothesis in the construction of test statistics in a manner similar to Kirby (1997), Richardson and Smith (1991; 1994), and Hodrick (1992). In our sample we find that failure to account for these issues tends to lead to results which incorrectly tend to reject the null hypothesis that returns are unpredictable.

The results of the unit root tests and multiperiod regressions for the Australian market are compared to those found in LMS (1999). The results seem to highlight a marked contrast between US and Australian markets, namely that, along with the other instruments considered, the composite intrinsic value measure does not appear to be an adequate measure of a stock's or portfolio's value. Several possible reasons are offered for this difference, including the differing market structures, the use of a different index or the use of alternate statistical tests.

The paper proceeds as follows: in section 2 a brief overview of the construction the portfolio index and intrinsic value measure is presented; section 3 develops the distribution properties of the test statistics employed along with testing methodology used to assess both the tracking ability and the predictability of various instruments on returns; section 4 reports the results of these testing procedures; and section 5 concludes.

2. A Review of the Construction of the ASX Portfolio Index and the Intrinsic Value Measure: An Application of Ohlson's Residual Income Valuation Model (1990)

The APELS was introduced in Australia in September 1999. Its aim was to provide a suitable benchmark measure for investable products. In contrast to the All Ordinaries Accumulation Index, the APELS comprises only the top 35 stocks by market capitalisation trading on the Australian Stock Exchange (ASX) and is rebalanced annually. Using this index (or a proxy thereof, which we will denote as the `ASX' portfolio), we seek to investigate the relative merits of various measures which seek determine a stock's or a portfolio's fundamental (intrinsic) value.

The model used by LMS (1999) to measure intrinsic value is one based on a discounted residual income model that relies on the assumption of clean surplus accounting. It takes an opposite view to more traditional valuation approaches that assume a security's price is the best available estimate of intrinsic value. They argue that price-value parity implied by the traditional approaches relies too heavily on the assumption of insignificant arbitrage (2) costs. When a security's fundamental value is difficult to measure and/or trading costs are significant, then the adjustment process takes time. The process is one of continuing convergence rather than static equality. LMS (1999) argue that the time series relation between intrinsic value and observed price can be modelled as a cointegrated system. In this way price and value only require to be convergent in the `long run'. By adopting this alternative valuation approach as opposed to traditional dividend discount valuation models, a better measure of a stock's or market's fundamental value can be achieved through its ability to track prices over time and forecast future returns.

LMS (1999) present their argument in the following manner. Consider the traditional dividend discount valuation model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where: [V.sup.*.sub.t] = the stock's intrinsic value at time t.

Since [V.sup.*.sub.t] is not directly observable most researchers treat the price of the traded security, [P.sub.t] as the stock's intrinsic value. They argue however that [P.sub.t] is merely an estimate of [V.sup.*.sub.t] and suggest that in the long run arbitrage forces will cause price to converge to the firm's intrinsic value. However in the short run, costs of arbitrage may be sufficiently large to prevent this convergence from occurring instantaneously. If we consider:

(1.2) log([P.sub.t]) = log([V.sup.*.sub.t]) + [[epsilon].sub.t]

or any estimate [V.sub.t] of the firm's `true' intrinsic value:

(1.3) log([V.sub.t]) = log([V.sup.*.sub.t]) + [[omega].sub.t],

then the relative accuracy of alternative value measures will be reflected in the time-series properties of the error term, [[omega].sub.t]. Superior measures are then those that have error terms with smaller first and second moments with faster mean reversion to its long run mean. However [[omega].sub.t] is not directly observable, and so inferences about the relative accuracy of different value measures must be drawn from the time series properties of empirical instruments such as the value to price ratios. Consider the difference between the (1.2) and (1.3):

(1.4) log([V.sub.t] / [P.sub.t]) = [[omega].sub.t] - [[epsilon].sub.t]

If P is an unbiased estimator of [V.sup.*] then [[epsilon].sub.t] should be mean zero. LMS (1999) suggest that, given arbitrage, it is reasonable to assume that [epsilon] is mean reverting (stationary). If we assume that the correlation between [epsilon] and [omega] is <1, LMS (1999) argue that the V/P ratio can serve as an instrument to evaluate alternative measures of a security's value.

Two distinct performance criteria emerge from which to assess alternative estimates of intrinsic value. The first is based on the estimate's: (1) price tracking ability; and (2) its predictive power over future security returns. Tracking ability relates to the property that a better estimate (V) results in V/P ratios that have lower standard deviation and a faster rate of mean reversion. Conditional on a particular correlation structure between [[omega].sub.t] and [[epsilon].sub.t], faster mean reversion in V/P implies faster mean reversion in [[omega].sub.t]. Predictive power relates to the fact that a better estimate (V) results in V/P ratios that better predict future returns. LMS (1999) empirically evaluate several alternate measures for intrinsic value based on these two criteria, among them traditional value measures such as book values, dividends and earnings, as well as the value estimate obtained using the residual income valuation model explained below.

2.1 The Residual-Income Valuation Model

As long as a firm's earnings and book value are forecast in a manner consistent with `clean surplus' accounting, (3) LMS (1999) argue that a firm's intrinsic value can be expressed as the firm's reported book value plus an infinite sum of discounted residual income:

(1.5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)

This expression is described by LMS (1999) as their `intrinsic value' model and is based on the valuation model derived by Ohlson (1990). The expression splits equity value into two components--a measure of the capital invested and a measure of the present value of all future wealth creating activities (abnormal earnings in each period). If abnormal earnings are equal to the cost of equity, then:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and the firm's intrinsic value will equal its book value: [V.sub.t] = [B.sub.t].

LMS (1999) argue that historical book value, reported earnings and dividends are inadequate proxies for measuring a firms fundamental value, because such measures do not incorporate the value of future wealth creating activities. We argue however that since the intrinsic value measure presented by LMS (1999) can be viewed as a composite measure utilising current and forecasted dividends, earnings, as well as reported book values. We would expect that the `intrinsic' measure should at best, perform equally as well as the more conventional measures.

2.2 Model Implementation Issues 

To operationalise the intrinsic valuation model of (1.5), explicit forecast periods must be specified, which implies a terminal value must be estimated for the infinite sum term. For ease of exposition, we adopt the following conventions similar to LMS (1999) and consider only a 3-year horizon model. An estimate for the intrinsic value of a firm or stock is then given by:

(1.6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where: [B.sub.t] = book value from the most recent financial statements divided by the number of shares outstanding in the current month from I/B/E/S;

[r.sub.e] = cost of equity capital. This value is computed as the sum of a time-varying riskless rate (the 90 day bank bill rate), plus and a consistent risk-premium above that rate. The risk premium was computed as the 20 year average excess return of the Australian All Ordinaries Index;

FRO[E.sub.t + 1] = forecasted ROE for period [sub.t+i], computed as FEP[S.sub.t+i]/[B.sub.t+i-1], where FEP[S.sub.t+i] is the IBES mean forecasted EPS for year [sub.t+i] and [B.sub.t+i-1] is the Book Value per share for year [sub.t+i+1]; and

[B.sub.t+i] = [B.sub.t+i-1] + FEP[S.sub.t+i] - FDP[S.sub.t+i] where FDP[S.sub.t+i] is the forecasted dividend per share for year [sub.t+i], estimated using the current dividend payout ration (k). Specifically, we assume FDP[S.sub.t+i] = FEP[S.sub.t+i]*k.

Utilising this procedure then allows us to compute the intrinsic value estimate for a stock or portfolio of stocks.

2.3 The Data Set

Our sample consists of firms traded on the Australian Stock Exchange during the period September 1990 to September 1998. We construct a portfolio using the top 30 stocks by market capitalisation selected at September each year. The portfolio was constructed in this way to broadly match the newly introduced APELS index. The APELS was introduced in Australia in September 1999 with the aim to provide a suitable basis for investable products. In contrast to the All Ordinaries Accumulation Index the APELS comprises only the top 35 stocks by market capitalisation, trading on the Australian Stock Exchange (ASX). This index is the closest match in Australia to the US Dow Jones Index series used by LMS (1999).

Financial data on these firms was supplied by SSGA (5) and was primarily sourced from the I/B/E/S data set. The following data was collected for the portfolio of firms: Share Price (closing monthly share price as reported on the ASX), number of Shares outstanding (this was then used to calculate market capitalisation). Monthly book value per share, earnings per share, dividends per share as reported by I/B/E/S were used to calculate the earnings yield (EP), dividend yield (DP) and book to market (BP) ratios. I/B/E/S consensus, 1 year and 2 year ahead, EPS forecasts are also collected in order to construct forecasted 1 and 2 year ahead earnings yields. This process involved searching through all I/B/E/S estimates (each analyst's forecasts for each company) for each month. Only the most recent estimate for each analyst is used and any stale estimates (over 90 days) are discarded. The average forecast for each company is then calculated to construct the 1 and 2 year ahead monthly forecasts. (6) Under the three period residual income model, an estimate for the three-year ahead earnings forecast must be made. In this case, as in LMS (1999) we set FEP[S.sub.t+3] = EP[S.sub.t+2](1 + g), where g is equal to the composite growth rate implicit in the forecast earnings for the previous two years. Any firms with missing data were excluded from the portfolio and were replaced with the next highest ranked firm by market capitalisation. So as to distinguish this index proxy from the true APELS index we call the constructed index the ASX portfolio.

