...product-market well as capital-market imperfections that give rise to well-founded concerns with risk management and capital allocation; (ii) some, but not all, of the risks they face can be frictionlessly hedged in the capital market; and (iii) the distribution of their cash flows may be asymmetric, which alters the demand for underwriting and hedging. We show these features result in three-factor model that determines the optimal pricing and allocation of risk and capital structure of the firm. This approach allows us to integrate these features into: (i) the pricing of risky investment, underwriting, reinsurance, and hedging; and (ii) the allocation of risk across all of these opportunities, and the optimal amount of surplus capital held by the firm.

INTRODUCTION

The cost of bearing risk is a crucial concept for any corporation. Most financial policy decisions, whether they concern capital structure, dividends, capital allocation, capital budgeting, or investment and hedging policies, revolve around the benefits and costs of a corporation holding risk. The costs are particularly important for financial service firms, where the origination and warehousing of risk constitutes the core of value added. And because financial service firms turn their assets more frequently than nonfinancial firms, risk pricing and repricing are needed more frequently.

Insurers and reinsurers are an important class of financial firm. They encounter financial risk in their underwriting and reinsurance portfolios, as well as in their investment and hedge portfolios. Often they have a large number of clients who view their insurance contracts as financially large and important claims. Two basic features make insurers and reinsurers especially sensitive to the costs of holding risk.

The first feature is that customers--especially retail policyholders--face contractual performance risks. Premiums are paid, and thereafter policyholders worry whether their future policy claims will be honored swiftly and fully. Customers are thought to be more risk averse to these product performance issues than are bondholders. There are several mechanisms for this greater risk sensitivity, some behavioral and others rational.

The behaviorist story is formalized in Wakker, Thaler, and Tversky (1997). They argue that "probabilistic insurance"--the name given by Kahneman and Tversky (1979) to an insurance contract that sometimes fails to pay the contractually legitimate claims of the insured--is deeply discounted by an expected utility maximizer who pays an actuarially fair premium. They also provide survey evidence that the discount is striking in size: in comparison to a contract with no default risk, a contract with 1 percent independent default risk is priced 20-30 percent lower by survey participants.

The rational argument owes most to Merton (1993, 1995a,b). He argues that customers of financial firms value risk reduction more highly than do investors because customer costs of diversifying are higher. Insurance contracts are informationally complex documents and claims payments often require customer involvement. Buying from a single insurer reduces costs. Furthermore, insurance pays off when the marginal utility of customer wealth is high. If absolute risk aversion is declining in wealth, as many suspect it is, then a customer will be more averse to an insurer's failure to perform than to a debtor's failure to perform, even if the performance failure is of equivalent size. Higher costs of diversification and greater impact on utility therefore makes risk aversion higher for customers than investors.

This motivates our assumption that when an insurer's financial circumstances decline, customer demand falls. Indeed it falls more than investor demand. There is evidence in the literature to support this view of "excess" sensitivity. Phillips, Cummins, and Allen (1998), for example, estimate directly price discounting for probability of insurer default. They find discounting to be 10 times the economic value of the default probability for long-tailed lines and 20 times for short-tailed lines. These numbers are too large to be consistent with capital markets pricing. (1) In this article, we take the excess sensitivity hypothesis at face value and trace out the implications for firm value-maximization.

There is a second feature that makes insurers and reinsurers especially sensitive to the costs of holding risk: they often face negatively asymmetric or skewed distributions of outcomes. Many insurance and reinsurance portfolios contain important exposures to catastrophic risks--natural and man-made perils of sufficient size and scope to generate correlated losses across large numbers of contracts and policies. Such events can be particularly damaging to insurers and reinsurers and can be expected to have first-order effects on risk allocation, pricing, and capital structure decisions.

Surprisingly, there has been relatively little work that demonstrates how the shape of the payoff distribution affects key decisions. (2) Perhaps one reason is that an infinite number of moments is required to fully describe a distribution's shape. Another is that higher-order moments appear only rarely in the capital markets literature. This is because discrete-time asymmetric distributions can be derived from continuous-time normally distributed innovations. We adopt here a functional approach to describing asymmetric distributions, treating them as functional transformations of symmetrically distributed normals. This allows us to generate general pricing and allocation results without having to specify moments. In this way, this article takes a step toward explicitly incorporating asymmetrically distributed risks in formal corporate pricing and allocation metrics.

