The Effects of the Financial Crisis on Risk Premia in the
Banking Sector
Jan-Willem Geut
Student number: s1882317
Master’s Thesis Finance
Supervisor: Dr. T.M. Katzur
13 June 2016
Abstract
This paper investigates the effects of the financial crisis on risk premia in the banking sector, as measured by the market. First, risk exposures are estimated as the correlation of individual bank returns with the market portfolio. Second, these exposures are translated into risk premia. In order to examine the effects of the financial crisis, both exposures and premia are measured before and after the financial crisis. The contribution of this article is that it separates risk exposures into operating and leverage components. As a result, it is possible to distinguish between different types of risk premia. Results show that the post-crisis risk premium on financial leverage increased, compared to the pre-crisis. The post-crisis risk premium on operating leverage shows negative signs but does not proof to be statistically significant. Moreover, results provide preliminary evidence for higher risk premia in European banks, compared to US banks.
Keywords: risk premium, financial crisis, operating leverage, financial leverage, market risk
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1. Introduction
Capital regulations in the banking sector that were in place before the 2007-2009 economic crisis resulted in high amounts of criticism and especially bank equity capital positioned itself as a central point of discussion. During and after the crisis, public demand for higher levels of bank capital significantly increased because excessive leverage proved to a substantially contributing factor to the economic turmoil (Berger & Bouwman, 2013). Calomiris & Nissim (2014) find that in the pre-crisis period leverage and its inherent effects were associated with higher value whereas in the post-crisis period, leverage and its inherent effects are associated with lower value. The financial crisis appears to have had an effect on perceived risk in the banking sector. This paper examines the effects of the financial crisis on the risk premia that are rewarded for exposure to these risks.
The years before the financial crisis showed relatively low market volatility, which is also referred to as the “Great Moderation”. It was believed that improvements in risk-sharing within and between different economies had led to a stabilized macroeconomic state. Option prices in this period reveal that implied volatility had been downwardly adjusted. Figure 6 in appendix A demonstrates that market volatility mostly remained between 10 and 20% in the period 2004 up until 2007. In these same years, the financial sector grew and the percentage of leverage per company grew along (Acharya, Viswanathan, 2011). One of the consequences of the disastrous results of this leverage build-up is that regulatory bodies in countries all over the world started revising capital regulations. There are two important trends in regulatory approaches: minimum capital requirements increased and regulatory frameworks shifted from a microprudential to a macroprudential approach.
The leverage ratio requirement that has been implemented in Basel III is a measure that increases the minimum amount of required capital in the banking sector. Blum (2008) already stated that Basel II should include a leverage ratio requirement because regulatory authorities are only able to analyze bank risk to a certain degree. Kiema and Jokivuolle (2014) state that this non-risk-weighted leverage ratio requirement provides an effective measure against the risk from the incorrect rating of loans, as happened before the financial crisis. Before the financial crisis, regulatory bodies mostly took a microprudential approach, whereas current regulation is increasingly macroprudential. Microprudential regulation mostly relates to the regulation and protection of individual institutions and macroprudential regulation aims to take into the account the economy as a whole. Examples of macroprudential regulation are temporary and time-varying capital buffers that are linked to the cyclicality of the economy (Hanson et al., 2011; Repullo, Suarez, 2013; Adrian, Shin, 2014; Aiyar et al., 2014; Behn et al., 2015).
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Rob, 1999). Jensen and Meckling (1976) described this agency problem related to risk-shifting. This implies that after a borrower (the agent) raises debt, he extracts value from the lenders by investing in riskier assets. This happens because the borrower is not exposed to the downside risk but instead has a chance of a high positive payoff as a result of the risky investment. Also in the banking sector this implies that in general, banks try to exploit their limited liability. VanHoose (2007) reviewed academic studies of bank capital regulation and concludes that the literature does not show consensus on the consequences of risk-based capital regulation on risk-taking. Tightening capital regulation is intended to create a safer banking environment but this does not always proof to be the case.
By investigating market returns in relation to bank returns before and after the financial crisis, this paper examines how the market perceived the effects of the financial crisis. More specific, examining risk premia that are awarded for market exposure (systematic risk) provides a measure of investigating perceived risk. If risk is perceived to be high, the market will demand a higher risk premium and vice versa. Changes in risk premia can be seen as a form of market discipline. Martinez Peria and Schmukler (2001) explain market discipline in the banking sector as the actions that stockholders, depositors or creditors take when they are confronted with costs that increase as banks engage in risky behavior. Consequently, changes in risk premia in the banking sector reflect changes in perceived risks. By examining risk premia before and after the financial crisis, this paper investigates how the market reacted to the effects of the financial crisis. The contribution of this paper is the separation of risk exposures and premia into operating and financial components. This is valuable information because it allows one to separate the nature of the risk of operations (operating risk) from the financial risk. The answers to the previous questions are found by focusing on market returns in relation to individual bank returns. By applying the Fama-MacBeth (1973) two-step approach it is possible to “let the market speak”. First, this approach quantifies risk exposure and second, it translates these exposures to risk premia.
Compared to the pre-crisis period, results indicate evidence for post-crisis shifts in market exposure in the banking sector, measured by beta. The levered market beta tends to have increased, whereas the unlevered market beta tends to have decreased. Regarding the perceived risk of financial leverage measured by the risk premium, the results show that in the years after the financial crisis the risk premium on financial leverage increased, compared to before the crisis. Results on the operating risk premium show negative signs, indicating a post-crisis decrease, compared to the pre-crisis. However, these effects are not robustly significant. Moreover, interesting differences in findings between US and European banks could be related to different regulatory approaches and financial systems.
