Long-term U.S. infrastructure returns and portfolio selection

Journal of Banking & Finance 42 (2014) 314–325

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Long-term U.S. infrastructure returns and portfolio selection Robert J. Bianchi, Graham Bornholt, Michael E. Drew, Michael F. Howard ⇑ Griffith Business School, Department of Accounting, Finance and Economics, Griffith University, Australia

a r t i c l e

i n f o

Article history: Received 12 December 2011 Accepted 17 January 2014 Available online 5 February 2014 JEL classification: G11 G12 G17

a b s t r a c t Our understanding of the long-term return behavior and portfolio characteristics of public infrastructure investments is limited by a relatively short history of empirical data. We re-construct U.S. listed infrastructure index returns by mapping their monthly performance to received systematic and industry risk factors from 1927 through 2010. Our findings reveal that the infrastructure returns in recent years may understate the tail-risk that investors could experience over the long-term, however, this tail-risk is commensurate with holding a broad portfolio of U.S. stocks. For mean-variance and mean-CVaR investors, we report the benefits of holding public infrastructure assets in investment portfolios. Ó 2014 Elsevier B.V. All rights reserved.

Keywords: Infrastructure Portfolio management Risk exposure Asset pricing

1. Introduction The OECD (2007) has reported a U.S.$1.8 trillion per annum projected requirement for global infrastructure spending through to 2030, yet there is a paucity of research on the portfolio benefits of these types of investments. From a United States perspective, the Department of the U.S. Treasury (2012) is allocating $476 billion in the coming years towards the development of new infrastructure initiatives which require both public and private investment. To better understand the characteristics of infrastructure, it is imperative that investors (such as pension funds) understand the long-term reward/risk behavior of infrastructure and its portfolio diversification characteristics. Furthermore, pension plan sponsors have a fiduciary duty to understand the role of infrastructure investment in a portfolio context. For most investments, this is achieved by evaluating the indexes that track the performance of a particular asset class. The challenge with infrastructure is the limited number of indexes (and associated history) with which to evaluate this asset class over the long-term. The challenge becomes more formidable in an asset allocation framework, as portfolio selection models require a large number of data observations that are simply not available for infrastructure investments. ⇑ Corresponding author. Address: Griffith Business School, Department of Accounting, Finance and Economics, Gold Coast Campus, Griffith University, Parklands Drive, Southport, Queensland 4222, Australia. Tel.: +61 7 3735 7078; fax: +61 7 3735 3719. E-mail address: m.howard@griffith.edu.au (M.F. Howard). http://dx.doi.org/10.1016/j.jbankfin.2014.01.034 0378-4266/Ó 2014 Elsevier B.V. All rights reserved.

Our study addresses these empirical challenges by investigating five U.S. listed infrastructure indexes. This research employs the methodology that follows Agarwal and Naik (2004) by utilizing the Fama and French (1993)/Carhart (1997) asset pricing models as the foundations to construct monthly returns for these U.S. listed infrastructure indexes over the long-term. By mapping U.S. infrastructure returns onto the Fama and French (1993)/Carhart (1997) risk factors and industry returns, we reconstruct U.S. listed infrastructure index monthly returns from 1927 to 2010. We acknowledge that any approach to the backfilling of data has limitations. This study takes the approach of Agarwal and Naik (2004), a methodology that allows researchers to construct historical infrastructure index returns based on the assumption that short-term empirical returns modeled on systematic risk factors and industry returns are a good proxy of their behavior over the long-term. From an asset pricing perspective, this study shows that a significant proportion of the variation of U.S. listed infrastructure index returns can be explained by systematic risk factors and industry returns. We use a five-factor asset pricing model which shows that approximately half of the total variation of returns can be explained by the four Carhart (1997) risk factors while the remaining variation of returns can be explained by the U.S. utilities industry returns orthogonalized to the Fama and French (1993)/Carhart (1997) factors. The asset pricing analysis in this study suggests that U.S. listed infrastructure index returns do not exhibit statistically significant excess returns. We model these indexes from 1927 through 2010 and find that, in general, U.S. listed infrastructure exhibit similar mean returns,

R.J. Bianchi et al. / Journal of Banking & Finance 42 (2014) 314–325

correlations and tail-risks as U.S. stocks. Furthermore, we show that the empirical tail-risks from recent empirical infrastructure returns understate their VaR and CVaR estimates over the longterm, however, their levels of tail-risk is commensurate with the systematic risk from U.S. stocks. This commonality between listed infrastructure and broad U.S. stocks is an interesting finding given that infrastructure indexes are heavily concentrated in sufficiently different industries including oil/gas storage and transportation, electricity and other broad based utilities. The risk estimates calculated in this study perhaps challenge the perception of infrastructure as a low-risk and steady-return investment. Our findings support the notion that U.S. listed infrastructure is perhaps not a separate asset class, but rather, a sub-set of the wider universe of U.S. stocks. From an investors’ perspective, we employ these long-term U.S. infrastructure returns to the problem of portfolio selection. We are motivated here to evaluate the long-term portfolio diversification benefits of publicly listed infrastructure. In a post Global Financial Crisis (GFC) world, tail-risk analysis is important within the Markowitz (1952, 1959) Mean-Variance framework. The estimation of tail-risk motivates us to examine these investments in the MeanVariance (MV) and Mean-Conditional-Value-at-Risk (M-CVaR) portfolio selection settings. In general, we find that most infrastructure indexes exhibit characteristics that can improve the risk/reward profile of an investment portfolio. While the various infrastructure indexes exhibit common risk factors, their desirability in a portfolio context is a function of the mean returns, volatilities, correlations and tail-risks of each index. This study is structured as follows. Section 2 reviews the relevant literature, Section 3 describes the data, and Section 4 outlines the methodology employed to evaluate listed infrastructure returns over the long-term. Section 5 presents the empirical analysis and Section 6 offers concluding remarks.

2. Related literature The OECD (2007) and the U.S. Treasury (2012) note the current deficit in infrastructure investment in electricity transmission, roads, rail, telecommunication and water (in addition to the need for critical maintenance of other sectors including ports, bridges and airports). However, against this imperative for infrastructure investment globally, there is a paucity of studies that consider the behavior of infrastructure returns over time (and associated characteristics for portfolio investors). The lack of literature may stem from the debate regarding whether infrastructure is, or is not an asset class distinct from listed stocks (Finkenzeller et al., 2010). Beeferman (2008) emphasizes that infrastructure returns are derived mainly from large individual idiosyncratic projects which increase the difficulty for investors to evaluate infrastructure as an asset class in a conventional portfolio analysis. Infrastructure investments are potentially attractive to pension funds because these long-term income generating assets complement the long duration of pension fund liabilities (Croce, 2011). Beeferman (2008) notes that infrastructure appears to be an attractive investment proposition for pension funds, however, the lack of knowledge of the reward and risk characteristics complicates the assessment of their diversification benefits. Furthermore, Inderst (2009) acknowledge that there is confusion with the investments options available, the expected and realized returns, the diversification benefits and the specific risks associated with infrastructure investments. One of the few studies that have considered the behavior of infrastructure returns was contributed by Bird et al. (forthcoming). The work of Bird et al. (forthcoming) take an augmented Fama and French (1993) approach to the asset pricing problem and find that

