# The Impact of Financial Leverage on Shareholders’ Systematic Risk

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Prior Works

_{U}). First, he measured the levered beta estimates and used Hamada’s method for estimating the unlevered betas. His initial results were in accordance with Hamada’s findings. He found that the mean value of the levered beta estimate was considerably larger than the mean of the unlevered beta estimate. Then, Chance divided his sample firms into four homogeneous risk classes according to four ranges of the unlevered beta (0.65–0.85, 0.65–0.75, 0.7–0.8, and 0.75–0.85), and tested Hamada’s relationship directly. Moreover, he tested how closely his observed slope was to Hamada’s implied theoretical slope [β

_{U}(1-T

_{C})], where T

_{C}is the corporate tax rate. Chance’s results indicated a positive beta–leverage relationship that supports Hamada’s equation. Second, Chance concluded that the penalty for financial leverage, which is captured by the implied slope using Hamada’s equation compared to the actual slope’s results, was higher. However, the difference was not consistently significant. These results, however, were based on relatively small, overlapping samples and were confined to the 1974 to 1978 period.

## 3. The Theoretical Framework and Hypotheses

_{E,i}= β

_{U,i}+ β

_{U,i}[L]

_{i}+ u

_{i},

_{E,i}= β

_{U,i}+ β

_{U,i}[(1 − T

_{C})L]

_{i}+ u

_{i},

_{E,i}= β

_{U,i}+ β

_{U,i}[TL]

_{i}+ u

_{i}.

_{E,i}= β

_{U,i}+ [(β

_{U}− β

_{D})L]

_{i}+ u

_{i},

_{E,i}= β

_{U,i}+ [(β

_{U}− β

_{D})(1 − T

_{C})L]

_{i}+ u

_{i},

_{E,i}= β

_{U,i}+ [(β

_{U}− β

_{D})TL]

_{i}+ u

_{i},

_{E,i}= β

_{U,i}+ [(β

_{U}(1 + q/T) − β

_{D})TL]

_{i}+ u

_{i},

_{C})(1 − T

_{E})/(1 − T

_{D}), where T

_{C}, T

_{E}and T

_{D}are the tax rates applicable to the corporation, equity holders, and debt holders, respectively; q is the bankruptcy costs coefficient and is given by q = C/D, where C is the expected value of the bankruptcy costs; and D is the value of the debt. The subscripts U and E represent the unlevered firm and the equity of the levered firm, respectively.

_{E}) is given by the sum of the unlevered beta (β

_{U}) and the leverage (L) multiplied by a positive coefficient given by (β

_{U}(1 + q/T) − β

_{D})T.

_{E,i}= γ

_{0}+ γ

_{1}[(β

_{U}(1 + q/T) − β

_{D})TL]

_{i}+ ε

_{i},

_{0}): γ

_{0}= β

_{U}, and, γ

_{1}= 1.

_{E,i}= γ

_{0}+ γ

_{1}[TL]

_{i}+ ε

_{i},

_{0}: γ

_{0}= β

_{U}, and, γ

_{1}= β

_{U}. Given that in the real world debt is usually risky, γ

_{1}should be equal to 1, which is the theoretical value in the direct estimated regression of Model (4b) given by Equation (5), rather than β

_{U}, which is the theoretical value in the direct estimated regression of Model (3a) given by Equation (6). This estimation method involves the comparison of the observed regression γ

_{0}, γ

_{1}with their theoretical counterparts γ

_{0}*, γ

_{1}*. For Equation (5), for example, γ

_{1}should be equal to 1 (γ

_{1}*), because the term in the squared brackets serves as the explanatory variable. Similarly, γ

_{0}should be equal to β

_{U}(γ

_{0}*), where β

_{U}is derived from the theoretical Model (4b).

_{E,i}= γ

_{0}+ γ

_{1}[(β

_{U}− β

_{D})TL]

_{i}+ ε

_{i},

_{0}: γ

_{0}= β

_{U}, and, γ

_{1}= 1. Therefore, the next hypothesis is that given that debt in reality is risky, γ

_{0}and γ

_{1}will approximate the theoretical values given by Model (3b) rather than their corresponding values in the risk free debt Model (3a). In other words, γ

_{1}in Equation (7) will approximate 1, which is the theoretical value of γ

_{1}in Equation (7), rather than that of β

_{U}, which is the theoretical value of γ

_{1}in Equation (6).

_{E,i}= γ

_{0}+ γ

_{1}[(β

_{U}− β

_{D})(1 − T

_{C})L]

_{i}+ ε

_{i},

_{0}: γ

_{0}= β

_{U}, and, γ

_{1}= 1.

_{E,i}= γ

_{0}+ γ

_{1}[(β

_{U}− β

_{D})L]

_{i}+ ε

_{i},

_{0}: γ

_{0}= β

_{U}, and, γ

_{1}= 1.

_{E,i}= γ

_{0}+ γ

_{1}[(1 − T

_{C})L]

_{i}+ ε

_{i},

_{0}): γ

_{0}= β

_{U}, and, γ

_{1}= β

_{U}.

_{0,}γ

_{1}coefficients should be the closest to the coefficient of L in Case (b), which includes risky debt models, rather than the risk free models described above in Case (a). Moreover, given that in reality personal taxes exist, and debt is risky and is associated with bankruptcy costs, Model (4b) is hypothesized to have the closest γ

_{0,}γ

_{1}coefficients compared to the other expressions.

_{0}, γ

_{1}) given in Equation (5) will reflect the existence of corporate taxes and personal taxes as well as the risky debt and bankruptcy costs in the theoretical beta–leverage expression in Model (4b).

## 4. Data and Variables Measurement

#### 4.1. Data and Construction of the Sample

#### 4.2. Measurement of Variables

_{E}), the business systematic risk (unlevered beta, β

_{U}), the debt systematic risk (β

_{D}), the corporate tax rate (T

_{C}), the tax rate applicable to the debt holders (T

_{D}), and to the equity holders (T

_{E}), and finally the bankruptcy costs factor (q). In this section, we review our proxies and measurements of the variables followed by a discussion of the relevant empirical literature.

#### 4.2.1. The Equity Systematic Risk (β_{E})

_{E}) using the so-called market model. This model involves a regression of the stock’s rate of return against the market index’s rate of return. We used 60 monthly returns for both the stock and the market index. Given that the sample consisted of NYSE (New York Stock Exchange) stocks, the market index employed here was the NYSE Composite Index. Details of the descriptive statistics are reported in Table 1 and will be discussed in Section 5.

#### 4.2.2. Financial Leverage (L)

_{1}= LTD/Equity

_{BV}; (2) Lev

_{2}= LTD/Equity

_{MV}; (3) Lev

_{3}= (LTD + CL)/Equity

_{BV}, and (4) Lev

_{4}= (LTD + CL)/Equity

_{MV}, where Lev denotes financial leverage, LTD is long-term debt, Equity is the value of common equity, CL is current liabilities, and the subscripts BV and MV stand for book and market values, respectively. Equity

_{MV}includes common equity in MV given by the product of the number of common shares outstanding and the mean value of the 12 monthly closing stock prices. The estimate of financial leverage (Lev) for each year is based on the mean value of the preceding five years. Two such estimates were also constructed: “Relative” and “Absolute.” The Relative Lev estimate for a given year is the mean value of the Lev variable across the preceding five years, while the Absolute Lev is given by the 5-year mean value of the “debt” numerator divided by the 5-year mean value of the “equity” denominator. Table 1 presents the full descriptive statistics of the financial leverage ratios, and a full discussion is also provided in Section 5.

