Bank Capital and the Cost of Equity
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund
  • | 2 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Contributor Notes

Using a sample of publicly listed banks from 62 countries over the 1991-2017 period, we investigate the impact of capital on banks’ cost of equity. Consistent with the theoretical prediction that more equity in the capital mix leads to a fall in firms’ costs of equity, we find that better capitalized banks enjoy lower equity costs. Our baseline estimations indicate that a 1 percentage point increase in a bank’s equity-to-assets ratio lowers its cost of equity by about 18 basis points. Our results also suggest that the form of capital that investors value the most is sheer equity capital; other forms of capital, such as Tier 2 regulatory capital, are less (or not at all) valued by investors. Additionally, our main finding that capital has a negative effect on banks’ cost of equity holds in both developed and developing countries. The results of this paper provide the missing evidence in the debate on the effects of higher capital requirements on banks’ funding costs.

Abstract

Using a sample of publicly listed banks from 62 countries over the 1991-2017 period, we investigate the impact of capital on banks’ cost of equity. Consistent with the theoretical prediction that more equity in the capital mix leads to a fall in firms’ costs of equity, we find that better capitalized banks enjoy lower equity costs. Our baseline estimations indicate that a 1 percentage point increase in a bank’s equity-to-assets ratio lowers its cost of equity by about 18 basis points. Our results also suggest that the form of capital that investors value the most is sheer equity capital; other forms of capital, such as Tier 2 regulatory capital, are less (or not at all) valued by investors. Additionally, our main finding that capital has a negative effect on banks’ cost of equity holds in both developed and developing countries. The results of this paper provide the missing evidence in the debate on the effects of higher capital requirements on banks’ funding costs.

I. Introduction

The global financial crisis (GFC) provided compelling evidence that capital is a bank’s strongest defense against losses from adverse movements in asset values. During the crisis, banks operating with low capital levels were brought to the brink of insolvency as the crisis unfolded and losses accumulated. Many such banks were acquired by healthier ones while others escaped extinction only through government bailouts using public funds.2

Policymakers and regulators immediately reacted by stepping up capital requirements, with the aim of strengthening the resilience of individual banks, as well as the whole banking system, to shocks. Efforts to enhance bank capitalization had culminated in the adoption of the Basel III regulatory framework in 2010, which requires banks to hold higher capital ratios compared to those recommended by its predecessor, Basel II.3

Yet, eight years after adopting the new, more stringent, capital regulatory framework, bank capital continues to be the subject of a heated debate between numerous banking stakeholders, namely, bankers, regulators, politicians, and academics. In particular, the consequences of increased capital requirements for banks’ funding costs continue to be controversial among bankers on the one hand, and regulators and academics on the other. While the latter praise the merits of higher capital ratios on the grounds that they enhance banks’ loss-absorption capacities and spare society the heavy costs of bank failures, bankers argue that requiring banks to operate with more equity capital increases funding costs because “equity has a higher cost than debt.” To persuade policymakers and society at large, bankers assert that higher funding costs would be passed on to borrowers, which would eventually result in less credit and depress the real economy. For instance, in November 2016, The Economist reported that European banks were complaining that higher capital requirements “will crimp lending and growth—although research by the BIS suggests that better-capitalized banks have lower funding costs and lend more, not less.”4 On March 7, 2019, the Financial Times reported that “The Federal Reserve has voted against activating a key buffer aimed at guarding against financial stability risks in one of a trio of decisions by U.S regulators that will be greeted with relief by major financial groups.”5

The present paper contributes to this debate by empirically examining the impact of capital on banks’ costs of equity. We study a large sample of banks from 62 countries over the 1991–2017 period in order to gauge the effects of various bank capital measures on the cost of equity. Our starting point is the theoretical prediction that, as a firm shifts to a capital structure with more equity, its equity cost decreases. As debt decreases in the capital mix, equity becomes less risky, which should lead to a decrease in the risk premium required by equity holders. This, in turn, results in a lower cost of equity capital. From a bank’s overall cost of funding perspective and using the Modigliani and Miller (1958) framework (M-M hereafter), we infer that, as a bank increases equity’s weight in its capital structure, the equity cost decreases, making less of an impact on its weighted average cost of capital cost (overall funding cost) than would be the case were the cost of equity insensitive to capital structure. If, indeed, the cost of equity was to decrease significantly with the increase in bank equity capital, the impacts of more stringent capital requirements on banks’ overall funding costs might not be as severe as bankers claim. Subsequently, any impact from higher capital requirements on the cost of credit would be (extremely) limited. In fact, throughout the paper, our empirical analyses consistently provide evidence of a robust, statistically and economically significant negative relationship between bank capital and the cost of equity. Our baseline regression estimations suggest that a one percentage point increase in the equity-to-assets ratio reduces the cost of equity by about 18 basis points. At very low bank capital levels (first quartile of our sample), the magnitude of the impact of a one percentage point increase in the equity-to-asset ratio on bank cost of equity is even larger (79 basis points).