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infrastructure investments exhibit low systematic risks and high idiosyncratic risks. We contribute to the debate by extending the work of Bird et al. (forthcoming) by examining the role of industry returns on the performance of listed infrastructure. Evidence from Fama and French (1997) and Chou et al. (2012) suggest that conventional asset pricing models cannot sufficiently capture the variation of industry returns. One of the contributions of this study is the evaluation of the effect of the U.S. Utilities industry on U.S. listed infrastructure indexes for the first time in an asset pricing framework. From a portfolio diversification perspective, the literature to date provides limited information for investors to alleviate the confusion of the efficacy of infrastructure investments. Newell and Peng (2008) estimate a significant 0.70 correlation between U.S. listed infrastructure and stocks from 2000 to 2006, however, the reward for risk characteristics dramatically changed across sub-periods. Newell et al. (2011) report a 0.48 correlation between Australian listed infrastructure and stocks from 1995 through 2009. In the unlisted infrastructure setting, Hartigan et al. (2011) reveal portfolio diversification benefits for a balanced investment portfolio over a ten year sample period to 2008. However, despite the important insights that this literature brings to the field of infrastructure investing, the short observation periods considered in these studies may limit its usefulness to long-term investors (such as pension funds). Another challenge for investors considering infrastructure investment are the wide range of sub-segments within the investment universe (such as transport, water, airports and utilities). For example, the Australian study of Newell and Peng (2007) from 1995 through 2006 finds that toll roads exhibited the highest raw returns for investors. However, toll roads delivered inferior returns on a risk-adjusted basis when compared to utilities, infrastructure and infrastructure/utility composites. In short, the performance of infrastructure investments is not homogenous. To capture these ideas, we investigate the effect of the U.S. utilities industry returns across a variety of broad infrastructure indexes. A key challenge facing investors is the absence of long-term data. For instance, there are no infrastructure index returns available prior to the 1990s. To address this concern, we follow the two-step methodology of Agarwal and Naik (2004). We follow an in-sample/out-of-sample procedure, which employs recent empirical data to construct a dataset of historical returns for many decades. Our study will employ this procedure to construct long-term infrastructure returns which can be used as the inputs in the Markowitz (1952, 1959) mean-variance framework to construct optimal and minimum-variance portfolios. An assumption of the Markowitz (1952, 1959) framework is that investors define risk as the variability of expected returns of a portfolio. One of the limitations of employing the volatility of returns as a measure of risk is that it does not account for the extreme losses or tail-risk that occurs during times of financial crisis. The evolution from the mean-variance analysis has seen the development of the mean-VaR portfolio selection frameworks from Alexander and Baptista (2002), Campbell et al. (2001) among others. This approach of managing portfolio VaR has been critiqued by Acerbi and Tasche (2002), Artzner et al. (1997, 1999) and Szego (2002) who argued that VaR exhibits discontinuities in the loss distributions, and thus cannot yield a coherent measure of risk. To overcome the limitations of the mean-VaR framework, Uryasev (2000), Rockafellar and Uryasev (2000, 2002), Krokhmal et al. (2002) and Topaloglou et al. (2002) have developed the portfolio optimization problem in a Mean-Conditional Value-at-Risk (M-CVaR) framework. The recognized limitations of VaR in the tail-risk literature motivates this study to evaluate infrastructure investments in a M-CVaR portfolio optimization framework. As discussed, this study contributes to the infrastructure finance literature by employing the Agarwal and Naik (2004)

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methodology to construct long-term monthly return series for the various U.S. listed infrastructure indexes. This approach applies the systematic risk factors of Carhart (1997) and an orthogonal U.S. Utilities Industry return to develop the time series of infrastructure returns over the long-term. We validate the efficacy of the fivefactor asset pricing model by examining the zero-intercept criterion (see Fama and French, 2012; Griffin, 2002; Merton, 1973) and the conventional econometric evaluation of the model and variables. A second advantage of the Agarwal and Naik (2004) methodology is that it allows us to measure tail-risk over the long-term by employing this historical return information in a MV and M-CVaR framework.

opportunities that can be empirically earned by broadly investing in U.S. stocks. The U.S. bond proxy is a spliced return series of the U.S. government long interest rate developed from three sources. The first source comes from Professor Robert Shiller who employs his 30 year U.S. government treasury bond yield data from January 1970 to December 1972 and is transformed into monthly returns. The second data source for U.S. bond returns is the Lehman Brothers U.S. Government Long Term Bond Index which is employed for the period from January 1973 to December 1989. The third data source for U.S. bonds is the Citigroup U.S. Broad Investment Grade Index, which is employed from January 1990 to December 2010. 4. Methodology

3. Data This study employs a variety of U.S. listed infrastructure indexes, namely, the Morgan Stanley Capital International (MSCI) gross returns for the MSCI U.S. Infrastructure (MUSII), U.S. Broad Utilities (MUSBUI) and U.S. Small Utilities (MUSSUI) indexes. We also employ the Dow Jones Brookfield Americas Infrastructure Total Return Index (DJBAITRI) and the Macquarie Global Infrastructure North America Total Return Index (MGINATRI).1 The MSCI infrastructure indexes are based on the Global Industry Classification System (GICS) and are free float-adjusted market capitalization weighted indexes consisting of listed infrastructure companies, which are rebalanced quarterly. The securities are selected from the MSCI country and composite indexes (i.e. MSCI U.S. Equity Index) which fall into the appropriate category as dictated by the GICS. The MUSII aggregates the sub-industries of telecommunication services, utilities, energy, transportation, and social infrastructure sectors into a single index. The MUSBUI is constructed from listed companies that produce and supply electricity, gas, water or a combination of these. The MUSSUI comprises of small utility companies with low market capitalizations. The DJBAITRI is constructed from listed U.S. firms who derive more than 70% of their cash flows from infrastructure lines of business. As at 30th September 2011, over 68% of the index is invested in U.S. firms, 29% in Canadian firms with the remainder invested in Brazil and Mexico. The index has its primary industry concentration in U.S. oil/gas storage and transportation with lower sector allocations to transmission, distribution and communications. The MGINATRI is designed to invest in firms engaged in the management, ownership and operation of U.S. infrastructure and utility assets. At the time of writing, the MGINATRI was heavily concentrated with over 89% of the index invested in U.S. electricity utility firms. Panel A of Table 1 presents the descriptive statistics of the various infrastructure indexes, risk factors and asset classes employed in this study. An interesting feature is the negative mean return of the MUSII and it also possesses the second highest volatility statistics of all infrastructure indexes. Panel B presents two MSCI U.S. Infrastructure sub-indexes that reveal summary statistics that differ markedly to the MUSII. Panel C reports the three Fama and French (1992, 1993) risk factors (Rm-Rf, SMB and HML), the Carhart (1997) momentum (UMD) factor, and the Fama-French U.S. Utilities industry which are utilized in our asset pricing model to construct the long-term monthly returns for the indexes in Panels A and B. Panel D reports the summary statistics for the two major investable asset classes. These are represented by the MSCI U.S. Equity Index, which reflects the performance and investment 1 We do not employ the UBS U.S. Infrastructure Index due to the small number of constituents (less than five publicly listed firms) in the index, therefore, it cannot be regarded as a ‘broad’ investment in listed infrastructure.

One of the challenges with studying infrastructure returns is the lack of data and the different commencement dates of each index. This raises empirical difficulties in comparing the returns, risk measures and correlations for similar sample periods. Studies such as Fama and MacBeth (1973) and Fama and French (1992) show that the time period sampled may lead to different outcomes. Another problem in analyzing various infrastructure indexes is the short empirical history compared to other asset classes such as stocks and bonds. The longest dataset for U.S. listed infrastructure is the MUSSUI, which commenced in January 1995 while the shortest history is the MUSBUI, which began in June 2003. To complete a robust portfolio selection with listed infrastructure investments, it is necessary to include many periods of economic growth and contraction, which are driven by different macroeconomic factors over the long-term. It is for this reason that we develop the following methodology to construct the monthly returns of infrastructure investments from 1927 through 2010. 4.1. In-sample model To model the listed infrastructure returns over the long-term, this research follows the two-step procedure by Agarwal and Naik (2004). We divide our infrastructure data sample at their midpoint and regress the excess returns as the dependent variables against a five-factor model on the first half of each sample period (i.e. the in-sample). The previous work of Bird et al. (forthcoming) employs the Fama and French (1993) three-factor model on empirical infrastructure index returns and they find that these investments exhibit low levels of systematic risk. To address this issue, we extend our understanding of infrastructure asset pricing in two ways. First, we employ the Carhart (1997) four-factor model by including the momentum risk factor to the asset pricing framework. Our second contribution originates from evidence which suggests that asset pricing models cannot fully explain industry returns. We examine the impact of industry returns on listed infrastructure by including the Fama-French U.S. Utilities industry return as a fifth independent variable which is orthogonal to the four Carhart (1997) risk factors. The orthogonalization process removes the effect of the four independent variables, thereby, capturing the marginal impact of this industry sector.2 This study estimates the following ordinary least squares (OLS) regression on the in-sample data:

Rt  Rf ;t ¼ a þ b1 ðRm;t  Rf ;t Þ þ b2 ðSMBt Þ þ b3 ðHMLt Þ þ b4 ðUMDt Þ þ b5 ðUTILt  Rf ;t Þ þ et

ð1Þ

where Rt is the return of the respective infrastructure index; Rf,t is the risk-free rate estimated from the U.S. government 1 month 2 The authors would like to thank and acknowledge an anonymous referee for this suggestion.