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2.1 Theoretical Framework
In order to quantify risk exposures and risk premia it is necessary to further study these aspects. Throughout this paper, risk exposure is measured by applying the Capital Asset Pricing Model (CAPM). Sharpe (1963) found that an efficient portfolio is always a combination of lending or borrowing at the risk-free rate and investing in the market portfolio. Higher (lower) exposure to the market and higher (lower) lending at the risk-free rate results in a more (less) risky portfolio. Exposure to the market is measured by beta and a beta higher (lower) than one indicates more (less) risk compared to the market portfolio:
E(ri) = rf + βi(Rmp) (1)
where E(ri) is the expected return on asset i, rf is the risk-free rate of return, βi is the sensitivity to the market portfolio for asset i and (Rmp) is the market premium.
Next to general risk exposure as measured by CAPM, it is time to focus on specific parts of risk exposure: operating leverage and financial leverage. Hamada (1972) was one of the first researchers that tried to test the relationships between corporate finance, investments and portfolio analyses. The goal of his research was to investigate, through those different areas of expertise, the consequences of financial leverage on the systematic risk of common stock. Eventually he validates his findings of the aforementioned phenomenon by testing the Modigliani and Miller Theory. This theory, founded by Modigliani and Miller (1958) states that the capital structure of a firm is irrelevant for the value of that firm. Hamada finally concludes that in his sample 21 - 24% of the systematic risk of common stock is caused by the additional financial risk through debt and preferred stock.
Hamada investigates the effects of financial leverage by separating operating and financial leverage. Operating risk relates to the uncertainty of the nature of operations of a firm in a specific sector or industry. Financial leverage risk relates to the degree in which the operating risk is magnified by attracting debt. Hamada refers to the operating risk as the “would-have-been” rate of return on common stock. This is a company’s cost of capital in case it would not have had any debt or preferred stock. In other words, this is the rate of return according to the risk of the nature of the firm’s operations, excluding leverage. The rate of return including leverage is referred to as the observed rate of return on common stock. Hereafter, we will refer to the would-have-been rate and the observed return as the unlevered return and levered return, respectively. Below, Hamada’s approach to constructing levered and unlevered returns is be explained. In order to fully understand the construction of these two returns, equation (2) displays how total returns to the common stock holders of a company are constituted:
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where Xt represent the earnings before taxes, interest and preferred dividends in period t, It
represents the interest and other fixed charged paid during period t, taxt represents the
corporation income tax rate paid in period t, pt represents dividends paid in period t, ΔG
represents the change in capitalized growth in period t, dt represents the common dividends paid
in period t and cgt represents the capital gains of common stock in period t. The left-hand side
(LHS) and the right-hand side (RHS) of the equation represent total returns to the common stock holders of a company during period t. The key element of this equation is that it links together accounting measures with the holding period of investors. The LHS shows the returns to common stock holders after interest, taxes and preferred dividends. In order to arrive at the total earnings for the period, the change in capitalized growth must be added. These earnings are the actual observed earnings and relate to the company’s state in which it has to pay interest on debt and preferred stock (i.e. the levered state). Dividing these earnings (the RHS) by the value of common stock in period t-1 results in the levered rate of return on common stock as displayed by equation (3):
RBt = (dt + cgt) / SBt-1 (3)
where RBt represents the levered rate of return on common stock during period t and SBt-1
represents the market value of common stock at the end of period t-1.
In order to estimate the unlevered rate of return on common stock, preferred dividends and interest payments are added back to the actual returns to the common stock holders as displayed in equation (4a). This is because in the unlevered state the company would not have had any debt or preferred stock. Next, these unlevered returns are divided by the market value to the common shareholder if the firm had no debt and preferred stock.
RAt = (dt + cgt + pt + It(1-tax)t) / (V-tax*D)t-1 (4a)
where RAt represents the unlevered rate of return on common stock, and
Vt-1 = SBt-1 + Dt-1 + PSt-1 (4b)
where Vt-1 represents the observed market value at the end of period t-1, SBt-1 represents the
market value of common stock at the end of period t-1, Dt-1 represents the market value of debt at
the end of period t-1 and PSt-1 represents the market value of preferred stock at the end of period t-1.
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betas and levered betas, respectively. The former approach is a relatively data-intensive approach based on accounting measures in order to determine both the levered and unlevered returns on common stock. Hill and Stone (1980) confirm that, compared to market prices, applying accounting measures of operating and financial leverage has significant value for eventually estimating market betas and coping with instability.
A company’s exposure to (systematic) market risk should be rewarded with a risk premium. An article related to risk premia is one by Julliard and Ghosh (2012) who investigated whether rare events are able to explain the overall “equity premium puzzle” and find that this is “probably not” the case. This equity premium puzzle is the phenomenon that equity returns over the long run tend to be substantially higher than government bond returns. Their rationale of rare events leading to a higher equity premium is quite simple. If during each period there is a chance that an extreme event (e.g. a financial crisis) occurs, risk-averse equity owners will demand a higher risk premium to compensate for potential losses during these rare but catastrophic events. The key object of this paper is related to the previous concept. Does the post-crisis banking landscape reflect higher risk premia that are demanded by the market as compared to the pre-crisis period? In order to translate market exposures to market risk premia, the levered and unlevered betas that will be found using Hamada’s approach are tested using the Fama-MacBeth approach. This approach is a two-step way of firstly finding market exposures and secondly translating these to market risk premia. Former approach will be more thoroughly explained in section 2.2. Moreover, the first of these two steps has essentially already been captured by Hamada’s approach.
In order to properly investigate and interpret the operating and leverage exposures to the market it is important to create an overview of actual banking sector risk and return data. Figure 1 shows the yearly returns from 1996 to 2015 for the S&P 500 Financials, the S&P Europe 350 Financials and the S&P Global 1200 Financials. These indices are comprised of companies in the S&P500, the S&P Europe 350 and the S&P Global 1200 that are classified as financial sector companies according to the Global Industry Classification Standard (GICS). This classification
Fig 1. This figure shows the yearly stock returns from 1996 to 2016 for the indices of the S&P 500 Financials,
the S&P Europe 350 Financials and the S&P Global 1200 Financials. Source: DataStream.
