CAPM for estimating the cost of equity capital: Interpreting the empirical evidence

We argue that the empirical evidence against the capital asset pricing model (CAPM) based on stock returns does not invalidate its use for estimating the cost of capital for projects in making capital budgeting decisions. Because stocks are backed not only by projects in place, but also by the options to modify current projects and undertake new ones, the expected returns on stocks need not satisfy the CAPM even when expected returns of projects do. We provide empirical support for our arguments by developing a method for estimating firms' project CAPM betas and project returns. Our findings justify the continued use of the CAPM by firms in spite of the mounting evidence against it based on the cross section of stock returns.     

GOLBALIZATION, CORPORATE FINANCE, AND THE COST OF CAPITAL

International financial markets are progressively becoming one huge, integrated, global capital market—a development that is contributing to higher stock prices in developed as well as developing economies. For companies that are large and visible enough to attract global investors, having a global shareholder base means having a lower cost of capital and hence a greater equity value for two main reasons: First, because the risks of equity are shared among more investors with different portfolio exposures and hence a different “appetite” for bearing certain risks, equity market risk premiums should fall for all companies in countries with access to global markets. Although the largest reductions in cost of capital resulting from globalization will be experienced by companies in liberalizing economies that are gaining access to the global markets for the first time, risk premiums can also be expected to fall for firms in long-integrated markets as well. Second, when firms in countries with less-developed capital markets raise capital in the public markets of countries (like the U.S.) with highly developed markets, they get more than lower-cost capital; they also import at least aspects of the corporate governance systems that prevail in those markets. For companies accustomed to less-developed markets, raising capital overseas is likely to mean that more sophisticated investors, armed with more advanced technologies, will participate in monitoring their performance and management. And, in a virtuous cycle, more effective monitoring increases investor confidence in the future performance of those companies and so improves the terms on which they raise capital. Besides reducing market risk premiums and improving corporate governance, globalization also affects the systematic risk, or “beta,” of individual companies. In global markets, the beta of a firm's equity depends on how the stock contributes to the volatility not of the home market portfolio, but of the world market portfolio. For companies with access to global capital markets whose profitability is tied more closely to the local than to the global economy, use of the traditional Capital Asset Pricing Model (CAPM) will overstate the cost of capital because risks that are not diversifiable within a national economy can be diversified by holding a global portfolio. Thus, to reflect the new reality of a globally determined cost of capital, all companies with access to global markets should consider using a global CAPM that views a company as part of the global portfolio of stocks. In making this argument, the article reviews the growing body of academic studies that provide evidence of the predictive power of the global CAPM as well as the reduction in world risk premiums.     

Testing conditional asset pricing models: An emerging market perspective

The CAPM as the benchmark asset pricing model generally performs poorly in both developed and emerging markets. We investigate whether allowing the model parameters to vary improves the performance of the CAPM and the Fama–French model. Conditional asset pricing models scaled by conditioning variables such as Trading Volume and Dividend Yield generally result in small pricing errors. However, a graphical analysis reveals that the predictions of conditional models are generally upward biased. We demonstrate that the bias in prediction may be the consequence of ignoring frequent large variation in asset returns caused by volatile institutional, political and macroeconomic conditions. This is characterised by excess kurtosis. An unconditional Fama–French model augmented with a cubic market factor performs the best among some competing models when local risk factors are employed. Moreover, the conditional models with global risk factors scaled by global conditioning variables perform better than the unconditional models with global risk factors.     

Robust estimation with flexible parametric distributions: estimation of utility stock betas

The distributions of stock returns and capital asset pricing model (CAPM) regression residuals are typically characterized by skewness and kurtosis. We apply four flexible probability density functions (pdfs) to model possible skewness and kurtosis in estimating the parameters of the CAPM and compare the corresponding estimates with ordinary least squares (OLS) and other symmetric distribution estimates. Estimation using the flexible pdfs provides more efficient results than OLS when the errors are non-normal and similar results when the errors are normal. Large estimation differences correspond to clear departures from normality. Our results show that OLS is not the best estimator of betas using this type of data. Our results suggest that the use of OLS CAPM betas may lead to erroneous estimates of the cost of capital for public utility stocks.     

