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«Robert J. Bianchi*, Michael E. Drew and Timothy Whittaker Department of Accounting, Finance and Economics Griffith Business School Griffith ...»

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Once the two forecast series are found to be statistically different to each other, the second step in the Giacomini and White (2006) procedure is to determine which forecast model performs better. Giacomini and White (2006) suggest a decision rule based on the fitted values of the regression of on. The number of times the fitted values are positive in comparison to the competing model determines which forecasting model performs better. This decision rule is employed in this study. In this analysis, the predictive performance of the asset pricing models is compared over a number of different time periods, namely, one month, one year and two years.

5. Results

The results section is divided into two distinct parts. First, we report the historical performance of asset pricing models (ex post) to provide the reader with an econometric picture and understanding of the systematic risk factors that explain the variation of Australian listed infrastructure returns. The second part of the results section reports the predictive performance of asset pricing models using the Giacomini and White (2006) and compares their performance with fixed excess return models.

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I. Asset Pricing Models (Ex-Post) Table 3 presents the conventional single-factor CAPM regressions on Australian listed infrastructure and PPP returns from 1997-2012. This provides the reader with an ex-post perspective of the CAPM and the systematic risks that explain the variation of infrastructure and PPP returns. The regression results suggest that all infrastructure and PPP indices in this study exhibit low systematic risk as expressed by their market betas. The value-weighted and equal-weighted infrastructure indices report market betas of 0.64 and 0.81, respectively. It is unsurprising that the equal weighted index exhibits a higher beta due to the higher index weighting across smaller market capitalisation firms which generally tend to exhibit higher betas.

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An interesting empirical observation in Table 3 is the joint interactions between the intercept term, the beta, the adjusted R2, and the direct relevance to asset pricing. The econometric estimation of a systematic risk factor in asset pricing originates from the zero-intercept criterion proposed in Merton (1973). The zero-intercept criterion suggests that the systematic risk factors of an asset pricing model are captured when there is a statistically significant independent variable which coincides with an insignificant intercept term. The insignificant intercept terms in Table 3 suggest there are no other systematic risk factor that can explain the asset returns of listed The relatively low adjusted R2s signify that these infrastructure and PPPs.

infrastructure returns exhibit relatively high levels of idiosyncratic risk.

Furthermore, it is important to note that the extremely low coefficient of determination of 0.0698 for the PPP index is attributable to the portfolio of four listed stocks only, which by construction, carries a high level of idiosyncratic risk in these regression estimates.9 Table 4 extends the ex-post analysis with the Australian version of the Fama and French (1993) three-factor model. The regression results reveal that the SMB size premium and the HML value premium do not assist in explaining the variation of infrastructure and PPP returns whilst the market beta remains the primary explanatory variable. Again, there are no statistically significant intercept terms (ie. no alpha) in these regression estimates. The regression results in Tables 3 and 4 differ to Bird et.

al., (2012) who estimate statistically significant excess returns in Australian listed infrastructure returns in their study. The variation in our results and those of Bird et.

al., (2012) can be isolated to two main differences. First, their work examined a sample period from 1995-2009 while our study is from 1997-2012. The second difference is that Bird et. al., (2012) employed an augmented Fama and French (1993) three-factor model with GFR GARCH with t-statistic distributed errors while we employ a conventional asset pricing model.

The Merton (1973) zero-intercept criterion has been employed in other asset studies such as Griffin (2002) and Fama and French (2004) in the U.S. setting, and by Limkriangkai, Durand and Watson (2008) in the Australian setting.

Effectively, the underlying asset of BrisConnections was a single investment in Brisbane’s AirportlinkM7 toll road. The primary asset of Rivercity otorways was Brisbane’s CL 7 tunnel.

Connect ast was the owner and operator of elbourne’s astLink motorway. Transurban is an ASX listed firm that owns and operates numerous toll road assets in Australia and the United States.

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II. Predictive Performance of Asset Pricing Models (RMSFE and Bias) Panel A of Table 5 shows that the fixed excess return models ranging from 2% to 4% exhibit the lowest forecast errors for future one month returns for most indices.

