Estimating the cost of capital with basis assets
Highlights
► To estimate the cost of capital, risk-equivalent classes are required. ► Modigliani and Miller (1958) use industry groupings to form risk classes. ► Ross (1988) argues for risk classes according to historical risk/return instead. ► We show returns based risk classes improve cost of capital estimates. ► Such cost of capital estimates use risk-class membership not asset pricing models.
Introduction
A key assumption of Modigliani and Miller (1958) is that firms can be divided into homogeneous “risk-equivalent” classes. They argue that firms belong to the same risk class when their cash flows are correlated and that therefore a firm’s industry is a reasonable proxy for its risk class. The authors use risk-equivalent classes as a device to argue that two identical firms in the same risk-equivalent class with the same cash flows must have the same value, even if their capital structure differs.1
Ross (1988) argues that given the deus ex machina of modern arbitrage pricing, the notion of Modigliani and Miller’s (1958) risk class is superfluous. He then resurrects the risk class concept from a modern perspective: As long as a group of firms have the same systematic risk exposure to exogenous economic shocks, they belong to the same risk class, irrespective of whether their cash flows are correlated or not. In other words, we can use returns rather than cash flows (or other accounting information) to group firms into risk equivalent classes.
Consistent with Ahn et al. (2009), we call risk classes constructed using returns: basis assets. The power of basis assets is that they effectively make asset pricing models and industry groups redundant when estimating the cost of capital. This insight is significant. Using industry groups as a proxy for risk equivalent classes is somewhat controversial (see literature review) despite the seminal work of Modigliani and Miller (1958). Furthermore, with regards to the use of asset pricing models to estimate the cost of capital, Ross (1988, p. 130) argues that the concept of risk class has great power since it abstracts “the determination of the cost of capital from an allegiance to one or another of the competing asset pricing models” (italics added).2
Ross’s (1988) thesis is that the cost of capital can be directly estimated from basis assets. Grouping firms endogenously into risk classes that are exposed to a single systematic risk means that all those firms must earn the same commensurate systematic return.3 To estimate the commensurate systematic return, no industry grouping or asset pricing model is required: Using knowledge of a firm’s risk class membership, one can obtain the ex post average return of all firms in the same risk class and use it as the ex ante return prediction, that is, the cost of capital estimate for the firm.
We introduce for the first time a theoretically – and empirically – appropriate way to estimate Ross’s (1988) modern risk equivalent class. Our aim is to “operationalize” Ross’s conceptual framework and determine the basis assets to obtain better cost of capital estimates. To do so, we use a statistical clustering approach, namely, the generalized basis assets algorithm (GBA), to group firms into risk-equivalent classes using firm returns. This procedure was first used by Brown and Goetzmann (1997) as a returns-based approach to determining style classification in a mutual funds context. Brown et al. (2008) extended it to grouping stocks using returns.
Ultimately, this work compares the efficacy of Ross’s (1988) modern risk class concept (implemented with basis assets using the GBA) with Modigliani and Miller’s (1958) traditional risk class concept (implemented using industry groupings). We demonstrate empirically that the GBA provides greater risk class homogeneity, leading to more accurate and precise estimates of the cost of capital, when compared with standard industry groupings. We argue that these are significant findings since they provide researchers with an improved method of grouping risky assets and articulating the relation between class membership and returns. Consistent with Ross’s (1988) conception of risk class, our approach permits us to determine the discount rate appropriate to each risk class without relying on either an ad hoc asset pricing model (Cochrane, 2011, p. 1068) or industry groupings (which are motivated by economic activity rather than systematic risk exposure). Ultimately, our results represent an important step in generating more accurate and precise cost of capital estimates.
Section snippets
Literature review
The theoretical concept of a homogeneous risk class plays a crucial role in the seminal work of Modigliani and Miller (1958) and Miller and Modigliani (1966) on the cost of capital. To obtain a firm’s present value, the authors assume the firm’s income is in perpetuity and value it accordingly, dividing it by the discount rate. Then, by analogy, they extend this approach to the case of a firm with uncertain income by dividing the expected level of earnings by a cost of capital specific to the
Data
We obtain data from the merged database of the Center for Research in Security Prices (CRSP) and Compustat8 and Kenneth French’s online data
Methodology
This work operationalizes the approach of Ross (1998) to estimate the classic Modigliani–Miller (1958) risk equivalent class using the GBA procedure. Ross (1988) argues that it is possible to generalize the notion of risk class introduced by Modigliani and Miller (1958) so that firms with the same systematic risk exposure are grouped together, irrespective of their idiosyncratic risks.
The theoretical underpinnings for Ross’s (1988) risk equivalent class follows. Theoretically, a firm’s return
Results
Modigliani and Miller (1958) argue that industry acts as a proxy for equivalent risk classes due to cash flows being correlated from intra-industry firms. On the other hand, Ross (1988) modernizes the concept and argues that only systematic risk exposure is important in forming equivalent risk classes. We test both approaches next.
We claim that the GBA approach is superior to traditional industry-formed risk classes if, for any given basis asset, the returns of all the firms in the basis asset
Conclusion
We have shown that the power of basis assets is that they have the potential to effectively make asset pricing models and industry groups redundant when estimating the cost of capital. Risk homogeneous classes required to estimate the cost of capital accurately may be contaminated when using industry groups. Current industry classification systems generate industry groups that exhibit a high degree of intra-industry return heterogeneity, which implies heterogeneity in the cost of capital for
Acknowledgment
The first two authors would like to acknowledge the Australian Research council Grant: DP110103260.
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