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R.J. Bianchi et al. / Journal of Banking & Finance 42 (2014) 314–325 Table 1 Summary statistics. Name

Date

Mean

SD

Median

Skew.

Panel A: Broad infrastructure indexes MSCI U.S. Infrastructure DJ Brookfield Americas ITRI Macq. GI North America TR

01/1999 01/2003 07/2000

0.04 1.16 0.82

4.57 3.93 4.71

0.97 1.25 1.57

0.49 0.04 0.65

Panel B: MSCI infrastructure sub-indexes MSCI U.S. Broad Utilities MSCI U.S. Small Utilities

06/2003 01/1995

0.48 0.78

3.91 4.06

1.28 1.11

Panel C: Risk factors and industry returns U.S. Stocks Fama-French SMB factor Fama-French HML factor Carhart Momentum (UMD) factor Fama-French Utilities Industry U.S. Govt. 1 month T-Bill

01/1927 01/1927 01/1927 01/1927 01/1927 01/1927

0.92 0.25 0.40 0.70 0.87 0.30

5.47 3.34 3.59 4.82 5.68 0.25

Panel D: Asset classes MSCI U.S. Equity Index U.S. Bond Index

01/1970 01/1970

0.88 0.65

4.53 2.03

Kurt.

Max.

Min.

3.18 3.81 3.99

12.47 10.63 13.42

12.15 10.93 12.05

1.30 0.19

5.01 4.52

7.11 16.16

13.37 14.39

1.30 0.08 0.25 0.89 1.06 0.27

0.13 2.17 1.82 3.03 0.07 1.02

10.38 24.98 18.44 29.54 10.49 4.23

38.37 39.04 35.48 18.39 43.16 1.35

29.01 16.67 13.45 50.63 32.96 0.06

1.15 0.69

0.41 0.18

4.76 8.45

17.79 11.22

21.22 9.88

This table details the descriptive statistics for the data utilized in this study for the period ending December 2010. The first column is the name of the index, risk factors employed and asset class benchmarks employed in this study. This is followed by the commencement date of the time series, monthly means, monthly standard deviations (SD), medians, skewness (Skew), kurtosis (Kurt), maximum values (Max) and minimum values (Min) for each data series. Panel A reports the three broad infrastructure indexes, namely, the MSCI U.S. Infrastructure Index, Dow Jones Brookfield Americas Infrastructure Total Return Index (DJBAITRI) and the Macquarie Global Infrastructure North America Total Return Index (MGINATRI). Panel B reports a sample of MSCI Infrastructure sub-indexes which are components of the MSCI U.S. Infrastructure Index (MUSII). These indexes are the MSCI U.S. Broad Utilities Index (MUSBUI) and MSCI U.S. Small Utilities Index (MUSSUI). Panel C reports the U.S. Composite return, the Fama and French (1992, 1993) U.S. SMB and HML risk factors, the Carhart (1997) momentum risk factor, the Fama-French U.S. Utilities Industry and the U.S. Government one month treasury bill return data. Panel D presents the proxies for investable asset classes in U.S. stocks and bonds.

Treasury Bill; a is the intercept term or constant; b1to5 is the first to the fifth regression coefficient; Rm,t is the U.S. market proxy; SMBt is the Fama and French (1992, 1993) risk factor pertaining to portfolio size; HMLt is the Fama and French (1992, 1993) risk factor pertaining to the book-to-market value ratio; UMDt is the Carhart (1997) risk factor pertaining to the 12 month return momentum; UTILt is the Fama-French U.S. Utilities industry return orthogonal to Rm,t, SMBt, HMLt and UMDt; and, et is the regression error terms. A valid asset pricing model which captures the systematic risks of these infrastructure returns would observe significant betas, high R2 values and insignificant intercept terms. 4.2. Generating out-of-sample infrastructure stock index returns The regression coefficients estimated from Eq. (1) for the in-sample period are then used to construct a set of model returns in the out-of-sample period. The model returns are calculated (in the out-of-sample period) by summing the products of the in-sample regression coefficient and their respective risk factor return for every month across the out-of-sample period. To evaluate the efficacy of the asset pricing model in Eq. (1), we perform a statistical comparison between the out-of-sample model returns and the empirical returns. We achieve this by estimating the parametric t-test to assess for differences in means, non-parametric Wilcoxon signed rank test to evaluate the differences in medians and the non-parametric Kruskal–Wallis test to assess the equality of the distributions of the two time series. Finally, we employ the Chow test to evaluate the stability of our regression coefficients across our in-sample and out-of-sample periods. A valid asset pricing methodology would suggest that the empirical returns and the model returns are not significantly different in the out-of-sample period. If the out-of-sample model returns are statistically similar to their empirical returns, then the coefficients from the in-sample regressions can be used on the five systematic risk factor returns in Eq. (1) to construct the long-term monthly returns for each infrastructure index dating back to January 1927. With this new set of monthly returns for the infrastructure indexes, we can then compare the return/risk characteristics of the newly constructed

long-term returns versus the relatively short history of the empirical returns. 4.3. Long-term returns and risk The in-sample/out-of-sample procedure evaluates the stability of the regression coefficients over time. In the context of this study, we assume that the behavior of listed infrastructure over the shortterm is representative of the asset pricing model risk factors over the long-term. This modest assumption allows us to employ the five-factor asset pricing model to construct hypothetical monthly returns of the listed infrastructure indexes over the long-term from 1927. This means we can compare the behavior of the short-term empirical observations against the model returns estimated over the long-term. This provides us with the opportunity to examine various measures of risk over the long-term. It is well recognized that financial markets suffer from extreme losses in the left-tail of the distribution of returns, yet no literature to date has assessed the tail-risk characteristics of U.S. listed infrastructure indexes. This study will also investigate the CVaR characteristics of infrastructure by employing the Rockafellar and Uryasev (2000, 2002) M-CVaR portfolio framework. 4.4. Long term measures for portfolio selection One of the original contributions of this study is the long-term portfolio analysis of infrastructure from 1970 to 2010. The construction of the historical data observations allows us to evaluate the risk-reward characteristics of these returns across many decades. This is an important procedure in order to capture the effects of various macroeconomic conditions, monetary and fiscal policies on infrastructure returns over the long-term. A comparison of the mean, volatility and correlation characteristics of the various infrastructure indexes, U.S. stocks and U.S. T-Bills can be employed to determine the behavior of these infrastructure indexes. One of the criticisms of the Markowitz (1952, 1959) mean variance portfolio selection is that it utilizes variance as a measure of risk; however, this may be inappropriate when the return distribution is not normally distributed. This study examines the