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includes the subcategories Banks, Diversified Financials, Insurance and Real Estate. They do not solely include banks but they give a good proxy for the banking sector. As shown in the figure, post-crisis stock returns are lower than those of the pre-crisis period. Figure 2 shows the 12-month rolling yearly standard deviation for the same indices and time period as in figure 1. The figure clearly shows the sharp increase in volatility during the financial crisis. Moreover, it also shows that post-crisis volatility is higher than the relatively calm years preceding the crisis (i.e. The Great Moderation). Over the long run, post-crisis volatility did not appear to have substantially changed compared to the pre-crisis volatility. This is interesting since much of the post-crisis regulation was intended to lower risk in the banking sector. It is decided to further examine this by investigating historical banking leverage levels. Figure 3 displays historical leverage levels in the US and European banking sectors. In both cases, the figure shows a downward pattern. This pattern is more extreme for European banks than it is for US banks. Despite decreasing leverage levels, volatility did not decrease along. This could imply that post-crisis leverage levels, especially in Europe, must decrease even further in order for the market to be satisfied.
Fig. 2. This figure shows the 12-month rolling yearly standard deviations from 1996 to 2015 for the indices of the S&P 500 Financials, the S&P Europe 350 Financials and the S&P Global 1200 Financials. Source: DataStream.
Fig. 3. This figure shows the median total debt to equity (D/E) ratios over the period 1996-2015 for US and European banks. For the US banks, yearly median D/E ratios are taken from all 701 US banks in DataStream that have available data on D/E ratios. For the European banks, yearly median D/E ratios are taken from all 191 European banks that have available data on D/E ratios. Source: DataStream.
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After explaining how to measure and interpret operating and financial leverage, how to translate this into risk premia and after creating an overview of the banking sector it is possible to derive hypotheses. There are numerous factors influencing the post-crisis banking landscape. Regulatory bodies are implementing frameworks that are intended to decrease the amount of banking leverage. Banks are forced to comply with these frameworks but on the other hand want to optimize profits and exploit their limited liability. This can lead to increases in the risk of banking portfolios. Moreover, excessive pre-crisis leverage and its consequences increased awareness of the, rare, but potential dangers of financial leverage. As a result of these phenomena it is expected that the risk premium on financial leverage in the post-crisis period increased compared to the pre-crisis period, which leads to hypothesis one:
H1: Risk premium on financial leverage pre-crisis < Risk premium on financial leverage post-crisis
During and after the crisis, capital requirements and leverage ratios have become stricter in order to limit overall banking leverage and the according risk. Although Basel III has not been fully implemented yet, this new regulatory environment should have created a less risky banking environment. The overall effect of (leverage) regulations should have led to a less risky post-crisis banking sector in general. Therefore, regardless of leverage effects and the perceived risk of leverage, the risk-premium rewarded for exposure to the nature of operations (operating risk) in the banking industry should have decreased. This leads to the second hypothesis:
H2: Risk premium on operating leverage pre-crisis > Risk premium on operating leverage post-crisis
After putting forward main hypotheses one and two it is important to perform a sanity check the on the data. First of all, as Hamada stated before, part of systematic risk is explained by leverage. Therefore, the exposure of levered returns (levered beta) to the market should be larger than the exposure of unlevered returns (unlevered beta) to the market. Therefore, the average levered beta should be higher than the unlevered beta which leads to the third hypothesis:
H3: Levered beta > Unlevered beta
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2.2 Statistical implementation
In order to test previous hypothesis, it is necessary to create levered and unlevered betas for each bank in our sample. Because market values of preferred stock were not available it was decided to only include banks that had zero preferred stock in at least the six years before the crisis and after the crisis. This sample consisted of 246 banks in total: 152 US banks and 94 European banks. Next, it was decided to only include banks that have a minimum of 15 years of yearly return observations. This resulted in 94 banks having a minimum of 15 yearly observations on both levered and unlevered returns. An additional four banks only had a minimum of 15 observations on levered returns on not on unlevered returns. In equations (5a) – (6b) it was decided to distinguish between these two samples. In the panel data regressions that follow afterwards, only banks are included that have a minimum of 15 observations on both levered and unlevered returns and as a result the sample size reduces to 94 banks. The pre-crisis period ranges from 1992 to 2006 and the post-crisis period ranges from 2010 to 2015. Moreover, the total period refers to these two periods combined and excludes the crisis years (2007-2009).
The method that investigates differences in risk premia is based on the Fama-MacBeth approach. In their paper they state a two stage approach that tests the validity of the CAPM model. In this paper the first step determines what is the degree of exposure to the market. The second step determines what is the risk premium for these exposures. In order to estimate the levered and unlevered exposures (betas) for each bank, the natural log of the levered and unlevered excess returns are regressed on the natural log of the market premia in the US and Europe. In order to obtain these betas, regressions (5a) and (5b) are performed:
ln(RAit) = Aαi +Aβi*ln(RMPt) + εit (5a)
where ln(RAit) represents the natural log of the unlevered excess return for bank i in period t, Aαi
represents the constant for firm i, Aβ1 represents the unlevered market beta for firm i, ln(Rmpt)
represents the natural log of the market premium in period t and εit represents the disturbance
term and,
ln(RBit) = Bαi + Bβi*ln(RMPt) + εit (5b)
where ln(RBit) represents the natural log of the levered excess return for bank i in period t, Bαi
represents the constant for firm i and Bβi represents the levered market beta for firm i.
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over the entire period. This implies that a significant change in the post-crisis period has occurred. Statistical significance of this second beta is determined by an F-test. Equations (6a) and (6b) relate to the testing of the unlevered and levered betas, respectively.
ln(RAit ) = Aαi +AβCHOW1i*ln(RMPt) + AβCHOW2i*(RMPt)DPOST + εit (6a) where AβCHOW1i represents the unlevered market beta for firm i in the Chow model, AβCHOW2i
represents the market beta that measures the post-crisis difference in unlevered market beta and
DPOST represents a dummy variable that takes 1 for the post-crisis and 0 for the pre-crisis, and
ln(RBit) = Bαi +BβCHOW1i*ln(RMPt) + BβCHOW2i*(RMPt)DPOST + εit (6b) where BβCHOW1i represents the levered market beta for firm i in the Chow model and AβCHOW2i represents the market beta that measures the post-crisis difference in the levered market beta.