Another interesting observation is the relatively similar RMSFE values for models that are above and below the lowest RMSFE. This finding suggests that there may be negligible differences between the predictive performance of one asset pricing model versus another. This hypothesis can be verified in the next section of the analysis when the Giacomini and White (2006) test is estimated. Furthermore, Panel A shows that the Bias across all infrastructure indices are generally negative. The negative bias suggests that asset pricing models generally under-estimate future one month returns, on average.





Panel B of Table 5 reports the RMSFE and Biases for 1 year forecasts. The RMSFE values are generally larger than those reported for 1 month predictions, however, you cannot directly compare RMSFEs across different forecasting time horizons. The Bias in Panel B is generally positive for most predictive models. The positive bias suggests that the asset pricing models in Panel B are over-estimating one year future returns, on average.

Panel C of Table 5 reveals two interesting findings. First, the fixed excess return models for VWII and EWII report smaller RMSFEs over the 2 year time horizon than their equivalent models used to forecast 1 month and 1 year future returns. This suggests that the forecast errors over a two year time horizon are smaller than those reported in Panels A and B. In comparison, the MSCIAII and S&PUI exhibit the opposite behaviour whereby their RMSFEs based on 1 month forecast are smaller than the 1 year and 2 year forecasts. The PPPI reports smaller RMSFEs for one month returns and the largest for 1 year time horizons. Second, the Bias is almost always positive for the two year forecasts which suggests that both conventional asset pricing and fixed excess return models are generally over-estimating future two year returns, on average. Superannuation funds and investment managers need to be mindful that these asset pricing models exhibit a tendency to over-estimate expected infrastructure index returns across a longer two year time horizon.

Table 6 Relative Forecast Performance of Asset Pricing Model versus Fixed Excess Returns (pre-GFC) This table presents the number of times that a fixed excess return and asset pricing model forecast is statistically significantly better than all other alternatives using the Giacomini and White (2006) Conditional Predictive Ability test based on the null hypothesis at the 10% level. The sample period is from January 1997 to December 2007. The independent variables are denoted as follows. VWII denotes the Value-Weighted Infrastructure Index of 37 firms. EWII denotes the Equal Weighted Infrastructure Index of 37 firms. MSCIAII denotes the MSCI Australia Infrastructure Index. S&PUI denotes the S&P/ASX 200 Utilities Index. PPPII denotes the value-weighted PPP index. The asset pricing models being tested are denoted in the column headings. The numbers 1% to 10% are the constant fixed excess returns from 1% to 10% per year. FF denotes the Australian Fama and French (1993) three-factor asset pricing model. FFNI denotes the Australian Fama and French (1993) three-factor asset pricing model with no intercept term. CAPM denotes the Australian single-factor Capital Asset Pricing Model. CAPMNI denotes the Australian single-factor Capital Asset Pricing Model with no intercept term. The best predictive model for every time horizon is highlighted.

1% 2% 3% 4% 5% 6% 7% 8% 9% 10% FF FFNI CAPM CAPMNI

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Table 7 Relative Forecast Performance of Asset Pricing Model versus Fixed Excess Returns (Full Sample) This table presents the number of times that a fixed excess return and asset pricing model forecast is statistically significantly better than all other alternatives using the Giacomini and White (2006) Conditional Predictive Ability test based on the null hypothesis at the 10% level. The sample period is from January 1997 to December 2012. The independent variables are denoted as follows. VWII denotes the Value-Weighted Infrastructure Index of 37 firms. EWII denotes the Equal Weighted Infrastructure Index of 37 firms. MSCIAII denotes the MSCI Australia Infrastructure Index. S&PUI denotes the S&P/ASX 200 Utilities Index. PPPII denotes the value-weighted PPP index. The asset pricing models being tested are denoted in the column headings. The numbers 1% to 10% are the constant fixed excess returns from 1% to 10% per year. FF denotes the Australian Fama and French (1993) three-factor asset pricing model. FFNI denotes the Australian Fama and French (1993) three-factor asset pricing model with no intercept term. CAPM denotes the Australian single-factor Capital Asset Pricing Model. CAPMNI denotes the Australian single-factor Capital Asset Pricing Model with no intercept term. The best predictive model for every time horizon is highlighted.