2.4 Alternate Value Measures

The following set of value measures have been constructed allowing us to assess the relative price performance for a portfolio of stocks:

1. Dividends per share (DPS)--end of month value weighted average of dividend per share on the ASX portfolio;

2. Earnings per share (EPS)--end of month value weighted average of the earnings per share for the ASX portfolio;

3. I/B/E/S Consensus Analysts 1 and 2 year ahead forecast earnings per share (FEPS1 and FEPS2)--end of month value weighted average of the forecasted earnings per share for the ASX portfolio;

4. Book value per share (BPS) end of month value weighted average of the book value per share for the ASX portfolio; and

5. Intrinsic value per share (VPS)--end of month value weighted average of the intrinsic value per share using the 3 year forecast horizon and the short-term t-bill rate for the ASX portfolio.

Using the above data we construct the instruments used to evaluate a measure of a stock's value. The instruments are calculated by computing the value to price ratio for each of the measures considered. Thus for comparative purposes, apart from the intrinsic value to price ratio (V/P), we will consider other instruments which have served as more conventional measures of a stock's relative value; book to market ratio (B/P), earnings yield (E/P ratio), and dividend yield (D/P ratio). Furthermore, we consider the adequacy of consensus analysts' forecasts as value measures by treating their 1 and 2 year forecasted earnings yields (FE1/P and FE2/P) as instruments. Specifically, the instruments will be used to assess whether the value measure adopted possess any price tracking ability, and any predictive power over future returns over various horizons.

3. Theory and Test Methodology

3.1 Assessing the Tracking Ability of Value Measures

As highlighted by the studies of Frankel and Lee (1996) and LMS (1999), one of the performance criteria for a value measure is its tracking ability. They suggest that a better value estimate (V) results in value to price ratios (V/P) that have lower standard deviations and faster rates of mean reversion. This broadly translates to testing whether the value to price ratio is stationary. Consistent with the LMS (1999) study, we utilise the non-parametric testing procedure of Phillips and Perron (1988) to determine whether the set of instruments considered possess a unit root. Two regressions for each variable are run; one without a time trend: [y.sub.t] = [alpha] + [rho][y.sub.t-1] + [u.sub.t], and one with a time trend: [y.sub.t] = [alpha] + [delta]t + [rho][y.sub.t-1] + [u.sub.t]. The first case allows us to test the null of a unit root with drift, while the second case tests whether the series has a unit root with a time trend. We test the null hypothesis in both regressions whether the variable y has a unit root ([rho] = 1). Rejection of the null will thus indicate that the series is stationary. We report two statistics, a correlation coefficient based test statistic ([rho] stat) and an adjusted t-statistic. Construction of the Phillip-Perron test statistics is robust to heteroskedasticity and autocorrelation in the residuals by specifying an appropriate lag structure. Adequate value measures will tend to reject the hypothesis that their value to price ratios (the instruments: VP, BP, EP, DP FEY1 and FEY2) have a unit root.

3.2 Testing Multiperiod Returns Predictability

3.2.1 Deriving an Asymptotic Theory for a Joint System of Returns Regressions

There has been a long tradition among researchers investigating the predictable variation in market returns and whether or not the random walk theory of stock prices holds. Along with LMS (1999), Campbell and Shiller (1988), Hodrick (1992) and Fama and French (1988a,b; 1989) are examples of empirical studies which attempt to assess whether a particular set of instruments or variables have any predictive power over returns by employing long horizon regression analysis. The strategy of many of these studies translates to calculating covariance statistics (t ratios and Wald statistics for the OLS slope coefficients) over differing return periods, using any significant result as evidence that returns can be predicted by that instrument or set of instruments. The traditional instruments used in these studies include the dividend yield, earnings yield, book to market ratio and for LMS (1999), the intrinsic value to price ratio. However this long horizon approach, as Richardson and Smith (1991) highlight, ignores the joint implications of the null hypothesis being tested; that returns are unpredictable. This section seeks to develop a generalised procedure that directly allows a joint test of the hypotheses that multiperiod returns are unpredictable over a range of return horizons:

(2.1) cov([[summation of].sup.j.sub.i=1][r.sub.t+i],[z.sub.t]) = 0 [for all] j [greater than or equal to] 1,

where: [r.sub.t] = the single period return on a stock or portfolio at time t; and

[z.sub.t] = the value of the instrument (otherwise known as the forecasting variable) at time t.

3.2.2 Distributional Properties of Slope Estimators Consider the following OLS regressions:

(2.2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(2.3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

for arbitrary j and k, where [[summation of].sup.j.sub.i=1][r.sub.t+i] is the j-period excess return on the portfolio, [z.sub.t] is the time t vector of instrumental variables, and [[epsilon].sub.t+j] is a mean-zero error term. Similar definitions can be said for [[summation of].sup.k.sub.i=1] [r.sub.t+i] and [[epsilon].sub.t+k].

Utilising Hansen's (1982) generalised methods of moments (GMM) framework, we seek to obtain the asymptotic joint-distribution for the least-squares slope estimators of (2.2) and (2.3) under the null hypothesis that returns are unpredictable ([H.sub.0]: [[beta].sub.j] = [[beta].sub.k] = 0). A joint test of the null hypothesis is then constructed using the joint asymptotic distribution of the estimators. Utilising the OLS normal equations for this problem, it is straightforward to write the following vector consistent with the normal equations:

(2.4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where: [x.sub.t] = [[[summation of].sup.j.sub.i=1][r.sub.t+i], [[summation of].sup.k.sub.i=1] [r.sub.t+i], [z'.sub.t]]'; [theta] = [[[alpha].sub.j], [[beta].sub.j], [[alpha].sub.k], [[beta].sub.k]]'; and

h([x.sub.t],[theta]) = the disturbance vector which contains the OLS normal equations whereby E[h(x,[theta])]=0.

Given the system in (2.4) is exactly identified, the sample analog of the parameters in [theta] are just their least squares estimators. By employing the GMM framework, tests of the null hypothesis can be derived by considering the limiting distribution of the GMM estimator. Hansen (1982) shows given suitable regularity conditions, namely that [x.sub.t], is stationary and ergodic, the following results are true:

(2.5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where: D = E[[differential]h([x.sub.t],[theta])/[differential][theta]'];

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and

T = the number of observations in the data set.

Before test statistics can be constructed, the estimators for the variance-covariance matrix of this system of regressions must be derived and estimated. We can establish the following result using an approach that closely follows Kirby (1997) who derives the distributional properties for estimators in a single regression horizon setting:

3.2.3 Theorem Let {[r.sub.t],[z.sub.t]} be ergodic and stationary. Assuming that the regularity conditions of Hansen (1982) are satisfied, the limiting distribution of [beta] = [[[beta].sub.j] [[beta].sub.k]]' is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

V, variance-covariance matrix, is given by:

(2.6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where:

(2.7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[[summation of].sub.zz] = the variance covariance matrix of the instruments; and

[[mu].sub.z] = the expected value of the vector [z.sub.t]. (See Appendix for Derivation)

3.2.4 Estimation of the Variance Covariance Matrix: HAC Estimators That Impose the Null Firstly defining [[eta].sub.t+j] [equivalent to] [[epsilon].sub.t+j]([z.sub.t] - [[mu].sub.z]), the typical element in V, [[OMEGA].sub.jk], can be written as:

(2.8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In order to come up with a consistent estimate of this covariance matrix, we first note that under the Hansen and Hodrick (1980) assumptions, we can simplify the terms in [[OMEGA].sub.jk]. Under the null, non-overlapping errors for the regressions are serially uncorrelated, and hence the covariances of [[eta].sub.t+j][[eta].sub.t+k-l] are non-zero only up to the highest lag. Under these circumstances, if we define [S.sup.*] to be:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where: [k.sup.*] = the largest holding period, then a consistent estimator for [[OMEGA].sub.jk] can be computed, following Newey and West (1987) by using an HAC (Heteroskedastic and Autocorrelation Consistent) estimator:

(2.9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where: [[summation of].sup.-1.sub.zz] = the sample variance covariance matrix of the instruments; and [[eta].sub.t+j], [[eta].sub.t+k] = the sample analogues of [[eta].sub.t+j] and [[eta].sub.t+k] respectively.