#### 4.2.3. Beta of Debt (β_{D})

_{D}using the Bloomberg interface by applying the CAPM (Capital Asset Pricing Model) in each sample year to the iBoxx ETF (Exchange Traded Fund). This bond ETF includes a broad representation of U.S. dollar-denominated high and low yield liquid corporate bonds. The mean value and standard deviation of the ETF betas across the sample years came to 0.3 and 0.063, respectively. For compatibility purposes, we estimated the debt betas using the same approach used for estimating the equity betas including the employment of the same market index, the NYSE composite index. With regard to the equity betas, we followed the practice in the empirical literature and used an all-equity index for estimating the stock betas. Given this practice, also using the same index for bonds may reduce the bias resulting from the use of an alternative index such as an all-debt index or a debt-and-equity index. Indeed, Weinstein [42] also employed the NYSE index for estimating bond betas, implying that such an approach is not an uncommon practice. To compensate for a possible bias in the beta estimate, however, we used below a range of mean bond betas that may appear consistent with the mean bond beta values reported in the literature, and which very likely may contain the true unobservable mean bond betas. Consistent with the range of mean debt beta values obtained in the literature and reported above, we set the individual bond betas in our sample to be given by the mean bond beta value plus a component that is mainly a function of the individual company’s financial leverage. This adjustment procedure is described below. To be consistent with the mean bond betas found in the literature, we used a mean range of 0.1, 0.2, and 0.3, which may likely contain unobservable mean bond beta. This mean range has been employed for sensitivity purposes and to account for potential measurement errors. As noted in Section 5.3, the main results of the study are essentially similar for these three mean bond beta estimates.

_{D}for the entire sample were 0.3 and 0.063 (based on the Bloomberg ETF sample), the mean and standard deviation values for the financial leverage of the entire sample were 1.5 and 0.5, respectively, and the specific company’s financial leverage was 2.5. The estimate for the specific company’s β

_{D}will be given as follows: β

_{D}= 0.3 + 2 × 0.063 = 0.426, where the Z score of 2 is given by (2.5 − 1.5)/0.5 = 2.

#### 4.2.4. The Business Systematic Risk (β_{U})

_{U}) from the observable equity beta (β

_{E}), incorporating relevant adjustments that depend on the market imperfections considered (e.g., Bernardo, Chowdhry and Goyal [45], Cooper and Nyborg [46,47]. Another approach is to simply use zero leverage firms. However, Doshi et al. [48] stated that using such procedures may end in a relatively small sample and lead to a severe selection bias.

_{U}. Accordingly, the estimate for β

_{U}in Model (1b) is based on Model (1a). Similarly, the estimate for β

_{U}in Model (2b) is based on Model (2a), and the same applies to Models (3b) and (4b). The β

_{U}estimate for each year is based on the preceding 5-year period. It might be worth noting that the GICS (Global Industry Classification Standard) in COMPUSTAT for the industrial sector is considered here as roughly reflecting a similar level of business risk.

#### 4.2.5. Corporate and Personal Tax Rates (T_{C} and T_{E})

_{C}) and the personal tax rates for both equity holders (T

_{E}) and debt holders (T

_{D}). Most proxies for the corporate tax rate are based on the ratio of the total income tax expense to pre-tax income (see for example: Arena and Roper [49]; Dyreng, Hanlon and Maydew [50]; Fan, Titman and Twite [51], or by assuming a constant corporate tax rate (Kemsley and Nissim [52]; DeAngelo, DeAngelo and Whited [53]. Following the first set of studies, we used the total tax expense divided by pretax income as a proxy for the corporate tax variable. The estimate of the corporate tax rate (T

_{C}) for each year was based on the mean value of the preceding five years. As in the case of the other variables estimated, to account for potential measurement errors and for the sake of robustness analysis, we constructed two estimates for Tc: “Relative” and “Absolute.” The Relative T

_{C}estimate for a given year is the mean value of the T

_{C}variable across the preceding five years. The Absolute T

_{C}is given by the 5-year mean value of the firm’s total tax expense divided by the 5-year mean value of the firm’s taxable income (the annual means of the corporate tax rate variable are presented in Table 2). Butler, Mohr, and Simonds [54] set the outliers of corporate tax rates to 40% because such rates are likely to be associated with nonrecurring or unusual items. They stated that this procedure is necessary for approximately 15% of the sample firms. We followed this procedure for approximately 12% of the sample firms. Corporate tax rate values exceeding 60% were set to the mean value plus two standard deviations, while tax rate values lower than 20% were set to the mean value minus two standard deviations.

_{R}) is defined here as: T

_{R}= [(1 − T

_{E})/(1 − T

_{D})], where T

_{D}is the tax rate for debt holders, and T

_{E}is the tax rate applicable to equity holders. T

_{E}is a weighted-average tax rate on dividend and capital gains income. In other words, it is the tax rate on dividend (T

_{d}) and capital gains (T

_{cg}) income expressed as: T

_{E}= [d· T

_{d}+ (1 − d)·α·T

_{cg}], where d is the ratio of the most recent year’s net income that was paid out in dividends divided by the mean value of the total earnings over the prior three years. Accordingly, (1 − d) is the retention ratio. Following the procedure devised by Dhaliwal, Heitzman, and Li [55], we winsorized d at zero and one. T

_{d}is the personal tax rate on dividend income, which was set equal to the values of T

_{D}for the years prior to 2003, and 15% thereafter. T

_{cg}is set equal to the top statutory tax rate on long-term capital gains income, which equaled 20% for 1998 through 2002, and 15% thereafter. α is the benefit of capital gains deferral. Following Dhaliwal, Heitzman, and Li [55], van Binsbergen, Graham and Yang [56], and Graham [57], we assumed that α = 0.25. Following Dhaliwal, Heitzman, and Li [55], T

_{D}was measured as the highest statutory tax rate on interest income, which was 39.6% for 1998 through 2000, 38.6% for 2001 through 2002, and 35% thereafter.

_{C}, both Relative and Absolute), the dividend payout ratio (d) next to the personal tax rate (T

_{E}), and the taxes ratio (T

_{R}) are presented in Table 3, in panels A, B, and C. The right hand side of each panel summarizes the overall statistics for the entire sample time period.

#### 4.2.6. Bankruptcy Costs (q)

## 5. Empirical Findings

#### 5.1. Descriptive Statistics

_{E}estimates, which are the mean, median (Med), standard deviation (SD), coefficient of variation (CV), minimum (Min), and maximum (Max) values. The last row reports the overall mean value for the sample years. For example, the mean value of β

_{E}in 2006 was 1.15, and the overall mean value across the years was 1.13. As Table 1 demonstrates, the analysis across the sample years revealed that the mean value of the equity’s risk estimate in 2007 was the highest. This result is also evident in the corresponding median values. Apparently, the outbreak of the subprime crisis beginning in the middle of 2007 is related to the increase in market risk.

_{1}(which is the book value) was 0.81, while the mean value of Lev

_{2}(which is the market value) equaled 0.46. Similarly, the Lev

_{3}estimate equaled 1.61, and the corresponding market estimate (Lev

_{4}) was 0.93. Similar results were obtained for the mean value of the Absolute measures of leverage and with respect to the various median leverage values.

_{2}and Lev

_{4}) were more volatile than their corresponding book estimates (Lev

_{1}and Lev

_{3}). For example, the overall mean value of CV was 1.41 and 1.02 for the Relative measures of Lev

_{1}and Lev

_{2}, and 1.51 and 1.15 for Lev

_{3}and Lev

_{4}, respectively. The Absolute measures of leverage yielded similar findings. Analysis across the sample years in Table 1 revealed that the mean value of financial leverage estimates in 2007 was lower than other test years. Presumably, the outbreak of the subprime crisis in the middle of this year had an impact on the debt value.

_{C}), the payout ratio (d), the personal tax rate (T

_{E}), and the descriptive statistics for the taxes ratio (T

_{R}) given by (1 − T

_{E}/1 − T

_{D}).

_{C}. A detailed explanation for the construction of the tax estimates is given in Section 4.2.5.

_{C}in 2007 was 0.345, while the median value equaled 0.344. Similarly, the corresponding Absolute estimate equaled 0.342, and the median value equaled 0.341 (though not reported here). Overall, the Relative method of measurement, rather than the Absolute measure yielded similar values of T

_{C}.