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non-normality of infrastructure returns by investigating the standardized z-scores of their return distributions. These estimates will allow us to compare the estimated z-scores of infrastructure returns and compare them with a normal distribution. This provides us with information on the left tail of the distribution of returns in order to examine the potential losses from U.S. listed infrastructure under extreme market conditions over the longterm. Finally, this study employs a quantile regression approach to measure the CAPM betas of infrastructure investments at various quantile intervals. We estimate a quantile regression to verify the stability of the CAPM beta coefficients at specific points within the distribution of returns. This technique has been selected over the traditional CAPM model due to the preference for a five-factor asset pricing model in this study. The CAPM model utilizes the market risk premium only and ignores the SMB, HML, UMD and UTIL-Rf risk factors. The quantile beta estimation therefore creates CAPM beta coefficients which account for changes in the other four risk factors and would make the quantile beta coefficient volatile through time. The quantile beta technique allows us to measure whether the systematic risk (i.e. beta) of infrastructure investments varies across the distribution of returns. 4.5. Correlations and portfolio analysis The monthly infrastructure returns from 1970 to 2010 can be directly compared with investable U.S. stock and bond indexes due to the availability of this information. Correlation coefficients are estimated for infrastructure indexes, stocks and bonds. As the infrastructure indexes are sub-sectors of the entire U.S. Composite stock index, it is expected that they exhibit strong correlations with each other. The study will perform a variety of portfolio optimizations over the 1970–2010 sample period. We derive the Markowitz (1952, 1959) minimum-variance portfolio comprising of each individual infrastructure index and a combination of stocks and bonds. The mean-variance efficient portfolio is calculated by solving the following optimization:

min VarðRp Þ

ð2Þ

X

s:t: xi P 0; i ¼ 1;. .. ;n;

n X

xi ¼ 1; and EðRp Þ P Target Return

ð3Þ

i¼1

where Rp is the n-assets portfolio return; Var(Rp) = X0 VX is the n-assets variance, respectively; X = (x1, x2, . . . , xn)0 is the vector containing the asset weights in the portfolio; V is the n  n covariance matrix; and, E(Rp) is the expected return of the portfolio. We calculate the optimal risky portfolio (i.e. the market portfolio) that is realized at the tangency of the Capital Market Line. The returns, standard deviations, Sharpe ratio, VaR and CVaR at the 95% and 99% confidence levels and optimal portfolio weightings of the indexes are reported so that a comparison can be made in terms of the portfolio diversification benefits of each infrastructure index. Because investors are interested in minimizing their portfolio tail-risk, the study will also calculate M-CVaR portfolios that provide the highest monthly return for a given level of CVaR at the 99% confidence interval. It is acknowledged that practitioners would set a minimum return before deriving this final portfolio, therefore, the study will also complete a sensitivity analysis on the infrastructure index with different targeted returns and minimizing the CVaR levels. This study also follows the convex programming formulation of M-CVaR from Rockafellar and Uryasev (2000, 2002). The M-CVaR portfolio framework to address a discrete loss distribution can be expressed as follows. The a-VaR of the loss is presented as:

1a ðxÞ ¼ zka

The a-CVaR of the loss associated with the decision x is the value:

1 /a ðxÞ ¼ 1a

"

! # ka ka X X pk  a zka þ pk zk k¼1

ð4Þ

k¼ka þ1

where /a(x) is the mean of the tail distribution of z = f(x, y); fixing x let corresponding loss points be ordered as z1 < z2 <    < zn, with the probability of zk being pk > 0. 5. Results 5.1. In-sample five-factor model for infrastructure returns The results of the in-sample OLS regressions are presented in Table 2. The most significant systematic risk factors which explain U.S. infrastructure returns are the market betas (i.e. market risk premium) and the orthogonal U.S. utilities industry return. The SMB, HML and UMD factors vary in their statistical significance depending on the infrastructure index. This finding suggests that the design and construction of each index may cause the variation in the SMB, HML and UMD factor loadings of these indexes. Authors such as Beeferman (2008) argue that infrastructure are expected to exhibit a significantly positive value (HML) risk factor because many infrastructure projects are more likely to operate in an environment where expansion opportunities are subject to market regulation. As a result, this effect would reduce the potential for corporate growth opportunities for infrastructure firms. The findings in our study reveal that the HML risk factor is significantly positive in only three of the five infrastructure indexes. The intercept terms in Table 2 are effectively zero (and negative for MUSBUI) which supports the notion that the five-factor model in Eq. (1) captures the systematic risk factors of listed infrastructure returns. The relatively high R2s in the regressions suggest that the five-factor model seems to capture a large proportion of the variation of infrastructure index returns. The consistently strong and positive regression coefficients of market beta and the U.S. utilities industry returns indicate that these two risk factors are the primary explanatory variables of U.S. listed infrastructure returns. The interesting observation from these findings is the commonality of moderate market beta and the utilities industry return despite the variation in industry concentrations in the various indexes. For example, the Macquarie Global Infrastructure North America Total Return Index (MGINATRI) is heavily concentrated with electricity utility companies while the Dow Jones Brookfield America Infrastructure Total Return Index (DJBAITRI) has large exposures to oil/gas storage and transportation, yet both observe significant regression coefficients to market beta and the U.S. Utilities industry. We now proceed to test whether these regression coefficients can explain the out-of-sample returns of these infrastructure indexes. 5.2. Out-of-sample tests Table 3 presents the hypothesis test statistics that compare the means, medians and distributions of the empirical returns versus the five-factor model returns during the out-of-sample period. We also report the Chow test for stability of the regression coefficients between the two periods. The findings reveal that there are no statistically significant differences between the mean, medians and distributions of the empirical returns and the model returns with the exception of the MUSII. In general, these test results suggest that the in-sample regression coefficients from the five-factor model can be employed to construct infrastructure index returns over the long-term. The close relationship between the empirical

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R.J. Bianchi et al. / Journal of Banking & Finance 42 (2014) 314–325 Table 2 In-sample regression estimates. Variables

C

Rm-Rf

SMB

HML

UMD

UTIL-Rf

Adj R2

Panel A: MUSII: 1/1999–12/2004 (72 months) Coefficient 0.0072 Std. error 0.0038 t-statistic 1.9024 p-value 0.0615

0.8294 0.1055 7.8584 0.0000

0.2625 0.1163 2.2582 0.0272

0.1133 0.1190 0.9525 0.3443

0.0829 0.0905 0.9155 0.3633

0.1954 0.1055 1.8511 0.0686

0.5793

Panel B: DJBAITRI: 1/2003–12/2006 (48 months) Coefficient 0.0010 Std. error 0.0014 t-statistic 0.7601 p-value 0.4515

0.7986 0.0981 8.1368 0.0000

0.1231 0.1250 0.9842 0.3306

0.1055 0.1187 0.8888 0.3792

0.0690 0.0516 1.3371 0.1884

0.7491 0.0870 8.6121 0.0000

0.8209

Panel C: MGINATRI: 7/2000–9/2005 (63 months) Coefficient 0.0000 0.7696 Std. error 0.0019 0.0486 t-statistic 0.0446 15.8227 p-value 0.9646 0.0000

0.0591 0.0443 1.3333 0.1877

0.3649 0.0711 5.1357 0.0000

0.0051 0.0225 0.2256 0.8223

0.9913 0.0643 15.4218 0.0000

0.9526

Panel D: MUSBUI: 6/2003–3/2007 (46 months) Coefficient 0.0034 Std. error 0.0006 t-statistic 5.4755 p-value 0.0000

0.7895 0.0292 27.0035 0.0000

0.1560 0.0267 5.8409 0.0000

0.2817 0.0393 7.1772 0.0000

0.0434 0.0260 1.6679 0.1031

1.0007 0.0189 53.0495 0.0000

0.9854

Panel E: MUSSUI: 1/1995–12/2002 (96 months) Coefficient 0.0007 Std. error 0.0018 t-statistic 0.3849 p-value 0.7012

0.6928 0.0555 12.4854 0.0000

0.0623 0.0391 1.5932 0.1146

0.3522 0.0789 4.4658 0.0000

0.0599 0.0229 2.6191 0.0103

0.6333 0.0558 11.3495 0.0000

0.7809

This table presents the regression results of the five-factor model in Eq. (1) on the in-sample period returns for the various indexes. Panel A displays the estimates for the MSCI U.S. Infrastructure Index (MUSII). Panel B exhibits the estimates for the Dow Jones Brookfield America Infrastructure Total Return Index (DJBAITRI). Panel C presents the estimates for the Macquarie Global Infrastructure North America Total Return Index (MGINATRI). Panel D reports the estimates for the MSCI U.S. Broad Utilities Index (MUSBUI). Panel E reports the estimates for the MSCI U.S. Small Utilities Index (MUSSUI). The table reports the regression estimates with the intercept (C) and the Carhart (1997) four factors abbreviated as Rm-RFR, SMB, HML and UMD. UTIL-Rf is the Fama-French U.S. Utilities Industry Index orthogonal to the other four risk factors and the adjusted R2 for each regression is reported in the final column. The table displays the slope coefficients, heteroskedasticity and autocorrelation-consistent standard errors, tstatistics and the p-values for the five risk factors.