Many authors have challenged the claim that increased equity requirements are economically costly because they lead to increases in banks’ funding costs, which will subsequently be passed on to borrowers. In an open letter to the Financial Times in 2010, twenty prominent academics advocated the imposition of much higher capital requirements than those introduced by Basel III. They argued, “Some claim that requiring more equity lowers the banks’ return on equity and increases their overall funding costs. This claim reflects a basic fallacy. Using more equity changes how risk and reward are divided between equity holders and debt holders, but does not by itself affect funding costs. Bankers warn that increased equity requirements would restrict lending and impede growth. These warnings are misplaced.”6 In a sweeping paper intended to illuminate the debate over capital regulation, Admati et al. (2013, p.1) assert that “the view that equity is expensive is flawed in the context of capital regulation.” Part of their argument is based on the premise that greater equity in the capital mix should lower equity risk, leading to decreases in stockholders’ required returns, which would not necessarily elevate a bank’s overall funding cost. Given what they consider as a trivial cost of capital effect of capital requirements, Admati and Hellwig (2013) suggest that the other benefits of increasing bank capital justify setting the minimum equity-to-assets ratio at between 20 and 30 percent.

Applying the M-M model with taxes, Kashyap et al. (2010) attempt to quantify the impact of increased capital requirements on lending by assessing the cost of capital effect. Their estimations suggest that each 1 percentage point increase in capital raises a bank’s weighted average cost of capital by about 2.5 basis points. They conclude that the long-run steady-state impact of increased capital requirements on lending is likely to be modest.

We investigate a scarcely addressed question in the banking empirical literature. Our central contribution is to demonstrate that the theoretical assumption that the required return on equity falls as a bank’s financial leverage decreases holds empirically. By doing so, we provide evidence that, in reality, markets do spot and price the change in bank risk ensuing from additional equity in the capital mix. We thus provide a strong basis for using the M-M framework to quantify the effect of capital requirements on banks’ costs of funding and, thereby, on their lending costs. Even in the presence of distortions, such as taxes and government deposit and debt guarantees, this framework can still be used to analyze the trade-off between the costs of additional equity (due to such distortions) and benefits (resulting from safer banking systems).

By documenting a negative empirical impact of additional capital on the cost of equity, we provide a missing piece of evidence to the debate on funding cost’s effect of higher bank capital requirements. For instance, in defending the view that higher capital requirements come at a price, Elliott (2013) argues that “Modigliani-Miller relies on markets to correctly perceive the change in relative safety that results from adding more equity to the funding mix. However, there is a chance that markets will be too skeptical in this regard, in which case equity and debt costs will not fall as they should, and total funding costs will go up more than would be required by the other factors described above. Higher funding costs would then be passed on to borrowers in whole or part.” He adds, “Nonetheless, one can understand why markets may be somewhat skeptical of something on which academics assure them of the truth but have not conclusively proven with empirical evidence.” This paper’s findings represent a stark response to the skepticism expressed in the above statements about markets’ pricing of additional bank equity capital in line with the predictions of standard finance theory.

While strongly advocating higher bank capital requirements, Admati et al. (2013) also question the empirical validity of the assumption that the required return on equity would fall with a rise in equity in the funding mix. They state, “Despite its fundamental importance, empirically establishing this relationship is notoriously difficult” (p.16, footnote 33). Likewise, Kashyap et al. (2010) point to the difficulty of empirically validating the assumption that investors demand lower risk premiums for holding better capitalized banks’ stocks. They do, however, attempt to provide some supporting evidence by showing that the stock returns of less-levered banks tend to be less volatile and exhibit lower betas. Yet, they stop short of establishing a clear empirical link between these risk measures and equity returns. The work of Baker and Wurgler (2013) comes close to ours in its attempt to validate the bank-capital-cost-of-equity relationship empirically, after admitting that “the validity of the capital structure irrelevance argument is not so clear, and direct empirical evidence is lacking” (p. 2). To emphasize the lack of empirical work addressing the link between bank capital and the cost of equity, they further note that “Admati et al. (2013) cite seven theoretical papers in the relevant section but only one empirical paper, Kashyap, Stein, and Hanson (2010), which does not estimate the cost of equity directly” (p. 2). To estimate leverage’s effect on a bank’s equity cost, Baker and Wurgler (2013) use a sample of U.S. banks and proceed in two stages. First, they estimate the relationship between the leverage ratio and equity beta, and then estimate the relationship between the equity beta and realized return on equity. Their results point to a positive relationship between financial leverage and equity risk (beta). However, their estimations fail to validate the presence of a positive relationship between beta and stock returns. Rather, their findings reveal that banks with lower betas have higher costs of equity.