The Newey-West or Bartlett weighting procedure adopted here guarantees, by construction, positive semi-definite variance covariance estimators that are robust to various forms of heteroskedasticity and autocorrelation in the residuals. Similar estimators can be easily constructed for [[OMEGA].sub.jj], [[OMEGA].sub.kk] and [[OMEGA].sub.kj]. Furthermore, by directly incorporating the null hypothesis when constructing the estimator for the variance covariance matrix, much of the size properties of the test statistics can also be improved (see Richardson & Smith 1991, 1994; Kirby 1997). This implies the disturbance vectors, [[eta].sub.t+j] and [[eta].sub.t+k], simplify to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

whose sample analogues can be substituted in order to compute the HAC estimator of (2.9).

Observe that that the estimator in (2.9) serves as a direct counterpart to the standard estimator proposed by Newey and West (1987). The difference being that (2.9) reflects the Newey West estimator that imposes the null hypothesis in its construction. As a result we can make direct comparisons of test statistics that use estimators which impose the null to those which do not. The differences will reflect the impact of imposing the null on the size of the test statistics.

3.2.5 Estimation of the Variance Covariance Matrix: Analytical Estimators That Impose the Null The procedures considered thus far require in cases of large j and k, the estimation of numerous covariances, which can lead to poor size properties in small samples. Considering the small sample sizes employed in this study, we may consider an alternative method to construct statistics when testing the null hypothesis. While not described in this paper, an alternative approach, similar to Richardson and Smith (1994), aims at constructing an analytical variance covariance matrix estimator for the slope coefficients. The variance covariance matrix is constructed under the null of no predictability and no serial correlation in single period returns using the distributional results of Hansen's (1982) Generalised Method of Moments (GMM) framework. The approach aims to explicitly model the dependencies induced by the use of overlapping observations by viewing the multiperiod estimators as linear combinations of single period OLS estimators. By then imposing the null, the distributional properties of the estimators can be derived. Since the results are derived analytically, the estimation procedure avoids many problems associated with traditional sampling estimation techniques (Richardson & Smith 1991). It can be shown that the asymptotic joint distribution of the multiperiod slope estimators is given by:

(2.10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where:

(2.11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In future we will refer to [V.sup.*] in (2.11) as the analytical variance covariance estimator of the OLS slope estimates. This approach greatly reduces the sampling error that is present in the techniques described earlier as it does not involve the estimation of any cross equation correlations. It also mitigates the potential problem that the covariance matrix of the estimators fails to be positive semi-definite. Furthermore, as Richardson and Smith (1991) and Hodrick (1992) show, approaches that impose the null when constructing the variance covariance estimators for the slope coefficients can improve the size of the tests. Thus the probability of rejecting the null when it is true is reduced and can be attributed to the reduced sampling error in the estimation process.

3.2.6 Construction of Test Statistics Having derived the variance covariance matrix of slope coefficients across regression horizons for arbitrary j and k then allows us to construct statistics that test the parameter restrictions jointly as well individually. Having obtained the estimates for the variance covariance matrix of the slope coefficients along with the OLS slope estimates, various statistics can be constructed to test the null of no predictability. Apart from conventional t ratios for each slope coefficient, we can use the variance-covariance estimators to construct Wald statistics that test whether the set of instruments in a regression are jointly equal to zero. The distinction between a joint test versus a series of individual tests is of practical importance. Richardson and Smith (1991) show that for the Fama and French series of studies (1988a, b; 1989), rejecting the random walk hypothesis on the basis of individual test statistics may not be justified in a joint system, as the individual test statistics fail to account for the correlation among statistics induced by the use of overlapping observations. In subsequent analysis, we incorporate both individual testing and joint testing procedures to determine whether alternative value measures have any predictive power over returns. If we consider the k horizon regression of (2.3):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where: [[beta].sub.k] = an m-vector of slope parameters for the k-period horizon regression, we can test the hypothesis [H.sub.0]: [[beta].sub.k] = 0 with the following Wald statistic:

(2.12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where: [[beta].sub.k] = the vector of OLS slope coefficient estimates in the k-horizon regression.

Of considerable interest however is in testing these parameter restrictions in a joint system, whereby having constructed and estimated a series of regressions of differing horizons, we test whether the slope estimates across these horizons are jointly equal zero, [H.sub.0]: [[beta].sub.j] = ... = [[beta].sub.k] = 0. Again a Wald statistic can be constructed:

(2.13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where: N = the number of regression horizons; and

[beta] = the vector of slope coefficients across regressions: [beta] [equivalent to] [[[beta].sub.1] [[beta.sub.2] ... [[beta].sub.N]]'.

The variance covariance matrix estimator, Var([beta]), for the set of parameter estimates from each regression can then be obtained using the procedures outlined earlier in section 2 such as the HAC estimator of (2.9) or the analytical estimator of (2.11).

3.2.7 Small Sample Considerations What the analysis has not considered thus far is the impact of finite sample sizes on inference. Specifically, if the degree of overlap in the multiperiod returns is high relative to the sample size, the asymptotic results used to test the slope estimates may not be applicable. To address this small sample bias in our estimates, we generate finite sample (empirical) distributions for the test statistics involved using Monte Carlo simulations in a manner similar to Hodrick (1992).

A first order Vector-Autoregression (VAR) is fitted to the data and is then used to generate a series of observations for the instruments and single period returns which satisfy the null hypothesis of no predictability. This is achieved by setting the coefficients of the lagged variables in the return equation equal to zero, and setting the constant equal to unconditional mean. Conditional upon using this approach, it is necessary that the variables used in the VAR estimation are jointly covariance stationary to ensure stability of the system. This requires that the roots of the characteristic equation from the matrix of VAR coefficients all lie within the unit circle. In the case of the Australian data, this was satisfied. For each of the 1000 replications, the simulation strategy can be described as follows. Once the VAR is initiated, shocks for subsequent observations are generated by sampling without replacement from the actual VAR residuals to obtain 96 observations for the single period returns and the instruments. The single period returns generated form the basis of the dependent variable, and the instruments generated are used as the independent variable in the multiperiod regressions. For each replication, the multi-period regressions are run, with OLS estimates computed along with their appropriate test statistics. The result of the replications lead to the generation of empirical distributions for the OLS slope coefficients and the test statistics. We also compute the bias in the OLS estimates using the method described in Fama and French (1988); the bias is calculated by computing the mean of the empirical distribution of the slope estimators generated under the null hypothesis. The bias adjusted slopes are then used to test the null using the test statistics' empirical distributions.

4. Discussion of Results

4.1 Empirical Results: Time Series Properties of the Instruments and Returns

4.1.1 Descriptive Statistics Our analysis is conducted on a sample of firms ranked in the top 30 of the ASX based on market capitalization over the period September 1990 to September 1998. Monthly excess returns are computed for a value weighted portfolio (ASX portfolio) consisting of these firms over the period in question. The subsequent analyses are constructed from these single-period monthly portfolio returns. The forecasting variables or instruments were then constructed for the ASX portfolio and include: the `Intrinsic' Value-to-Price ratio (VP), the Book-to-Market ratio (BP), the Earnings yield (EP), the Dividend yield (DP), and the 1 and 2 year ahead consensus analyst forecast Earnings yields (FEY1, FEY2).

Table 1 presents summary statistics on the portfolio returns and forecasting variables for the period in question. Panel A reports the results for the ASX portfolio's monthly excess returns. For the period of study, the portfolio averaged an excess return of 0.095% (or 1.14% p.a.) with a range of -17% to 12% on a monthly basis. Inspection of the autocorrelations at various lags largely suggests a low order autoregressive, stationary process. While not reported, the plot of autocorrelations for multiperiod returns, by construction, exhibit higher order autocorrelation.

Panel B reports the descriptive statistics for the instruments adopted in this study. All instruments including the one based on the intrinsic value measure tend to exhibit significant, slow decaying autocorrelation structures, suggesting that the series are either non-stationary, or very close to being near unit root processes. This would suggest that, unlike the LMS study, the value measures constructed tend not to have the tracking properties that are desirable in measures of firm value.

Panel C reports the sample correlation structures across the instruments. This panel highlights several important differences between the Australian index investigated in this study and the US Dow Index. The high reported correlation between VP and BP (0.97) suggests that these series behave quite similarly; indeed this appears to be the case upon visual inspection of the time series plots in figure 1. The plots suggest that the difference between measures is minimal; both tend to have similar `mean reverting' characteristics. While these plots far from guarantee that the series are stationary, these results differ to those in the US study which reports that VP does not tend to deviate greatly from its long run mean unlike BP. Furthermore, with the exception of the 1 and 2 year ahead forecast yields, correlation among the traditional value measures (BP, EP and DP) all appear not to be as high as those reported for the US market.

[FIGURE 1 OMITTED]

4.1.2 Unit Root Tests: Testing Stationarity The very high first order autocorrelations reported in table 1 suggest further investigation as to whether the instruments possess a unit root or are near non-stationary. While rejection of a unit root suggests that process displays mean reversion around a long run trend, the reported results in table 1 at the very least exhibit very slow mean reversion.