_{E}). The mean value of the payout ratio (d) in 2007 was 0.174, while the median value equaled 0.162. In addition, the mean value across the five sample years was 0.205 with a Min–Max range of 0.174 to 0.236. Finally, the bottom of Panel B reports the T

_{E}estimates for the sample years. The mean value of T

_{E}in 2007, for example, was 0.057 with a standard deviation of 0.02.

_{R}= (1 − T

_{E})/(1 − T

_{D})], associated with debt, represents the relative tax disadvantage for individual investors of receiving a dollar of interest income versus a dollar of equity income. Larger values for the personal tax penalty imply that equity financing is more attractive, as potential stockholders will require a lower pretax return relative to potential lenders. Panel B shows that the penalty is quite steady, as indicated by both the mean and median values across the sample years. For example, the mean value of T

_{R}varied only from 1.440 to 1.451 through the sample years. Dhaliwal et al. [55] reported similar results to those obtained here. For example, their mean value of T

_{R}was 1.428, which is quite similar to the 1.445 reported here.

#### 5.2. Findings for the Risk Free Debt Models

#### 5.2.1. The Findings for the Perfect Capital Markets Case: Model (1a)

_{2}. We obtained similar results (not included in Table 3) when the financial leverage was based Lev

_{1}, Lev

_{3}or Lev

_{4}.

^{2}, and the significance of the slope (the significance level of the intercept is not reported here, because it was significant at the 1% level in all cases). The main result that emerges from Table 3, and perhaps the most important one, is that as financial theory dictates, there is a positive relationship between risk and leverage. This result holds for each year in the sample and for all four leverage estimates. All of the additional tests conducted (though not reported here) using other Lev estimates (that is, using LTD + CL in the numerator of the financial leverage ratio) were also significant at the 1% level. The significance of the results also holds, regardless of whether the Absolute or Relative method is employed. However, the results also indicate that the relationship between risk and leverage is stronger when using market measures of financial leverage rather than book measures. Finally, we obtained similar results not included in Table 3 when the financial leverage was based on the total debt (Lev

_{3}, Lev

_{4}), rather than the long-term debt (Lev

_{1}, Lev

_{2}). To obtain an indication about the results for an abnormal year, we tested the beta–leverage relationship for 2002. The findings imply that even for such an abnormal year, the relationship between beta and leverage was significantly positive. Note that the relationship between beta and leverage (as reported by R

^{2}) was weaker in 2007 than in any other sample year, possibly due to the outbreak of the subprime crisis in July 2007.

_{1}was lower than γ

_{0}in each year, supporting the idea that γ

_{1}might be taking other market imperfections into account. As will be discussed later in Section 5.4, in most cases, the differences between [γ

_{0}-β

_{U}

^{*}] and [γ

_{1}-β

_{U}

^{*}] were statistically significant. This result implies that while the relationship between beta and financial leverage is positive, the observed gap between γ

_{0}and γ

_{1}is possibly due to other market imperfections not considered here. The gap is evident in each of the sample years and for all financial leverage estimates employed. For example, for Lev

_{2}reported in Table 3, the mean values of γ

_{0}and γ

_{1}across all sample years were 0.945 and 0.381, respectively. As noted earlier, a possible explanation for this substantial difference between γ

_{0}and γ

_{1}may stem from the non-incorporation of capital market imperfections

_{E}and γ

_{0}. Given that the equity beta (β

_{E}) reflects both business and financial risk, it should be higher than γ

_{0}, which should reflect the business risk only. The various tests indeed indicate that β

_{E}> γ

_{0}. For example, the mean value of β

_{E}in 2006 was 1.15 (see the second line in Table 1), while the value of γ

_{0}was 0.929. This result holds for all financial measures and across all the sample years.

#### 5.2.2. The Findings for the Corporate Tax Case: Model (2a)

_{C}measure and the Relative Lev

_{2}estimate. However, the results were very similar when the Relative rather than the Absolute measure was employed, and when the financial leverage was based on Lev

_{1}, Lev

_{3}, or Lev

_{4}. As discussed in Section 4, we estimated the corporate tax rate (T

_{C}), like the financial leverage, using both Relative and Absolute methods.

_{E}, while the explanatory variable is [(1 − T

_{C})L], and by the null hypothesis (H

_{0}): γ

_{0}= β

_{U}, and, γ

_{1}= β

_{U}. The main estimation results of the corporate tax case [Model (2a)] in Table 3 were similar to those of the perfect capital markets case [Model (1a)]. Thus, all of the tests conducted here showed that both γ

_{0}and γ

_{1}were significant, and that as financial theory dictates, there is a positive relationship between beta and leverage. Note, too, that due to the incorporation of the corporate tax factor that exists in reality, the gap between γ

_{0}and γ

_{1}was relatively lower in Model (2a) than in Model (1a). For example, looking at the mean value of the intercept and slope at the end of the first two lines of Table 3, the gap between γ

_{0}and γ

_{1}across all five years was 0.364 (0.944–0.580) for Model (2a) compared with the corresponding gap of 0.564 (0.945–0.381) for Model (1a). This result may be related to the inclusion of the corporate tax factor in Model (2a). As in the preceding case, here too, the results for an abnormal year such as 2002 were generally similar to those reported above for the sample years. Once again, 2007 still remains a year with possibly a higher degree of business risk, as implied by the highest mean value of γ

_{0}compared with the rest of the sample years.

#### 5.2.3. The Findings for the Combined Tax Case: Model (3a)

_{C})(1 − T

_{E})/(1 − T

_{D}), L is the financial leverage variable, and by H

_{0}: γ

_{0}= β

_{U}, and γ

_{1}= β

_{U}. The estimation results of the regression equation presented in Table 3 show that the relationship between beta and leverage for Model (3a) were generally similar to those for Model (2a), and Model (1a). However, the gap between γ

_{0}and γ

_{1}corresponds to the magnitude of the explanatory variable underlying these three equations, as demonstrated in Models (1a)–(3a). As indicated by the corresponding regression Equations (7), (11), and (6), respectively, are as follows: [1], [(1 − T

_{C})L], and [TL] for Equations (1a), (2a), and (3a), respectively, where (1 − TC) < T < 1. Accordingly, the [γ

_{0}− γ

_{1}] gap should be highest for Model (1a) and lowest for Model (2a). An examination of the [γ

_{0}− γ

_{1}] gap in Table 3 verifies this result. Specifically, the mean gap across all sample years was equal to 0.564 (0.945–0.381), 0.364 (0.944–0.580), and 0.549 (0.945–0.396). Similar findings were obtained for the abnormal year 2002. The gap for the Absolute Lev

_{1}was equal to 0.73 (0.843–0.113), 0.646 (0.837–0.191), and 0.712 (0.840–0.128) for Models (1a)–(3a), respectively. These results are consistent with capital structure theory. While the impact of corporate taxes on the value of the firm was positive, the impact of the personal tax differential (T

_{D}− T

_{E}) was negative. Similarly, when personal taxes are present, the increase in the beta of the equity was lower when compared to the case of corporate taxes only. The reported results so far are for the case of risk free debt, which as discussed above, implies that the null hypothesis is γ

_{0}= β

_{U}, and γ

_{1}= β

_{U}. However, the null hypothesis is different when debt is risky, which is the case we examine next.

#### 5.3. Findings for the Risky Debt Models

_{0}and γ

_{1}) to the theoretical values (expressed here as γ

_{0}* and γ

_{1}*) will hopefully clarify the relationship between beta and leverage.

_{C}measure when β

_{D}= 0.1 and q = 7% for the estimation of Model (4b). Using other estimates in the framework of our robustness tests (that is, the Relative T

_{C}measure, other debt betas, Lev

_{1}, Lev

_{3}, and Lev

_{4}financial leverage estimates, and different bankruptcy measures) led to similar results in most cases, so we do not report them here. However, in Table 4, we do present the comparison tests obtained when β

_{D}is 0.2 and 0.3 for all of the risky models including Models (1b)–(3b).