Table 3 Out-of-sample stability tests. Index name

Obs.

t-test

Sign test

Kruskal–Wallis

Chow test

MUSII

72

Test statistic p-value

1.2286 0.2213

1.6681 0.0953

2.7893 0.0949

2.8584 0.0119

DJBAITRI

48

Test statistic p-value

0.1913 0.8487

0.1429 0.8864

0.0215 0.8835

1.4411 0.2087

MGINATRI

63

Test statistic p-value

0.0251 0.9800

0.0878 0.9300

0.0081 0.9281

1.9122 0.0847

MUSBUI

45

Test statistic p-value

0.0826 0.9344

0.1614 0.8718

0.0274 0.8686

0.9001 0.4987

MUSSUI

96

Test statistic p-value

0.0929 0.9261

0.2961 0.7671

0.0885 0.7662

2.0120 0.0640

This table presents a parametric t-test to assess for differences in means, the non-parametric Wilcoxon signed rank test for differences in medians, the non-parametric Kruskal–Wallis test for differences in the distributions and the Chow test for stability of the regression coefficients between the two periods. The data series comprises of the constructed returns derived from the five-factor model regression coefficient estimates for the out-of-sample period and the empirical returns of the various infrastructure indexes. The column Obs. denotes the number of monthly observations in each out-of-sample period. The MSCI U.S. Infrastructure Index (MUSII) is for the period January 2005–December 2010. The Dow Jones Brookfield America Infrastructure is for the period January 2007–December 2010. Macquarie Global Infrastructure North America Total Return Index (MGINATRI) is for the period October 2005–December 2010. The MSCI U.S. Broad Utilities Index (MUSBUI) is for the period April 2007–December 2010. The MSCI U.S. Small Utilities Index (MUSSUI) is for the period January 2003–December 2010.

out-of-sample returns and the five-factor model can be visualized by plotting some of these returns in Figs. 1–3. It can be seen that the model returns are efficient at tracking the out-of-sample empirical returns. We perform a second exercise to check the robustness of the out-of-sample model returns derived from the five-factor model. We estimate an OLS regression with the out-of-sample model returns as the dependent variable and the empirical infrastructure index returns as the independent variable. The adjusted R2 for the MUSII, DJBAITRI, MGINATRI, MUSBUI and MUSSUI regressions are 0.651, 0.821, 0.981, 0.977 and 0.731, respectively, which are

very similar to their in-sample adjusted R2s. These simple regressions provide further support that the five-factor model employed in this study provide explanatory power. The third and final method to verify the robustness of the model is the reversal of the abovementioned procedure. We reverse the data by treating the out-of-sample as the in-sample period to confirm the robustness of our model. We found again that there were no statistically significant differences between the means, medians and distributions. In the interests of brevity, we do not report these results. In short, these tests provide us with statistical confidence that the regression coefficients from the five-factor model can be

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15.00% 10.00% 5.00% 0.00% -5.00% -10.00% -15.00% -20.00% 2005

2007

2006

2008

Empirical Returns

2009

2010

Model Returns

Fig. 1. Out-of-sample results for MSCI U.S. Infrastructure Index.

10.00%

5.00%

0.00%

-5.00%

-10.00%

-15.00% 2007

2008

2009

Empirical Returns

2010

Model Returns

Fig. 2. Out-of-sample results for D.J. Brookfield Americas Infra. Index.

10.00%

5.00%

0.00%

-5.00%

-10.00%

-15.00%

Empirical Returns

2010. Although the infrastructure indexes broadly exhibit moderate market beta and strong U.S. Utilities industry characteristics, Table 4 shows that their long-term mean returns vary considerably which reflects the various concentrations of industry sectors within each index. The findings also reveal that infrastructure indexes exhibit a long-term return ranging from 0.09% to 1.02% per month depending on the index being examined. In terms of volatility, the standard deviation of returns over the long-term exhibits a range from 4.70% to 6.34% per month. In every case, the volatility of returns is higher over the long-term which is expected due to the greater number of major macroeconomic shocks, for example, the period of the Great Depression, World War 2, the oil shock of the 1970s and others. The historical estimates also reveal that the minimum monthly returns over the long-term are substantially worse than recent empirical history suggests, and the maximum monthly returns in the long-term are markedly greater than observed in their short-term empirical returns. From a tail-risk perspective, Table 4 shows that the 99% VaR and CVaR tail-risks calculated from their short term empirical history are understated in comparison to their long-term estimates. These findings suggest that investors analyzing empirical infrastructure returns are underestimating the tail-risk inherent in listed infrastructure investments. This finding must be tempered with the results in Panel P of Table 4, which show that all CVaR tail-risk statistics in listed infrastructure returns are commensurate with those reported for broad U.S. stock returns over the long-term. This similarity of CVaR tail-risk in infrastructure and broad U.S. stocks challenge the perception that listed infrastructure provides lowrisk returns due to their general positioning as monopoly operators in highly regulated markets. This evidence suggests that listed infrastructure cannot be considered as a low-risk proposition.

Model Returns

Fig. 3. Out-of-sample results for Macquarie Global Infra. N. America Index.

used to construct infrastructure monthly returns over the longterm.

5.3. Performance characteristics of infrastructure indexes Table 4 reports the summary statistics of the long-term returns modeled from 1927 to the commencement date of each index versus the empirical returns. For comparative purposes, Panel P of Table 4 reports the U.S. Composite Index returns from 1927 to

5.4. Infrastructure indexes over the long-term Given this new knowledge on the differences between the long and short term returns, we now examine the return and risk profile of infrastructure indexes in more detail. Table 5 reports the statistics of the infrastructure indexes whereby the long-term constructed returns are spliced with the short-term empirical returns to form a single time series for each index from 1927 to 2010. Panel A shows that all infrastructure indexes delivered a risk premium over and above the risk-free rate with the exception of the MUSII. In terms of relative performance, the DJBAITRI and MGINATRI indexes outperformed U.S. stocks whilst reporting similar standard deviation of returns. In general, the findings suggest that infrastructure indexes exhibit commensurate returns and volatility as U.S. stocks. To further examine the extreme tail behavior of infrastructure index returns, Panel B presents standardized z-scores and compares these with what is expected from a normal distribution. Panel B reports that all infrastructure indexes and U.S. stocks exhibit standardized z-scores which are less extreme at the 5% z-score interval of 1.6449, however, the left-tail nature of both infrastructure and U.S. stocks at the 1% z-score are fat-tailed with statistics that are more negative than 2.3263. The 1% z-scores indicate that the tail-risks of listed infrastructure are non-normally distributed, however, they are commensurate with broad U.S. stocks. To provide a clearer comparison of these tail-risks, Panel C compares the empirical VaR and CVaR estimates at the 95% and 99% confidence levels, respectively. Panel C shows that infrastructure index returns exhibit tail-risks which are similar to U.S. stocks, and any differences are negligible. Overall, we can conclude that U.S. listed infrastructure index returns in this study exhibit similar tail-risks as broad U.S. stocks over the long-term. The empirical evidence presented in Table 5 challenges the perception that

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R.J. Bianchi et al. / Journal of Banking & Finance 42 (2014) 314–325 Table 4 Differences in long-term versus empirical returns. Mean

SD

Median

Min.

Max.