Our paper differs from Baker and Wurgler (2013) in various respects. First, while they use realized stock returns as a proxy for the cost of equity, we use an ex-ante measure implied by stock prices and analysts’ earnings forecasts (COE hereafter). The recent literature argues that the ex-ante cost of equity implied by stock prices and analysts' earnings forecasts is a better measure of cost of capital than ex post returns (see Bekaert and Harvey, 2000; Hail and Leuz, 2006; Pastor et al., 2008). Pastor et al. (2008) empirically show that the implied cost of capital outperforms realized returns in detecting a risk-return trade-off. They advocate the use of COE rather than realized returns because the former is forward looking, with a better capacity to capture time-varying expected returns. Li et al. (2013) show that COEs are better than traditional ratios at predicting future stock returns.

Additionally, while Baker and Wurgler (2013) focus their analysis on the U.S. banking sector, we take a global perspective and analyze the cost of capital effects of higher capital requirements on an international sample that spans a large number of countries with various levels of economic development and different institutional setups. This global approach is of paramount importance in light of the increasing interconnectedness of national banking systems and the resulting potential vulnerabilities, which may have adverse effects beyond each banking sector’s national borders. It is also important to investigate the cost of capital impact of bank capital requirements at the international level, as regulatory capital agreements are intended to be implemented globally. We also exploit our rich dataset to provide insights on the variations in bank capital ratios and cost of equity across countries, geographical regions, levels of economic development, and time periods. Finally, Baker and Wurgler (2013) use a two-step test approach to examine the empirical relationship between leverage and the cost of equity. Instead, we employ a direct empirical specification, where the cost of equity is regressed on the capital ratio and various bank- and country-level controls.

We examine the bank-capital-cost-of-equity relationship in a cross-country setting using bank-level data covering listed banks in 62 countries over the period 1991–2017 (more than 16,000 bank-year observations). Our estimations indicate that banks with higher capital ratios enjoy a significantly lower cost of equity. We also find that investors value sheer equity capital most, as other forms of capital impact the cost of equity either very slightly (other components of Tier 1 capital) or insignificantly (Tier 2 capital). Our results are robust to a battery of controls for bank- and country-level factors, cost of equity measures, sample composition, and tests that account for potential endogeneity concerns. In additional tests, we find that the magnitude of the impact of capital on bank’s cost of equity is larger at banks with lower capital levels. In other words, banks with more binding (lower) capital ratios benefit more, in terms of cost of equity, from additional capital. Our findings also reveal that capital has a stronger effect on banks’ cost of equity in developing countries than in advanced countries.

This paper’s findings have important policy implications. The documented evidence suggests that the theoretical assumption that equity becomes cheaper as a bank funds itself with more equity capital is, in fact, empirically valid. Considering the scarcity of such empirical evidence, our study may open the door for a more enlightened debate concerning the merits of requiring banks to hold more capital. If, in addition to a decrease in cost of equity, bank cost of debt also declines due to higher capital (as is suggested by theoretical literature and some empirical evidence), the effect of higher capital requirements on the weighted average cost of capital could be far lower than that suggested by bankers. This would be the case even in the presence of distortions, such as taxes and implicit and explicit government guarantees of bank debt. Higher capital requirements can thus come at little or no cost to borrowers, and the benefits in terms of financial stability may outweigh the costs. Hence, the current actions taken by some countries to loosen bank capital regulations may be ill advised and should be reconsidered.

The remainder of this paper is organized as follows. In Section 2, we present our data and define the main variables used in the study. In Section 3, we discuss our empirical results. Section 4 provides additional analyses, and Section 5 concludes the paper.

II. Data and variables

A. Data

To examine the impact of capital on the cost of equity in the banking sector, we begin by extracting all available bank equities listed on all stock exchanges around the world from DataStream for the period 1991–2017. We then merge these data with other data from two other databases: Institutional Brokers Earnings Services (I/B/E/S) from Thomson Reuters, which provides analyst forecast data, and Thomson Reuters and Bloomberg, which provide bank financial statement information. We further extract country variables’ data from various databases, including the International Financial Statistics, World Development Indicators, Financial Structure database, etc. The result is a sample of more than 16,000 bank-year observations for 62 countries. Due to data availability, the number of observations varies from one country to another over the sample period. Likewise, the number of observations varies from variable to another.

B. The Implied Cost of Equity Capital

Following Hail and Leuz (2006) and Dhaliwal et al. (2006), we measure our dependent variable, the implied cost of equity (COE), as the average estimate obtained from four different models provided by Claus and Thomas (2001); Gebhardt et al. (2001); Easton (2004); and Ohlson and Juettner-Nauroth (2005). Using the average of four estimates, rather than relying on a single model, reduces the possibility of obtaining biased results (Dhaliwal et al., 2006). The individual estimates of the implied cost of capital we get using the models of Claus and Thomas (2001), Gebhardt et al. (2001), Easton (2004), and Ohlson and Juettner-Nauroth (2005) are denoted rCT, rGLS, rES, rOJN respectively. We note that rOJN is estimated in a closed form solution while rCT, rGLS, and rES involve numerical techniques wherein the solution is bounded between 0 and 100 percent.