^{2}values were consistently higher than their corresponding book measures. For example, the mean value of R

^{2}for the Relative and Absolute Lev

_{2}(which are market estimates) was 0.159, and the corresponding mean values for the Relative and Absolute Lev

_{1}were 0.102 and 0.116.

_{0}and γ

_{1}in each model corresponded to their counterpart theoretical models γ

_{0}* and γ

_{1}*. Again, given that the scale of iteration is extremely high, Table 3 presents only the results for the set of values for the Relative Lev

_{2}, when mean debt beta was 0.1 and bankruptcy costs were 7%. However, Table 4 presents additional findings when the mean debt beta were 0.2 and 0.3, and bankruptcy costs were 3%, 7%, and 11%. Using other estimates yielded similar results. As the two last lines in Table 3 for each risky model demonstrate, we accepted the null hypothesis for the equality of the observed intercept and slope with their theoretical counterparts. In other words, H0: γ

_{0}= β

_{U}, and γ

_{1}= 1 for the intercept and slope, respectively. These results imply that risky debt models capture the real beta-leverage relationship better than risk free debt models. To verify the latter conclusion, for the sake of sensitivity analysis, a more detailed discussion of this issue, combined with additional measures of the parameters, is given in Table 4 and described in the subsequent section.

#### 5.4. Comparative Analysis and Robustness Tests

_{0}and γ

_{1}) to the theoretical values (γ

_{0}* and γ

_{1}*, which are hypothesized to equal β

_{U}and 1, respectively, for the risky debt models, and β

_{U}for the risk free models) derived from the hypotheses mentioned earlier in Section 3.

_{E,i}= β

_{U,i}+ [(β

_{U}− β

_{D})(1 − T

_{C})L]

_{i}+ u

_{i},

_{E,i}= γ

_{0}+ γ

_{1}[(β

_{U}− β

_{D})(1 − T

_{C})L]

_{i}+ ε

_{i},

_{U}− β

_{D})(1 − T

_{C})L], the null hypothesis here is that γ

_{1}equals 1, which is expressed as γ

_{1}*. Accordingly, γ

_{0}should be equal to β

_{U}, which is derived from the theoretical Model (2b). As described in Section 3, Model (2a) is a risk free debt model, and Model (2b) is a risky debt model. In addition, while the null hypothesis in Equation (10) is that both γ

_{0}and γ

_{1}should be equal β

_{U}*, the null hypothesis in Equation (8) is that γ

_{0}will equal β

_{U}* and γ

_{1}will equal the value of 1. Therefore, the gaps are as follows: [γ

_{0}− β

_{U}*] and [γ

_{1}− β

_{U}*] for the risk free models, and [γ

_{0}− β

_{U}*] and [γ

_{1}− 1*] for the risky debt models.

_{2}is used. The first and second columns describe the model and the variants in its variables. Each year is divided into two columns. The first column shows the difference between γ

_{0}and its theoretical value by the null hypothesis, which is β

_{U}

^{*}. The second column presents the difference between γ

_{1}and its theoretical value, which is also β

_{U}

^{*}for the risk free models and 1 for the risky debt models. The upper part of Table 4 lists the results obtained for the risk free debt models (Models (1a)–(3a)) and the bottom part lists them for the corresponding risky debt models ((Models (1b)–(4b)).

_{C}, β

_{D}, and q measures. Each sample year in Table 4 is divided into two columns according to the statistical tests conducted for the differences between the observed regression intercepts and slopes and their theoretical counterparts. It is important to note that the value of β

_{U}* is the theoretical β

_{U}that should have been revealed in the estimation results if the specific model holds true. Each β

_{U}* is derived from the specific model and according to the relevant measures of market imperfections. Each line in Table 4 specifies the exact model tested with reference to the sensitivity analysis conducted. For example, the fourth line in the risk free debt models presents the empirical results achieved by testing Model (3a), according to the Relative corporate tax estimation method described in detail in Section 4. To summarize, Table 4 presents the significance tests for the differences between the observed parameters and their counterpart theoretical values, namely, [γ

_{0}− β

_{U}*] and [γ

_{1}− β

_{U}*] for the risk free debt models and [γ

_{0}− β

_{U}*] and [γ

_{1}− 1*] for the risky debt models. The first term of each pair in the squared parentheses represents the deviation of the observed intercept from its corresponding theoretical value, and the second term represents the deviation of the observed slope from the value of its theoretical counterpart. Note that for all risky debt models, γ

_{1}should be equal to γ

_{1}*, which is the value of 1. Finally, the last line in Table 4 presents the overall mean. Other financial leverage estimates as well as the beta of debt and bankruptcy costs were also tested and yielded similar results, so we do not report them here.

_{0}to β

_{U}* in 2006. In accordance with previous results with regard to the estimation of β

_{U}, Model (4b) was more accurate than any risk free model. While most of the differences were significant in 2006 for the risk free models, all of the gaps were insignificant in Model (4b). Furthermore, the mean gap in Model (4b) was 0.049, while the mean gap for the risk free models was 0.098. Therefore, using Model (4b) reduced the deviation by nearly 48%. A similar picture emerges when we compare any of the risk free models to Model (4b) across the sample years. While the majority of the tests conducted point to the significance of [γ

_{0}− β

_{U}*] for the risk free models, all of these gaps are insignificant for Model (4b). Similar results emerge when we compare γ

_{1}to γ

_{1}*. While most of the risk free models imply that γ

_{1}is significantly different from its theoretical counterpart, the opposite is true for Model (4b). In 2006, for example, four of the five tests conducted for the risk free models showed a significant difference between γ

_{1}and γ

_{1}* ([γ

_{1}− 1

^{*}]). However, for Model (4b), none of the tests showed a significant difference. These results imply that Model (4b) is preferable to the risk free models. Furthermore, a comparison between the mean gap of Model (4b) and the other risky models demonstrates that Model (4b) has the minimum mean value for the difference between γ

_{1}and γ

_{1}

^{*}([γ

_{1}− 1

^{*}]). The mean absolute value of the difference for Model (4b) was 0.089 and 0.194 for the rest of the three risky debt models, which improved the accuracy in this case by nearly 54% (note that we computed the mean value of the absolute differences rather than their natural values to avoid the possible bias of positive and negative gaps). However, this result holds only for 2005–2007. The improvement was even greater when we compared the value of 0.089 to the corresponding mean value of the risk free models, which was 0.253 (in absolute terms). The improvement in this case was nearly 64%. This rate of improvement is evident in each year of the sample. In fact, most of the results across the years show that the gap between γ

_{1}and γ

_{1}

^{*}is minimized when debt is considered risky rather than risk free.

_{1}− β

_{U}

^{*}] in the risk free model of Model (3a) were considerably higher than those of Model (3b), where the corresponding differences were 0.079 through 0.229 for [γ

_{1}− 1

^{*}]. It is important to underscore that these differences were statistically significant for Model (3a) (that is, the observed slope was statistically different from the theoretical slope), while for Model (3b) they were not.

