Estimating beta and Cost of Equity Capital for Non-traded Transportation Companies

Contents

I. Introduction

II. Background
A. CAPM and APT – A Review
B. The Risk Relevance of Accounting Variables
C. The Transportation Sector

III. Empirical Methodology
A. The Relevant Global Risk Factors
B. Estimating beta for Listed Companies
C. Relating Accounting Measures to Systematic Risk
D. beta and the Cost of Equity Capital of Non-traded Companies

IV. Data
A. The Sample
B. Global Risk Factors
C. Accounting Variables

V. Empirical Results
A. The Common Risk Factors
B. The Significance of Accounting Variables
C. The Estimated betas
D. The Expected Cost of Equity Capital
E. Evidence from the Field
F. Robustness Tests

VI. Conclusions

References

I. Introduction

Estimating the cost of equity capital has two major implications. First, it reflects the return to a company’s stock which an equity investor expects to receive from his investment. He makes his decision upon whether he could earn a higher rate of return in an alternative investment of equivalent risk. Second, a company must earn the cost of capital (both debt and equity) through its undertaken projects. It is hence relevant for decisions on undertaking positive net present value projects which are of similar risk as the company’s average business activities. It also substantially influences the pricing of an entire firm as far as the valuation is based on a discounted cash flow model.

A lot of effort has been done in the past to achieve accurate models which precisely determine this cost. Building on the modern portfolio theory of Harry Markowitz (1952), a widely used and commonly known model in this context is the Capital Asset Pricing Model (CAPM). Introduced by several researchers (Sharpe (1964), Lintner (1965) and Mossin (1966)) in the 1960s, it is still one of the most applied methods for practitioners (Graham and Harvey (2001)). However, it suffers from several shortcomings, including statistical caveats, economic assumptions, the absence of market frictions and the behaviour of market participants (Fama and French (2004) and King (2009)). An upgrade to this model was provided by Stephen Ross (1976) which has resulted in the Arbitrage Pricing Theory (APT). It combines several risk factors in addition to one market proxy, as it is the case in the CAPM, and is less restrictive in its assumptions (Reinganum (1980)).

But both CAPM and APT require observable market data, i.e. stock prices, of the analysed companies. These models thus only work for publicly listed firms. If research should be done on non-traded companies, however, an alternative methodology must be applied. In general, data from the balance sheet, the income statement and the cash flow statement are available for both listed and non-listed companies. While accounting data have widely been used in the past as well (Beaver et al. (1970), Thompson (1976) and Bowman (1979)) and have been assumed to provide valuable information in explaining stock returns, this line of research has dissipated over time. Only a few key figures, such as size and financial leverage, are still considered to be relevant. However, they can be used to indirectly estimate a firm’s beta by assessing their explanatory power in a CAPM or APT framework. This methodology is particularly beneficial for firms which are not listed because there cannot be observed any stock price movements. According to Ryan (1997), further motivations for using accounting data are: i) to make ex post risk measures more efficient, ii) to determine actual risk determinants, iii) to reduce the noise when estimating beta through stock returns and iv) to develop trading strategies.

In this thesis, I apply a methodology proposed by Brimble and Hodgson (2007) and Bowman and Bush (2006) to a sample of listed and non-listed European transportation companies.

Transportation has a substantial economic importance because it undertakes a spatiotemporal transformation where transport serves as the spatial bridging function and warehousing is the temporal bridging function (Pfohl (2010)). As it plays an important part in economic growth and globalization, the transportation sector is suggested to be highly cyclical and its performance should mainly depend on fundamental factors (Stopford (2009)) what implies that global economic trends are superior to firm-individual business risk. It can be subclassified into air transport, water transport, rail transport, road transport, transport via pipelines, warehousing and postal activities. Additionally, one can distinguish between passenger and freight transport (European Commission (2010)). It is surprising that little research has yet been done on examining the determinants of transportation stock movements in previous studies, while asset pricing literature provides a widely accepted methodology.

The rest of this thesis is organised as follows. The next section reviews previous results on both global risk factors and fundamental accounting variables. Section III describes the empirical methodology used to estimate beta and to relate accounting variables to systematic risk. Section IV presents the data and in section V, I discuss the empirical results. Section VI concludes.

