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

Diplomarbeit von Sascha Heller

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, a widely used and commonly known model in this context is the Capital Asset Pricing Model (CAPM). Introduced by several researchers in the 1960s, it is still one of the most applied methods for practitioners. However, it suffers from several shortcomings, including statistical caveats, economic assumptions, the absence of market frictions and the behaviour of market participants. An upgrade to this model was provided by Stephen Ross 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.

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 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, 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 and Bowman and Bush 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. 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 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. 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.

Table of Contents:

Text Sample:

Chapter 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. It is not pricing relevant in this context.

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 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. 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. The APT essentially requires three less restrictive assumptions: 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.

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. 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. and Rosenberg and McKibben 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, others used up to one hundred and one variables. Several studies focused on specific variables such as operating leverage, turnover and coverage ratio and variability in sales and financial leverage. In Figure I, Penman 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.