To calculate the implied cost of equity, we use the I/B/E/S database to obtain the positive one-, two-, and three- year-ahead mean forecasted earnings per share (FEPSt+j), as well as the long-term growth rate forecast. In line with Frankel and Lee (1998) and Hail and Leuz (2009), we substitute the missing or negative FEPSt+j with the historical earnings per share, estimated using the beginning of the year book value per share and the three-year median return on equity in the same year, country, and industry. In this paper, we consider only banks with sufficient I/B/E/S forecasts. We discard bank-year observations for which none of the implied cost of equity estimates converge (Easton, 2004; Claus and Thomas, 2001; and Gebhardt et al., 2001 models), or are undefined (Ohlson and Juettner-Nauroth, 2005 model).

The implied cost of capital is the discount rate (r) that equates the present value of future dividends (Dt + τ) to the current stock price (Pt):

Pt=τ=1Dt+τ(1+r).(1)

In Appendix B, we provide a brief presentation of the four cost of equity models we rely on in this paper.

C. Bank Capital Variables

Our main test variable is bank capital. Throughout the paper, we use three alternative measures of bank capital. Our first measure of capital is a bank’s financial leverage, calculated as the ratio of total equity to total assets (EQUITY). It is reasonable to assume that this is the primary measure of capital that equity investors rely on when assessing a bank’s financial risk for at least two main reasons. First, it is a simple calculation that reflects the amount of a bank’s high-quality capital—with the highest loss-absorption capacity—relative to its total non-risk-weighted exposure. Second, it avoids the drawbacks of risk-weighted capital ratios, which are highly sensitive to risk weights. The latter are, in turn, sensitive to the risk models used and perceived riskiness of assets, and can therefore change from one bank to another, and across countries for the same type of asset.7 Hence, investors can use this simple leverage ratio to compare the financial risks of banks within a single jurisdiction, as well as across jurisdictions. The second capital measure we use is the Tier 1 regulatory capital ratio, which we obtain by dividing Tier 1 capital by risk-weighted assets (TIER1). Finally, our third measure of capital is the total capital ratio, calculated as the sum of Tier 1 and Tier 2 capital to risk-weighted assets (TOTCAP). Despite their flaws, these two ratios may be followed by equity holders, along the leverage ratio, to assess a bank’s financial risk and determine the required rate of return – cost of equity. Tier 1 capital includes common stock and retained earnings, as well as perpetual noncumulative preferred stock. Tier 2 capital is composed of hybrid capital, subordinated debt, revaluation reserves, and loan loss reserves.

D. Control Variables

Our regression equations also include a number of bank- and country-level variables intended to capture the potential effects of factors other than capital on banks’ cost of equity. In particular, we control for a set of bank-level factors that can shape investors’ perceptions of a bank’s risk profile, and potentially influence the risk premium they require for investing in the bank’s equity. We control for a bank’s asset quality using the ratio of loan loss provisions to total loans (PROV). Banks with riskier loan portfolios set up higher provisions to face losses when they materialize. Equity investors may thus require greater compensation from banks with higher provisions (higher risks), which result in a higher cost of equity. We also include a control for a bank’s quality of management, measured by the ratio of salaries and benefits to total assets. We label this variable INEFF (for inefficiency). We expect it to be positively associated with the cost of equity, as banks with higher personnel expenses per dollar of assets may be seen by investors as inefficient and penalized with a higher cost of equity. Bank earnings are closely monitored by equity investors and are expected to affect the cost of equity significantly. We thus include the return on assets (ROA) as another control variable in our cost of equity regression equation. We further control for the ratio of deposits to total assets (DEP). The more deposits a bank has, the more stable its funding structure, which would reduce its susceptibility to liquidity problems (e.g., Beltratti and Stulz, 2012; Berger and Bowman, 2013). This can, in turn, lower investors’ required return on equity. As a final bank-level control, we include the natural logarithm of total assets (SIZE). Equity investors may perceive larger banks as a source of lower risk due to better asset diversification (e.g., Demsetz and Strahan, 1997) and better monitoring executed by supervisory and regulatory bodies. Additionally, larger banks may be viewed by investors as too big to fail (e.g., Deng et al. 2007; Belkhir, 2013), and the risk premiums they have to pay equity holders may be lower than those required from smaller banks.

Our second set of controls comprises country-level variables. As in prior cross-country equity cost studies (e.g., Hail and Leuz, 2006; Chen et al., 2009; Chen et al., 2011; Belkhir et al., 2019), we include the natural logarithm of GDP per capita (LGDPC), the expected inflation rate (INFL), and the level of a country’s stock market development as country-level controls. Per capita GDP is used as a control for a country’s income level. The latter reflects various country characteristics, such as institution(al) quality, investor protection, and regulation, which can impact investors’ perceptions of bank risk. In particular, investors may be less concerned with banks located in richer countries compared to those in less rich ones. We control for expected inflation because the higher the expected inflation rate and the higher the return on equity required to preserve a constant real rate of return for investors. We use annual realized inflation as a proxy for expected inflation. We also control for a country’s stock market development using the ratio of stock market capitalization to GDP (MCAP). Appendix A provides more detailed descriptions of the variables and their sources.