II. Background

A. CAPM and APT – A Review

In a CAPM or APT framework, systematic risk refers to a firm’s stock price movement, i.e. its return, which depends on a set of risk factors. This type of risk cannot be diversified away. It must be taken into account by both investor and company when deciding on an optimal asset allocation or the true value of either a business project or the entire firm. Unsystematic risk, however, is firm-individual and can thus be eliminated when a broadly diversified portfolio is built up (Brealey and Myers (2008)). It is not pricing relevant in this context (Fu (2009)).

Hence, literature has focused on estimating systematic risk which is measured by beta in the CAPM. This model proposes that a firm’s expected stock return can be explained as a one-dimensional linear combination of a market proxy’s return in excess of a risk-free rate (i.e. the market risk premium) plus the risk-free rate. It makes the following restrictive assumptions (Black et al. (1972) and Bowman (1979)): i) investors are single-period, risk-averse maximisers of the expected utility of terminal wealth, ii) they can make their optimal portfolio decisions solely on the basis of mean and standard deviation of the probability distributions of terminal wealth, iii) they have homogeneous expectations about the mean and standard deviation of the probability distributions, iv) they have the same decision horizon and can lend and borrow at the same risk-free rate and v) there are perfect capital markets.

In addition to this single-factor model, a set of macroeconomic risk factors has been added over time and found to contain valuable information to assess stock price movements (King (1966), Chen et al. (1986) and Ferson and Harvey (1993)).¹ The risk factors refer to macroeconomic shocks which may affect required excess returns by expectations about either future dividend payments or future real interest rates or future risk premia (Campbell and Mei (1993)). The APT essentially requires three less restrictive assumptions (Reinganum (1981)): i) there are perfect capital markets, ii) investors prefer more wealth to less wealth with certainty and iii) the process generating stock returns can be expressed as a K-factor model. However, additional assumptions are needed in an international context, i.e. perfect integration of national equity markets and the absence of distorting taxes and transaction costs (Drobetz et al. (2009)).

But research solely relates to publicly listed firms for which movements in stock prices are observable. Then exposures to a set of risk factors can be estimated. If stock prices are not available, one has to implement a more sophisticated empirical methodology to estimate the cost of equity capital. It was some 40 years ago when asset pricing literature was in the fledgling stages and much research was done on determining the drivers of stock prices. Researchers developed different methods in estimating beta which included both market measures of risk (i.e. stock returns and macroeconomic factors) and key figures derived from accounting data (i.e. balance sheet, income statement and cash flow statement). While the latter approach has disappeared for several years, some key variables are still assumed to have a substantial influence in explaining stock price movements. Essentially, these are, among others, firm size, price- earnings ratio and market-to-book ratio (Fama and French (1995) and Penman (1996)). They have turned out to provide good explanatory power and are used in several ways.

B. The Risk Relevance of Accounting Variables

The models always require data which are observable on the market. Thus, one cannot relate them to estimations focused on non-traded companies. Another methodology first provided by Beaver et al. (1970) and Rosenberg and McKibben (1973), among others, is based on indirect measures of systematic risk. In this framework, a set of variables derived from accounting data is used to explain a previously estimated beta using a CAPM or APT model, respectively. In early studies, empirical work examined multiple accounting variables. While most researchers applied a set of three to seven accounting variables (Logue and Merville (1972), Breen and Lerner (1973), Ben-Zion and Shalit (1975) and Patel and Olsen (1984)), others used up to one hundred and one variables (Rosenberg and Marathe, 1975). Several studies focused on specific variables such as operating leverage (Lev (1974)), turnover and coverage ratio (Bildersee (1975)) and variability in sales and financial leverage (Lev and Kunitzky (1974)). In Figure I, Penman (2001) presents a model which illustrates the theoretical relationship between systematic risk and accounting variables. This model divides systematic risk into two fundamental risk measures, growth risk and return on common equity risk. The latter is then broken down into operating risk and financial risk. Operating risk is measured by profit margin risk which is determined by expense risk and operating leverage risk, asset turnover risk and operating liability leverage risk. Financing risk is further subdivided into financial leverage risk and borrowing cost risk.