A Comparison of Cost of Equity Estimates of Local and Global CAPMs

Cost of equity estimates are compared for three pricing models: the traditional local CAPM, the single (market) factor global CAPM, and the two‐factor global CAPM, with both market and currency index factors. For 2989 US stocks, the average difference in the cost of equity estimates is about 48 basis points between the local CAPM and the single‐factor global CAPM, and is about 61 basis points between the two global models. For 70 developed‐market ADRs, the corresponding average differences are 76 and 47 basis points, respectively. For 48 emerging‐market ADRs, the corresponding average differences are 57 and 70 basis points.     

What slice of the pie? The corporate bond market boom in emerging economies

This paper studies the determinants of shifts in debt composition among emerging market non-financial corporates. We show that the determinants of bond market access in EMs vary with global cyclical conditions and across local and foreign currency markets. We find that the role for institutions and macro fundamentals in creating an enabling environment for markets increased during the post-crisis period for local currency markets. Foreign bank linkages additionally explain why local currency bond markets increasingly substituted for banks in channeling liquidity to EMs. In the case of foreign currency markets, in turn, global cyclical factors accounted for most of the variation. Furthermore, a country’s relative sensitivity to global factors appears to vary with the size of its foreign currency bond market rather than local fundamentals. Our results highlight the risk of capital flow reversal in those EMs that benefited from the upturn in the global financial cycle mostly due to the relative size of their bond markets rather than strong fundamentals.     

Fama's Ratio and the Effect of Operating Leverage on the Cost of Capital Under CAPM

The firm's operating leverage is its ratio of fixed to variable costs. It is widely understood that production settings with higher fixed costs and lower variable costs are high risk. Well-rehearsed CAPM arguments show how the firm's beta and cost of capital is higher when its proportion of fixed costs is higher. Importantly, that generalization holds under CAPM if expected total costs are constant and merely re-apportioned between fixed and variable, but does not hold if expected total costs change. In actual business contexts, higher fixed costs are intended to bring lower unit variable costs and often lower expected total costs. Allowing for such efficiency gains, the firm's risk-adjusted cost of capital might typically fall despite the higher operating leverage. Formal proof follows directly from the payoffs or ‘certainty equivalent’ expression of CAPM. The CAPM insights and new CAPM equations brought to light in this proof are surprising and useful.     

The Cost of Capital of Cross‐listed Firms

This paper analyses the cost of capital of firms with foreign equity listings. Our purpose is to shed light on the question whether international and domestic asset pricing models yield a different estimate of the cost of capital for cross‐listed stocks. We distinguish between (i) the multifactor ICAPM of Solnik (1979) and Sercu (1980) including both the global market portfolio and exchange rate risk premia and (ii) the single factor domestic CAPM. We test for the significance of the cost of capital differential in a sample of 336 cross‐listed stocks from nine countries in the period 1980–99. Our hypothesis is that the cost of capital differential is substantial for firms with international listings, as these are often large multinationals with a strong international orientation. We find that the asset pricing models yield a significantly different estimate of the cost of capital for only 12% of the cross‐listed companies. The size of the cost of capital differential is around 50 basis points for the US, 80 basis points for the UK and 100 basis points for France.     

Accounting‐based Risk Management and the Capital Asset Pricing Model: An Empirical Comparison

Accounting‐based risk management (ABRM) is a theoretically consistent and practical tool for calculating the cost of capital from underlying financial ratios. In this paper, a sample of ABRM‐generated discount factors is used to generate risk‐adjusted returns, which are compared to CAPM equivalent discount factors. In view of the debates about CAPM's validity, alternative models, the nature and scale of the equity risk premium, and the importance of discount rates in capital budgeting and asset valuation, ABRM's characteristics and resulting discount rates offer a potentially useful alternative. Results suggest that although average discount rates are comparable, their cross‐sectional distributions are dissimilar, so that investors in an average risky firm are overcompensated for systematic risk when using CAPM discount rates, because CAPM discount factors overestimate risk arising from fixed costs in most firms.     