All data used to construct levered and unlevered returns are yearly data. This means that, especially the post-crisis period, contains a relatively low number of observations. Since this low number of observations is likely to result in statistically less significant results it is decided to further test the hypotheses. Adding the two betas in each Chow model provides an estimation of the post-crisis beta. Therefore, comparing these two betas with the original market betas estimated by equations (5a) and (5b) tests if a significant change occurred. These comparisons are performed by conducting Wilcoxon Signed Rank Tests.
Equations (5a) – (6b) imply separate time series regressions for each bank. After these time series, step two of the Fama-MacBeth approach implies the estimation of panel data regressions that estimate the risk premia for exposure to the market. Equations (7a) and (7b) regress the natural log of the unlevered and levered excess bank returns on the betas calculated in equations (5a) and (5b), respectively
ln(RAit) = Aλ0i + Aλ1i*Aβi + εit (7a)
where Aλi represents the risk premium awarded for exposure to the factor loading related to the unlevered returns and Aβi represents the unlevered betas for entities 1 to 94 calculated in the time
series regressions of equation (5a), and
ln(RBit) = Bλ0i + Bλ1i*Bβi + εit (7b)
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the levered betas of all 94 banks in the sample. Equation (7c) shows the Fama-MacBeth regression using the natural log of the actual yearly excess stock returns as dependent variable:
ln(RCit) = Cλ0i + Cλ1i*Bβi + εit (7c)
where RCit represents the natural log of the actual yearly excess stock return of bank i in period t, Cλi represents the risk premium awarded for exposure to the factor loading related to the levered betas and Bβi again represents the levered betas for entities 1 to 94 calculated in the time series regressions of equation (6b). After testing the CAPM output by applying the Fama-MacBeth equations it is time to further extend these regressions. Equations (8a) – (8c) are extended with the ratio of the levered return over the unlevered return, hereafter referred to as the leverage ratio proxy. Moreover, just like equations (7a) – (7c), equations (8a) – (8c) again include the unlevered and levered betas as calculated in equations (5a) and (5b). Note again that these betas only change in the cross-sections.
ln(RAit) = Aλ0i + Aλ1i*Aβi + Aλ2i*(RBit/RAit) + εit (8a) where (RBit/RAit) represents the leverage ratio proxy, and
ln(RBit) = Bλ0i + Bλ1i*Bβi + Bλ2i*(RBit/RAit) + εit (8b)
where Bλ2i represents the risk premium for exposure to the factor loading related to the leverage ratio proxy, and
ln(RBit) = Cλ0i + Cλ1i*Bβi + Cλ2i*(RBit/RAit) + εit (8c)
where Cλ2i represents the risk premium for exposure to the factor loading related to the leverage ratio proxy. Next, the previous equations are extended with a dummy variable in order to measure post-crisis effects on the risk premia.
ln(RAit) = Aλ0i + Aλ1i*Aβi + Aλ2i*(RBit/RAit) + Aλ3i* Aβi*DPOST + εit (9a) where DPOST is a dummy variable that takes value 1 for the post-crisis period and value 0 for the
pre-crisis period, and
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dummy. As mentioned before, there was made a distinction between US and European banks. Again, the first equation (10a) includes the natural log of the unlevered excess return as dependent variable, the second equation (10b) includes the natural log of the levered excess return as dependent variable and the third equation (10c) includes the natural log of the actual excess stock return:
ln(RAit) = Aλ0i + Aλ1i*Aβi + Aλ2i*(RBit/RAit) + Aλ3i*Aβi*DPOST +
Aλ4i*DEUROPE*Aβi + εit (10a)
where DEUROPE is the dummy variable that takes value 1 for Europe and value 0 for the US, and
ln(RBit) = Bλ0i + Bλ1i*Bβi + Bλ2i*(RBit/RAit) + Bλ3i*Bβi*DPOST +
Bλ4i*DEUROPE*Bβi + εit (10b)
ln(RCit) = Cλ0i + Cλ1i*Bβi + Cλ2i*(RBit/RAit) + Cλ3i* Bβi*DPOST +
Cλ4i*DEUROPE*Bβi + εit (10c)
In the total sample there was a number of banks that went bankrupt during the years of measurement. These bankruptcies lead to extreme values when levered and unlevered returns are calculated. Therefore, as a robustness check all panel data regressions are run after a truncation of the highest and lowest 1% of the bank return data (levered, unlevered and actual returns).
3. Data
Sample selection
The initial sample consisted of 1301 banks with yearly data ranging from 1992 to 2015. 1093 are from the US and 208 are from Europe. The US sample consists of all US banks according to DataStream. The European sample consists of all banks in countries of the European Union, according to DataStream as well. However, since market values of preferred stock were not able to obtain, it was decided to only include banks with zero preferred stock in the six years before the crisis and the six years after the crisis. After correcting for banks with zero preferred stock, the remaining sample consists of 246 banks in total: 152 from the US and 94 from Europe. The eventual sample that meets the threshold of a minimum of 15 yearly return observations on both levered and unlevered returns is 94: 46 banks from the US and 48 banks from Europe.
Common dividends
These are the yearly dividends to common stock, according to DataStream.
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These are the yearly changes in market value of common stock for each bank, calculated as the market value of common stock at time t minus the market value of common stock at time t-1. Value from DataStream.
Preferred dividends
Since only banks were included with zero preferred stock, preferred dividends were not relevant anymore.
Interest and other fixed charges
For this input the total yearly interest expense according to DataStream is selected. Other fixed charges were not available and are therefore excluded from the estimations.
Tax rate
Aswath Damodaran is a Professor of Finance at the Stern School of Business in New York and on his website he displays an overview of industry betas and levered betas for both the US and Europe and the according effective tax rate. The effective tax rates for the US and European banking sectors were taken from this database because these most closely reflect the amount of taxes that have actually been paid.