E. Summary Statistics

Panel A of Table 1 reports country-by-country median values of COE and our three measures of bank capital. Column 1 of panel A reveals a large cross-country variation in the median cost of equity, with a minimum COE recorded in Australia (9.8 percent) and a maximum observed in Lebanon (25.1 percent). Likewise, columns 2, 3, and 4 show a great deal of cross-country variation in the median values of our three bank capital measures. EQUITY varies between a minimum of 3.1 percent in Belgium and a maximum of 15.7 percent in Serbia. As regards TIER1, the lowest median value is recorded in Italy (7.4 percent), whereas the largest median value is observed in Serbia (18 percent). Italy has the lowest median value of TOTCAP (11.3 percent), while Nigeria has the highest median value of TOTCAP (20.4 percent).

Table 1.

Descriptive Statistics and Correlation Matrix

Panel A. Medians of the main variables by country

Panel B. Median values of COE, EQUITY, TIER1 and TOTCAP by year.

Panel C. Full sample summary statistics of the main variables used in the regression analysis.

Panel D. Correlation matrix

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This table reports descriptive statistics and Pearson’s correlation coefficients for the variables used in the main regressions. Panel A reports the medians (Median) and the number of observations (N) by country of the main variables used in our regressions. Panel B reports the medians (Median) and the number of observations (N) by year of the main variables used in our regressions. Panel C reports descriptive statistics for all the explanatory variables. In Panel C, the labels Mean, P25, P50, P75, STD, and N stand for the mean, the 25th percentile, the median, the 75th percentile, the standard deviation, and the number of observations. Panel D reports Pearson’s correlation coefficients for the main variables. In Panel D, correlation coefficients in bold are significant at the 1% level. The total sample consists of 16,776 observations from 62 countries between 1991 and 2017. Appendix A provides definitions and data sources for all the variables

Columns 1 and 2 in panel B of Table 1, and panel A of Figure 1 trace the movement of the median values of COE and our first measure of bank capital (EQUITY) over the sample period for the full sample. They both document COE’s tendency to decrease during periods of financial expansion (and stability), and to increase sharply during episodes of financial turmoil. This can be clearly seen in the 1998–2000 period (Russian and LTCM crises) and in the 2008–2010 period (the GFC). Despite these momentary sharp rises in equity cost, overall, there is a cumulative fall in the cost of equity of about 3 percentage points between 1991 and 2017 (from 12.9 percent to 10 percent). By contrast, one can spot a clear upward trend in the ratio of banks’ equity to assets (EQUITY). Over our sample period, there is a cumulative 4 percentage point increase in EQUITY, from 6 percent in 1991 to 10 percent in 2017. A closer look at panel A of Figure 1 and the figures reported in column 2 of panel B (Table 1) reveals that an important part of this incremental bank capital has been added since the GFC’s breakout; EQUITY has increased from 8.3 percent in 2007–2008 to 10 percent in 2017. If anything, this proves that banks and regulators across the globe have sought to improve bank capitalization in the GFC’s aftermath. Columns 3 and 4 of the same table also document substantial increases in the two Basel regulatory capital ratios (TIER1 and TOTCAP) over the 27-year sample, with the gains split (roughly) evenly between the pre- and post-GFC periods.

Figure 1.
Figure 1.

Bank Cost of Equity and Equity-to-Assets Ratio

Citation: IMF Working Papers 2019, 265; 10.5089/9781513519807.001.A001

Panel B of Table 1 shows the median cost of equity and the median equity-to-assets ratio by year, across two subsamples (advanced economies and developing countries). Panel B of Figure 1 records the movement(s) of these two medians across the two country groups over time. Overall, we note a persistent gap of about 3 percentage points between the median bank cost of equity for developing countries and the one for advanced economies. Except during the GFC’s peak (2008–2009), banks in advanced countries enjoy a lower cost of equity compared to those in developing countries. Interestingly, bank capitalization seems to follow the same path over the years across developing and advanced countries, and the typical bank seems to operate at the same capital ratio level, whether located in a developed or developing country. Global factors, especially international capital regulation, may be thought of as the main driving forces behind this common path of bank capitalization.

Panel C of Table 1 presents the sample descriptive statistics for all of the variables used in our analysis of the bank-capital-cost of equity relationship. A sample bank has a mean COE of 12.1 percent (median: 10.8 percent), and a mean financial leverage ratio (EQUITY) of 8.7 percent (median: 8.3 percent). The average bank has a logarithm of total assets equal to 2.246 (median: 1.979), a ratio of loan loss provisions to loans of 76.4 percent (median: 44 percent), a ratio of salaries and benefits to assets of 1.3 percent (median: 1.3 percent), a return on assets of 1.0 percent (median 1.1 percent), and a ratio of deposits to assets of 66.8 percent (median: 71.3 percent). Further, the different variables’ standard deviations in the table suggest that the banks in our sample have different characteristics in terms of capitalization, size, asset quality, profitability, liquidity, etc. The standard deviations of our country-level variables also suggest that our sample banks come from countries with varying levels of income, inflation, and financial development. As previously indicated, the number of observations varies from one variable to another due to missing observations for some variables.