We adopt the Phillips and Perron (1988) testing procedure for the set of instruments; VP, BP, EP, DP, FEY1 and FEY2. As described earlier, two cases are investigated: (a); and (b). We report two statistics, a correlation based test statistic and the adjusted t-statistic under each case. We report the results for the instruments in table 2 allowing for serial correlation of 2 and 12 lags. Unlike LMS (1999), the ASX portfolio results suggests that all instruments including the one based on the intrinsic value measure at 12 lags generally do not reject the null of a unit root. All instruments appear to have poor mean reverting qualities, as we only reject the null on only a few instances. This also suggests that, unlike the Dow portfolio, the inclusion of time-varying interest rates in constructing VP does not produce a stationary, mean reverting process.

4.2 Empirical Results: Predictability of Multiperiod Returns

The first set of analyses focuses directly on the univariate regressions using the instruments over a number of return horizons as conducted by LMS (1999). These results correct for the induced autocorrelation and heteroskedasticity in the residuals using the variance covariance estimators derived by Newey and West (1987).

We then make a direct comparison of the impact of imposing the null hypothesis on the size of the tests by constructing variance covariance estimators using the HAC estimation procedure of (2.9). Imposing the null in the construction of the parameters' covariance matrix can improve the size properties of the test statistics. Having considered the univariate regressions results, multivariate regression results

The final set of analyses focus on the regressions results using the analytical variance covariance estimator. This approach allows us to improve the size of the tests by reducing the sampling error inherent in the previous approaches. Given the small sample size, the reduced sampling error of this technique allows us to focus more on the testing the joint restriction; whether the OLS estimators for the instruments are jointly equal to zero across horizons. By doing so, we are better able to assess whether the construction of a superior measure of value, as prescribed by LMS (1999), results in better returns prediction (exhibiting high R-squared values and significant estimates) or whether the initial significance observed using standard testing techniques are the result of the overlapping observations used in the multiperiod regressions. We consider the relative significance of each measure by first considering the univariate regression case, and second by considering the multivariate regression case for a selected set of instruments.

4.2.1 Univariate Regression Results: Tests Using Standard HAC Covariance Matrix Estimators We report in table 3 the univariate regression results for the series of instruments: VP, BP, DP, EP, FEP1 and FEP2. Using the same procedure as LMS (1999), the results have been corrected for heteroskedasticity and autocorrelation resulting from overlapping observations using the approach of Newey and West (1987). The t ratios for each instrument are compared against their finite sample distributions as summarised by their p-values. The results demonstrate that utilising heteroskedastic and autocorrelation consistent (HAC) techniques seem to produce significant results for most of the instruments at various horizons even after accounting for small sample bias. On inspection, we find the t ratios across all instruments are not greatly significant in the shorter horizon regressions, but become more significant as the length of the return horizon increases. The earnings and dividend based yields seem to produce significant statistics at more horizons (k = 3 ,6, 9, and 12) than the intrinsic value measure (k = 12 and 18), with book value fairing poorly as a significant predictor of returns. We also report for all instruments, that the R-squared values tend to increase dramatically with the return horizon; a result consistent with LMS (1999). While this initial inspection highlights modest results for the intrinsic value measure, the results nevertheless seem to indicate that for a broad range of measures, returns appear to have a predictable component, thus violating the notion of market efficiency.

4.2.2 Univariate Regression Results Using HAC Covariance Matrix Estimators That Impose the Null Hypothesis Table 4 seeks to reassess the findings obtained in table 3. Table 4 reports the univariate regression results using the HAC covariance matrix estimator that imposes the null. Rather than employing the standard Newey-West estimator directly to estimate the variance covariance matrix, the Newey-West based HAC estimator of (2.9), which imposes the null condition that the slope estimates are equal to zero, is used. In this way, we can assess how the size of the tests change once we impose the null on the estimator. We also report Wald statistics (the d statistic) from (2.13) that jointly test whether the slope estimates for a particular instrument are zero across all the horizons: [H.sub.0]: [[beta].sup.i.sub.1] = [[beta].sup.i.sub.3] = ... = [[beta].sup.i.sub.18] = 0. We find strong evidence suggesting that addressing the size properties of the test statistics in this fashion results in test statistics that fail to reject the null hypothesis. This applies when considering each regression independently (as reported by the t statistics and [W.sub.k] values), or as a joint system (as reported by the J values). We find this to be true for all the instruments considered, with reported p-values for the J statistics ranging from 16.1% for BP to 32.4% for VP.

The t statistics which report the results of one sided tests, shows that the significance of each statistic is diminished for all the instruments across each horizon. While earnings and dividend yields provide some evidence of marginal significance at the 10% level for various horizons, the other instruments, including the intrinsic value measure, VP, fair poorly across all horizons. These results contrast with results reported in table 3 and can be attributed to the fact that we are directly imposing the null that returns are unpredictable when constructing test statistics.

4.2.3 Multivariate Forecasting Regression Results: A Comparison of HAC Covariance Matrix Estimators Table 5 extends the comparison between the covariance estimation procedures used in tables 3 and 4, by running multivariate regressions involving the instruments: VP, BP, EP and DP:

(3.1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

for k = 1, 3, 6, 9, 12 and 18. In panel A we report the results of the multivariate regressions using the HAC estimation approach of Newey and West (1987) without imposing the null. We display the slope estimates along with standard errors, t statistics and p values, as well as the R-squared for each regression. Panel A reports that for the longer regression horizons (k = 6 to 18), we find some indication at the 10% level, of predictive power among the various measures. Specifically we find that VP with BP seem to be poor regressors, while DP seems to be marginally significant at the 6 and 12 month horizons. Furthermore, the reported R-squared values seem to dramatically increase as the horizon increases, peaking at a value of 43.08% for k = 12.

In panel B the HAC estimator of (2.9) which imposes the null is used to construct the variance covariance matrix. We first report individual t statistics to test whether individual instruments in each regression are significant, and the Wald statistics ([W.sub.k]) from (2.12) which tests for each regression, whether the set of instruments used are jointly equal to zero. As reported in table 4, the t statistics and Wald statistics of panel B indicate that we cannot reject the null hypothesis at any reasonable level of significance. Thus despite the significant reported R-squared values, constructing the test statistics in this way demonstrates that the marginal significance observed under the previous procedures is no longer evident. We also report the Wald based or statistic for each instrument, and find that none of the instruments seem to be jointly significant across horizons as exhibited by very poor p-values. On comparing the or statistics computed for each instrument, we find that Earnings Yield, EP, displays the greatest significance amongst the 4 regressors, with a reported value of 5.91 followed by BP (3.212), VP (3.111) and DP (1.149).

4.2.4 Univariate Forecasting Regression Results Using the Analytical Variance Covariance Matrix Estimator Table 6 reports the univariate regression results using the analytical variance covariance estimator of (2.11). As with all the regressions conducted, we report the bias calculated in the slope estimates and find that for all instruments, the degree of bias increases with horizon, k. We report three sets of statistics; the individual t statistics and [W.sub.k] statistics which test whether each instrument is significant in a single horizon setting, as well d which tests whether an instrument is jointly significant across the set of horizons. The test statistics for all the instruments consistently highlight a lack of predictive power. Earnings and Dividend yields again appear the most significant among the instruments considered in predicting returns. Earnings appears marginally significant at the 10% level for the k = 9 month horizon regression, while DP appears to be marginally significant at the 10% level over various horizons (k = 1,3,6 & 9). The intrinsic value and other measures seem to fair less well. On comparing d statistics, the conclusions drawn from the individual t tests are confirmed; with each instrument reporting large p-values for their respective d statistic. On comparing these values, EP and DP report the largest statistics with values of 14.823 and 11.7696 respectively, followed by VP (10.041) and BP (8.2705), and then by the 1 and 2 year ahead analysts earnings forecasts (8.0439 & 7.2059, respectively).

4.2.5 Multivariate Forecasting Regression Results Using The Analytical Variance Covariance Matrix Estimator Table 7 considers the multivariate case for the 4 instruments of interest, VP, BP, EP and DP:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

for k = 1, 3, 6, 9, 12 and 18. The individual t statistics overwhelmingly suggest a lack of predictive ability of the instruments across all horizons. No instrument appears to be significant in this setting for any of the horizons. Furthermore, the [W.sub.k] statistics computed for each regression overwhelmingly suggests there is little evidence of rejecting the null, with p-values all exceeding 68%. This conclusion is supported by large p-values reported for the J statistics which test whether the slope coefficients for each instrument across regressions are jointly zero. On inspection of these values we find EP with a J statistic of 8.770 is the most significant of the instruments, followed by DP with a value of 8.563, VP (6.065) and BP (3.976).