## 6. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Modigliani, F.; Miller, M.H. The Cost of Capital, Corporation Finance and the Theory of Investment. Am. Econ. Rev.
**1958**, 48, 261–297. [Google Scholar] - Modigliani, F.; Miller, M.H. Corporate income taxes and the cost of capital: A correction. Am. Econ. Rev.
**1963**, 53, 433–443. [Google Scholar] - Hamada, R.S. Portfolio analysis, market equilibrium, and corporation finance. J. Financ.
**1969**, 24, 13–31. [Google Scholar] [CrossRef] - Hamada, R.S. The effect of the firm’s capital structure on the systematic risk of common stocks. J. Financ.
**1972**, 27, 435–452. [Google Scholar] [CrossRef] - Rubinstein, M.E. A mean variance synthesis of corporate financial theory. J. Financ.
**1973**, 28, 167–181. [Google Scholar] [CrossRef] - Conine, T.E. Corporate debt and corporate taxes: An extension. J. Financ.
**1980**, 35, 1033–1037. [Google Scholar] [CrossRef] - Yagil, Y. On valuation, beta, and the cost of equity capital: A note. J. Financ. Quant. Anal.
**1982**, 17, 441–449. [Google Scholar] [CrossRef] - Bowman, R.G. The importance of a market-value measurement of debt in assessing leverage. J. Account. Res.
**1980**, 18, 242–254. [Google Scholar] [CrossRef] - Chance, D. Evidence on a Simplified Model of Systematic Risk. Financ. Manag.
**1982**, 11, 53–63. [Google Scholar] [CrossRef] - Marston, F.; Perry, S. Implied Penalties for Financial Leverage: Theory versus Empirical Evidence. Q. J. Bus. Econ.
**1996**, 35, 77–97. [Google Scholar] - Beaver, W.H.; Kettler, P.; Scholes, M. The association between market determined and accounting-determined risk measures. Account. Rev.
**1970**, 45, 654–682. [Google Scholar] - Bildersee, J.S. The Association between a Market-Determined Measure of Risk and Alternative Measures of Risk. Account. Rev.
**1975**, 50, 81–98. [Google Scholar] - Myers, S. The relationship between real and financial measures of risk and return. In Risk and Return in Finance; Friend, I., Bicksler, J., Eds.; Ballinger Publishing Company: Cambridge, UK, 1977. [Google Scholar]
- Gahlon, J.; Gentry, J. On the relationship between systematic risk and the degree of operating and financial leverage. Financ. Manag.
**1982**, 11, 15–23. [Google Scholar] [CrossRef] - Mandelker, G.; Rhee, S. The impact of the degrees of operating and financial leverage on systematic risk of common stocks. J. Financ. Quant. Anal.
**1984**, 19, 45–57. [Google Scholar] [CrossRef] - Darrat, A.F.; Mukherjee, T.K. Inter-industry differences and the impact of operating and financial leverages on equity risk. Rev. Financ. Econ.
**1995**, 4, 141–155. [Google Scholar] [CrossRef] - Lin, C.; Schmid, T.; Xuan, Y. Employee representation and financial leverage. J. Financ. Econ.
**2018**, 127, 303–324. [Google Scholar] [CrossRef] - Vo, X.V. Leverage and corporate investment–Evidence from Vietnam. Financ. Res. Lett.
**2019**, 28, 1–5. [Google Scholar] [CrossRef] - Kini, O.; Shenoy, J.; Subramaniam, V. Impact of financial leverage on the incidence and severity of product failures: Evidence from product recalls. Rev. Financ. Stud.
**2016**, 30, 1790–1829. [Google Scholar] [CrossRef] - Bărbuță-Mișu, N.; Madaleno, M.; Ilie, V. Analysis of Risk Factors Affecting Firms’ Financial Performance—Support for Managerial Decision-Making. Sustainability
**2019**, 11, 4838. [Google Scholar] [CrossRef] - Di Pietro, F.; Bontempi, M.E.; Palacín-Sánchez, M.J.; Samaniego-Medina, R. Capital Structure across Italian Regions: The Role of Financial and Economic Differences. Sustainability
**2019**, 11, 4474. [Google Scholar] [CrossRef] - Lassala, C.; Apetrei, A.; Sapena, J. Sustainability matter and financial performance of companies. Sustainability
**2017**, 9, 1498. [Google Scholar] [CrossRef] - Saretto, A.; Tookes, H.E. Corporate Leverage, Debt Maturity, and Credit Supply: The Role of Credit Default Swaps. Rev. Financ. Stud. Forthcom.
**2013**, 26, 1190–1247. [Google Scholar] [CrossRef] - Denis, D.J.; McKeon, S.B. Debt Financing and Financial Flexibility Evidence from Proactive Leverage Increases. Rev. Financ. Stud.
**2012**, 25, 1897–1929. [Google Scholar] [CrossRef] - Giroud, X.; Mueller, H.M.; Stomper, A.; Westerkamp, A. Snow and leverage. Rev. Financ. Stud.
**2012**, 25, 680–710. [Google Scholar] [CrossRef] - George, T.J.; Hwang, C.Y. A resolution of the distress risk and leverage puzzles in the cross section of stock returns. J. Financ. Econ.
**2010**, 96, 56–79. [Google Scholar] [CrossRef] - Brav, O. Access to capital, capital structure, and the funding of the firm. J. Financ.
**2009**, 64, 263–308. [Google Scholar] [CrossRef] - Lemmon, M.L.; Roberts, M.R.; Zender, J.F. Back to the beginning: Persistence and the cross-section of corporate capital structure. J. Financ.
**2008**, 63, 1575–1608. [Google Scholar] [CrossRef] - Chang, X.; Dasgupta, S. Target behavior and financing: How conclusive is the evidence. J. Financ.
**2009**, 64, 1767–1796. [Google Scholar] [CrossRef] - Frank, M.Z.; Goyal, V.K. Capital Structure Decisions: Which Factors Are Reliably Important? Financ. Manag.
**2009**, 38, 1–37. [Google Scholar] [CrossRef] - Billet, M.; King, T.D.; Mauer, D.C. Growth opportunities and the choice of leverage, debt maturity, and covenants. J. Financ.
**2007**, 62, 697–730. [Google Scholar] [CrossRef] - Barclays, M.J.; Morellec, E.; Smith, C.J. On the debt capacity of growth options. J. Bus.