In panel D of Table 1, we report the Pearson correlation coefficients among the different variables we use in our main analysis. Consistent with (the) finance theory predictions, COE is negatively and significantly correlated (at the 99 percent level) with our three measures of bank capital, with the highest correlation coefficient observed for EQUITY (-0.09). Additionally, most of the control variables are correlated with COE in line with theoretical predictions and the findings of prior empirical literature. Importantly, the control variables generally exhibit low correlations, reassuring us that multicollinearity is not a major challenge to our empirical analyses.

III. Empirical results

A. Graphical Evidence

Our primary conjecture is that banks operating with more equity capital in their capital mix bear a lower cost of equity capital. As a preamble to our multivariate analysis of the bank-capital-cost of equity relationship, in this section, we present scatterplots that display the relationship between COE and our measures of bank capital. In panel A of Figure 2, we use the full sample and report a clear negative association between the cost of equity (on the Y-axis) and EQUITY (on the X-axis). This negative relationship holds when we use TIER1 (panel B) and TOTCAP (panel C) as measures of bank capital. In the remainder of Figure 2 (panels D, E, F, G, H, and I), we provide scatterplots illustrating the bank capital-cost of equity relationships for selected advanced economy countries (Germany, U.K, and U.S) and developing countries (India, Malaysia, and Thailand). These graphs point to the presence of a negative association between the cost of equity and bank capital in each of the selected countries. This observation holds for most of the countries in our sample. Hence, graphic evidence suggests that bank capital and the cost of equity are negatively associated. We now turn to multivariate regression techniques to investigate the precise link between capital and the cost of equity.

Figure 2.
Figure 2.

Cost of Equity (Y-axis) vs. Bank Capital (X-axis)

Citation: IMF Working Papers 2019, 265; 10.5089/9781513519807.001.A001

Figure 2.1:
Figure 2.1:

Cost of Equity (Y-axis) vs. EQUITY (X-axis) – selected countries

Citation: IMF Working Papers 2019, 265; 10.5089/9781513519807.001.A001

B. Main Evidence

In this section, we investigate bank capital’s impact on the cost of equity using a multivariate regression analysis. To this end, we estimate various specifications of the regression model below. Specifically, we regress COE on a measure of bank capital (CAPITAL: EQUITY, TIER1, or TOTCAP) and a set of firm- and country-level control variables (CONTROLS):

COEt=α0+β1CAPITALt1+β2CONTROLSt1+FE+εt.(1)

In the above model, represents an error term and FE represents a set of country and year fixed effects. Due to the nature of our sample, which includes banks from many countries, the country and year fixed effects are intended to control for any country- and time-specific factors that may affect banks’ cost of equity or the potential association between bank capital and the cost of equity. As indicated in Demirguc-Kunt et al. (2013), such factors may include differences in interest rates and other macroeconomic variables, cross-country disparities relating to the severity of the financial crisis and its economic repercussions, authorities’ different policy responses, variations in the quality of bank regulation and supervision, and differences in accounting and regulatory standards. By including country and year fixed effects we reduce the potential bias caused by omitted variables.

Table 2 presents our main evidence of the bank capital-cost of equity relationship. Columns (1)–(3) report the results of our estimations using EQUITY as a measure of bank capital. Column 1, which includes only bank-level controls, shows that, consistent with our expectations, EQUITY is negative and statistically significant at the 1 percent level. This suggests that banks with higher ratios of equity capital to assets bear lower costs of equity. This evidence is in favor of the theoretical prediction that an increase in equity capital reduces a bank’s financial risk and eventually leads investors to require lower equity returns. This, in turn, translates into lower costs of equity. The impact of EQUITY is not only statistically significant, but also economically meaningful. The coefficient estimate for EQUITY in column (1) suggests that a one standard deviation increase in EQUITY (0.039) leads to a 72-basis-point drop in the cost of equity (-0.186*0.039 = -0.0072), all else being equal. Similarly, a 10-percentage-point increase in EQUITY would reduce the cost of equity by a significant 1.86 percentage points. In columns (2)-(3), we gradually augment the COE regression model with country-level variables. In column (2), we add the natural logarithm of GDP per capita and the inflation rate. In column (3), we further add a measure of stock market development, namely, stock market capitalization to GDP. Adding any of these variables alters neither the statistical nor the economic significance of our main variable of interest, EQUITY. The latter continues to load negative and statistically significant at the 1 percent level, with roughly the same economic magnitude.

Table 2.