5. Concluding Remarks

This study attempts to reassess the findings from the US market where a significant relationship has been established between the intrinsic value measures and future returns, particularly over long horizons. In our sample of Australian stocks we find little evidence to suggest predictability of multiperiod returns using both the traditional measures of value as well as the intrinsic value measure in question. In particular, we find that traditional value measures such as those based on dividends and earnings, although somewhat small, will tend to have more significance in explaining future returns than book value or composite-based measures based on the model by Ohlson (1990) and adopted in LMS (1999). These results contrast with the results obtained for US markets by LMS (1999), which suggest these intrinsic value measures display better performance. In terms of tracking ability, all measures using Australian data appear to behave poorly, including the intrinsic value measure. We suggest several possible reasons for the differing results.

Firstly, the Australian and US companies use fundamentally different accounting practices. Specifically, Australian companies (8) are not restricted to reporting book values as historical cost value. As in the US system, Australian companies must write down the value of an asset if the market value falls below the current book value. However, in contrast to the US, Australian companies also have the option to mark up the book value of an asset if the market value exceeds the current book value. Recall that the Intrinsic Value measure splits equity value into two components--a measure of the capital invested and a measure of the present value of all future wealth-creating activities. If the measure of capital invested is upwardly biased due to revaluations to current market value, then the Intrinsic Value measure may also be inflated. We therefore propose that the ability of Australian companies to upwardly revalue book values may explain why the intrinsic value measure faired so poorly in the Australian sample relative to the other value measures.

Another possible reason for the differing results may simply be the use of a different sample. The Index used to assess the value measures was constructed from the top thirty stocks listed on the Australian Stock Exchange. Although this was the closest proxy to the Dow Jones Index used in the LMS (1999) study, it was constructed using different criteria and therefore may have affected the results. Evidence of this is shown in tables 1 and 2 where, unlike the US results, all instruments appear to have poor mean-reverting qualities. We tend to find the market instruments display significant slow decaying autocorrelation structures. This highlights significant differences in the time-series properties of the US and Australian samples.

The differing results may also be explained when investigating whether the testing methodology used by LMS (1999) is robust to issues relating to overlapping observations. Despite using well established techniques to account for serial correlation and heteroskedasticity, such as approaches of Newey and West (1987) and White (1980), LMS (1999) fail to explicitly incorporate the serial dependence by imposing the null hypothesis in the construction of the variance covariance matrix. LMS (1999) accept that the slopes of these regressions may be correlated, and propose a joint test by computing an average slope statistic, testing whether the slopes at various horizons are equal. However, these tests do not take into account the correlation inherent among the slope estimates and test statistics across regressions that result from the use of overlapping observations. Therefore, the tests employed by LMS (1999) may not mitigate the problems associated with Type I errors.

We have demonstrated marked differences in the significance of the test statistics that result when applying different variance covariance estimators. By incorporating the null hypothesis of no predictability in the construction of these test statistics, we find that results that previously demonstrated significance no longer displayed those properties. Specifically, we demonstrate that, on initial inspection of the ASX portfolio, various measures seem to have some return predictability. However, once accounting for the implied effects of overlapping observations by imposing the null when constructing the variance covariance estimators, we find that none of the measures seems to perform well as predictors. In fact, on comparison of the J statistics for each instrument, the traditional market instruments such as earnings and dividends yield fair marginally better than the intrinsic-value measure in terms of significance.

While this may or may not be a factor influencing the results in the US study that report the superiority of the residual income valuation models over traditional approaches, our results at least point to the fact that valuation techniques which are effectively composite measures of publicly available information sets should only do as well as those directly observable and publicly available market measures. Our results suggest, when conditioning on pubic information, it seems unlikely that a violation of the market efficiency hypothesis is possible.

Ultimately by appropriately accounting for the statistical properties of the tests employed, we find that we require more than simply a set of existing public information to predict future returns. While it is reasonable to suggest that there are information measures that can predict returns, it should be apparent that they will not be ones based on existing public information. We would expect that a predictable measure would be one based private information sets which have not been fully incorporated into prices.

Appendix

We begin with the disturbance vector for the system described in (2.4) and derive D analytically by taking the expected value of the Jacobian of h([x.sub.t], [theta]) with respect to [theta]; yielding the following block diagonal matrix:

(A.1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The inverse of D can easily be constructed owing to its block diagonality:

(A.2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The variance covariance matrix of the moment conditions, S, can be expressed as:

(A.3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where:

(A.4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

By Hansen (1982), we can write the variance-covariance matrix of the estimators as V [equivalent to] = [D.sup.-1][SD'.sup.-1]. Substituting in (A.3) and (A.4) thus yields:

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

To obtain [[OMEGA].sub.jk] = cov([square root of (T [[beta].sub.j])], [square root of (T [[beta].sub.k])]) (the covariance between slope estimators) is straightforward; owing to the block diagonality of [D.sub.-1], [[OMEGA].sub.jk] can be computed as

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

Using similar arguments:

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

and

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

Thus the asymptotic joint-distribution for [beta] = [[[beta].sub.j] [[beta].sub.k] is given by:

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

with V given by

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

Table 1
Summary Statistics for Monthly Returns and Forecasting Variables

The summary statistics are computed using monthly data from (Sept 1990
to Sept 1998). Returns on the ASX portfolio are continuously compounded
returns in excess of the 90 day bank accepted bill rate expressed in
percent. DP refers to the annual dividend yield, EP is the annual
earnings yield, BP is the annual book to market ratio, and FEY1 & FEY2
are the consensus analyst's 1 and 2 year ahead forecast earnings yields
(all measures are calculated on the ASX portfolio). VP is the
value-to-price ratio based on the value measure outlined in Section 1.
TB is the annualised end-of-month yield on the 90 day bank accepted
bills. The autocorrelations are calculated for lags 1,3,6,9,12 and
18. (7)

Panel A: Univariate Statistics for Returns--Full Period
(Sept 1990 to Sept 1998)

                                                             Auto-
                                                          correlation
                                                             at lag

  Variable       Mean    Standard     Min       Max      1        3
                         Deviation

ASXp[f.sub.1]    0.095     4.85      -17.16    12.22   -0.192   0.060

Panel B: Univariate Statistics for Forecasting Variables--Full Period
(Sept 1990 to Sept 1998)

                                                             Auto-
                                                          correlation
                                                             at lag

  Variable       Mean    Standard     Min       Max      1        3
                         Deviation

DP               1.797     0.243       1.40     2.60    0.874   0.603
EP               2.798     0.900       0.60     4.90    0.873   0.436
BP              54.213     8.346      41.30    79.60    0.893   0.662
VP              56.477     6.280      45.50    76.40    0.856   0.546
FEY1             6.481     1.206       4.50    10.20    0.909   0.669
FEY2             5.653     1.293       3.30     9.20    0.928   0.738
TB               6.916     0.218       4.800   13.40    0.937   0.810

Panel A: Univariate Statistics for Returns--Full Period
(Sept 1990 to Sept 1998)

                        Autocorrelation at lag

  Variable         6        9       12       18

ASXp[f.sub.1]   -0.059    0.078    0.051   -0.040

Panel B: Univariate Statistics for Forecasting Variables--Full Period
(Sept 1990 to Sept 1998)

                        Autocorrelation at lag

  Variable         6        9       12       18

DP               0.217    0.069    0.034   -0.090
EP              -0.141   -0.079    0.076   -0.412
BP               0.360    0.210    0.087    0.194
VP               0.179    0.005   -0.148    0.074
FEY1             0.343    0.193    0.004   -0.228
FEY2             0.457    0.289    0.134   -0.157
TB               0.606    0.386    0.163   -0.146

Panel C: Correlation Among Forecasting Variables--Full Period
(Sept 1990 to Sept 1998)

Variable    DP      EP      BP      VP     FEY1    FEY2

EP         0.568    --      --      --      --      --
BP         0.557   0.379    --      --      --      --
VP         0.612   0.447   0.970    --      --      --
FEY1       0.880   0.615   0.520   0.603    --      --
FEY2       0.898   0.579   0.396   0.479   0.962    --
TB         0.708   0.432   0.707   0.643   0.774   0.728
Table 2
Phillip-Perron Unit Root Tests

This table summarises the results of the Phillip-Perron Unit Root
tests on VP, BP, EP, DP, FEY1 and FEY2. The tests have been
performed under two cases: (a) without a time trend; and (b)
with a time trend. The regressions are run for cases (a) and
(b) respectively:

a. [y.sub.t] = [alpha] + [rho][y.sub.t-1] + [u.sub.t]

b. [y.sub.t] = [alpha] + [delta]t + [rho][y.sub.t-1] + [u.sub.t]

Two sets of test statistics are constructed to test the null
hypothesis under (a) and (b) that [rho] = 1, or that the
series possesses a unit root and hence is non-stationary.
The tests allow regression residuals to be serially
correlated up to a specified order. Test statistics
are reported for both 2 and 12 lags.