Figure I

The Relationship between Systematic Riks and Accounting Variables

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Systematic risk is divided in both ROCE risk and Growth Risk, where ROCE is rate of return on common equity, RNOA is rate of return on net operating assets, FLEV is financial leverage, NBC is net borrowing cost. NOA is net operating assets and ATO is asset turnover. ROCE Risk is then subdivided into Operating Risk and Financing Risk. OI is defined as operating income and OL is operating liabilities. NFO is net financial obligations, CSE is common shareholder equity and NFE is net financial expense. Source: Penman (2001)

A number of studies has attempted to relate accounting measures of the aforementioned types of risk to a firm’s systematic risk (Lakonishok et al. (1994), Laveren et al. (1997), Kim et al. (2002) and Lee and Jang (2007)). The seminal empirical work used a set of seven accounting variables (i.e. dividend payout ratio, growth in assets, financial leverage, asset size, liquidity, earnings variability and accounting beta) where only dividend payout ratio, asset growth and variability in earnings turned out to be significantly correlated with systematic risk (Beaver et al. (1970)). While other studies determined different sets of relevant accounting measures, there is still little agreement over which variables are most relevant, and even less evidence whether there are substantial differences across industries and countries. In addition, coefficient signs, i.e. the direction of contribution to systematic risk, are somewhat different to what is theoretically expected.

C. The Transportation Sector

From a financial research perspective, transportation companies are somewhat curious. Gong et al. (2002) ask “A High Risk – Low Beta Business?” what best describes the intuition behind a substantial and ongoing examination. This industry sector is assumed to be highly cyclical and, hence, should bear a remarkably high amount of systematic risk. Its performance should depend on stock market-related factors and the industrial and economy-wide development. Previous findings, however, report relatively low market betas (Alexander et al. (1999), Kavussanos and Marcoulis (2000), Gong et al. (2002), Morrell and Turner (2003) and Yamada (2005)) which stand in contrast to theoretical expectations.² The studies suggest that betas may differ across transportation sectors and may be time-variant. Kavussanos and Marcoulis (1997) report betas which are on average higher for the subperiod January 1990 to June 1995 as compared to the subperiod July 1984 to December 1989, where water and rail transportation industries betas significantly differ in the entire period and the second subperiod. Allen et al.

(1990) document the time-dependent character of airline, motor carrier and railroad industries betas in the period from January 1963 to June 1987, while betas remained relatively stable for different 5-year to 10-year subperiods. betas also substantially differed across industries.

In this thesis, I focus on European transportation companies, both traded and non- traded. While even some big players, measured by sales, in this sector are not listed on any stock exchange (e.g. Deutsche Bahn AG, Condor Flugdienst GmbH, Hapag-Lloyd AG, La Poste), issuing stock is attractive mainly for well-established firms. Most firms in this industry stay privately held and, thus, market data are not observable. They are, however, expected to face the same risky environment, as do big companies. Hence, practitioners must apply a precise valuation method including estimations on the cost of capital.

III. Empirical Methodology

In order to finally estimate the cost of equity capital for non-traded companies, I need several steps including estimations based on listed and non-listed companies as well as macroeconomic data and accounting data. My empirical analysis is based on transportation-related companies where all models are estimated for both transportation and transportation service companies, and for each of those subsectors individually. First, exposures to a set of global macroeconomic factors are estimated using a market model regression with one market proxy and a methodology proposed by Ferson and Harvey (1994) for several global risk factors, respectively. This framework is also used in Chen at al. (1986) and in Drobetz et al. (2009) who focus on shipping companies. In a second step, I apply a methodology provided by Bowman and Bush (2006) and Brimble and Hodgson (2007) to assess an applicable set of accounting variables which can explain systematic risk for traded companies. Afterwards, I estimate betas for non- traded companies using the previous results. Fourth, I use a CAPM-linked model to determine the expected cost of equity capital for non-listed firms. Econometric assumptions and guidelines for the regression models are provided in Campbell et al. (1996) and Wooldridge (2002).

