«Robert J. Bianchi*, Michael E. Drew and Timothy Whittaker Department of Accounting, Finance and Economics Griffith Business School Griffith ...»
The analysis of Australian publicly listed firms means that we employ the Australian All Ordinaries Accumulation Index (AAOAI) as the proxy for market beta. We also design and construct the Australian versions of the Fama and French (1993) size (SMB) and value (HML) risk factors. The Australian equivalent of the Fama and Fench (1993) size factor (SMB) was constructed by sorting ASX listed firms according to market capitalisation using the Sirca SPPR database. Sirca data only identifies stocks as ‘infrastructure’ from the end of 1996 onwards, therefore, this is the commencement date of our study. Consistent with Fama and French (1992), the Small and Big portfolios were formed based on the median market capitalisation as the midpoint. The Australian version of the Fama and Fench (1993) value factor (HML) is constructed by sourcing the book values of ASX listed firms from the Morningstar FinAnalytics database. The limited time series of these book values limits the construction of our customised infrastructure indices to a commencement date of January 1997 because the first ASX listed infrastructure (ie. Hills Motorway) company commenced in this year. Consistent with Fama and French (1992), the High and Low HML portfolios were formed based on companies sorted by their bookvalue-to-market-value with breakpoints at the 30/40/30 intervals. Both SMB and HML risk factor portfolios are calculated as at December each year.
Table 2 Summary Statistics and Distributions This table presents the summary statistics and distributions of the data employed in this study. AOAAI denotes the Australian All Ordinaries Accumulation Index. VWAII denotes the Value-Weighted Australian Infrastructure Index constructed from 37 ASX listed firms in the MSCI Infrastructure and S&P Utilities indices. EWAII is the Equal-Weighted Australian Infrastructure Index which is the equal weighted version of the VWAII. MSCI Infra. denotes the MSCI Infrastructure Index. S&P Utilities denotes the S&P Utilities Index. PPPI denotes the market-weighted index of the four ASX listed PPP companies. SMB denotes the Fama and French (1993) Small-Minus-Big risk factor portfolio return which captures the Australian size premium. HML denotes the Fama and French (1993) High-MinusLow risk factor portfolio return which captures the Australian value premium. The heading Start denotes the commencement month and year of the respective time series. Mean denotes the mean monthly rate of return. Std. Deviation denotes the standard deviation of monthly returns. The 5 th percentile, median and 95th percentile headings denote the 5th, median and 95th percentile rates of returns of the empirical distribution of returns of the time series. The numbers reported in parentheses are annualised statistics.
All time series are stationary based on the Augmented Dickey-Fuller (ADF) test.
5th percentile 95th percentile Start Mean Std. Deviation Median
In terms of the risk-free rate, the data sample in our study straddles the period of the John Howard federal government where budget surpluses were delivered resulting in Australian Commonwealth Government Treasury Notes no longer being issued from 2003 to 2008. This large five year gap without Treasury Notes means that there are no monthly returns available for these short-term liquid and low-duration risk-free assets. As an alternative, one option is to employ the monthly returns of an Australian Commonwealth government 1 year bond, however, a methodology such as this ignores the interest rate or duration risk exposed to the investor. To offer a pragmatic alternative, this study employs the UBS Australia Bank Bill Index as a proxy for the risk-free rate. The index comprises of seven parcels of 90 day bank accepted bills which mature every 7 days and are reinvested in the index at the current bank bill rate.
Furthermore, other studies such as Brailsford, Handley and Maheswaran (2008) also employ bank bills as a proxy for the Australian risk-free rate. It is important to note that records to date show that no Australian bank accepted bill has ever defaulted in the history of the Australian financial system.6 Table 2 presents the summary statistics of the variables of interest. Panel A reports the infrastructure and PPP indices while Panel B presents the statistics of the All Ordinaries Accumulation Index (AAOAI). Panel A shows that the value-weighted infrastructure index (VWII) and the equal-weighted infrastructure index (EWII) outperformed the AAOAI over the same sample period. All infrastructure indices exhibit marginally higher levels of volatility in returns. It is unsurprising that the EWII exhibits the highest level of volatility given that smaller capitalisation stocks are more heavily weighted in this index. The median, 5th and 95th percentiles all suggest that the distribution of infrastructure indices are similar to the AAOAI.