95% VaR

99% VaR

95% CVaR

99% CVaR

Panel A: MUSII long-term returns: 1/1927–12/1998 0.09 4.73 0.09

27.96

34.96

6.43

14.31

11.15

18.79

Panel B: MUSII empirical returns: 1/1999–12/2010 0.04 4.57 0.97

12.15

12.47

8.92

11.71

10.41

11.96

Panel C: Panel A–Panel B 0.13 0.16

15.81

22.49

2.49

2.60

0.74

6.83

Panel D: DJBAITRI long-term returns: 1/1927–12/2002 1.01 5.28 1.24

29.15

37.86

7.45

14.45

11.93

19.78

Panel E: DJBAITRI empirical returns: 1/2003–12/2010 1.16 3.93 1.25

10.93

10.63

6.30

9.96

8.86

10.93

Panel F: Panel D–Panel E 0.15 1.35

18.22

27.23

1.15

4.49

3.07

8.85

0.88

0.01

Panel G: MGINATRI long-term returns: 1/1927–6/2000 1.02 6.34 1.03

34.64

53.68

8.43

16.91

13.78

23.94

Panel H: MGINATRI empirical returns: 7/2000–12/2010 0.82 4.71 1.57 12.05

13.42

9.22

11.93

11.28

12.02

Panel I: Panel G–Panel H 0.20 1.63

22.59

40.26

0.79

4.98

2.50

11.92

Panel J: MUSBUI long-term returns: 1/1927–5/2003 0.48 5.88 0.48

33.69

44.56

8.21

16.06

13.51

22.65

Panel K: MUSBUI empirical returns: 6/2003–12/2010 0.48 3.91 1.28

13.37

7.11

6.51

11.78

10.04

13.37

Panel L: Panel J–Panel K 0.00 1.97

0.54

20.32

37.45

1.70

4.28

3.47

9.28

Panel M: MUSSUI long-term returns: 1/1927–12/1994 0.84 4.85 0.87

27.06

36.52

6.72

14.26

10.90

18.35

Panel N: MUSSUI empirical returns: 1/1995–12/2010 0.78 4.06 1.11

14.39

16.16

5.84

9.46

8.44

12.58

Panel O: Panel M–Panel N 0.06 0.79

12.67

20.36

0.88

4.80

2.46

5.77

Panel P: U.S. Composite Index returns: 1/1927–12/2010 0.92 5.47 1.30 29.01

38.37

7.85

14.93

12.24

20.05

0.80

0.24

This table reports the mean returns, standard deviations (SD), medians, minimum monthly returns (Min), maximum monthly returns (Max), empirical Value-at-Risk (VaR) and empirical Conditional Value-at-Risk (CVaR) (reported as the magnitude of losses) at the 95% and 99% confidence levels for the long term versus empirical returns of the various indexes. All statistics in this table are expressed as a percentage return. MUSII denotes the MSCI U.S. Infrastructure Index. DJBAITRI denotes the Dow Jones Brookfield America Infrastructure Total Return Index. MGINATRI denotes the Macquarie Global Infrastructure North America Total Return Index. MUSBUI denotes the MSCI U.S. Broad Utilities Index. MUSSUI denotes the MSCI U.S. Small Utilities Index. Panels A to O report the long-term, empirical returns and difference in the returns for the MUSII, DJBAITRI, MGINATRI, MUSBUI and MUSSUI, respectively. As a comparison, Panel P reports the statistics for the U.S. Composite returns for the entire 1927–2010 period.

infrastructure investments earn consistently high returns with low levels of volatility. To better understand the systematic risk behavior of infrastructure indexes, Panel D reports the CAPM betas based on quantile regression estimates from the 1st to 99th quantile range. We employ a quantile regression approach to address the non-normality of returns that may lead to misleading relative risk measures of CAPM beta when employing the OLS approach. Panel D reveals that the CAPM beta estimates for all infrastructure indexes are generally stable throughout the quantile range. The estimated betas for all infrastructure indexes are less than unity, which lends further support to the notion that these investments are indeed a low/moderate market beta proposition over the long-term. Overall, the marginally higher return of some listed infrastructure indexes can be explained by the utilities industry sector which comprises of firms operating in less competitive markets with higher levels of regulation. Whilst some listed infrastructure investments exhibit marginally higher returns than broad U.S. stocks, these rewards are offset by potential losses at the extreme left-tail in the distribution of returns. This finding is consistent with the classical return/risk relationship in finance theory. The issue of concern in these findings is the significant underperformance of the MUSII, yet it exhibits similar levels of risk as the other risky assets in this study. These findings motivate us to ex-

plore the returns and risk of listed infrastructure index returns over the long-term in a portfolio setting. 5.5. Portfolio selection and infrastructure The portfolio analysis section of this study begins with the mean-variance framework. We examine the first two moments of the distribution (i.e. mean and standard deviation) and the correlation coefficients of the infrastructure indexes, U.S. stocks and U.S. bonds. There are three rationales for employing the mean-variance framework on U.S. data for the sample period from January 1970 to December 2010. First, there are no U.S. bond index returns available before 1970. This study will maximize the usage of bond index returns as it is well understood that the characteristics of bond index returns are distinctly different to the return characteristics of a single bond. Second, for U.S. stocks, we employ the MSCI U.S. Equity Index as it represents the authentic investable returns that are likely to be earned by investors in U.S. stocks. The data available for the MSCI U.S. Equity Index commences on 31st December 1969. Third, we restrict the mean-variance analysis to U.S. assets only because monthly bond index returns for non-U.S. countries before the 1970s is virtually non-existent. The means, volatilities and correlations for the assets in the mean-variance analyses are presented in Table 6. The

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Table 5 Long-term measures of return and risk. MUSII

DJBAITRI

MGINATRI

MUSBUI

MUSSUI

Stocks

T-Bills

Panel A: Moments of the distribution Mean 0.07 Std. dev. 4.70 Skewness 0.35 Kurtosis 12.84

1.02 5.17 0.05 9.93

0.99 6.16 0.61 13.60

0.48 5.73 0.14 11.07

0.83 4.71 0.24 11.10

0.92 5.47 0.13 10.38

0.30 0.25 1.02 4.23

Panel B: Standardized tail z-scores 1st qtile 2.96 5th qtile 1.56 95th qtile 1.27 99th qtile 2.34

2.95 1.62 1.36 3.02

2.79 1.57 1.38 2.87

2.68 1.50 1.40 2.97

2.94 1.55 1.36 2.83

2.90 1.60 1.66 2.29

1.21 1.16 2.33 3.27

7.36 14.22 11.63 19.29

8.67 16.21 13.54 22.58

8.11 14.86 13.23 21.95

6.48 13.04 10.45 17.51

7.85 14.93 12.24 20.05

0.80 0.80 0.86 0.81 0.79 0.80 0.80 0.81 0.86 0.87 0.84

0.87 0.91 0.80 0.79 0.82 0.80 0.77 0.84 0.96 0.92 0.84

0.88 0.85 0.81 0.76 0.76 0.76 0.77 0.81 0.85 0.75 0.82

0.74 0.75 0.76 0.69 0.69 0.67 0.70 0.72 0.70 0.76 0.76

Panel C: Empirical tail risk measures 95% VaR 7.26 99% VaR 13.83 95% CVaR 11.20 99% CVaR 17.94 Panel D: Quantile single-factor CAPM betas Q 1st 0.77 Q 2.5th 0.83 Q 5th 0.83 Q 10th 0.82 Q 25th 0.81 Q 50th 0.80 Q 75th 0.81 Q 90th 0.81 Q 95th 0.78 Q 97.5th 0.77 Q 99th 0.82

