شواهد جدید در مورد تاثیر اهرم مالی بر ریسک بتا: یک روش سری زمانی

The traditional estimation of a project’s cost of capital often requires leverage adjustments to beta. Several researchers have empirically investigated the relationship between the debt/equity ratio (D/E) and beta implied by such leverage adjustments. Typically, this has involved cross-sectional analysis of a sample of U.S. firms in selected industry classifications. The major contribution of the current study is to extend this evidence by investigating the relationship between financial leverage and beta using a time-series approach. This has several advantages over the cross-sectional approach. Our results reveal that while the estimated unlevered beta produced by the time-series approach is quite close to the theoretically implied unlevered beta, the mean difference between the two measures across our sample of 348 U.S. stocks is highly significant. The analysis also reveals that 30–40% of our full sample rejects a theoretical D/E restriction on the time-series model. Moreover, the results suggest that the restriction is much more likely to be rejected for stocks with high debt/equity ratios, which in general have low unlevered betas. Further, there is a considerable cross-sectional variation in the proportion of these rejections across industry groupings. Accordingly, these results suggest that due care needs to be applied when taking the traditional view of delevering beta risk.

In the application of the capital asset pricing model (CAPM) to the estimation of a project’s cost of capital, modern finance theory has been substantially influenced by the work of Hamada (1972), Bowman (1980), Conine (1980) and others, regarding the need to make leverage adjustments to beta, under certain circumstances.1 In a recent paper, Marston and Perry (1996) empirically investigate the relationship between financial leverage and beta. Their approach involves a series of cross-sectional analyses across a sample of U.S. firms in selected two-digit and four-digit SIC industry classifications. They investigate three subperiods over the interval 1974–1988 and compare the regression results to those predicted by the Hamada (1972) leverage adjustment. Generally, their results indicate that the techniques which are commonly applied for the purposes of unlevering beta, tend to over-penalize beta when higher levels of financial leverage are being utilized. The current study aims to extend the evidence contained in the existing literature by investigating the impact of financial leverage on beta using a time-series approach. This delivers several major advantages over the cross-sectional approach used in all previous work. First, and perhaps the primary advantage, is that the time-series approach provides a much stronger control for operating or business risk, as it avoids having to make a strong assumption of constant systematic business risk across a chosen industry grouping (see Marston & Perry, 1996). Instead, we make the more reasonable assumption that systematic operating or business risk is constant for a given firm (although even this assumption can be tested and relaxed if necessary). A second important advantage of our time-series approach is that it delivers a level of statistical power not possible in the cross-sectional studies. As discussed later, our sample involves 348 stocks which represents a much larger sample than is allowed by industry regressions or by the matched-pair sample approach of Marston and Perry (1996), for example. Thus, with more observations, the current study has more power to reject the hypothesis that the difference between the empirical and the implied theoretical unlevered betas is equal to zero. Third, following on from the preceding point, our time-series approach allows the examination of a number of industries that would be precluded in the cross-sectional approach due to an insufficient number of firms within the industry. A fourth advantage of our time-series methodology is that it allows for the time variation in debt/equity (D/E) ratios, which has been found to be quite substantial for most companies over certain periods in their life history. The notion that the time variation in the D/E ratio causes time variation in beta risk and risk generally, is widely cited in the finance literature (see, for example, Black, 1976 and Christie, 1982). Indeed, the relatively recent proliferation of generalized autoregressive conditional heteroskedasticity (GARCH) model applications and, in particular, the popularity of the asymmetric variations thereof (for example, see Nelson, 1991; Glosten et al., 1993 and Engle and Ng, 1993) have invoked leverage arguments to explain their empirical success. A fifth advantage is that, unlike Marston and Perry (1996) and others, financial firms can be validly included in this analysis, despite their extreme values of D/E, without compromising the homogeneity of the sample. This is so because the time-series approach means that the results of such extreme D/E ratio firms are produced independently of the results of firms with less extreme financial leverage. Accordingly, the evidence we provide considerably broadens the scope of our understanding in this area. A sixth advantage relates to the fact that an unlevered beta can be estimated directly using data for a single company in isolation of all other companies (except for the need to utilize a market index return). Moreover, the estimated unlevered beta can be used in conjunction with the time-series of D/E to generate a series of time-varying (levered) equity betas. A seventh and final advantage of the time-series approach is that it gives new insight to an issue that has traditionally been tested in a cross-sectional way. 2 In general, our results reveal that while the estimated unlevered beta produced by the time-series approach is quite close to the theoretically implied unlevered beta, the mean difference between the two measures across the sample of 348 U.S. stocks is highly significant. Further, our analysis also reveals that 40% (29.3%) of our sample rejects a theoretical restriction on the time-series model in the no-taxes (tax-adjusted) setting. Moreover, the results suggest that the restriction is much more likely to be rejected for stocks with high and variable debt/equity ratio’s which in general have low unlevered betas. Further, there is considerable cross-sectional variation in the proportion of these rejections across industry groupings. Hence, the principal message that this study delivers is the need for particular care to be taken in these ‘high-risk’ situations when applying the unlevered beta approach. Specifically, our analysis generally re-enforces the implication of Marston and Perry (1996), namely, that we must be careful when using traditional techniques so as not to over-penalize beta in situations of high leverage. The remainder of this paper is organized as follows. In Section 2, the empirical framework is briefly outlined, while Section 3 presents and analyses the results. The final section presents a summary and conclusion