MEASURING THE COST OF CAPITAL IN AN INTERNATIONAL CAPM FRAMEWORK

This paper can be viewed as extending the traditional CAPM framework in two important ways. The first expands the concept of the market portfolio to include international securities. The second extends the definition of systematic risk to include currency risk.
What becomes clear in estimating the cost of capital for an international asset is that both extensions have become necessary if the traditional CAPM is to remain relevant. International markets have become increasingly integrated over the past two decades and so all assets might now be considered "international" and priced accordingly. The inclusion of the currency risk factor is not an ad hoc addition to the CAPM but rather results quite naturally from the fact that foreign returns need to be converted into a domestic currency.
Based on an examination of 18 companies, the article shows that the use of a broader market portfolio will tend to lower the estimated cost of capital for most firms, but in some cases could actually raise it. (In the case of Singapore Airlines, for example, the currency risk factor adds substantially to the cost of capital, while materially reducing it in the case of Nestlé.) Using a simple regression, the authors also attempt to show how the specifics of a particular company—for example, the currencies that are part of their cost/ revenue structure—determine the impact of currency risk on the cost of capital.     

The evolution of capital asset pricing models

The capital asset pricing models (CAPM) has been the benchmark of asset pricing models and has been used to calculate asset returns and the cost of capital for more than four decades. Many researchers have tried to relax the original assumptions and generalize the static CAPM. We survey the important alternative theoretical models of capital asset pricing and provide a complete review of the evolution of asset pricing models. We also discuss the interrelationships among these models and suggest several possible directions for future research. Our results might be used as a guideline for future theoretical and empirical research in capital asset pricing.     

Common risk factors in bank stocks

This paper provides evidence on the risk factors that are priced in bank equities. Alternative empirical models with precedent in the nonfinancial asset pricing literature are tested, including the single-factor CAPM, three-factor Fama–French model, and ICAPM. Our empirical results indicate that an unconditional two-factor ICAPM model that includes the stock market excess return and shocks to the slope of the yield curve is useful in explaining the cross-section of bank stock returns. However, we find no evidence that firm specific factors such as size and book-to-market ratios are priced in bank stock returns. These results have a number of important implications for the estimation of the banks’ cost of capital as well as regulatory initiatives to utilize market discipline to evaluate bank risk under Basel II.     

Estimating the Cost of Equity for Property-Liability Insurance Companies

Due to the highly skewed and heavy‐tailed distributions associated with the insurance claims process, we evaluate the Rubinstein‐Leland (RL) model for its ability to improve the cost of equity estimates of insurance companies because of its distribution‐free feature. Our analyses show that there is as large as a 94‐basis‐point difference in the estimated cost of insurance equity between the RL model and the capital asset pricing model (CAPM) for the sample of property‐liability insurers with more severe departures from normality. In addition, consistent with our hypotheses, significant differences in the market risk estimates are found for insurers with return distributions that are asymmetrically distributed, and for small insurers. Third, we find significant performance improvements from using the RL model by showing smaller values of excess return of the expected return of the portfolio to the model return for a portfolio of insurers with returns that are more skewed and for a portfolio of small insurers. Finally, our panel data analysis shows the differences in the market risk estimates are significantly influenced by firm size, degree of leverage, and degree of asymmetry. The implication is that insurers should use the RL model rather than the CAPM to estimate its cost of capital if the insurer is small (assets size is less than $2,291 million), and/or its returns are not symmetrical (the value of skewness is greater than 0.509 or less than ?0.509).     

An international CAPM for partially integrated markets: Theory and empirical evidence

This article proposes a theoretical testable capital asset pricing model for partially segmented markets. We establish that if some investors do not hold all international assets because of direct and/or indirect barriers, the world market portfolio is not efficient and the traditional international CAPM must be augmented by a new factor reflecting the local risk undiversifiable internationally. We also introduce a suitable framework to test this model empirically. Using a sample of six emerging markets and three mature markets, we find that the degree of stock market integration varies through time and that most of the sample emerging markets have become more integrated in the recent years. The local risk premium for emerging markets represents the most important component of the total risk premium, but its relative importance has decreased recently. Differently, the total risk premium for developed countries is largely driven by global factors.     

Alternative Models for Estimating the Cost of Equity Capital for Property/Casualty Insurers

This paper estimates the cost of equity capital for Property/Casualty insurers by applying three alternative asset pricing models: the Capital Asset Pricing Model (CAPM), the Arbitrage Pricing Theory (APT), and a unified CAPM/APT model (Wei (1988). The in-sample forecast ability of the models is evaluated by applying the mean squared error method, the Theil U2 (1966) statistic, and the Granger and Newbold (1978) conditional efficiency evaluation. Based on forecast evaluation procedures, the APT and Wei's unified CAPM/APT models perform better than the CAPM in estimating the cost of equity capital for the PC insurers and a combined forecast may outperform the individual forecasts.     