A level of critique may be aimed towards the UBS Australia Bank Bill Index is an inadequate proxy for the risk-free rate, however, other researchers including Brailsford et. al., (2008) also employ Australian bank bills as a proxy for the risk-free rate. In our study, the Australian Commonwealth 1 year Treasury Bond earned a 5.22% annual rate of return which is 6 basis points less than the 5.28% annual return from the bank bill index. In short, the 6 basis point difference between these two risk-free proxies is negligible.
An interesting observation in Panel A is the higher levels of return and risk characteristics of the PPP index in comparison to the infrastructure counterparts.
There are a number of reasons for this finding. First, the PPP index exhibits higher mean returns than its infrastructure counterparts because PPPs generally own assets that do not possess a long-term terminal value as these assets revert back to government hands at the end of their concession period. As a result, PPP equity holders must accumulate the capital value of the PPP asset throughout its concession period, which results in a higher mean return for PPPs than for conventional asset returns where the proceeds of an asset sale can occur at some point in the future.
Second, the PPP index exhibits substantially higher levels of risk which is attributable to the fact that all four listed PPPs are toll-road assets which have experienced severe traffic demand risks when shifting from the construction phase to the operations phase (Bureau of Infrastructure, Transport and Regional Economics, 2011; Black, 2014) Whilst PPPs are regarded in the investment industry as a relatively ‘low-risk’ proposition, the empirical evidence from ASX listed toll road PPPs challenges this perspective.
Panel C presents the Australian versions of the Fama and French (1993) SMB and HML risk factors while Panel D reports the statistics of the risk-free proxy over the sample period. The interesting features here is the Australian SMB and HML risk factors recorded lower mean returns than the risk-free rate during the sample period, although the median of the HML factor was marginally higher than the risk-free rate.
These interesting Australian based SMB and HML statistics are unsurprising given the previous works of Faff (2001) who revealed the negative performance of these Australian risk factors from 1991-1999. Overall, the summary statistics presented in Table 2 reflect the salient empirical features of the time series returns being employed in this study.
This section of the paper is divided into three distinct parts. The first section details the asset pricing models employed in this study. The second section explains the rationale for employing a constant fixed excess return benchmark as a comparison for the competing asset pricing models. The third section details the state-of-the-art Giacomini and White (2006) methodology to determine the predictive performance of the best asset pricing model.
(i) Asset Pricing Models Tested:
Previous studies in the U.S. setting by Lewellen and Nagel (2006), Simin (2008) and Welch and Goyal (2008) show that conditional models report the worse predictive performance of asset pricing models in comparison to unconditional models. In the Australian setting, Durack et. al., (2004), Nguyen et. al., (2007) and Whittaker (2013) all demonstrate the conditional versions of asset pricing models do not improve the predictive power of their unconditional counterparts. Given these previous findings in the literature, this study examines the predictive power of the following Australian
asset pricing models:
Unconditional Fama and French (1993);
Unconditional CAPM with intercept suppressed;
Unconditional Fama and French (1993) with intercept suppressed;
Simin (2008) demonstrates that the suppression of the intercept when estimating the asset pricing model factors, results in an increase in the precision of the regression coefficient estimates. However, the increase in precision of the coefficient estimates is at the cost of increasing forecast bias. This study will follow Simin (2008) and include both types of regressions in the analysis.
The derivation of the forecasted returns follows the methodology of Simin (2008) and Fama and French (1997). Asset pricing parameters are estimated over a 60 month training period and are then multiplied by the average factor returns during the training period.7 These are then used to predict the returns in the subsequent month.