A considerable volume of empirical research has investigated the relationship between the debt/equity ratio and beta, encouraged by the theoretical work produced by Hamada (1972), Bowman (1980), Conine (1980) and others. Typically, such empirical analysis, most recently represented by Marston and Perry (1996), has adopted a cross-sectional approach. Generally, their results indicate that the techniques which are commonly applied for the purposes of unlevering beta, tend to over-penalize beta when higher levels of financial leverage are being utilized. The major contribution of the current study is to extend this evidence by investigating the impact of financial leverage on beta risk using a time-series approach. This time-series methodology, which has never before been utilized, offers several advantages over the widely employed cross-sectional approach. First, and perhaps most important, is that the time-series approach provides a much stronger control for operating or business risk, as it avoids strong assumptions of constant systematic business risk across a chosen industry grouping. Second, the time-series approach delivers a level of statistical power not possible in the cross-sectional studies. Third, our time-series approach allows the examination of a number of industries that would be precluded in the cross-sectional approach due to an insufficient number of firms within the industry. Fourth, it allows for the time variation in debt/equity (D/E) ratios, which have been found to be quite substantial for most companies over certain periods in their life history. Fifth, financial firms can be validly included in this analysis, despite their extreme values of D/E. A sixth advantage relates to the fact that an unlevered beta can be estimated directly using data for a company in isolation of all other companies. A final advantage of the time-series approach is that it gives a new perspective on an issue which has traditionally been tested in a cross-sectional way. Our study reveals several principal findings. First, we find that while the estimated unlevered beta produced by the time-series approach is quite close to the theoretically implied unlevered beta, the mean difference between the two measures across the sample of 348 U.S. stocks is highly significant. Second, the analysis also reveals that 40% (29.3%) of our sample rejects a theoretical restriction on the time-series model in the no-taxes (tax-adjusted) setting. Third, the results suggest that the restriction is much more likely to be rejected for stocks with high and variable debt/equity ratio’s, which in general have low unlevered betas. Further, there is a considerable cross-sectional variation in the proportion of these rejections across industry groupings. Fourth, we find that in the context of testing within a given four-digit SIC grouping, the hypothesis of equality between the unlevered beta risk of individual companies was soundly rejected. Accordingly, the major thrust of our analysis can be stated as follows. First, given that we find a high proportion of our sample supports the time-series leverage restriction, we can conclude that making such leverage adjustments is in general justified. Second, the above conclusion warrants a careful qualification as our analysis suggests that traditionally applied adjustments work reasonably well in some circumstances but not universally so. Specifically, it is found that only for relatively low D/E (in the order of 1:1 or below), do the leverage adjustments of beta risk seem well specified. Hence, our results suggest that due care needs to be applied when taking the traditional view of delevering beta risk. Moreover, this finding is important because it serves to confirm and re-enforce the conclusion drawn by Marston and Perry (1996) that traditionally applied leverage adjustments tend to over-penalize beta, particularly when high levels of financial leverage are being employed. A third and final major thrust of our study is that given the appreciably greater support for the tax-adjusted leverage adjustment, our findings commend the use of taxation-adjusted techniques. While this may at first seem a trivial confirmation of long-held wisdom, it should be remembered that one version of the equilibrium outcome of the Miller (1977) model (that incorporates both corporate and personal taxes), effectively produces an outcome ‘as if’ a no-taxes scenario was in force. Thus, empirical discrimination between these alternatives is important.