The Relationship Between Bank Cost of Equity and Capital Measures

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This table reports cross-sectional regression results of the following model: C0Et = α0 + β1CAPITALt_1 + β2C0NTR0LSt_1 + FE + εt. The dependent variable COE is a proxy for the cost of equity calculated as the average of the four implied cost of capital models described in Section 2.2. The CAPITALt_1 variables consist of either lagged EQUITY, or TIER1, or TOTCAP. The set of control variables (CONTROLSt_1) consist of lagged bank-level and/or lagged country-level variables. FE is the set of fixed effects dummy variables at the country and/or year levels. Thelagged bank-level control variables are: PROV, INEFF, ROA, DEP, and SIZE. The lagged country-level control variables are: LNGDPC, INF, and MCAP. The total sample consists of 16,776 observations from 62 countries between 1991 and 2017. Appendix A provides definitions and data sources for all the variables. Beneath each coefficient is the robust /-statistic.

indicate significance at the 10%, 5%, and 1% levels, respectively.

Across the three models reported in columns (1)-(3) of Table 2, the coefficient estimates for our bank- and country-level control variables are generally consistent with our predictions and the prior literature. In particular, the positive, significant coefficient estimate for PROV suggests that the cost of equity increases as the quality of a bank’s loan portfolio deteriorates. The negative and significant coefficient estimate on ROA indicates that more profitable banks enjoy a lower cost of equity. Likewise, banks with a lower liquidity risk (higher DEP) face a lower cost of equity. In addition, the coefficient estimate for SIZE is consistently negative and significant across all three COE models, implying that larger banks enjoy a lower cost of equity, all else being equal. Our estimations also reveal that banks’ cost of equity depends on their home countries’ income levels; as suggested by the negative and significant coefficient for LGDPC, banks located in richer countries enjoy a lower cost of equity. As expected, a rise in expected inflation is conducive to a higher bank cost of equity. Additionally, stock market development contributes to the lowering of banks’ cost of equity; the coefficient estimate on MCAP is negative and significant at the 1 percent level.

In columns (4)-(9) of Table 2, we replicate the analyses reported in columns (1)-(3) using TIER1 and TOTCAP as alternative measures of bank capital. The findings suggest that using the ratio of Tier 1 capital to risk-weighted assets as an alternative bank capital measure substantiates our initial finding on the influence of bank capital on the cost of equity. Specifically, our estimates reveal a negative association between the ratio of Tier 1 capital to risk-weighted assets and the cost of equity. The coefficient estimate for TIER1 is consistently negative and significant at the 1 percent level across columns (4)–(6). The economic significance of TIER1’s coefficient estimate is, however, smaller than EQUITY’s. Using the estimated coefficient on TIER1 in column (4), a one standard deviation increases in TIER1 (0.078) translates into a mere 26-basis-point drop in the cost of equity (-0.034*0.078 = - 0.0026). This is a reasonable finding given that the additional forms of capital that enter the composition of Tier 1 capital (besides equity capital) have lower loss-absorption capacities and are therefore not valued by equity investors as they value pure equity capital. The results reported in columns (7)-(9) are qualitatively similar to those reported in columns (4)-(6). The coefficient estimate on TOTCAP is negative and significant at the 1 percent level and has the same magnitude as the coefficient on TIER1. This result suggests that the additional capital entering the composition of bank total capital on top of Tier 1 capital (i.e., Tier 2 capital) is not priced by stockholders. Indeed, our results imply that investors perceive Tier 2 capital as having no effect on their financial risk. Overall, the results reported in Table 2 suggest that investors do not value Tier 2 capital, and their perceived financial risk is only affected by sheer equity and, to a lesser extent, by the other components of Tier 1 capital. To validate this inference, we re-estimate the cost of equity model using the ratio of Tier 2 to risk-weighted assets as a measure of bank capital. Our results (unreported) confirm that Tier 2 capital is not a factor that determines banks’ cost of equity; the coefficient estimate on Tier 2 capital is statistically insignificant at the conventional level.

In sum, our estimations indicate that a bank’s cost of equity declines with the amount of equity capital with which it operates. In other words, as predicted by financial theory, equity capital lowers a bank stockholder’s financial risk, which eventually leads to a lower cost of equity. This result holds, even when we control for various bank- and country-level factors that may affect banks’ cost of equity.