Total debt
Market values of debt were not available. Therefore, book values of total debt were taken from DataStream.
Value of common stock
Yearly market values of common stock were taken from DataStream.
Market Premium
For the US banks the market return of the S&P 500 was taken. DataStream provides a total return index (capital gains and dividends). By using this return index the yearly returns were calculated. Next, the one-year government interest yield was deducted in order to obtain the market premium. For the European banks the market return of the S&P 350 Euro was taken. Next, the one-year interest yields for the Euro Area were deducted in order to obtain the market premium.
4. Results
13 # of regressions run # of betas significantly different from zero
Average Median Standard
Deviation Equation (5a) 94 15 Aβ1 0,133 0,141 0,198 AR2 0,104 0,051 0,130 Equation (5b) 98 23 Bβ1 0,413 0,334 0,441 BR2 0,128 0,059 0,157
Table 1: Summary statistics of equations (5a) and (5b). The table shows the summary statistics of all separate OLS regressions of equations (5a) and (5b) over the period 1992-2015 (excluding 2007-2009). Column one states each equation and the type of variable and statistics that are reported. Column two states the total number of regressions that were run for either equation (5a) or (5b). Column three states for both equations, out of the total number of regressions, the number of βs that are significantly different from zero. Column four states the averages of the βs and R2 reported in column one. Column five states the medians of the βs and R2 reported in column one. Column six states the standard deviations of the βs and R2 reported in column one.
shows that the average of the coefficients resulting from regressing the 94 unlevered returns on the market premia is 0,133. In other words, the average unlevered beta of the 94 regressions is 0,133. Column five shows that the median of the unlevered betas is 0,141 and column six shows that the standard deviation of the unlevered betas is 0,198. Moreover, the average R2 of the aforementioned 94 regressions is 0,104.
Table 1 column two also shows that for the levered returns (equation (5b)), 98 regression were run. Column three shows that of these 98 regressions, 23 levered betas are significantly different from zero. Column four shows that the average of the levered betas of all 98 regressions is 0,413. Column five shows that the median of all 98 levered betas is 0,334 and column six shows that the standard deviation of all 98 betas is 0,441. Lastly, the average R2 for the total 98 regressions is 0,128. Figures 4 and 5 show the distribution of the unlevered and levered betas, respectively. The levered betas have a higher standard deviation than the unlevered betas and this is also reflected by the relatively wide distribution of figure 5.
Fig. 4: Histogram showing the distribution of the 94 unlevered betas resulting from the regressions of
equation (5a). The horizontal axis shows the different intervals of unlevered betas that were measured. The vertical
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Fig. 5: histogram showing the distribution of the 98 levered betas resulting from the regressions of equation
(5b). The horizontal axis shows the different intervals of levered betas that were measured. The vertical axis shows
the frequency of occurrence of these intervals.
Table 2 shows the results of equations (6a) and (6b) that relate to the Chow tests. These Chow tests determine if the market betas in the post-crisis period are significantly different from the market betas in the pre-crisis period. The second column, just like table 1, shows that for the unlevered and levered returns 94 and 98 banks had a minimum of 15 years of observations, respectively. The third column states that in the Chow models, 18 and 19 unlevered and levered betas are significantly different from zero, respectively. The fourth column shows that in case of both equations (6a) and (6b) there are 10 banks in each sample that show significant change in market beta in the post-crisis period.
Total number of regressions Number of β1CHOW betas significantly different from zero Number of β2CHOW betas significantly different from zero
Average Median Standard
deviation Equation (6a) 94 18 10 Aβ1CHOW 0,204 0,205 0,256 Aβ2CHOW -0,306 -0,280 0,483 AR2 0,180 0,143 0,143 Equation (6b) 98 19 10 Bβ1CHOW 0,402 0,313 0,464 Bβ2CHOW 0,087 0,090 0,940 BR2 0,181 0,143 0,143
Table 2: Summary statistics of equations (6a) and (6b) showing the results of the Chow tests. The table shows the summary statistics of all OLS regressions of equations (6a) and (6b) over the period 1992-2015 (excluding 2007-2009). Column one states each equation and the type of variable and statistics that are reported. Column two states the total number of regressions that were run for either equation (6a) or (6b). Column three states for each equation, out of the total number of regressions, the number of β1CHOW betas that are significant. Column four states for each
equation, out of the total number of regressions, the number of β2CHOW betas that are significant. Column five shows
the averages of the values of the variables and R2 reported in column one. Column six shows the medians of the values of the variables and R2 reported in column one. Column seven shows the standard deviations of the values of the variables and R2 reported in column one.
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Table 1 and 2 indicated that a relatively small number of betas is significantly different from zero. As a result, it is not surprising that, measured by the Chow test, only a small number of betas show significant change in the post-crisis period. As mentioned before, Hamada’s approach of separating levered and unlevered returns requires yearly accounting data. Especially in the case of the post-crisis period this results in a relatively low number of observations. Therefore, previous results will be subject to further empirical testing in order to improve estimates of the determinants of pre- and post-crisis positions on market exposure.
Since analysis of the individual regressions does not provide convincing empirical evidence it is decided to investigate the different groups of coefficients that were estimated. Adding the first Chow beta to the second Chow beta results in an estimate of the post-crisis beta. Comparing these combined betas to the regular market betas over the total period shown in table 1 provides an estimate of post-crisis change in betas. In order to determine statistical differences between these two groups, the Wilcoxon Signed Rank Test is applied by comparing the medians of the two sets. The null hypothesis that the median of (Aβ1CHOW + Aβ2CHOW)1-94 is equal to the median of (Aβ1)1-94 is rejected at the 1% level. Next, the groups of variables are reversed and again the null hypothesis that the median (Aβ1)1-94 is equal to the median of (Aβ1CHOW + Aβ2CHOW)1-94 is rejected at the 1% level. After testing the post-crisis difference of the unlevered betas it is time to similarly test the post-crisis difference of the levered betas. The Wilcoxon Signed Rank Test finds that the null hypothesis that the median of (Bβ1CHOW + Bβ2CHOW)1-98 is equal to the median of (Bβ1)1-98 is rejected at the 5% level. Next the groups of variables are reversed and again the null hypothesis that the median of (Bβ1)1-94 is equal to the median of (Bβ1CHOW + Bβ2CHOW)1-98 is rejected at the 10% level. Previous tests provide preliminary evidence that compared to the pre-crisis period, levered market betas in the banking sector increased in the period after the crisis. It is also found that unlevered market betas decreased in the post-crisis period. However, this evidence is less convincing. After equations (5a) and (5b) calculated market exposure, the next step relates to applying these exposures to determine risk premia.