0 0 0 0

This table presents the long-term behavior of the MSCI U.S. Infrastructure Index (MUSII), Dow Jones Brookfield Americas Infrastructure Total Return Index (DJBAITRI), Macquarie Global Infrastructure North America Total Return Index (MGINATRI), MSCI U.S. Broad Utilities Index (MUSBUI), MSCI U.S. Small Utilities Index (MUSSUI), the Fama and French U.S. market raw monthly returns and the U.S. Government 1 month Treasury-Bill monthly returns for the period from January 1927–December 2010. The statistics are calculated from splicing the Long-term constructed monthly returns and the short-term empirical monthly return data for each respective index. Panel A reports the mean, standard deviation, skewness and kurtosis. Panel B reports the standardised returns of each index. The 1%, 5%, 95% and 99% quantiles for a normal distribution are 2.3263, 1.6449, 1.6449 and 2.3263, respectively. Panel C presents the empirical VaR and CVaR estimates at the 95% and 99% confidence intervals, respectively. Panel D reports the quantile regression single-factor CAPM beta estimates of the excess returns of the infrastructure indexes against U.S excess returns at the 1st, 2.5th, 5th, 10th, 25th, 75th, 90th, 97.5th and 99th quantile levels.

mean-variance analysis estimated in this study is designed to reflect the realistic assumptions and investment governance guidelines of a typical pension fund. To facilitate this, we impose a restriction on leverage by not allowing any asset weight to be greater than 100% and requiring the sum of all weights to also equal 100%. No short sales are allowed in the portfolio optimizations. Table 6 exhibits the summary statistics of the monthly returns that are employed in the MV analysis from January 1970 to December 2010. The infrastructure index returns are all derived

by combining the long-term and short-term returns over the 1970–2010 sample period. Panel A of Table 6 reports that the DJBAITRI exhibits the highest mean return of 1.05% per month (12.60% per year). All infrastructure index returns report a higher return than T-Bills with the exception of the MUSII which exhibits a historical mean return of 0.16% per month (1.92% per year), and therefore, historically underperformed in comparison to other risky and risk-free assets. The low return of the MUSII is not reflected in its volatility of 3.83%

Table 6 Moments and correlations (1970–2010). Stocks Panel A: First two moments Mean 0.88 SD 4.53 Panel B: Correlation coefficients Stocks 1 Bonds MUSII DJBAITRI MGINATRI MUSBUI MUSSUI

Bonds

MUSII

DJBAITRI

MGINATRI

MUSBUI

MUSSUI

T-Bills

0.65 2.03

0.16 3.83

1.05 3.95

1.02 4.33

0.52 4.23

0.88 3.58

0.45 0.25

0.27 1

0.88 0.32 1

0.76 0.39 0.79 1

0.50 0.40 0.90 0.85 1

0.59 0.43 0.92 0.90 0.97 1

0.64 0.38 0.75 0.88 0.90 0.92 1

This table reports the first two moments of the distribution of returns and the correlation coefficients employed in mean-variance analyses for the period January 1970– December 2010. The infrastructure index based returns are derived by combining the empirical monthly return observations and the constructed model’s monthly returns. MUSII denotes the MSCI U.S. Infrastructure Index. DJBAITRI denotes the Dow Jones Brookfield America Infrastructure Total Return Index. MGINATRI denotes the Macquarie Global Infrastructure North America Total Return Index. MUSBUI denotes the MSCI U.S. Broad Utilities Index. MUSSUI denotes the MSCI U.S. Small Utilities Index. Panel A reports the first two moments of the distribution of returns for each investment. Panel B exhibits the correlation coefficients between each investment. All correlation coefficients are statistically significant at the 1% level.

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Ret.

SD.

Sharpe

95% CVaR

99% CVaR

W% Stocks (%)

W% Bonds (%)

W% Inf. (%)

0.07 0.12 0.01

3.81 4.19 4.68

6.98 7.09 6.54

0.0 29.3 0.0

88.1 70.7 53.1

11.9 0.0 46.9

Panel B: Dow Jones Brookfield Americas Infrastructure Total Return Index (DJBAITRI) MVP 0.67 1.99 0.11 3.80 ORP 0.89 2.79 0.16 5.53 M99%CVaR 0.77 2.16 0.15 4.03

7.14 7.43 6.84

8.2 0.0 0.0

91.8 40.0 71.0

0.0 60.0 29.0

Panel C: Macquarie Global Infrastructure North America Total Return Index (MGINATRI) MVP 0.67 1.99 0.11 3.80 ORP 0.83 2.64 0.14 4.96 M99%CVaR 0.79 2.40 0.14 4.30

7.14 7.02 6.56

8.2 13.2 0.0

91.8 46.5 63.5

0.0 40.4 36.5

Panel D: MSCI U.S. Broad Utilities Index (MUSBUI) MVP 0.67 1.99 ORP 0.72 2.20 M99%CVaR 0.61 2.31

0.11 0.12 0.07

3.80 4.19 4.33

7.14 7.09 6.74

8.2 29.3 0.0

91.8 70.7 68.1

0.0 0.0 31.9

Panel E: MSCI U.S. Small Utilities Index (MUSSUI) MVP 0.68 1.98 ORP 0.76 2.32 M99%CVaR 0.72 2.08

0.11 0.13 0.13

3.73 4.32 3.84

6.93 6.51 6.32

4.3 9.3 0.0

87.4 51.1 69.9

8.3 39.6 30.1

Panel A: MSCI USA Infrastructure Index (MUSII) MVP 0.59 1.98 ORP 0.72 2.20 M99%CVaR 0.42 2.37

This table reports the mean-variance (MV) optimizations for the minimum variance portfolio (MVP), the optimal risky portfolio (ORP) and the portfolio that will minimize the Mean return for the Conditional-Value-at-Risk at the 99% confidence level calculated from the monthly returns for the January 1970–December 2010 period. These returns are derived by combining the actual monthly return observations and the constructed model’s monthly returns up to the commencement of the empirical returns. The investment universe in this analysis includes U.S. stocks, U.S. bonds and the five infrastructure indexes. MUSII denotes the MSCI U.S. Infrastructure Index. DJBAITRI denotes the Dow Jones Brookfield America Infrastructure Total Return Index. MGINATRI denotes the Macquarie Global Infrastructure North America Total Return Index. MUSBUI denotes the MSCI U.S. Broad Utilities Index. MUSSUI denotes the MSCI U.S. Small Utilities Index. Ret. denotes the mean monthly portfolio return, SD. denotes the portfolio standard deviation, Sharpe denotes the monthly Sharpe ratio of portfolio returns, and CVaR is the Conditional-Value-at-Risk at the 95% and 99% confidence levels, respectively. W% denotes the optimal portfolio weights allocated to each asset class and W% Inf. denotes the optimal portfolio weighting of the respective infrastructure index.

per month, which is comparable with the other infrastructure indexes. These metrics do not bode well for the MUSII when it is employed in a portfolio optimization. Another interesting observation is that the MUSBUI delivered similar returns as U.S. bonds but with higher levels of volatility. Panel B of Table 6 reports large and positive correlation coefficients between U.S. listed infrastructure indexes and U.S. stocks. The high correlations and the high R2s of the five-factor asset pricing model (previously reported in Table 2) provide us with sufficient evidence to conclude that U.S. listed infrastructure index

returns are simply a sub-sector of U.S. stocks, and do not represent a distinctly separate asset class. There is no evidence in this study to suggest that the source of the return behavior of U.S. listed infrastructure indexes are sufficiently different to broad U.S. stock returns. Table 7 exhibits the mean-variance portfolio (MV) optimizations for the minimum-variance portfolio (MVP), the optimal risky portfolio (ORP) (i.e. the portfolio that is tangent to the Capital Market Line) and the optimal portfolio that minimizes the CVaR at the 99% confidence level. The portfolio optimizations reveal that the

Table 8 Mean-conditional-value-at-risk for a targeted return. Monthly return (%)

99% CVaR (%)

Std. dev. (%)

Sharpe

W% Stocks (%)

W% Bonds (%)

W% DJBAITRI (%)

0.650 0.675 0.700 0.725 0.750 0.766 0.775 0.800 0.825 0.850 0.875 0.890 0.900 0.925 0.950 0.975 1.000 1.025 1.050

7.48 7.05 6.89 6.87 6.85 6.84 6.86 6.92 6.97 7.03 7.25 7.43 7.60 8.13 8.77 9.45 10.15 10.84 11.56