**2006**, 79, 37–58. [Google Scholar] [CrossRef] - Fama, E.F.; French, K. ‘Financing Decision: Who Issues Equity’. J. Financ. Econ.
**2005**, 76, 549–582. [Google Scholar] [CrossRef] - Molina, C.A. Are firms underleveraged? An examination of the effect of leverage on default probabilities. J. Financ.
**2005**, 60, 1427–1459. [Google Scholar] [CrossRef] - Aharon, D.Y.; Yagil, Y. The Impact of Financial Leverage on the Cost of Equity. Int. J. Econ. Financ. Issues
**2019**, 9, 175–188. [Google Scholar] - Aharon, D.Y.; Yagil, Y. The Impact of Financial Leverage on the Variance of Stock Returns. Int. J. Financ. Stud.
**2019**, 7, 14. [Google Scholar] [CrossRef] - Boquist, J.A.; Racette, G.A.; Schlarbaum, G.G. Duration and risk assessment for bonds and common stocks. J. Financ.
**1975**, 30, 1360–1365. [Google Scholar] [CrossRef] - Lanstein, R.; Sharpe, W. Duration and Security Risk. J. Financ. Quant. Anal.
**1978**, 13, 653–668. [Google Scholar] [CrossRef] - Livingston, M. Duration and Risk Assessment for Bonds and Common Stocks: A Note. J. Financ.
**1978**, 33, 293–295. [Google Scholar] - Reilly, F.K.; Joehnk, M.D. The Association Between Market-Determined Risk Measures for Bonds and Bond Ratings. J. Financ.
**1976**, 31, 1387–1403. [Google Scholar] - Alexander, G.J. Applying the market model to long term corporate bonds. J. Financ. Quant. Anal.
**1980**, 15, 1063–1080. [Google Scholar] [CrossRef] - Weinstein, M. The Systematic Risk of Corporate Bonds. J. Financ. Quant. Anal.
**1981**, 16, 257–278. [Google Scholar] [CrossRef] - Cornell, B.; Green, K. The investment performance of low-grade bond funds. J. Financ.
**1991**, 46, 29–48. [Google Scholar] [CrossRef] - Conine, T.E.; Tomarkin, M. Divisional cost of capital estimation: Adjusting for leverage. Financ. Manag.
**1985**, 14, 54–58. [Google Scholar] [CrossRef] - Bernardo, A.E.; Chowdhry, B.; Goyal, A. Growth options, beta, and the cost of Capital. Financ. Manag.
**2007**, 36, 5–17. [Google Scholar] [CrossRef] - Cooper, I.A.; Nyborg, K.G. The value of tax shields is equal to the present value of tax shields. J. Financ. Econ.
**2006**, 81, 215–225. [Google Scholar] [CrossRef] [Green Version] - Cooper, I.A.; Nyborg, K.G. Tax adjusted discount rates with investor taxes and risky debt. Financ. Manag.
**2008**, 37, 365–379. [Google Scholar] [CrossRef] - Doshi, H.; Jacobs, K.; Kumar, P.; Rabinovitch, R. Leverage and the Cross-Section of Equity Returns. J. Financ.
**2019**, 74, 1431–1471. [Google Scholar] [CrossRef] - Arena, M.P.; Roper, A.H. The effect of taxes on multinational debt location. J. Corp. Financ.
**2010**, 16, 637–654. [Google Scholar] [CrossRef] [Green Version] - Dyreng, S.; Hanlon, M.; Maydew, E. The effects of executives on corporate tax avoidance. Account. Rev.
**2010**, 85, 1163–1189. [Google Scholar] [CrossRef] - Fan, J.P.; Titman, S.; Twite, G. An International Comparison of Capital Structure and Debt Maturity Choices. J. Financ. Quant. Anal.
**2012**, 47, 23–56. [Google Scholar] [CrossRef] [Green Version] - Kemsley, D.; Nissim, D. Valuation of the debt-tax shield. J. Financ.
**2002**, 57, 2045–2073. [Google Scholar] [CrossRef] - DeAngelo, H.; DeAngelo, L.; Whited, T. Capital structure dynamics and transitory debt. J. Financ. Econ.
**2011**, 99, 235–261. [Google Scholar] [CrossRef] - Butler, K.C.; Mohr, R.M.; Simonds, R.R. The Hamada and Conine Leverage Adjustments and the Estimation of Systematic Risk for Multisegment Firms. J. Bus. Financ. Account.
**1991**, 18, 885–901. [Google Scholar] [CrossRef] - Dhaliwal, D.; Heitzman, S.; Li, O. Taxes, leverage, and the cost of equity capital. J. Account. Res.
**2006**, 44, 691–723. [Google Scholar] [CrossRef] - Van Binsbergen, J.; Graham, J.; Yang, J. The cost of debt. J. Financ.
**2010**, 65, 2089–2136. [Google Scholar] [CrossRef] - Graham, J. Do personal taxes affect corporate financing decisions. J. Public Econ.
**1999**, 73, 147–185. [Google Scholar] [CrossRef] [Green Version] - Warner, J.B. Bankruptcy, Absolute Priority, and the Pricing of Risky Debt Claims. J. Financ. Econ.
**1977**, 4, 239–276. [Google Scholar] [CrossRef] - Weiss, L.A. Bankruptcy resolution: Direct costs and violation of priority of claims. J. Financ. Econ.
**1990**, 27, 285–314. [Google Scholar] [CrossRef] - Miller, M.H. Debt and taxes. J. Financ.
**1977**, 32, 261–275. [Google Scholar] - Altman, E. A further empirical investigation of the bankruptcy cost question. J. Financ.
**1984**, 39, 1067–1089. [Google Scholar] [CrossRef] - Andrade, G.; Kaplan, S.N. How costly is financial (not economic distress)? Evidence from highly leveraged transactions that became distressed. J. Financ.
**1998**, 53, 1443–1494. [Google Scholar] [CrossRef] [Green Version] - Lubben, S.J. The direct costs of corporate reorganization: An empirical examination of professional fees in large Chapter 11 cases. Am. Bankruptcy Law J.
**2000**, 509, 508–552. [Google Scholar] - Bris, A.; Welch, I.; Zhu, N. The costs of bankruptcy: Chapter 7 liquidations vs. Chapter 11 reorganizations. J. Financ.
**2006**, 61, 1253–1303. [Google Scholar] [CrossRef] - Garlappi, L.; Yan, H. Financial Distress and the Cross-section of Equity Returns. J. Financ.
**2011**, 66, 789–822. [Google Scholar] [CrossRef] - Hortaçsu, A.; Matvos, G.; Syverson, C.; Venkataraman, S. Indirect Costs of Financial Distress in Durable Goods Industries: The Case of Auto Manufacturers. Rev. Financ. Stud.
**2013**, 26, 1248–1290. [Google Scholar] [CrossRef] [Green Version]