                  Panel A: Lag Structure = 2

Variable      Without Trend           With Trend

                          t                     t        #
             [rho]     Adjust      [rho]     Adjust    Obser-
           Statistic    Stat.    Statistic    Stat.    vation

VP          -14.46 *   -3.03 *    -18.80      -3.17      95
BP          -10.26     -2.71      -16.82      -3.03      95
EP          -16.10 *   -2.88      -16.35      -2.89      95
DP          -11.53     -3.17 *    -10.32      -2.87      95
FEY1        -10.07     -3.10 *     -9.20      -2.86      95
FEY2         -7.80     -2.66       -7.43      -2.66      95

                  Panel A: Lag Structure = 12

Variable      Without Trend           With Trend

                          t                     t        #
             [rho]     Adjust      [rho]     Adjust    Obser-
           Statistic    Stat.    Statistic    Stat.    vation

VP          -10.87     -2.76      -13.48      -2.72      84
BP           -7.99     -2.55      -12.40      -2.64      84
EP           -8.09     -2.07       -8.46      -2.10      84
DP           -9.50     -3.15 *     -6.61      -2.89      84
FEY1        -10.56     -3.10 *     -8.79      -2.85      84
FEY2         -8.75     -2.70       -6.92      -2.66      84

Note: * = significant at the 5% level; and

** = significant at the 1% level.
Table 3
Univariate Forecasting Regression Results Using Standard HAC
Variance Covariance Estimators

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Table 3 summarises the univariate forecasting regression results for
each instrument. The regressions are run for the monthly horizons of
k = 1, 3, 6, 9, 12 and 18. For k > 1, the regressions use overlapping
observations. The dependent variable is the excess return on the ASX
portfolio. [[beta].sub.k] refers to the slope coefficient from the
regression and z refers to the instrument used. The t-ratios are
corrected for heteroskedasticity and autocorrelation up to k lags
in the residuals using the method of Newey and West (1987).
The test statistics are compared to their small sample distributions,
as summarised by the p-values in a one-sided test of the null
([[beta].sub.k] > 0). The small sample distributions were generated
using 1000 replications of a Monte Carlo simulation under the null
that returns are not predictable following the approach used by
Hodrick (1992). Bias refers to the mean of the empirical distribution
of the slope estimates generated under the null of no predictability
and are used in adjusting the slope estimates when constructing the
test statistics.

     [[beta].
k     sub.k]     Bias    Std Err   t-Stat   p-Value   N    [R.sup.2]

                             Panel A: Z = VP

1      0.0636   0.0087    0.0817   0.6730    0.2410   95      0.69
3      0.1720   0.0226    0.1707   0.8755    0.2310   93      2.45
6      0.2728   0.0366    0.2953   0.7998    0.2770   90      3.78
9      0.5521   0.0482    0.2931   1.7191    0.1280   87     12.76
12     0.8867   0.0610    0.2532   3.2617    0.0300   84     28.83
18     0.8027   0.0876    0.2092   3.4186    0.0390   78     24.20

                             Panel B: Z = BP

1      0.0415   0.0067    0.0605   0.5764    0.2620   95      0.52
3      0.1059   0.0178    0.1295   0.6802    0.2680   93      1.63
6      0.1686   0.0292    0.2352   0.5927    0.3360   90      2.52
9      0.3607   0.0389    0.2414   1.3329    0.1860   87      9.40
12     0.5887   0.0482    0.2079   2.6006    0.0760   84     21.81
18     0.4936   0.0670    0.1763   2.4206    0.1020   78     15.84

                              Panel C: Z = EP

1      0.5220   0.0248    0.4428   1.1231    0.1350   95      0.93
3      1.7940   0.0655    0.8182   2.1127    0.0540   93      5.16
6      3.7366   0.1009    1.3700   2.6538    0.0380   90     13.72
9      5.9578   0.1358    1.7544   3.3184    0.0250   87     28.88
12     6.5119   0.1697    1.6157   3.9254    0.0200   84     30.36
18     4.1996   0.2639    2.0886   1.8844    0.1710   78     13.65

                              Panel D: Z = DP

1      2.8145   0.2131    2.2558   1.1532    0.1370   95      2.00
3      8.6954   0.5805    4.4741   1.8138    0.0810   93      9.37
6     17.5716   1.0315    3.9176   4.2221    0.0070   90     23.89
9     20.7759   1.4413    3.4581   5.5910    0.0050   87     27.69
12    22.5066   1.8566    3.3575   6.1504    0.0010   84     28.61
18    19.2618   2.8315    2.2347   7.3525    0.0100   78     24.24

                              Panel E: Z = FEY1

1      0.2321   0.0582    0.3924   0.4432    0.2910   95      0.34
3      1.0761   0.1612    0.8376   1.0923    0.1860   93      3.55
6      2.7479   0.2761    0.8850   2.7931    0.0330   90     14.31
9      3.4400   0.3798    1.2159   2.5167    0.0710   87     18.67
12     3.9152   0.4694    1.4716   2.3416    0.1000   84     21.46
18     3.0837   0.6653    1.2863   1.8802    0.1620   78     14.97

                              Panel F: Z = FEY2

1      0.2494   0.0576    0.4056   0.4730    0.2910   95      0.45
3      1.0243   0.1624    0.8625   0.9993    0.2070   93      3.70
6      2.5848   0.2962    0.9931   2.3046    0.0720   90     14.70
9      3.1713   0.4060    1.2731   2.1721    0.1040   87     18.46
12     3.3442   0.4814    1.6059   1.7826    0.1680   84     18.25
18     2.6708   0.6085    1.2650   1.6302    0.2250   78     13.50
Table 4
Univariate Forecasting Regression Results using HAC Covariance
Matrix Estimators that Impose the Null

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Table 4 summarises the univariate forecasting regression results
for each instrument by imposing the null on the covariance matrix
estimators. The t-ratios and Wald Statistics are computed by imposing
the null that the slopes are equal to zero when constructing the
estimate for the variance-covariance matrix. They are corrected for
heteroskedasticity and autocorrelation using the method of Newey and
West (1987). [W.sub.k] refers to the Wald statistic constructed for
each individual regression and tests whether, for regression k,
[H.sub.0]: [[beta].sub.k] = 0. d refers to the Wald statistic
constructed for the system of regressions and tests whether [H.sub.0]:
[[beta].sub.1] = [[beta].sub.2] = ... = [[beta].sub.k] = 0 across
regression horizons. The t statistics are compared using the p-values
from a one-sided test ([[beta].sub.k] > 0). The t statistics are
compared to their empirical distributions as summarised by the
p-values from a 1-sided test, whereas the Wald statistics are
summarised by p-values from a 2-sided test; all generated under the
null from 1000 replications of a Monte Carlo Simulation. Bias refers
to the mean of the empirical distribution of the slope estimates
generated under the null of no predictability and are used in
adjusting the slope estimates when constructing the test statistics.

     [[beta]                                p-     [W.sub    p-
k    .sub.k]    Bias    Std Err   t-Stat   Value    .k]     Value

                             Panel A: Z = VP

1     0.0636   0.0087    0.0852   0.6451   0.246   0.4161   0.547
3     0.1720   0.0226    0.1884   0.7932   0.263   0.6291   0.564
6     0.2728   0.0366    0.3479   0.6789   0.312   0.4609   0.648
9     0.5521   0.0482    0.4867   1.0354   0.226   1.0721   0.476
12    0.8867   0.0610    0.5968   1.3836   0.149   1.9143   0.323
18    0.8027   0.0876    0.5174   1.3823   0.142   1.9108   0.340

                                                             p-
                                                     J      Value

                                                   4.4635   0.324
                             Panel B: Z = BP

1     0.0415   0.0067    0.0631   0.5533   0.271   0.3061   0.612
3     0.1059   0.0178    0.1404   0.6274   0.293   0.3936   0.625
6     0.1686   0.0292    0.2701   0.5159   0.364   0.2662   0.722
9     0.3607   0.0389    0.3722   0.8647   0.282   0.7477   0.582
12    0.5887   0.0482    0.4440   1.2174   0.209   1.4821   0.443
18    0.4936   0.0670    0.3591   1.1881   0.210   1.4115   0.470

                                                             p-
                                                     J      Value

                                                   6.6547   0.161
                             Panel C: Z = EP

1     0.5220   0.0262    0.5318   0.9324   0.164   0.8694   0.371
3     1.7940   0.0690    1.0206   1.6902   0.075   2.8569   0.189
6     3.7366   0.1091    2.0419   1.7765   0.064   3.1561   0.161
9     5.9578   0.1439    3.3138   1.7544   0.074   3.0781   0.188
12    6.5119   0.1840    3.5050   1.8054   0.073   3.2594   0.179
18    4.1996   0.2376    2.8250   1.4025   0.181   1.9671   0.402