Table 3 shows the summary results of the Fama-MacBeth regressions that were carried out. These regressions estimate the risk premia that are rewarded for market exposures that were calculated by equations (5a) and (5b). In all three panel regressions the λ1 and λ1 have the correct signs because both are positive. Moreover, both parameter estimates λ0 and λ1 in equations (7a) and (7b) are significantly different from zero. In equation (7c) only the constant is significantly different from zero. Table 7 in appendix B shows the results of equations (7a) – (7c) after truncating the data by discarding the highest 1% and lowest 1% of the bank returns. This robustness test does not lead to substantial changes in either the parameter estimates or the explanatory power of the models. Both the R2 within and adjusted R2 slightly increase, which is on average a logical consequence of removing extreme values.
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are included. Of these 94 banks, only one bank does not have a minimum of 15 years of yearly actual stock return data and is therefore excluded. For comparability reasons it is decided to also exclude those four banks from regressions (7a) – (7c).
Equation λ0 λ1 i N R2 within R2 adj. F-stat. (7a) 0,113*** (24,546) 0,085*** (4,291) 94 1798 0,222 0,218 10,234 (7b) 0,107*** (10,912) 0,055*** (3,447) 94 1801 0,185 0,180 19,777 (7c) 0,028*** (3,995) 0,014 (1,223) 93 1764 0,246 0,238 27,164
Table 3: Descriptive statistics regressions (7a) – (7c). The table shows the descriptive statistics of the Fama-MacBeth regressions (7a) – (7c) estimated with fixed effects panel models. Estimated period 1992-2015 (excluding 2007-2009). Column one states each equation. Column two (λ0) shows the values of the constants. Column three (λ1)
shows the values of the previously estimated betas that are included as independent variables. Columns four – eight for each equation show the number of cross-sections, the total number of observations, the R2 within, the adjusted R2 and the F-statistic, respectively. t-ratios in parentheses and ***, ** and * indicate significance at the 1%, 5% and 10% level, respectively. Equation λ0 λ1 λ2 i N R2 within R2 adj. F-stat. (8a) 0,139*** (25,142) 0,090*** (4,457) -0,009*** (-5,166) 94 1637 0,224 0,232 23,500 (8b) 0,102*** (10,196) 0,050*** (3,105) 0,018*** (6,224) 94 1637 0,172 0,189 18,364 (8c) 0,026*** (3,479) 0,023** (1,981) 0,010*** (4,644) 93 1595 0,249 0,253 25,514
Table 4: Descriptive statistics of regressions (8a) – (8c). The table shows the descriptive statistics of the Fama-MacBeth regressions estimated with fixed effects panel models, extended with the leverage ratio proxy. Estimated period 1992-2015 (excluding 2007-2009). Column one states each equation. Column two (λ0) shows the values of
the constants. Column three (λ1) shows the values of the previously estimated betas that are included as independent
variables. Column four (λ2) shows the values of the leverage ratio proxy. Columns five – nine for each equation
show the number of cross-sections, the total number of observations, the R2 within, the adjusted R2 and the F-statistic, respectively. t-ratios in parentheses and ***, ** and * indicate significance at the 1%, 5% and 10% level, respectively.
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parameters. Only λ2 in equation (8a) is slightly negative but this could be due to the relatively high premia rewarded to the first two parameters of this equation. The risk premia on the leverage ratio proxy in equations (8b) and (8c) are positive and highly significant. This confirms that higher (lower) financial leverage results in a higher (lower) risk premium demanded by the market. Table 8 in appendix B shows the results of equations (8a) – (8c) after truncating the data by discarding the highest 1% and lowest 1%. Again this robustness test does not lead to substantial changes in either the parameter estimates or the explanatory power of the models.
Table 5: Descriptive statistics of regressions (9a) – (9c). The table shows the descriptive statistics of the Fama-MacBeth regressions estimated with fixed effects panel models, extended with the leverage ratio proxy and the dummy variable indicating post-crisis effects. Estimated period 1992-2015 (excluding 2007-2009). Column one states each equation. Column two (λ0) shows the values of the constants. Column three (λ1) shows the values of the
previously estimated betas that are included as independent variables. Column four (λ2) shows the values of the
leverage ratio proxy. Column five (λ3) shows the values of the dummy variable indicating post-crisis effects.
Columns six – ten for each equation show the number of cross-sections, the total number of observations, the R2 within, the adjusted R2 and the F-statistic, respectively. t-ratios in parentheses and ***, ** and * indicate significance at the 1%, 5% and 10% level, respectively.
Table 5 shows the results of the former equations extended with a dummy variable that takes 1 for the crisis period and 0 for the pre-crisis period. The negative sign on the post-crisis estimator for the unlevered return premium (λ3 equation (9a)) indicates a decrease in risk premium. This could imply that in the post-crisis period a lower risk premium is rewarded to operating leverage in the banking sector, compared to the pre-crisis period. This is also in line with previous findings of the Chow tests that indicate that a decrease in post-crisis unlevered beta. However, this parameter is not significantly different from zero and therefore it is not possible to state conclusive findings. The first three parameters of equation (9b) again indicate positive and significant signs on risk premia in relation to levered returns. Moreover, λ3 indicates a post-crisis increase in risk premium that is significant at the 10% level. This is in line with previous findings regarding the Chow tests that provided evidence for a post-crisis increase in beta. Equation (9c) shows positive and highly significant signs on parameters one, three and four. This again confirms a positive risk premium related to financial leverage. Moreover, λ3 indicates that this risk premium increased in the post-crisis period. Furthermore, this post-crisis increase is significant at the 1% level. Table 9 in appendix B shows the results of equations (9a) – (9c) after truncating the data by discarding the highest 1% and lowest 1%. It is found that the parameters and the explanatory power of the model do not substantially change.