β_{E} | Mean | Med | SD | CV | Min | Max |

2007 | 1.31 | 1.20 | 0.78 | 0.60 | −0.34 | 4.78 |

2006 | 1.15 | 1.02 | 0.73 | 0.64 | −0.56 | 4.91 |

2005 | 1.14 | 1.03 | 0.75 | 0.66 | −0.62 | 4.60 |

2004 | 1.05 | 0.98 | 0.70 | 0.66 | −0.63 | 4.37 |

2003 | 1.01 | 0.93 | 0.67 | 0.66 | −0.44 | 4.16 |

Mean | 1.13 | 1.03 | 0.73 | 0.64 | −0.52 | 4.56 |

Lev_{1} | Mean | Med | SD | CV | Min | Max |

2007 | 0.77 | 0.43 | 1.14 | 1.48 | 0.00 | 7.94 |

2006 | 0.81 | 0.44 | 1.18 | 1.46 | 0.00 | 7.94 |

2005 | 0.80 | 0.47 | 1.09 | 1.37 | 0.00 | 8.33 |

2004 | 0.88 | 0.50 | 1.23 | 1.40 | 0.00 | 8.59 |

2003 | 0.92 | 0.59 | 1.23 | 1.34 | 0.00 | 7.82 |

Mean | 0.84 | 0.49 | 1.17 | 1.41 | 0.00 | 8.12 |

Lev_{2} | Mean | Med | SD | CV | Min | Max |

2007 | 0.40 | 0.22 | 0.64 | 1.59 | 0.00 | 5.39 |

2006 | 0.46 | 0.24 | 0.75 | 1.65 | 0.00 | 6.12 |

2005 | 0.51 | 0.27 | 0.80 | 1.57 | 0.00 | 6.11 |

2004 | 0.57 | 0.34 | 0.81 | 1.43 | 0.00 | 5.19 |

2003 | 0.59 | 0.37 | 0.78 | 1.32 | 0.00 | 5.95 |

Mean | 0.51 | 0.29 | 0.76 | 1.51 | 0.00 | 5.75 |

Lev_{3} | Mean | Med | SD | CV | Min | Max |

2007 | 1.56 | 1.01 | 1.63 | 1.05 | 0.13 | 9.00 |

2006 | 1.61 | 1.05 | 1.69 | 1.05 | 0.15 | 9.00 |

2005 | 1.60 | 1.09 | 1.59 | 0.99 | 0.13 | 9.00 |

2004 | 1.71 | 1.15 | 1.73 | 1.01 | 0.15 | 9.00 |

2003 | 1.78 | 1.20 | 1.75 | 0.98 | 0.15 | 9.00 |

Mean | 1.65 | 1.10 | 1.68 | 1.02 | 0.14 | 9.00 |

Lev_{4} | Mean | Med | SD | CV | Min | Max |

2007 | 0.82 | 0.55 | 0.99 | 1.21 | 0.04 | 8.44 |

2006 | 0.93 | 0.61 | 1.13 | 1.22 | 0.04 | 9.00 |

2005 | 1.03 | 0.66 | 1.21 | 1.18 | 0.05 | 9.00 |

2004 | 1.13 | 0.80 | 1.24 | 1.10 | 0.06 | 8.20 |

2003 | 1.19 | 0.85 | 1.22 | 1.02 | 0.06 | 7.42 |

Mean | 1.02 | 0.69 | 1.16 | 1.15 | 0.05 | 8.41 |

Panel A | ||||||

Rel T_{C} | 2007 | 2006 | 2005 | 2004 | 2003 | Mean |

Mean | 0.345 | 0.350 | 0.355 | 0.364 | 0.374 | 0.358 |

Med | 0.344 | 0.342 | 0.353 | 0.359 | 0.373 | 0.354 |

SD | 0.073 | 0.078 | 0.083 | 0.085 | 0.073 | 0.078 |

CV | 0.211 | 0.223 | 0.235 | 0.232 | 0.195 | 0.219 |

Min | 0.202 | 0.203 | 0.207 | 0.201 | 0.210 | 0.205 |

Max | 0.562 | 0.567 | 0.569 | 0.595 | 0.567 | 0.572 |

Panel B | ||||||

d | 2007 | 2006 | 2005 | 2004 | 2003 | Mean |

Mean | 0.174 | 0.184 | 0.205 | 0.227 | 0.236 | 0.205 |

Med | 0.162 | 0.164 | 0.200 | 0.182 | 0.140 | 0.170 |

SD | 0.177 | 0.199 | 0.211 | 0.250 | 0.274 | 0.222 |

CV | 1.018 | 1.082 | 1.028 | 1.101 | 1.161 | 1.078 |

Min | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

Max | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

T_{E} | ||||||

Mean | 0.057 | 0.058 | 0.061 | 0.063 | 0.064 | 0.061 |

Med | 0.056 | 0.056 | 0.060 | 0.058 | 0.053 | 0.057 |

SD | 0.020 | 0.022 | 0.024 | 0.028 | 0.031 | 0.025 |

CV | 0.349 | 0.385 | 0.391 | 0.446 | 0.482 | 0.411 |

Min | 0.038 | 0.038 | 0.038 | 0.038 | 0.038 | 0.038 |

Max | 0.150 | 0.150 | 0.150 | 0.150 | 0.150 | 0.150 |

T_{R} | ||||||

Mean | 1.451 | 1.449 | 1.445 | 1.441 | 1.440 | 1.445 |

Med | 1.453 | 1.452 | 1.446 | 1.449 | 1.456 | 1.451 |

SD | 0.031 | 0.034 | 0.036 | 0.043 | 0.047 | 0.038 |

CV | 0.021 | 0.024 | 0.025 | 0.030 | 0.033 | 0.027 |

Min | 1.308 | 1.308 | 1.308 | 1.308 | 1.308 | 1.308 |

Max | 1.481 | 1.481 | 1.481 | 1.481 | 1.481 | 1.481 |

Risk Free Debt Models | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Lev_{2}(Mv) Rel | 2007 | 2006 | 2005 | 2004 | 2003 | Mean | Min | Max | ||

Model (1a) | Perfect capital market | Intercept | 1.130 | 0.929 | 0.933 | 0.860 | 0.872 | 0.945 | 0.860 | 1.130 |

Slope | 0.444 | 0.486 | 0.415 | 0.336 | 0.225 | 0.381 | 0.225 | 0.486 | ||

R^{2} | 0.132 | 0.247 | 0.195 | 0.152 | 0.070 | 0.159 | 0.070 | 0.247 | ||

HO: γ_{1} = 0 | Slope Sig | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |

Model (2a) | Corporate taxes | Intercept | 1.135 | 0.931 | 0.928 | 0.863 | 0.865 | 0.944 | 0.863 | 1.135 |

Slope | 0.644 | 0.720 | 0.651 | 0.507 | 0.378 | 0.580 | 0.378 | 0.720 | ||

R^{2} | 0.134 | 0.247 | 0.192 | 0.144 | 0.074 | 0.158 | 0.074 | 0.247 | ||

HO: γ_{1} = 0 | Slope Sig | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |

Model (3a) | Corporate and Personal taxes | Intercept | 1.135 | 0.932 | 0.929 | 0.864 | 0.866 | 0.945 | 0.864 | 1.135 |

Slope | 0.439 | 0.490 | 0.445 | 0.347 | 0.260 | 0.396 | 0.260 | 0.490 | ||

R^{2} | 0.136 | 0.249 | 0.194 | 0.145 | 0.074 | 0.160 | 0.074 | 0.249 | ||

HO: γ_{1} = 0 | Slope Sig | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |

Risky Debt Models | ||||||||||

Model (1b) | Perfect capital market | Intercept | 1.155 | 0.935 | 0.913 | 0.826 | 0.825 | 0.931 | 0.825 | 1.155 |

Slope | 0.671 | 0.826 | 0.809 | 0.681 | 0.543 | 0.706 | 0.543 | 0.826 | ||

R^{2} | 0.054 | 0.128 | 0.162 | 0.146 | 0.103 | 0.118 | 0.054 | 0.162 | ||

HO: γ_{1} = 0 | Slope Sig | 0.002 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.002 | |

HO: γ_{0} = β_{U}^{*} | Sig | 0.048 | 0.291 | 0.183 | 0.259 | 0.106 | 0.177 | 0.048 | 0.291 | |

HO: γ_{1} = 1 | Sig | 0.523 | 0.892 | 0.606 | 0.289 | 0.030 | 0.468 | 0.03 | 0.892 | |

Model (2b) | Corporate taxes | Intercept | 1.119 | 0.899 | 0.910 | 0.836 | 0.819 | 0.917 | 0.819 | 1.119 |

Slope | 1.086 | 1.273 | 1.130 | 0.900 | 0.806 | 1.039 | 0.806 | 1.273 | ||

R^{2} | 0.095 | 0.200 | 0.173 | 0.147 | 0.114 | 0.146 | 0.095 | 0.200 | ||

HO: γ_{1} = 0 | Slope Sig | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |

HO: γ_{0} = β_{U}^{*} | Sig | 0.074 | 0.390 | 0.154 | 0.444 | 0.366 | 0.286 | 0.074 | 0.444 | |

HO: γ_{1} = 1 | Sig | 0.752 | 0.749 | 0.296 | 0.298 | 0.438 | 0.507 | 0.296 | 0.752 | |

Model (3b) | Corporate and Personal taxes | Intercept | 1.120 | 0.899 | 0.908 | 0.831 | 0.813 | 0.914 | 0.813 | 1.120 |

Slope | 0.818 | 0.966 | 0.863 | 0.696 | 0.631 | 0.795 | 0.631 | 0.966 | ||

R^{2} | 0.090 | 0.192 | 0.170 | 0.148 | 0.117 | 0.143 | 0.090 | 0.192 | ||

HO: γ_{1} = 0 | Slope Sig | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |

HO: γ_{0} = β_{U}^{*} | Sig | 0.090 | 0.499 | 0.265 | 0.269 | 0.243 | 0.273 | 0.09 | 0.499 | |

HO: γ_{1} = 1 | Sig | 0.750 | 0.515 | 0.907 | 0.357 | 0.178 | 0.541 | 0.178 | 0.907 | |

Model (4b) | Corporate and Personal taxes, B. Costs | Intercept | 1.158 | 0.944 | 0.914 | 0.838 | 0.820 | 0.935 | 0.820 | 1.158 |

Slope | 0.928 | 1.121 | 1.062 | 0.775 | 0.517 | 0.881 | 0.517 | 1.121 | ||

R^{2} | 0.051 | 0.127 | 0.191 | 0.218 | 0.209 | 0.159 | 0.051 | 0.218 | ||

HO: γ_{1} = 0 | Slope Sig | 0.002 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.002 | |

HO: γ_{0} = β_{U}^{*} | Sig | 0.057 | 0.326 | 0.342 | 0.334 | 0.256 | 0.263 | 0.057 | 0.342 | |

HO: γ_{1} = 1 | Sig | 0.426 | 0.976 | 0.382 | 0.357 | 0.326 | 0.493 | 0.326 | 0.976 |

2007 | 2006 | 2005 | 2004 | 2003 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Risk Free Debt Models HO: γ_{0} * = β_{U} *; γ_{1} * = β_{U} * | |||||||||||