2.03 2.00 2.04 2.07 2.12 2.16 2.19 2.29 2.41 2.55 2.69 2.79 2.85 3.02 3.19 3.38 3.56 3.75 3.95

0.0978 0.1116 0.1215 0.1322 0.1409 0.1454 0.1473 0.1517 0.1546 0.1563 0.1570 0.1571 0.1571 0.1567 0.1559 0.1549 0.1538 0.1526 0.1514

0.0 10.9 15.7 9.8 3.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

100.0 89.1 80.7 77.0 73.4 71.0 68.8 62.5 56.3 50.0 43.8 40.0 37.5 31.2 25.0 18.7 12.5 6.2 0.0

0.0 0.0 3.6 13.2 22.8 29.0 31.2 37.5 43.7 50.0 56.2 60.0 62.5 68.8 75.0 81.3 87.5 93.8 100.0

This table reports the minimum conditional-value-at-risk for a targeted portfolio mean monthly return as a percentage for the Dow Jones Brookfield Americas Infrastructure Total Return Index (DJBAITRI), U.S. stocks and U.S. bonds. The portfolio analysis is for the sample period January 1970–December 2010. The table reports the targeted portfolio mean monthly return and the mean-conditional-value-at-risk that can be attained, the portfolio standard deviation, the Sharpe ratio and W% denotes the portfolio weightings allocated to each asset class.

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DJBAITRI, MGINATRI and MUSSUI exhibit large asset allocations in their ORPs, however, the MUSII and MUSBUI do not. The marginally higher returns and marginally lower volatility estimates of some infrastructure indexes are sufficiently different for the MV framework to prefer listed infrastructure than broad U.S. stocks. The MUSII does not feature in the ORP as its historical mean return is lower than the risk-free rate. Another interesting observation is the portfolios that minimize 99% CVaR (i.e. M-CVaR optimal portfolios) all exhibit a higher allocation to infrastructure indexes than to broad U.S. stocks. The preference of the 99% CVaR portfolio to infrastructure can be highlighted by the portfolio optimization’s higher allocation towards the MUSII than to stocks. These portfolio optimization results are consistent with the previous findings in Table 5 that indicate that the CVaR estimates of all infrastructure indexes exhibit comparable tail risk to broad U.S. stocks. Whilst the differences in tail-risk are negligible, the findings in Table 7 demonstrate that these small differences are sufficiently (sensitive) enough for MCVaR investors to re-allocate their portfolio weighting from broad U.S. stocks to infrastructure indexes. 5.6. Mean-CVaR portfolio selection Table 8 reports the minimum CVaR for a targeted mean return of M-CVaR of one of the portfolio optimizations. Table 8 demonstrates the investment tradeoff between the CVaR and the Sharpe ratio. This is important for pension funds who have a fiduciary responsibility to maximize risk-adjusted returns for their investors while minimizing the potential for extreme losses. Table 8 reveals that the 99% CVaR continues to decrease until the 0.766% monthly mean return after which this tail-risk statistic begins to deteriorate. The highest Sharpe ratio occurs at a monthly return of 0.89–0.90%. The findings clearly show the investment tradeoff facing pension funds in achieving higher risk-adjusted returns versus minimizing tail-risk when including U.S. listed infrastructure in a stock/bond portfolio optimization. The portfolio analysis of these infrastructure index returns over the long-term provides us with a number of important findings which are of interest to academia and pension funds. First, infrastructure index returns deliver return characteristics, which are related to moderate market beta and strong U.S. utilities industry characteristics, yet the associated risks of these investments are commensurate with broad U.S. stocks. Second, infrastructure index returns may exhibit common risk factors, however, they possess sufficient differences in their mean returns and standard deviations to cause sufficient variations in portfolio weightings when calculating optimal portfolio choice in a MV framework. Conversely, the tail-risks of these infrastructure indexes are sufficiently different which causes similar optimal portfolio outcomes with these investments in a M-CVaR framework. The high sensitivity to the input values in MV and M-CVaR frameworks must be well understood by investors before making long-term investment decisions with infrastructure. These findings are important to pension fund managers and other industry professionals in developing their understanding of the risk-reward characteristics and portfolio diversification benefits of U.S. listed infrastructure investments. 6. Conclusion This research addresses the paucity of knowledge relating to U.S. listed infrastructure index returns, asset pricing and optimal portfolio choice. This study employed the procedure from Agarwal and Naik (2004) to model infrastructure returns over the longterm. A five-factor asset pricing model was employed to construct

long-term returns from 1927 to 2010. Asset pricing theory informs us that the Fama and French (1993)/Carhart (1997) four-factor model may explain asset returns and this study revealed that this framework with the inclusion of the U.S. Utilities industry returns can generally explain the variation of U.S. listed infrastructure returns over the long-term. With this new information, this study estimated higher levels of risk in infrastructure index investments over the long-term than those experienced in the recent past. The contribution of this study shows that U.S. listed infrastructure index returns exhibit the characteristics of low/moderate market beta and a strong positive relationship with the U.S. utilities industry even though each index possesses differences in design methodology and industry sector concentration. Another major finding of this study is that U.S. listed infrastructure is simply a sub-sector of U.S. stocks. This finding stems from the evidence which demonstrates that the mean returns, correlations and tailrisks of U.S. listed infrastructure indexes and broad U.S. stocks are sufficiently similar, therefore, these investments cannot be considered as a separate asset class. MPT informs us that an asset with a high return, combined with a low standard deviation and a correlation of less than one is desirable in a mean-variance analysis. This study found that the correlation coefficients between all risky assets were positive. Unique to this study, mean-variance portfolios were constructed by employing both long-term and short-term U.S. listed infrastructure index returns. It was established that most infrastructure indexes dominate MV due to the marginally higher return and lower risk than broad U.S. stocks. Furthermore, M-CVaR (99%) portfolios preferred listed infrastructure over U.S. stocks due to their relatively marginally smaller tail-risk. Whilst these infrastructure index returns report common risk factors, they exhibit sufficient differences in mean returns and tail-risks to cause differences in optimal portfolio choice. Pension funds must recognize that the optimal asset allocation to U.S. listed infrastructure index returns is not readily transferable from one index to another due to the similarities in their common risk factors, but rather, their differences in expected return and tail-risk remain the variables that ultimately drive optimal portfolio decision making. Acknowledgement We gratefully acknowledge the Australian Research Council Grant LP0989743 for financial assistance. Any remaining errors or ambiguities are our own. References Acerbi, C., Tasche, D., 2002. On the coherence of expected shortfall. Journal of Banking and Finance 26 (7), 1487–1503. Agarwal, V., Naik, N.Y., 2004. Risk and portfolio decisions involving hedge funds. The Review of Financial Studies 17 (1), 63–98. Alexander, G., Baptista, A., 2002. Economic implications of using a mean-VaR model for portfolio selection: a comparison with mean-variance analysis. Journal of Economic Dynamics and Control 26 (7/8), 1159–1193. Artzner, P., Delbaen, F., Eber, J.M., Heath, D., 1997. Thinking coherently. Risk 10 (11), 68–71. Artzner, P., Delbaen, F., Eber, J.M., Heath, D., 1999. Coherent measures of risk. Mathematical Finance 9 (3), 203–228. Beeferman, L.W., 2008. Pension fund investment in infrastructure: a resource Paper. Occasional Paper Series: Pension and Capital Stewardship Project Labor and Worklife Program Harvard Law School. Bird, R., Liem, H., Thorp, S., forthcoming. Infrastructure: real assets and real returns. European Financial Management. http://dx.doi.org/10.1111/j.1468036X.2012.00650.x. Campbell, R., Huisman, R., Koedijk, K., 2001. Optimal portfolio selection in a valueat-risk framework. Journal of Banking and Finance 25 (9), 1789–1804. Carhart, M.M., 1997. On persistence in mutual fund performance. Journal of Finance 52 (1), 57–82. Chou, P., Ho, P., Ko, K., 2012. Do industries matter in explaining stock returns and asset-pricing anomalies? Journal of Banking and Finance 36 (2), 355–370.

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