18 Equation λ0 λ1 λ2 λ3 λ4 i N R2 within R2 adj. F-stat. (10a) 0,126*** (24,349) 0,057*** (2,749) -0,004*** (-5,305) -0,045 (-1,077) 0,051** (2,088) 94 1637 0,215 0,234 21,823 (10b) 0,106*** (10,296) 0,005 (-0,140) 0,017*** (5,851) 0,063* (1,793) 0,042 (1,364) 94 1637 0,173 0,191 17,068 (10c) 0,028*** (3,791) 0,029 (-1,218) 0,009*** (4,206) 0,086*** (3,346) 0,033 (1,459) 93 1595 0,253 0,258 24,092
Table 6: Descriptive statistics of regressions (10a) – (10c). The table shows the descriptive statistics of the Fama-MacBeth regressions estimated with fixed effects panel models, extended with the leverage ratio proxy, a dummy variable indicating post-crisis effects and a dummy variable indicating location effects. Estimated period 1992-2015 (excluding 2007-2009). Column one states each equation. Column two (λ0) shows the values of the constants.
Column three (λ1) shows the values of the previously estimated betas that are included as independent variables.
Column four (λ2) shows the values of the leverage ratio proxy. Column five (λ3) shows the values of the dummy
variable indicating post-crisis effects. Column six (λ4) shows the values of the dummy variable indicating effects of
European banks compared to US banks. Columns seven – eleven for each equation show the number of cross-sections, the total number of observations, the R2 within, the adjusted R2 and the F-statistic, respectively. t-ratios in parentheses and ***, ** and * indicate significance at the 1%, 5% and 10% level, respectively.
Table 6 shows that equation (10a) again shows positive signs on the first two parameters and a negative sign on the third parameter. The fourth parameter that relates to the post-crisis period implies that after the crisis the risk premium on operating risk exposure decreased. However, this estimate lies outside the significance level of 10% and is therefore not statistically significant. The fifth parameter that relates to the country dummy indicates that the risk premium on the unlevered returns is larger in European banks than in US banks. Moreover, this effect is significant at the 5% level. Equation (10b) shows positive signs on all five parameters. λ3 again shows that the post-crisis increase in risk premium is significant at the 10% level. The country effect in this regression is again positive but not significant. Equation (10c) that relates to the actual stock returns shows positive signs on all parameters as well. Moreover, λ0, λ2 and λ3 are significant at the 1% level. Again a robustness test is performed by discarding the highest 1% and lowest 1% of the bank return data. Table 10 shows that after the data trim, λ4 of equation (10c) is significant at the 10% level, indicating a larger risk premium on leverage in Europe compared to the US.
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5. Conclusions and limitations
After the financial crisis there has been a high amount of research that relates to the investigation of capital regulation approaches. Despite a high variety of focus areas, a majority of recent literature describes a trend towards macroprudential frameworks. Moreover, the literature also shows that capital requirements have become stricter in the years after the financial crisis. Excessive (bank) leverage in the years preceding the crisis was found to be a substantially contributing factor related to the economic turmoil that followed.
This paper investigated a sample of US and European banks over the period 1992-2015 and finds interesting insights regarding market exposures and according risk premia. By applying an approach initially used by Hamada it was possible to distinguish between operating and financial risk. After determining market exposures (beta) to both of these risks, the second step of the Fama-MacBeth approach translated these market exposures to risk premia. By linking market returns to individual bank returns it was made possible “to let the market speak”. Logically, unlevered excess returns related to the risk premia on the unlevered market exposure and levered excess returns related to the risk premia on the levered market exposure. As a robustness check, in addition to the levered excess returns, it was also decided to relate the actual excess stock returns to the risk premia on the levered market exposure.
Results showed that in the post-crisis period (2010-2015) market exposure relating to leverage risk, measured by the levered market beta, increased compared to the pre-crisis period. Market exposure regarding operating risk, measured by the unlevered beta, indicated a post-crisis decrease. However, this second effect did not proof to be robustly significant. Analyses of the levered return exposures by regressing the levered excess returns on the previously calculated levered betas revealed that a post-crisis increase in risk-premia has occurred. Moreover, this same effect was found when the actual excess stock returns were regressed on the same set of levered betas. This implied that in both the US and European banking systems after the crisis, the market demands a higher premium for risk as a result of financial leverage, compared to before the crisis. After including the levered betas as explanatory variables, the model was also extended with a leverage ratio proxy. This proxy was calculated by dividing the levered returns by the unlevered returns. In both models (levered and actual excess returns) this proxy was positive and highly significant. Analyses of the unlevered return exposures showed negative signs regarding post-crisis risk-premia, compared to the pre-crisis period. However, these effects were not found to be significant. Including location effects that distinguished between US and European banks revealed positive signs for European banks. In the unlevered return model this effect was significant and in the levered return model this effect lied just outside the 10% significance level. Former results indicate a stronger effect in European banks compared to US banks, although statistical evidence is limited.
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frameworks focus on market values related to the financial system as a whole. Research has found that market values provide effective indicators of bank stability and compared to book values they can lead to substantial changes regarding optimal capital adequacy (Acharya et al., 2014; Acharya and Steffen, 2014). Focusing on market values can therefore provide a correction compared to focusing on book values because book values do not fully reflect risk drivers put forward by the market. Taking into account fluctuations in risk premia demanded by the market helps to identify risk drivers that in turn explain bank stability.