The performance of cross-sectional regression tests of the CAPM with non-zero pricing errors

We show that in the presence of non-zero pricing errors, the Fama–MacBeth (FM) cross-sectional regression test is very likely to either reject the Capital Asset Pricing Model (CAPM) when it (almost) holds or accept the model when it grossly fails. We investigate the case when pricing errors are correlated with betas and demonstrate that the test performance depends crucially on the correlation, cross-sectional distribution of betas, and several other parameter values. Even when the CAPM holds exactly (pricing errors are zero) the FM test is equally likely to either reject or accept the model when typical sample sizes are used.     

Controlling shareholder share pledging and the cost of equity capital: Evidence from China

We propose and test the incentive view—that the margin call pressure and ownership-control discrepancy associated with insider share pledging increase investors’ perceived risk, and thus also the cost of equity capital, in an emerging market. Using a controlling shareholder share pledging sample for Chinese listed firms, we find that firms with share pledging have a cost of equity capital that is 23.7 basis points higher than firms without share pledging. Further, share pledging increases the cost of equity capital through the information risks and agency conflicts channels. Cross-sectional analyses show that share pledging has a stronger effect on the cost of equity capital in non-state-owned enterprises, firms without monitoring of multiple large shareholders, firms with controlling shareholders assuming the position of chairperson, and firms with a weak institutional environment. In addition, using the global financial crisis and the outbreak of the coronavirus (COVID-19) as quasi-natural experiments, we disentangle the potential confounding effect of firm fundamentals and show that share pledging is positively associated with the cost of equity capital. Overall, the results are consistent with our incentive view that share pledging increases the cost of equity capital in an emerging market.     

New estimates of the cost of capital for pharmaceutical firms

Academic researchers, as well as pharmaceutical firms themselves, often use the Capital Asset Pricing Model (CAPM) to estimate a firm's cost of capital. But the CAPM implicitly assumes that cash flows follow a random walk. This assumption is inconsistent with our finding that large U.S.-based pharmaceutical firms' cash flow growth rates display either momentum or mean-reversion. We show that growth rate momentum implies: (1) the systematic risk of a project increases monotonically with time to maturity of the cash flows; and (2) longer duration projects require a higher cost of capital. One of the practical implications of our results is that the traditional CAPM underestimates the cost of capital for some pharmaceutical firms by as much as 2.8%. These findings are quite relevant for the policy debate about the high rates of return earned by pharmaceutical companies, which some claim are pure rents and are not necessary to attract investors. Our theoretical and empirical analysis shows that high returns are often required to compensate for the higher systematic risk of long-duration pharmaceutical cash flows.     

Estimating the Cost of Equity Capital for Property-Liability Insurers

This article presents new evidence on the cost of equity capital by line of insurance for the property‐liability insurance industry. To do so we obtain firm beta estimates and then use the full‐information industry beta (FIB) methodology to decompose the cost of capital by line. We obtain full‐information beta estimates using the standard one‐factor capital asset pricing model and extend the FIB methodology to incorporate the Fama–French three‐factor cost of capital model. The analysis suggests the cost of capital for insurers using the Fama–French model is significantly higher than the estimates based upon the CAPM. In addition, we find evidence of significant differences in the cost of equity capital across lines.     

交叉上市的资本成本效应之实证研究

交叉上市的资本成本效应是从公司理财角度研究交叉上市的核心领域。本文以截止2008年6月30日在内地、纽约与香港交叉上市的11家中国公司为样本,分别采用CAPM和Gordon模型估算分析公司在内地、纽约和香港三个市场的资本成本,结果表明:(1)在A股市场CAPM模型下的资本成本要高于Gordon模型下的资本成本,而在N股市场和H股市场,结果相反;(2)采用CAPM模型与Gordon模型均证明公司在A股市场的资本成本(β系数)低于其在N股和H股市场的资本成本。A股市场较低的资本成本反映出我国股票市场对投资者利益保护不足,我国股票市场亟需加强对投资者利益的保护。