A. The Relevant Global Risk Factors

According to Ferson and Harvey (1994) and Drobetz et al. (2009), among others, I apply a multi-factor model which includes K-1 risk factors in addition to one market proxy. In this context, I first estimate a linear fixed-effects (within) cross-sectional time- series regression model³ to determine which factors have a significant impact on predicting returns on transportation stocks:

illustration not visible in this excerpt

where [illustration not visible in this excerpt] is the continuously compounded return for firm i in period t-1 to t and r ft is the ⁴ risk-free rate. [illustration not visible in this excerpt] denotes the intercept term and [illustration not visible in this excerpt] is the exposure against the [illustration not visible in this excerpt] macroeconomic risk factor [illustration not visible in this excerpt]. beta is a measure of systematic risk and can be expressed by the covariance between a stock’s return and the market return, standardised with the variance of the stock’s return. [illustration not visible in this excerpt] is an error term and indicates the unsystematic risk which is not priced in an asset pricing context (Fu (2009)). A fixed- effects model takes into account a firm-specific constant term. This estimation method results in one pooled beta for each risk factor. The model is estimated in a step-wise procedure, i.e. risk factors which are not significant in at least one subsample (all companies, transportation companies and transportation service companies) are excluded and the reduced model is then re-estimated. The estimation process is repeated successively until all coefficients are significant.

B. Estimating beta for Listed Companies

The market model regression is an OLS regression⁵ with one market proxy. This single beta model separately estimates one risk exposure, i.e. market beta, for each company:

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where [illustration not visible in this excerpt] and [illustration not visible in this excerpt] are the same as in model (1). [illustration not visible in this excerpt] is the return on the market proxy. [illustration not visible in this excerpt] is a firm-individual intercept term and [illustration not visible in this excerpt] is a firm’s sensitivity against a market proxy’s return. [illustration not visible in this excerpt] is an error term. alpha, beta and epsilon have the same economic interpretation as in model (1). Consequently, this model provides one beta for each company and is applied exclusively to traded companies.

In a next step, a multi-factor model (OLS)⁶ is estimated which includes solely K’ significant risk factors:

illustration not visible in this excerpt

where [illustration not visible in this excerpt] is the sensitivity against the [illustration not visible in this excerpt] macroeconomic risk factor [illustration not visible in this excerpt] for firm i, while the remaining variables and coefficients are the same as in model (2). This model is separately estimated for each listed firm and results in an array of N betas for each risk factor.

C. Relating Accounting Measures to Systematic Risk

The next section assesses the contribution to risk of several accounting variables. The model in Bowman and Bush (2006) differs slightly from that applied in Brimble and Hodgson (2007), in that Bowman and Bush estimate their results for one point in time, while the estimations in Brimble and Hodgson are based on accounting variables averaged over a specific time period. I use the latter in order to take into account changes in the economic environment. However, I do not use time-series betas what implicitly assumes stationarity throughout the whole period (Beaver et al. (1970)). This model (OLS)⁷ proposes that market beta can be explained by a set of L accounting variables:

illustration not visible in this excerpt

where [illustration not visible in this excerpt] is the market beta for traded firm i estimated by (2).[illustration not visible in this excerpt] is the exposure against the l-th accounting variable [illustration not visible in this excerpt] for firm i, averaged over the time period [illustration not visible in this excerpt], and [illustration not visible in this excerpt] is the error term. In my analysis, I exclude the intercept because a firm without any business activities and thus with accounting variables equal to zero has no exposure to a certain risk factor, i.e. beta is zero. A positive gamma indicates a positive relationship between systematic risk and the respective accounting measure, and vice versa. This results in one pooled gamma for each accounting variable. The model is estimated in a step-wise procedure, i.e. non-significant accounting variables are excluded and the reduced model is then re-estimated. The estimation process is repeated successively until all coefficients are significant. The model (OLS)⁸ finally delivers L’ significant accounting variables:

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This allows for an applicable model to calculate the expected cost of equity capital.