Next to the practical implications, this paper has a number of important limitations. Because of the unavailability of market values of preferred stock it was decided to only include banks that have zero preferred stock. There are various reasons for the issuance of preferred stock. Since preferred stock is treated as equity, it provides a way of increasing capital without increasing the leverage ratio. Moreover, it provides a company with relative flexibility regarding non-dividend related reasons. Therefore, excluding banks from the sample that have preferred stock outstanding could bias the sample in the sense that the sample only contains banks that do not specifically need the advantages of preferred stock.
Former analyses of the banking industry relates to a broad classification of banks. This classification does not distinguish amongst different types of banks. Different types of banks (e.g. investment versus savings banks) can have different risk profiles and therefore, placing all banks under one umbrella could bias results.
Since macroprudential regulation increasingly relies on risk drivers put forward by the market, further research should increasingly focus on the relation between operating and financial risk premia, as measured by the market.
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Appendix A
23 Appendix B Equation λ0 λ1 i N R 2 within R2 adj. F-stat. (7a) 0,114*** (28,280) 0,064*** (3,685) 94 1762 0,228 0,227 25,603 (7b) 0,104*** (13,196) 0,047*** (3,592) 94 1765 0,223 0,221 24,802 (7c) 0,028*** (3,995) 0,014 (1,223) 93 1764 0,246 0,238 27,164
Table 7: Descriptive statistics of regressions (7a) – (7c) after truncating the data by discarding the highest 1%
and lowest 1% bank rates of return. The table shows the descriptive statistics of the Fama-MacBeth regressions
(7a) – (7c) estimated with fixed effects panel models. Estimated period 1992-2015 (excluding 2007-2009). Column one states each equation. Column two (λ0) shows the values of the constants. Column three (λ1) shows the values of
the previously estimated betas that are included as independent variables. Columns four – eight for each equation show the number of cross-sections, the total number of observations, the R2 within, the adjusted R2 and the F-statistic, respectively. t-ratios in parentheses and ***, ** and * indicate significance at the 1%, 5% and 10% level, respectively. Equation λ0 λ1 λ2 i N R 2 within R2 adj. F-stat. (8a) 0,128*** (29,048) 0,062*** (3,513) -0,004*** (-5,353) 94 1687 0,228 0,237 24,869 (8b) 0,102*** (12,578) 0,047*** (3,477) 0,008*** (5,015) 94 1693 0,221 0,227 23,599 (8c) 0,024*** (3,449) 0,024** (2,081) 0,006*** (4,567) 93 1668 0,257 0,257 27,172
Table 8: Descriptive statistics of regressions (8a) – (8c) after truncating the data by discarding the highest 1%
and lowest 1% bank rates of return. The table shows the descriptive statistics of the Fama-MacBeth regressions
estimated with fixed effects panel models, extended with the leverage ratio proxy. Estimated period 1992-2015 (excluding 2007-2009). Column one states each equation. Column two (λ0) shows the values of the constants.
Column three (λ1) shows the values of the previously estimated betas that are included as independent variables.
Column four (λ2) shows the values of the leverage ratio proxy. Columns five – nine for each equation show the
24 Equation λ0 λ1 λ2 λ3 i N R2 within R2 adj. F-stat. (9a) 0,128*** (28,994) 0,077*** (3,588) -0,005*** (-5,337) -0,046 (-1,241) 94 1687 0,220 0,238 23,862 (9b) 0,102*** (12,595) 0,038** (2,385) 0,008*** (4,971) 0,028 (0,983) 94 1693 0,221 0,227 22,614 (9c) 0,025*** (3,465) 0,001 (0,082) 0,006*** (4,512) 0,081*** (0,199) 93 1668 0,258 0,261 26,582
Table 9: Descriptive statistics of regressions (9a) – (9c) after truncating the data by discarding the highest 1%
and lowest 1% bank rates of return. The table shows the descriptive statistics of the Fama-MacBeth regressions
estimated with fixed effects panel models, extended with the leverage ratio proxy and the dummy variable indicating post-crisis effects. Estimated period 1992-2015 (excluding 2007-2009). Column one states each equation. Column two (λ0) shows the values of the constants. Column three (λ1) shows the values of the previously estimated betas that
are included as independent variables. Column four (λ2) shows the values of the leverage ratio proxy. Column five
(λ3) shows the values of the dummy variable indicating post-crisis effects. Columns six – ten for each equation show
the number of cross-sections, the total number of observations, the R2 within, the adjusted R2 and the F-statistic, respectively. t-ratios in parentheses and ***, ** and * indicate significance at the 1%, 5% and 10% level, respectively. Equation λ0 λ1 λ2 λ3 λ4 i N R2 within R2 adj. F-stat. (10a) 0,126*** (28,010) 0,057** (2,301) -0,005*** (-5,427) -0,045 (-1,208) 0,051* (1,721) 94 1687 0,221 0,239 23,018 (10b) 0,105*** (12,671) 0,000 (0,001) 0,007*** (4,800) 0,029 (1,012) 0,042 (1,620) 94 1693 0,222 0,228 21,803 (10c) 0,027*** (3,758) -0,035 (-1,455) 0,006*** (4,324) 0,082*** (3,260) 0,040* (0,815) 93 1668 0,258 0,262 25,647
Table 10: Descriptive statistics of regressions (10a) – (10c) after truncating the data by discarding the highest
1% and lowest 1% bank rates of return. The table shows the descriptive statistics of the Fama-MacBeth
regressions estimated with fixed effects panel models, extended with the leverage ratio proxy, a dummy variable indicating post-crisis effects and a dummy variable indicating location effects. Estimated period 1992-2015 (excluding 2007-2009). Column one states each equation. Column two (λ0) shows the values of the constants.
Column three (λ1) shows the values of the previously estimated betas that are included as independent variables.
Column four (λ2) shows the values of the leverage ratio proxy. Column five (λ3) shows the values of the dummy
variable indicating post-crisis effects. Column six (λ4) shows the values of the dummy variable indicating effects of
