Managing the Invisible: Identifying Value-Maximizing Combinations of Risk and Capital

Abstract

This article demonstrates the linkage—often asserted but seldom described—between Enterprise Risk Management (ERM) and maximizing a firm's value. I show that knowing a firm's aggregate risk exposure (via ERM), when combined with a valuation model like the one presented here, can enable the firm's managers to identify and choose value-maximizing combinations of risk and capital. Using value maximization as the criterion for choosing a firm's capital structure is quite distinct from rules of thumb that CFOs often use for such decisions. The valuation model shows that increasing an insurer's surplus from an initially low level typically increases the present value of future cash flows that take into account the probability of impairment from extreme losses. In contrast to traditional literature on the risk of ruin, impairment here is taken to mean a loss of creditworthiness such that the firm's business model is no longer sustainable, whether or not the firm is solvent. However, beyond a certain optimal level relative to a firm's risk, further increases in surplus actually reduce a firm's value added measured in this fashion. Sensitivity analyses presented here show how these conclusions are affected by changes in the values of crucial variables. In particular, the article shows how managers can use this model to identify specific actions that their firm can take to increase its value added, and it emphasizes the practical importance of making a firm's value both visible and manageable.

Acknowledgments

The original version of this article was presented at the CAS/SOA/PRMIA Enterprise Risk Management Symposium in April 2006, where it received the first ERM Research Excellence Award, an annual prize established by The Actuarial Foundation. I am indebted to Richard Goldfarb and Richard Derrig for valuable discussions and encouragement in preparing the original version. Since then, stimulated by discussions with David Ingram, Daniel Bar Yaacov, and Chuck Thayer, and especially by an anonymous referee's superb comments and suggestions, I have substantially extended it to encompass new results. As with all my work, SDG.

Notes

The real significance of these authors’ path-breaking work was its use of arguments based on arbitrage—arguments that have fundamentally affected the evolution of finance as well as of financial securities and markets. For succinct reviews of portions of the voluminous relevant literature see Rubinstein (2003), Modigliani (1988), and Giesecke and Goldberg (2004).

Examples of this literature include Hancock, Huber, and Koch (2001), Chandra and Sherris (2007), Yow and Sherris (2007, 2008), Smith, Moran, and Walczak (2003), Exley and Smith (2006), and Major (2009a, 2009b), who further extend this emerging frictional cost framework to considerations of pricing, optimal capitalization, and firm value.

A refreshingly frank admission is found in Copeland, Weston, and Shastri (2005), p. 611: “How Does a Practitioner Use the Theory to Determine Optimal Capital Structure? The answer to this question is the Holy Grail of corporate finance. There is no completely satisfactory answer.”

I am indebted to Richard Goldfarb for his numerous insights on this topic.

In finance, the phrase “value of the firm” refers to the value of its assets, not the value of its equity. Here, by contrast, I will use the phrase to mean the value of a firm to its shareholders, as imperfectly reflected in its market capitalization—the aggregate value of its stock—either as observed or as estimated by the model presented later.

For a critique of and correction to that approach, see Panning (1994, 2006).

The experience described here has also been discussed in Panning (2003a).

Growth is an issue with numerous facets that cannot be adequately treated in the space available and so will be treated in a subsequent article. One well-known issue is that high growth rates cannot be sustained indefinitely. Dealing with this issue requires a more complex model than the one presented here.

For an earlier model of franchise value see Panning (1994), which focused on the risk to franchise value of changes in interest rates. Unfortunately, the concluding equation of that paper is marred by an egregious printing error. The correct equation is readily derived from the two that precede the final one. Panning (2006) is a briefer and more sophisticated treatment of that topic, which corrects that error but likewise excludes consideration of default risk. Hancock, Huber, and Koch (2001), Smith, Moran, and Wolczak (2003), and Exley and Smith (2006) present results very similar to some of those presented here and that are based on current financial theory and its rather strong assumptions rather than on the simpler approach adopted here. Fernandez (2002) provides a thorough survey of the huge variety of valuation approaches that have been proposed or are in use. Damodaran (2005) provides a survey of rival approaches and associated evidence. Leibowitz (2004) presents a synthesis of his earlier work on estimating franchise value, and Koller, Goedhart, and Wessels (2010) provide textbook models for valuing corporations. Avanzi (2009) provides a valuable review of the extensive literature on dividend discount models and the strategies they imply, and Dickson (2005) surveys the huge relevant actuarial literature on the risk of ruin and its implications for firm strategy and valuation. The links between corporate strategy, risk, and valuation are explored in books by Coleman (2009), Pettit (2007), Schroeck (2002), Segal (2011), and Woolley (2009). Major (2011) provides an excellent overview of the principal approaches to modeling the effect of risk on valuation. Venter and Underwood (2010), Bodoff (2011), and Ingram and Bar Yaacov (2012) extend the model presented here to strategy choice and risk hedging. Finally, articles such as Brockman and Turtle (2003) and Episcopos (2008) present models for pricing corporate securities based on a barrier option pricing framework, which has important similarities to the model presented here.

See Boland (2007), p. 48, for details.

One additional implication is worth pointing out. Expected losses conditional on the firm's survival are necessarily lower than unconditional expected losses. Consequently, observed rates of return on premiums or on surplus are likely to be biased upwards. Firms that experience extremely high losses will be reorganized and disappear from view. So unless the underlying data-gathering process is extremely thorough, both the industry and the firms within it will appear to be more profitable than underlying risk exposures would warrant. A similar phenomenon occurs in the investment world, where funds that significantly underperform market averages are liquidated or merged, and statistics concerning their poor results disappear with them. Given the cyclical nature of property-casualty insurance, such upward bias could significantly distort the view and actions of both regulators and investors. Seminal papers on survival bias include Brown et al. (1992) and Brown, Goetzmann, and Ross (1995).

See Elton et al. (2001) for an analysis of the components of a risk premia on bonds, Derrig and Orr (2004) for a comprehensive review of the empirical literature on the equity risk premium, and Eling (2012) for a compendium of post-2004 research on risk premia.

The numerical precision of the results shown in Table 2 is misleading, since the precision of a model's results depends upon the correctness of the valuation model and the precision with which its inputs are measured. The several decimal places shown for the values in Tables 1 and 2 are intended to enable readers to check the model and are not indicative of the precision with which the model's inputs can actually be estimated or its results applied to real firms. I note, however, that most of the key inputs to the model can be reasonably measured or estimated. Consequently, it would not be unreasonable to conclude that, for this hypothetical firm, optimal surplus is likely to be closer to 80 than to 50 or 110.

Optimal surplus is not always positive. The model implies that there are certain circumstances—partly defined by combinations of expected loss and standard deviation of loss—in which optimal surplus is zero. In other words, there are boundaries beyond which risks are, in effect, economically uninsurable or expected profits are so low as to preclude a viable business model.

Some of the ideas stated here draw on Panning (2003a, 2003b).

This definition is quite similar to that of the CAS Advisory Committee on ERM: “ERM is the process by which organizations in all industries assess, control, exploit, finance, and monitor risks from all sources for the purpose of increasing the organization's short and long term value to its stakeholders.”