C. Robustness Checks

In this section, we subject our main finding of a negative impact of bank capital on the cost of equity to a variety of robustness tests. We first check the robustness of our results to additional control variables. Next, we use alternative measures of the cost of equity to check whether our findings are sensitive to the use of the specific cost of equity measure, COE. We then estimate the cost of equity model using alternative methods to address potential endogeneity issues that might have biased our initial results. Finally, we test the robustness of our results to the composition of our sample. Interestingly, our main results are robust to all these checks. Table 3 reports our estimation results when we include additional control variables. In columns (1)–(6), we add controls for market risk, as this has been shown by prior literature to impact the cost of equity (e.g., Botosan et al., 2011; Chen et al., 2016). In particular, in columns (1)–(3), we use the standard deviation of a bank’s stock returns (RSTD) as a measure of market risk and include it as an additional variable in our cost of equity model. The coefficient estimate on RSTD appears positive and significant at the 1 percent level only in column 1, where we use EQUITY as a measure of capital. Our main variable of interest, EQUITY, TIER1, or TOTCAP, continues to have a negative and significant association with COE across columns (1)-(3). In columns (4)-(6), we replace RSTD with the stock beta, BETA, as a measure of the market risk of equity. The BETA coefficient is positive and highly significant across columns (4)–(6), regardless of the bank capital measure we use. This result is consistent with theoretical predictions suggesting that a firm’s cost of equity should rise with its systematic risk. Importantly, the coefficient estimates for our three bank capital variables continue to be negative and significant. The economic impacts of EQUITY, TIER1, and TOTCAP on the cost of equity are the same as those reported in Table 2. This result suggests that, apart from the indirect effect it might exert through stock beta (as suggested by Baker and Wurgler, 2013), bank capital has a significant direct effect on a bank’s cost of equity. In columns (7)-(9), we include the stock market turnover, MTOV, as a control for stock market liquidity. Prior literature on nonbanking firms’ cost of equity suggests that firms listed in stock markets with a higher liquidity levels face lower costs of equity (e.g., Belkhir et al., 2019; Saad and Samet, 2017). Our estimations in column (7) corroborate this finding for banking firms. Using EQUTIY as a measure of bank capital, we estimate a negative and significant impact of MTOV on bank cost of equity. Yet, this does not alter our main conclusion concerning the bank-capital-cost of equity relationship, as we continue to find a negative and significant coefficient estimate for each of the bank capital variables (EQUITY, TIER1, and TOTCAP).

Table 3.

Robustness Tests Controlling for Additional Variables

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This table reports cross-sectional regression results of the following model: C0Et = α0 + β1CAPITALt_1 + β2C0NTR0LSt_1 + FE + εt. The dependent variable COE is a proxy for the cost of equity calculated as the average of the four implied cost of capital models described in Section 2.2. The CAPITALt_1 variables consist of either lagged EQUITY, or TIER1, or TOTCAP. The set of control variables (CONTROLSt_1) consist of lagged bank-level and/or lagged country-level variables. FE is the set of fixed effects dummy variables at the country and/or year levels. Thelagged bank-level control variables are: PROV, INEFF, ROA, DEP, and SIZE. The lagged country-level control variables are: LNGDPC, INF, and MCAP. The total sample consists of 16,776 observations from 62 countries between 1991 and 2017. Appendix A provides definitions and data sources for all the variables. Beneath each coefficient is the robust /-statistic.

indicate significance at the 10%, 5%, and 1% levels, respectively.

In columns (10)-(12), we report the results of adding the ratio of nonperforming loans to total loans (NPL) as a control variable for the quality of a bank’s assets. Our estimations show that NPL is positively and highly significantly associated with COE, suggesting that banks with more nonperforming loans incur a higher cost of equity. This, however, does not affect our main finding of a negative and significant relationship between our three measures of bank capital and the cost of equity; we continue to report negative coefficient estimates for EQUITY, TIER1, and TOTCAP. Finally, in line with Berger et al. (2018), in columns (13)-(15), we control for a bank’s book-to-market ratio (BTM) and find that banks with a higher BTMs bear a higher cost of equity. Nonetheless, the reported negative association between bank capital and the cost of equity is unaffected by this additional control variable.

In Table 4, we investigate whether our results are sensitive to the specific cost of equity measure we have used so far. As a reminder, COE is calculated as the arithmetic average of four implied cost of equity measures (rCT, rGLS, rES, rOJN). To alleviate the potential effect of this specific cost of equity measure on our results, we re-estimate the cost of equity model using different measures. In columns (1)-(12), we verify that our results continue to hold if we use the individual measures of the cost of equity instead of the average of the four measures. The reported results reveal that bank capital (EQUITY, TIER1, and TOTCAP) has a negative and significant effect on each of the individual cost of equity measures.

Table 4.

Alternative Measures of the Cost of Equity and Risk Premium

Panel A. Alternative measures of the cost of equity

Panel B. Risk premium

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In Panel A of this Table, columns (1) –(12) repeat the same analysis as in Table 2 models 3, 6, and 9 after replacing COE with each of R CT, R ES, R GLS, and R OJ, that represent the implied cost of equity estimates of Claus and Thomas (2001), Easton (2004), Gebhardt et al. (2001), and Ohlson and Juettner-Nauroth (2005) , respectively. Columns (16-18) replaces COE with the average of R ES and R GLS implied cost of equity. Columns (16-18) replaces COE with the principal component (R PCA ) of R CT, R ES, R GLS, and R OJ . Panel B replace COE by the risk premium (RPM) which is calculated as COE minus the 10-year U.S. Treasury bond yield. The total sample consists of 16,776 observations from 62 countries between 1991 and 2017. Appendix A provides definitions and data sources for all the variables. Beneath each coefficient is the robust t -statistic.

indicate significance at the 10%, 5%, and 1% levels, respectively.