But neither the sensitivity of customer demand nor the asymmetric nature of underwriting exposures can invalidate the Modigliani-Miller irrelevance theorems. (3) A firm with perfect access to capital could fund investment opportunities using any combination of instruments. It could raise external finance at the same cost regardless of the strength of its capital base. It could not add to its market value by managing its risk, holding different amounts of capital, or pricing customer risk exposures differently from the outside capital market. Thus, if M&M is to fail, some form of capital-market imperfection is needed. (4)

The approach we take here follows Froot and Stein (1998). It employs two realistic capital-market imperfections. The first is that internal capital is assessed a "carry" charge. Carry costs imply that, all else equal, an additional dollar of equity capital raises firm market value by less than a dollar. The most straightforward source of carry costs would be corporate income taxation. Taxes on additional interest are zero if the dollar is instead deposited in a mutual fund or other pass-through savings vehicle. Another source is agency costs: perhaps management will not use the dollar in shareholders' best interest. Both sources suggest that the market should place limits on how much equity capital a firm can feasibly raise. Indeed, the market does this. (5)

The second imperfection is an "adjustment" cost of capital. This is a standard approach, used in models of financing under asymmetric information (e.g., Myers and Majluf, 1984), where raising external funds becomes expensive when existing capital is low. It provides another motivation--in addition to the product-market and asymmetry concerns above--for the firm to get around paying carry costs by holding too little capital. Following Froot, Scharfstein, and Stein (1993), if the firm allows internal funds to run down, it will increasingly have to choose between cutting highly rewarding investments or incurring the high costs of external finance. In the insurance and reinsurance industries, adjustment costs of capital appear most clearly in the aftermath of catastrophic events, when depleted industry capital results in high prices and reduced availability of insurance and reinsurance. (6)

With capital-market imperfections, product-market sensitivity to risk, and exposure asymmetry, the firm exhibits strong valuation effects from risk and capital management. As one might expect, these latter factors tend to make the insurer or reinsurer more conservative in accepting risk, more eager to diversify investment and underwriting exposures, more aggressive in hedging, and more willing to carry costly equity capital. As in Merton and Perold (1993) and Myers and Read (2001), our framework jointly and endogenously determines optimal hedging, capital budgeting, and capital structure policies. (7)

We find that product-market considerations contribute additively to capital-market distortions in reducing the desire to hold risk and to price risk at fair market levels. Product-market considerations also tilt the optimal level of capital and surplus toward higher levels. In addition, we prove the firm will price distributional asymmetries in payoffs which are unpriced in the capital market. Negatively skewed exposures impose costs that in general are higher than those of positively skewed exposures, and this causes firms to seek more aggressive reinsurance and hedging and less aggressive and more diversified underwriting and investment.

We also demonstrate that the capital- and product-market imperfections bias firms toward removing risks. Firms maximize value by removing a risk source completely unless: (i) illiquidity makes the risk costly to trade or (ii) the firm has expertise in that risk source that allows it to outperform. Thus, even though the firm's hurdle for bearing negatively asymmetric insurance exposures is higher than that of the capital market, insurers nevertheless derive their value by earning returns on insurance exposures that, after acquisition costs, exceed required capital market hurdles. This has the normative implication that financial intermediaries should shed all liquid risks in which they have no ability to outperform and devote their entire risk budgets toward an optimally diversified portfolio in exposures where they have an edge. For insurers specifically, this means warehousing insurance risks, where they arguably have informational advantages, and shedding all others. Their warehoused insurance risks will generally be those that are also illiquid--after all, if any were frictionlessly available, shareholders could directly provide their own capital to back them, and average returns would be competed down to rates required by the capital market. Thus, insurers also generally should not hold perfectly liquid insurance risks unless they have private information that allows them to cherry pick among them. This is all the more true because of the negative skew in "long'-position insurance returns.

In practice, of course, insurance and reinsurance companies, do not seem to eliminate all liquid exposures. While beyond the scope of this article, the reasons for this might be several. One is that our assumed capital- and product-market imperfections do not exist, or have limited financial impact. Most articles do not dispute the existence of at least some of these imperfections, though their exact specifications are a matter of debate. (8) A second potential reason is that as financial investors, insurers and reinsurers have a real or perceived ability to outperform capital market hurdles. Realized insurer returns on their investment portfolios probably do not provide evidence that this ability is real, Berkshire Hathaway notwithstanding. This leaves corporate overconfidence concerning capital market investment opportunities as a possible explanation. This is an area with interesting new evidence. (9)

THE MODEL: TIMING AND ASSUMPTIONS

The model, which follows Froot and Stein (1998), has three time periods, 0, 1, and 2. In the first two periods, time and 1, the insurer chooses its capital structure and then makes underwriting and hedging decisions. These two periods highlight the fact that consumers will pay less for an insurance contract written by a firm with low surplus with given risk or by a firm with more negatively asymmetric risk. The last period closes the model by allowing the insurer to raise additional capital after paying (or defaulting on) its losses. At this stage additional frictional costs of raising capital are added.

Time 0: Insurer Capital Structure Decision

At time 0, the insurer chooses how much equity capital, K, to hold. The capital goes toward financing various risks, in both investments and underwriting. There are, however, distortions that make the use of capital expensive. First are the deadweight costs of carrying capital, which can be thought of as arising from corporate income taxes or from agency costs associated with shareholders' imperfect controls over management. These costs make it expensive for a firm to carry large amounts of capital. We summarize these deadweight costs as [tau]K, where...

NOTE: All illustrations and photos have been removed from this article.




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