Model | γ_{0}- β_{U} * | γ_{1}- β_{U} * | γ_{0}- β_{U} * | γ_{1}- β_{U} * | γ_{0}- β_{U} * | γ_{1}- β_{U} * | γ_{0}- β_{U} * | γ_{1}- β_{U} * | γ_{0}- β_{U} * | γ_{1}- β_{U} * | |

1a | 0.194 * | −0.496 * | 0.141 * | −0.302 * | 0.178 * | −0.340 * | 0.191 * | −0.333 * | 0.237 * | −0.410 * | |

Rel T_{C} | 2a | 0.093 | −0.368 * | 0.043 | −0.133 | 0.082 | −0.237 * | 0.064 | −0.160 | 0.103 | −0.282 * |

Abs T_{C} | 2a | 0.098 | −0.393 * | 0.048 | −0.232 * | 0.074 | −0.203 * | 0.099 * | −0.257 * | 0.129 * | −0.358 * |

Rel T_{C} | 3a | 0.182 * | −0.491 * | 0.127 * | −0.289 * | 0.168 * | −0.348 * | 0.145 * | −0.271 * | 0.180 * | −0.343 * |

Abs T_{C} | 3a | 0.187 * | −0.509 * | 0.132 * | −0.310 * | 0.161 * | −0.323 * | 0.182 * | −0.335 * | 0.209 * | −0.397 * |

Mean Risk Free | 0.151 | −0.451 | 0.098 | −0.253 | 0.133 | −0.290 | 0.136 | −0.271 | 0.172 | −0.358 | |

Risky Debt Models HO: γ_{0} * = β_{U} *; γ_{1} * = 1 | |||||||||||

Model | γ_{0}- β_{U} * | γ_{1}- 1 * | γ_{0}- β_{U} * | γ_{1}- 1 * | γ_{0}- β_{U} * | γ_{1}- 1 * | γ_{0}- β_{U} * | γ_{1}- 1 * | γ_{0}- β_{U} * | γ_{1}- 1 * | |

β_{D} = 0.2 | 1b | 0.153 * | −0.165 | 0.072 | 0.027 | 0.091 | −0.041 | 0.077 | −0.165 | 0.106 | −0.325 * |

β_{D} = 0.3 | 1b | 0.113 | 0.082 | 0.025 | 0.329 | 0.075 | 0.106 | 0.034 | 0.051 | 0.058 | −0.134 |

Mean Δ 1b | 0.133 | 0.124 | 0.049 | 0.178 | 0.083 | 0.074 | 0.056 | 0.108 | 0.082 | 0.230 | |

β_{D} = 0.2 | 2b Rel | 0.050 | 0.213 | −0.018 | 0.435 * | 0.025 | 0.214 | −0.013 | 0.197 | 0.003 | 0.052 |

β_{D} = 0.3 | 2b Rel | 0.047 | 0.323 | −0.027 | 0.626 * | 0.005 | 0.428 | −0.043 | 0.453 | −0.032 | 0.305 |

β_{D} = 0.2 | 2b Abs | 0.045 | 0.239 | −0.030 | 0.484 * | 0.004 | 0.327 | 0.010 | 0.083 | 0.019 | −0.018 |

β_{D} = 0.3 | 2b Abs | 0.042 | 0.358 | −0.040 | 0.706 * | −0.016 | 0.565 | −0.026 | 0.343 | −0.020 | 0.237 |

Mean Δ 2b | 0.046 | 0.283 | 0.029 | 0.563 | 0.013 | 0.384 | 0.023 | 0.269 | 0.019 | 0.153 | |

β_{D} = 0.2 | 3b Rel | 0.133 | −0.100 | 0.056 | 0.079 | 0.096 | −0.066 | 0.049 | −0.062 | 0.058 | −0.160 |

β_{D} = 0.3 | 3b Rel | 0.138 | −0.092 | 0.056 | 0.168 | 0.077 | 0.085 | 0.012 | 0.156 | 0.015 | 0.066 |

β_{D} = 0.2 | 3b Abs | 0.128 | −0.079 | 0.044 | 0.124 | 0.076 | 0.021 | 0.071 | −0.144 | 0.075 | −0.215 |

β_{D} = 0.3 | 3b Abs | 0.136 | −0.076 | 0.045 | 0.229 | 0.058 | 0.184 | 0.028 | 0.085 | 0.028 | 0.013 |

Mean Δ 3b | 0.134 | 0.087 | 0.050 | 0.150 | 0.077 | 0.089 | 0.040 | 0.112 | 0.044 | 0.114 | |

β_{D} = 0.2 | Rel T_{C} | ||||||||||

q = 3% | 4b | 0.125 | −0.148 | 0.052 | −0.015 | 0.102 | −0.179 | 0.068 | −0.210 | 0.086 | −0.317 * |

q = 7% | 4b | 0.136 | −0.190 | 0.063 | −0.066 | 0.114 | −0.222 | 0.081 | −0.262 * | 0.100 | −0.369 * |

q = 11% | 4b | 0.147 | −0.230 | 0.073 | −0.114 | 0.125 | −0.262 * | 0.095 | −0.308 * | 0.116 | −0.414 * |

β_{D} = 0.3 | Rel T_{C} | ||||||||||

q = 3% | 4b | −0.009 | 0.309 | −0.071 | 0.336 | 0.029 | −0.013 | 0.050 | −0.241 | −0.024 | −0.072 |

q = 7% | 4b | 0.111 | −0.079 | 0.033 | 0.074 | 0.079 | −0.097 | 0.044 | −0.140 | 0.061 | −0.258 |

q = 11% | 4b | 0.120 | −0.126 | 0.042 | 0.016 | 0.089 | −0.148 | 0.058 | −0.201 | 0.077 | −0.319 * |

β_{D} = 0.2 | Abs T_{C} | ||||||||||

q = 3% | 4b | 0.122 | −0.141 | 0.047 | −0.004 | 0.085 | −0.114 | 0.094 | −0.298 * | 0.104 | −0.375 * |

q = 7% | 4b | 0.134 | −0.186 | 0.059 | −0.060 | 0.098 | −0.165 | 0.107 | −0.341 * | 0.119 | −0.420 * |

q = 11% | 4b | 0.146 | −0.228 | 0.070 | −0.111 | 0.110 | −0.212 | 0.119 | −0.379 * | 0.132 | −0.459 * |

β_{D} = 0.3 | Abs T_{C} | ||||||||||

q = 3% | 4b | 0.098 | −0.016 | 0.016 | 0.160 | 0.050 | 0.036 | 0.052 | −0.164 | 0.061 | −0.249 |

q = 7% | 4b | 0.109 | −0.070 | 0.027 | 0.089 | 0.062 | −0.030 | 0.066 | −0.223 | 0.077 | −0.311 * |

q = 11% | 4b | 0.119 | −0.120 | 0.038 | 0.025 | 0.075 | −0.091 | 0.079 | −0.274 * | 0.092 | −0.365 * |

Mean Δ 4b | 0.115 | 0.154 | 0.049 | 0.089 | 0.085 | 0.131 | 0.076 | 0.253 | 0.087 | 0.327 | |

Mean Risky Models | 0.107 | 0.162 | 0.046 | 0.194 | 0.070 | 0.164 | 0.058 | 0.217 | 0.067 | 0.248 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Aharon, D.Y.; Yagil, Y.
The Impact of Financial Leverage on Shareholders’ Systematic Risk. *Sustainability* **2019**, *11*, 6548.
https://doi.org/10.3390/su11236548

**AMA Style**

Aharon DY, Yagil Y.
The Impact of Financial Leverage on Shareholders’ Systematic Risk. *Sustainability*. 2019; 11(23):6548.
https://doi.org/10.3390/su11236548

**Chicago/Turabian Style**

Aharon, David Yechiam, and Yossi Yagil.
2019. "The Impact of Financial Leverage on Shareholders’ Systematic Risk" *Sustainability* 11, no. 23: 6548.
https://doi.org/10.3390/su11236548