                                                             p-
                                                     J      Value

                                                   3.7841   0.488

                            Panel D: Z = DP

1     2.8145   0.2131    2.0760   1.2531   0.097   1.5702   0.260
3     8.6954   0.5805    5.0259   1.6146   0.089   2.6070   0.210
6    17.5716   1.0315    9.2253   1.7929   0.065   3.2146   0.175
9    20.7759   1.4413   13.8463   1.3964   0.135   1.9499   0.325
12   22.5066   1.8566   17.0038   1.2144   0.186   1.4748   0.437
18   19.2618   2.8315   15.2218   1.0794   0.223   1.1651   0.513

                                                             p-
                                                     J      Value

                                                   1.2146   0.708

                             Panel E: Z = FEY1

1     0.2321   0.0599    0.4019   0.4285   0.292   0.1836   0.688
3     1.0761   0.1681    0.9064   1.0019   0.186   1.0037   0.429
6     2.7479   0.2901    1.6525   1.4874   0.115   2.2123   0.294
9     3.4400   0.3953    2.4787   1.2283   0.179   1.5087   0.426
12    3.9152   0.4904    3.0678   1.1163   0.224   1.2462   0.514
18    3.0837   0.6147    2.6763   0.9225   0.303   0.8511   0.636

                                                             p-
                                                     J      Value

                                                   2.0017   0.757

                             Panel F: Z = FEY2

1     0.2494   0.0576    0.4097   0.4683   0.290   0.2193   0.669
3     1.0243   0.1624    0.9282   0.9286   0.218   0.8623   0.514
6     2.5848   0.2962    1.6274   1.4063   0.148   1.9777   0.357
9     3.1713   0.4060    2.3102   1.1970   0.213   1.4328   0.469
12    3.3442   0.4814    2.7804   1.0296   0.260   1.0601   0.549
18    2.6708   0.6085    2.3932   0.8617   0.319   0.7426   0.664

                                                             p-
                                                     J      Value

                                                   0.3893   0.839
Table 5
Multivariate Forecasting Regression Results: A
Comparison of HAC Covariance Matrix Estimators

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Table 5 compares the multivariate forecasting regression results
for a selected set of instruments (VP, BP, EP and DP). The dependent
variable in these regressions is the k period excess return on the
ASX portfolio. The regressions are run for the monthly horizons of
k = 1,3,6,9,12 and 18. For k > 1, the regressions use overlapping
observations. [[beta.sup.i.sub.k] refers to the [i.sup.th] bias
adjusted slope coefficient from the k horizon regression. Panel A
represents the regression results without imposing the null on the
covariance matrix estimator. They are corrected for heteroskedasticity
and autocorrelation using the method of Newey and West (1987). In
panel B the t-ratios and Wald Statistics are computed by imposing
the null that the slopes are equal to zero when constructing the
estimate for the variance-covariance matrix and are also corrected for
heteroskedasticity and serial correlation in the residuals using the
method Newey and West (1987). [W.sub.k] refers to the Wald statistic
constructed for the regression and tests whether, for regression k,
[H.sub.0]: [[beta].sup.1.sub.k] = [[beta].sup.2.sub.k] =
[[beta].sup.3.sub.k] = [[beta].sup.4.sub.k] = 0. J refers to the Wald
statistic for the system of regressions and tests whether [H.sub.0]:
[[beta].sub.1] = [[beta].sub.2] = ... = [[beta].sub.k] = 0 across
regression horizons. Standard Errors are reported in parentheses.
The test statistics are compared to their small sample distributions,
as summarised by the p-values.

              Panel A: Multivariate Regression Results

k       VP      t-Stat   p Value      BP      t-Stat    p Value

1     0.0833    0.2396    0.407    -0.0744    -0.3215    0.390
     (0.3478)                      (0.2315)
3     0.2935    0.4894    0.362    -0.2863    -0.6814    0.302
     (0.5998)                      (0.4202)
6     0.1083    0.1598    0.472    -0.3159    -0.6036    0.365
     (0.6782)                      (0.5234)
9     0.6240    0.8756    0.305    -0.5126    -0.9538    0.291
     (0.7126)                      (0.5374)
12    1.9193    2.1362    0.126    -1.1259    -1.5483    0.208
     (0.8984)                      (0.7272)
18    3.1128    2.7709    0.104    -2.0699    -2.0851    0.175
     (1.1234)                      (0.9927)

k       EP      t-Stat   p Value      DP      t-Stat   p Value

1     0.2269    0.3611    0.422     1.6245    0.4207    0.312
     (0.6285)                      (3.8614)
3     0.7642    0.6602    0.330     5.8313    0.8241    0.261
     (1.1575)                      (7.0759)
6     1.7716    1.0843    0.248    14.8074    2.5165    0.067
     (1.6338)                      (5.8842)
9     4.2311    2.0670    0.106     7.4440    1.0854    0.261
     (2.0470)
12    3.7752    2.3863    0.087     0.5480    0.0742    0.506
     (1.5820)                      (7.3847)
18    0.3089    0.1416    0.451     3.4871    0.4229    0.432
     (2.1810)                      (8.2450)

k    [W.sub.k]   P value   [R.sup.2]

1      1.4149     0.920       2.04
3      5.0954     0.691      10.06
6     27.2862     0.161      27.12
9     43.2669     0.149      35.29
12    73.4954     0.109      43.08
18    51.4972     0.352      38.21

    Panel B: Regression Results using Covariance Matrix
               Estimator that Imposes the Null

k       VP      t-Stat   p Value      BP      t-Stat    p Value

1     0.0833    0.2307    0.409    -0.0744    -0.3055    0.394
     (0.3612)                      (0.2436)
3     0.2935    0.4879    0.359    -0.2863    -0.6952    0.300
     (0.6017)                      (0.4119)
6     0.1083    0.1040    0.484    -0.3159    -0.4307    0.405
     (1.0417)                      (0.7335)
9     0.6240    0.6109    0.354    -0.5126    -0.6055    0.361
     (1.0215)                      (0.8465)
12    1.9193    1.2580    0.206    -1.1259    -1.0079    0.269
     (1.5257)                      (1.1171)
18    3.1128    2.0615    0.094    -2.0699    -2.0198    0.103
     (1.5100)                      (1.0248)
J     3.1105              0.483     3.2122               0.482

k       EP      t-Stat   p Value      DP       t-Stat   p Value

1     0.2269    0.3260    0.429      1.6245    0.4290    0.304
     (0.6963)                       (3.7865)
3     0.7642    0.7907    0.298      5.8313    0.8000    0.244
     (0.9665)                       (7.2894)
6     1.7716    0.9734    0.247     14.8074    1.3464    0.120
     (1.8200)                      (10.9978)
9     4.2311    1.5380    0.130      7.4440    0.6446    0.322
     (2.7510)                      (11.5479)
12    3.7752    1.6712    0.108      0.5480    0.0335    0.511
     (2.2590)                      (16.3401)
18    0.3089    0.3102    0.412      3.4871    0.2949    0.442
     (0.9957)                      (11.8245)
J     5.9082              0.234      1.1487              0.749

k    [W.sub.k]   P value

1     1.1815      0.939
3     3.0349      0.826
6     4.6252      0.636
9     3.9962      0.733
12    3.8557      0.779
18    5.2932      0.709
J
Table 6
Univariate Forecasting Regression Results Using The
Analytical Variance Covariance Matrix Estimator

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Table 6 summarises the univariate forecasting regression results for
each instrument using the analytical variance-covariance estimator.
[W.sub.k] and t-stat refer to the t-statistic and Wald statistic
constructed for each individual regression and test whether, for
regression k, [H.sub.0]: [[beta].sub.k] = 0. J refers to the Wald
statistic for the system of regressions and tests whether [H.sub.0]:
[[beta].sub.1] = [[beta].sub.2]2 = .... = [[beta].sub.k] = 0 across
regression horizons. The test statistics are compared to their small
sample distributions, as summarised by the p-values. The small sample
distributions were generated using 1000 replications of a Monte Carlo
simulation under the null that returns are not predictable. Bias
refers to the mean of the empirical distribution of the slope
estimates generated under the null of no predictability and are used
in adjusting the slope estimates when constructing the test
statistics.