(ii) Evaluation of Constant Benchmark Models:
We follow Simin (2008) and employ a fixed excess return model from a range of 1% to 10%. There are two rationales for a constant benchmark framework. First, we are interested in whether a fixed excess return model is a better predictor of asset returns than conventional asset pricing models. Simin (2008) finds that a constant U.S.
equity risk premium return of 6% per annum is a better predictor of future returns than any unconditional or conditional asset pricing model. Second, the work of Bishop, Fitzsimmons and Officer (2011) suggest that the market risk premium in Australia is between 6-7% while Brailsford et. al., (2008) estimate an Australian equity risk premium of 6.8% over bank bills from 1958-2008. In our study, we are interested whether the predictive performance of asset pricing models on infrastructure deliver similar approximations of an excess return of 6% per year (ie.
commensurate returns) over the sample period of the available infrastructure data from 1997-2012.
(iii) Evaluation of Predictive Performance This study follows Simin (2008) as it represents the state-of-the-art methodology for evaluating the predictive performance of asset pricing models to date. Consistent with Simin (2008), unconditional versions of the CAPM and the Fama and French (1993) three-factor model are examined and their performances are compared against a constant (or fixed excess return) benchmark. Following Simin (2008), we employ the fixed benchmark of six per cent per annum however, the performance of various other fixed benchmarks is also included.
Test 1: RMSFE Following Simin (2008), the Root Mean Square Forecast Error (RMSFE) is employed as a measure of forecast accuracy. RMSFE quantifies the average squared distance between the expected return from the model and the realised return over the specified time horizon. According to Simin (2008), the advantage of the RMSFE is that it can disaggregate a measure of forecast bias to allow for the differentiation in forecasting The term ‘training period’ is employed to remain consistent with the terminology in Simin (2008).
models. The equation below shows how the forecast bias can be disaggregated from the Mean Square Forecast.
( ̂ ) is the Mean Square Forecast Error for the model under S where is the actual return of the portfolio under examination at time t; ̂ is consideration;
the forecast return of the portfolio under examination at time t; var( ) is the variance of the difference between the actual and forecast returns of the portfolio under examination; and, bias( ) is the measure of forecast bias. By identifying the sign of the forecast bias, it is possible to identify the tendency of models to over or under predict subsequent returns. The RMSFE is simply the square root of the MSFE.
Test 2: Bias Following Simin (2008), we derive the Bias from Equation (1). Bias is defined as the tendency of over- or under- prediction around the RMSFE. The nature of the RMSFE as a quadratic function means that under- and over- estimations of a similar magnitude are given an equal weighting in the calculation. By calculating the Bias, this allows us to identify systematic under- or over- estimation of the forecast errors.
This Bias is informative for users interested in asymmetric preferences. For example, investment managers may be interested in models that consistently under-estimate long-term rates of return as you would employ those in an investment process rather than models that consistently over-estimate future rates of return.
Test 3: Giacomini and White (2006) Test As an alternative test of model performance, the Giacomini and White (2006) conditional predictive ability test is employed. The Giacomini and White (2006) test enables the best performing forecast model to be identified. The Giacomini and White (2006) test is a two-step procedure. The first step of the Giacomini and White (2006) test examines whether there is a statistical difference between two sets of
forecast errors. The null hypothesis for this test is given as:
[̂ -̂ | ]0 (2) where ̂ is the forecast error (or the difference between actual and forecast) for model i at time t. The test statistic according to Giacomini and White (2006) for one period ahead forecast is given by. Where n is the number of forecasts examined and is the un-centred multiple correlation coefficient from the regression of on.
Giacomini and White (2006) define as the difference between the forecast error functions, or ̂ -̂ where m observations are employed as the estimation window. The term is defined by both Giacomini and White (2006) and Simin (2008) as the vector (1 ). The null hypothesis is rejected at the α test level when the test statistic is greater than the (1- α) quartile of the χ2 distribution. For the purposes of this study, the chosen α of significance is ten percent, consistent with Simin (2008).