The model (OLS)⁹ is also estimated for each significant beta derived from the multi- factor model in (3):

illustration not visible in this excerpt

where [illustration not visible in this excerpt] is the exposure against the k-th global risk factor for firm i and [illustration not visible in this excerpt] is the sensitivity against the l-th averaged accounting variable [illustration not visible in this excerpt] for firm i for [illustration not visible in this excerpt]. [illustration not visible in this excerpt] is the error term. As in (4), a step-wise estimation procedure (OLS)¹⁰ is applied and delivers L’ significant [illustration not visible in this excerpt] -coefficients:

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D. beta and the Cost of Equity Capital of Non-traded Companies

I then estimate market betas and multi-factor betas, respectively, for a sample of non- traded companies using the estimated gammas from (5) and (7) and the appropriate accounting variables:

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for a market beta estimation where [illustration not visible in this excerpt] is the exposure against a market proxy for the [illustration not visible in this excerpt]- th non-traded company and [illustration not visible in this excerpt]is the l -th estimated coefficient for the market beta. [illustration not visible in this excerpt] is accounting variable l for non-traded firm j, averaged over the time period [illustration not visible in this excerpt]

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is utilised for estimating multi-factor betas where [illustration not visible in this excerpt] is the exposure against the [illustration not visible in this excerpt] global risk factor for non-traded firm [illustration not visible in this excerpt] kl is the [illustration not visible in this excerpt] estimated coefficient for the [illustration not visible in this excerpt] beta from (5) and (7), respectively. [illustration not visible in this excerpt] is defined as above. To compare results, models (8) and (9) are also estimated for traded companies where index j changes to index i.

Using a CAPM-linked methodology and the estimated market beta from (8), I calculate the expected cost of equity capital for non-listed companies. In addition to a risk-free rate and a market risk premium, this model takes into account a liquidity risk premium which corrects for the risk of a stock’s thin trading. This concept is provided by Acharya and Pedersen (2005) and Amihud et al. (2005), among others. While Amihud et al. give four possible explanations for illiquidity¹¹, Acharya and Pedersen estimate a risk premium when correcting for the level of liquidity. The expected cost of equity capital is determined as follows:

illustration not visible in this excerpt

where [illustration not visible in this excerpt] is the annual return for non-traded firm [illustration not visible in this excerpt], [illustration not visible in this excerpt] is the annual risk-free rate and R m is the annual market return. [illustration not visible in this excerpt] is the estimated systematic risk from (8) for firm j and [illustration not visible in this excerpt] is the annual liquidity risk premium. E is the expectation operator and E ([illustration not visible in this excerpt]) – [illustration not visible in this excerpt] is the expected market risk premium.

IV. Data

The models explained in III require observable market data and (observable) accounting data taken from a firm’s balance sheet, income statement and cash-flow statement. Stock prices and macroeconomic data are provided by Thomson Reuters Datastream and accounting data are taken from Bureau van Dijk’s Amadeus dataset and Standard & Poor’s Compustat. All data are on a Euro basis, except for interest rates, over the period from 29 January 1999 to 31 December 2008.

A. The Sample

I use a sample of 64 publicly traded and 20717 non-listed transportation-related companies from France, Germany, Italy, Spain, Switzerland and the United Kingdom which can be divided into transportation and transportation service companies. The sample covers 37 traded and 13673 non-traded transportation firms and 27 traded and 7044 non-listed transportation service firms. According to the “Nomenclature des Activités Economiques dans la Communauté Européenne“ (NACE; “General Name for Economic Activities in the European Union“) (European Commission (2010)), the sample can further be subdivided into five major categories, i.e. land transport and transport via pipelines, water transport, air transport (NACE codes 49, 50, 51; transportation companies)¹² and warehousing and support activities for transportation, postal and courier activities (NACE codes 52, 53; transportation service companies)¹³. This allows for a detailed analysis and an examination of structural differences in the risk profile within the transportation sector.

I use monthly stock prices which are adjusted for capital actions and dividends. The transportation stocks must provide a sufficient length of available data of at least 36 months and the company must be listed at 31 December 2008.¹⁴ I calculate continuously compounded returns in excess of the Euro Currency 1-month interest rate as the risk- free rate. Descriptive statistics on monthly returns and excess returns are reported in Table I. Except for the water transport sector, average returns and, hence, average excess returns are negative over the entire period. While there are remarkably high differences between the different sectors in monthly returns (ranging from -.07% to 1.0%) and monthly excess returns (ranging from -4.0% to -2.2%), aggregate means do not differ.