1% 2% 3% 4% 5% 6% 7% 8% 9% 10% FF FFNI CAPM CAPMNI

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Overall, the RMSFE and Bias estimates in Table 5 provide a summary of the forecast errors calculated from every asset pricing model. Whilst the RMSFE and Bias estimates are an indication of which asset pricing model provides the lowest forecast errors, they do not provide a statistical test to evaluate the predictive performance of these models. To address this issue, we proceed to compare the predictive performance of these asset pricing models by employing the Giacomini and White (2006) test.

III. Predictive Performance using the Giacomini and White (2006) Test

This section of the study evaluates the predictive performance of asset pricing models using the Giacomini and White (2006) test and is divided into two parts. The section of the analysis examines the predictive performance of asset pricing models on infrastructure returns prior to the GFC from the period 1997 through 2007. The second part of the analysis carries the tests forward and reports the evaluation for the full sample period from 1997-2012. The objective of this analysis is to evaluate the sensitivity of the Giacomini and White (2006) test to changes in market conditions (ie. the 2008 GFC) and to ascertain the differences in the overall results by comparing the two sets of tests.

Table 6 presents the summary of the Giacomini and White (2006) tests on 14 predictive asset pricing models (four asset pricing models and ten constant return benchmarks) on the four infrastructure indices and the PPP index from 1997-2007 which is the sample period prior to the GFC. 10 Panel A reports the predictive performance of asset pricing models based on their 1 month forecasts and reveals that both CAPM and Fama-French asset pricing models outperformed all of the fixed excess return models. The very low numbers reported in Panel A signifies that it is difficult for any one single asset pricing model to significantly outperform the predictive performance of other asset pricing models. Panel B presents the predictive performance of asset pricing models in their 1 year forecasts and reports that the 10% fixed excess return model is the best predictor of future returns. In fact, Panel B shows that all fixed (ie. constant) excess return models from 2% to 10% per annum The detailed output of the Giacomini and White (2006) tests from 1997-2007 which compare every asset pricing model with its alternatives are available upon request.

outperformed both Fama-French models and the conventional CAPM model. Panel C summarises the predictive performance of asset pricing models based on their 2 year forecasts and reveals that the CAPM with no intercept (CAPMNI) marginally outperformed all other alternatives. The 5% fixed excess return model was the second best predictor of future returns. The results in Panel C are similar to the findings in Simin (2008) who estimate a 6% constant return model outperforms all other U.S. asset pricing models.

Table 7 reports the Giacomini and White (2006) tests on the 14 predictive asset pricing models across the full sample period from 1997 trough 2012 which includes the GFC.11 This allows us to compare the results of Tables 6 and 7. Panel A reveals similar results to the sample period prior to the GFC. Both CAPM and Fama-French asset pricing models outperform the constant fixed return models although the low numbers suggest that the magnitude of outperformance against the alternative models is negligible. Panel B shows that the 10% fixed excess return model continues to be the best predictor of infrastructure returns across the entire 1997-2012 sample period.

Again, the 1 year forecasts reveal that all constant return models outperform both CAPM and Fama-French models in predicting returns over 1 year time horizons.

Panel C reveals that the best predictor of returns 2 years forward is the 10% fixed excess return model which is closely followed by the strong performance of the 9% fixed excess return. Again, the CAPM and Fama-French asset pricing models are the worst performers in predicting returns 2 years forward. The finding in Panel C of the 10% excess return model shows that the dynamics of the GFC in 2008 and the subsequent market improvement afterwards has reduced the predictive performance of the 5% model (see Panel C in Table 6) and the 10% excess return model is now the best predictor of returns 2 year forward. Another interesting finding in Panel C is the predictive performance of the CAPM with no intercept has deteriorated somewhat since the GFC.



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