Panel A: Z = VP

k    [[beta].sub.k]    bias     Std     t-Stat   p Value
                               Error

1        0.0636       0.0087   0.0788   0.6973    0.230
3        0.1720       0.0226   0.1380   1.0827    0.244
6        0.2728       0.0366   0.1984   1.1903    0.275
9        0.5521       0.0482   0.2471   2.0390    0.166
12       0.8867       0.0610   0.2904   2.8431    0.095
18       0.8027       0.0876   0.3691   1.9375    0.184

k    [W.sub.k]   p Value   [R.sup.2]   N

1     0.4862      0.513       0.69     95
3     1.1722      0.517       2.45     93
6     1.4168      0.563       3.78     90
9     4.1574      0.357      12.76     87
12    8.0831      0.218      28.83     84
18    3.7538      0.374      24.20     78
         J       p Value
      10.0410     0.621

Panel B: Z = BP

k    [[beta].sub.k]    bias     Std     t-Stat   p Value
                               Error

1        0.0415       0.0067   0.0593   0.5881    0.254
3        0.1059       0.0178   0.1039   0.8482    0.286
6        0.1686       0.0292   0.1493   0.9335    0.326
9        0.3607       0.0389   0.1860   1.7303    0.210
12       0.5887       0.0482   0.2186   2.4733    0.132
18       0.4936       0.0670   0.2778   1.5360    0.243

k    [W.sub.k]   p Value   [R.sup.2]   N

1     0.3459      0.578       0.52     95
3     0.7195      0.604       1.63     93
6     0.8714      0.649       2.52     90
9     2.9938      0.443       9.40     87
12    6.1172      0.280      21.81     84
18    2.3594      0.483      15.84     78
         J       p Value
      8.2705      0.671

Panel C: Z = EP

k    [[beta].sub.k]    Bias     Std     t-Stat   p Value
                               Error

1        0.5220       0.0248   0.5500   0.9041    0.185
3        1.7940       0.0655   0.9628   1.7953    0.149
6        3.7366       0.1009   1.3841   2.6267    0.118
9        5.9578       0.1358   1.7242   3.3766    0.078
12       6.5119       0.1697   2.0262   3.1301    0.110
18       4.1996       0.2639   2.5752   1.5283    0.281

k    [W.sub.k]   p Value   [R.sup.2]   N

1      0.817      0.410       0.93     95
3      3.223      0.326       5.16     93
6      6.899      0.262      13.72     90
9     11.402      0.183      28.88     87
12     9.798      0.236      30.36     84
18     2.336      0.561      13.65     78
         J       p Value
      14.823      0.458

Panel D: Z = DP

k    [[beta].sub.k]    Bias     Std     t-Stat   p Value
                               Error

1        2.8145       0.2131   2.0369   1.2771    0.098
3        8.6954       0.5805   3.5657   2.2758    0.076
6       17.5716       1.0315   5.1260   3.2267    0.062
9       20.7759       1.4413   6.3854   3.0280    0.095
12      22.5066       1.8566   7.5037   2.7520    0.122
18      19.2618       2.8315   9.5370   1.7228    0.234

k    [W.sub.k]   p Value   [R.sup.2]   N

1     1.6311      0.245       2.00     95
3     5.1794      0.188       9.37     93
6     10.4118     0.155      23.89     90
9     9.1685      0.222      27.69     87
12    7.5734      0.271      28.61     84
18    2.9680      0.471      24.24     78
         J       p Value
      11.7696     0.510

Panel E: Z = FEY1

k    [[beta].sub.k]    Bias     Std     t-Stat   p Value
                               Error

1        0.2321       0.0582   0.4104   0.4237    0.295
3        1.0761       0.1612   0.7185   1.2733    0.204
6        2.7479       0.2761   1.0329   2.3931    0.127
9        3.4400       0.3798   1.2867   2.3783    0.154
12       3.9152       0.4694   1.5120   2.2789    0.182
18       3.0837       0.6653   1.9218   1.2584    0.303

k    [W.sub.k]   p Value   [R.sup.2]   N

1     0.1795      0.683       0.34     95
3     1.6213      0.465       3.55     93
6     5.7268      0.283      14.31     90
9     5.6563      0.344      18.67     87
12    5.1934      0.375      21.46     84
18    1.5837      0.614      14.97     78
         J       p Value
      8.0439      0.671

Panel F: Z = FEY2

k    [[beta].sub.k]    Bias     Std     t-Stat   p Value
                               Error

1        0.2494       0.0576   0.3831   0.5009    0.283
3        1.0243       0.1624   0.6706   1.2854    0.209
6        2.5848       0.2962   0.9640   2.3741    0.139
9        3.1713       0.4060   1.2008   2.3028    0.177
12       3.3442       0.4814   1.4111   2.0287    0.212
18       2.6708       0.6085   1.7935   1.1499    0.332

k    [w.sub.k]   p Value   [R.sup.2]   N

1     0.2509      0.647       0.45     95
3     1.6522      0.481       3.70     93
6     5.6363      0.320      14.70     90
9     5.3031      0.401      18.46     87
12    4.1154      0.466      18.25     84
18    1.3222      0.673      13.50     78
         J       p Value
      7.2059      0.733
Table 7
Multivariate Forecasting Regression Results Using
The Analytical Covariance Matrix Estimator

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Table 7 summarises the multivariate forecasting regression results
for a selected set of instruments (VP, BP, EP and DP) using the
analytical variance covariance estimator. The dependent variable in
these regressions is the k period excess return on the ASX portfolio.
The regressions are run for the monthly horizons of k = 1,3,6,9,12
and 18. For k > 1, the regressions use overlapping observations,
[[beta].sup.i.sub.k] refers to the ith slope coefficient from the k
horizon regression. [W.sub.k] refers to the Wald statistic constructed
for the regression and tests whether for regression k, [H.sub.0]:
[[beta].sub.k] = 0. J refers to the Wald statistic constructed to
test whether [H.sub.0]: [[beta].sub.1] = [[beta].sub.2] = .... =
[[beta].sup.i.sub.k] = 0 across regression horizons. The test
statistics are compared to their small sample distributions, as
summarised by the p-values. The small sample distributions were
generated using 1000 replications of a Monte Carlo simulation under
the null that returns are not predictable. Bias refers to the mean
of the empirical distribution of the slope estimates generated under
the null of no predictability and are used in adjusting the slope
estimates when constructing the test statistics. Bias adjusted slope
coefficients are reported. Standard Errors are reported in
parentheses.

k       VP      t-Stat   p Value      BP      t-Stat    p Value

1     0.0833    0.2326    0.414    -0.0744    -0.2924    0.400
     (0.3583)                      (0.2545)
3     0.2935    0.4681    0.394    -0.2863    -0.6427    0.356
     (0.6272)                      (0.4455)
6     0.1083    0.1202    0.489    -0.3159    -0.4932    0.419
     (0.9016)                      (0.6405)
9     0.6240    0.5556    0.402    -0.5126    -0.6424    0.392
     (1.1231)                      (0.7979)
12    1.9193    1.4542    0.257    -1.1259    -1.2008    0.303
     (1.3198)                      (0.9376)
18    3.1128    1.8558    0.204    -2.0699    -1.7370    0.238
     (1.6774)                      (1.1917)
J     6.0653              0.805     3.976                0.899

k       EP      t-Stat   p Value      DP       t-Stat   p Value

1     0.2269    0.3291    0.423      1.6245    0.5700    0.268
     (0.6896)                       (2.8501)
3     0.7642    0.6330    0.373      5.8313    1.1687    0.212
     (1.2072)                       (4.9893)
6     1.7716    1.0208    0.317     14.8074    2.0644    0.132
     (1.7355)                       (7.1726)
9     4.2311    1.9572    0.180      7.4440    0.8332    0.339
     (2.1618)                       (8.9347)
12    3.7752    1.4860    0.231      0.5480    0.0522    0.511
     (2.5405)                      (10.4996)
18    0.3089    0.0956    0.458      3.4871    0.2613    0.460
     (3.2289)                      (13.3447)
J     8.7701              0.650      8.5634              0.652

k    [W.sub.k]   p Value

1      1.2161     0.932
3      4.6215     0.841
6     10.4148     0.688
9     11.5545     0.709
12    11.7104     0.710
18     5.8844     0.864
J

(1.) From this point on LMS (1999)

(2.) A true arbitrage relationship requires the construction of a tradeable portfolio that facilitates a profitable riskless trading strategy. As such, it is questionable that an arbitrage argument can be used to describe price-value parities, as it is unclear how a value measure can be used to form a tradeable portfolio.

(3.) All gains and losses affecting book value are also included in earnings ([B.sub.t] = [B.sub.t-1] + N[I.sub.t] - DI[V.sub.t])

(4.) For details, see LMS (1999).

(5.) We would like to thank David Walsh and Jonathon Whiteoak at SSGA for providing the data.

(6.) These ratios are used both in the construction of the Intrinsic Value measure (V) and the forecasting instruments.

(7.) Due to a shorter data set in constructing the ASX portfolio we have used a different lag structure than that of LMS

(8.) Refer to Australian Accounting Standard: AASB 1010

(Date of receipt of final transcript: May 2001. Accepted by Gary Twite, Area Editor.)

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Ron Guido ([dagger]) Kathleen Walsh ([dagger])

([dagger]) Australian Graduate School of Management, University of New South Wales, Sydney, NSW 2052. Email: [e-mail]; [e-mail]

The authors would like to thank John Lyon, Tom Smith, Garry Twite, Chris Kirby, David Walsh and an anonymous referee for comments on this paper. We would also like to thank Jonathon Whiteoak at SSGA for his considerable contribution in the construction of a unique data set drawing from internal and I/B/E/S resources.