B. Global Risk Factors

The global risk factors are based on macroeconomic data. Previous empirical studies have examined individual risk factors in different pricing models. I apply a set of nine factors which are commonly used in the multi-beta asset pricing literature (Chen et al. (1986), Ferson and Harvey (1994), Drobetz et al. (2002) and Harvey et al. (2002)). They capture several sources of systematic risk in an international context. This APT framework is supposed to better explain stock price movements than does a single-beta asset pricing model, i.e. a market model. According to Drobetz et al. (2009), four of the nine risk factors are aggregate risk measures using data from the G7 countries, i.e. Canada, France, Germany, Italy, Japan, the United Kingdom and the United States. The remaining five global factors use macroeconomic data which are taken from indices, exchange rates and interest rates of different countries.¹⁵ The risk factors are calculated as follows:

The market risk premium is proxied by a sector-related regional measure. I use the monthly log change of the MSCI Europe Transport index less the Euro Currency 1- month interest rate as the risk-free rate (F_MSCIETR). This measure is assumed to capture additional information compared to a global equity index.

Trading and transportation is a global business. As parties from multiple currency areas are involved in a single transaction, a measure for currency risk is included. Additionally, previous literature reports that currency risk is pricing relevant (Dumas and Solnik (1995) and De Santis and Gérard (1998)).

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[...]

¹ Instead of adding macroeconomic factors, portfolio returns derived from mimicking portfolios for firm size and market-to-book ratio can also serve as risk proxies (Fama and French (1993))

² Some studies find betas equal to or higher than market average (Allen et al. (1990) and Lee and Jang (2007)

³ xtreg command in Stata with robust standard errors allowing for intragroup correlation (vce(cluster) command in Stata)

⁴ Economically, a positive alpha indicates a stock’s underpricing where the return is lower than expected by the CAPM. A negative alpha indicates that the stock is overpriced (Kavussanos et al. (2003)

⁵ reg command in Stata

⁶ reg command in Stata

⁷ reg command in Stata with robust standard errors (vce(robust) command in Stata)

⁸ reg command in Stata with robust standard errors (vce(robust) command in Stata)

⁹ reg command in Stata with robust standard errors (vce(robust) command in Stata)

¹⁰ reg command in Stata with robust standard errors (vce(robust) command in Stata)

¹¹ These are: i) exogenous transaction costs, ii) demand pressure and inventory risk, iii) private information about fundamentals of the security and order flow, and iv) search friction.

¹² Land transport and transport via pipelines include passenger rail transport (interurban), freight rail transport, urban and suburban passenger land transport, taxi operation, other passenger land transport n.e.c, freight transport by road, removal services, and transport via pipelines. Water transport includes sea and coastal passenger water transport, sea and coastal freight water transport, inland passenger water transport, and inland freight water transport. Air transport includes passenger air transport, freight air transport, and space transport

¹³ Warehousing and support activities for transportation include warehousing and storage, service activities incidental to land transportation, service activities incidental to water transportation, service activities incidental to air transportation, cargo handling, and other transportation support activities. Postal and courier activities include postal activities under universal service obligation, and other postal and courier activities

¹⁴ As a result, survivorship bias may affect the results. However, there exists a possible trade-off between survivorship bias and the effect of thin trading, i.e. firms which are close to bankruptcy are less frequently traded (Racine (1998)). I suggest that the problem of thin trading may be superior to that of a survivorship bias in this sample because the listed firms are relatively small and thus inherently not

continuously traded (Scholes and Williamson (1977), Dimson (1979) and Gong et al. (2006)). Also, one could argue that survivorship bias implicitly excludes bankruptcy risk which is, however, part of unsystematic risk (Dichev (1998)).

¹⁵ Although the sample solely covers firms from European countries, the performance of the transportation sector is supposed to be dependent on the global economic state.