Value from Hedging Risk with Reinsurance

Transcription

1 Value from Hedging Risk with Reinsurance Nicos A. Scordis 1 and Petra Steinorth 2 Abstract: Reinsurance is a transaction insurance firms use to hedge risk. Existing studies have only investigated the demand for reinsurance. Thus, we do not have direct evidence on whether the use of reinsurance creates value. Our study provides this evidence. We find a positive relation between the use of reinsurance and value. This relation is nuanced. Our results suggest that shareholders fully recognize the value of hedging only in the absence of noise in the firm s environment. Our results also suggest that the use of hedging creates value for shareholders because hedging may be a less expensive substitute to holding capital. H INTRODUCTION edging risk through the purchase of reinsurance is a trade off between its costs and its benefits. Borch (1961:35) was the first to observe that when an insurance company reinsures a part of its portfolio, it buys security and pays for it. The company will forgo a part of its expected profits in order to reduce the possibility of inconvenient losses. The management of the company has to weigh expected profit against possible loss. This trade off between increased safety and increased costs raises the question of whether the use of reinsurance enhances shareholder value. We investigate this question and make two contributions to the literature. First, we contribute to the insurance literature as we establish an empirical link between the use of reinsurance and value. While such link is indirectly implied in the literature, it has not been directly tested before. This is important in light of Solvency II, a uniform system of insurance 1 St. John s University, School of Risk Management, 101 Murray Street, New York, NY 10007, scordisn@stjohns.edu 2 St. John s University, School of Risk Management, 101 Murray Street, New York, NY 10007, steinorp@stjohns.edu 210 Journal of Insurance Issues, 2012, 35 (2): Copyright 2012 by the Western Risk and Insurance Association. All rights reserved.

2 VALUE FROM HEDGING RISK WITH REINSURANCE 211 regulatory standards adopted by the European Union, and efforts to recognize the current risk based capital solvency system in the United States, as functionally equivalent. This regulatory regime will fully recognize the effect of reinsurance on risk reduction and will allow the use of reinsurance to substitute for capital. Such substitution has implications for the future as today s capital management decisions will influence future solvency capital requirements. In turn, today s capital management decisions influence future growth. Second, we contribute to the risk management literature as we clarify the available empirical results of the relation between hedging risk and value. Four studies that have directly investigated the relation between hedging and value are Allayanis and Weston (2001), Carter et al. (2006), Jin and Jorion (2006), and Mackay and Moeller (2007). These studies use Tobin s q as their measure of value. The use of Tobin s q as a measure of value, however, creates ambiguity in the interpretation of their results. We explain why later in our paper. Our study proceeds to explain how the use of reinsurance may add value, and then to review the empirical literature on the relation between hedging and value. In the section after that we explain our data. We then follow with our analysis section. We conclude with a non technical summary and a discussion of our results. THE POSSIBLE VALUE OF REINSURANCE We do not know whether the purchase of reinsurance creates value for shareholders because existing empirical studies examine only why insurance firms demand reinsurance. Regardless of what drives demand for reinsurance, its use creates value only when shareholders perceive that its benefits outweigh its costs. Results vary across the empirical literature on the demand for reinsurance. For example, eight studies (Mayers and Smith, 1990; Adams, 1996; Garven and Lamm Tennant, 2003; Shortridge and Avila, 2004; Cole and McCullough, 2006; Powell and Sommer, 2007; Adams et al., 2008; Lei and Schmit, 2010) find that larger insurance firms use less reinsurance while four studies (Hoerger, Sloan, and Hassan, 1990; Adiel, 1996; Wang et al., 2008; Kader et al., 2010) find no relation between the size of insurance firms and their use of reinsurance. Furthermore, Shiu (2011), depending on which of the several econometric models he uses, finds both a positive and a negative relation between the size of insurance firms and their use of reinsurance. We believe it is beyond the scope of this paper to review the empirical literature on the demand for reinsurance. It is sufficient to recognize that all authors who investigate such demand

3 212 SCORDIS AND STEINORTH conclude that individual insurance subsidiaries with a higher likelihood of bankruptcy purchase more reinsurance. Eling and Schmeiser (2010), however, provide a non technical explanation of why financial events at individual insurance subsidiaries do not faithfully transmit to the insurance holding company level. Thus, preventing bankruptcy of a downstream insurance company, which directly benefits its policyholders, its managers, and its regulators, is not the same as increasing value for the diversified owners of the upstream insurance holding firm. One way the bankruptcy reduction effect of reinsurance can benefit shareholders is by enabling the now safer firm to take on more debt. One way shareholders benefit from debt is through the creation of tax shields (Leland, 1998; Graham and Rogers, 2002). In the case of insurance firms, debt often takes the form of selling more insurance policies, which creates tax deductible liabilites. Staking and Babbel (1995) explain that insurers effectively borrow in the less efficient insurance market, rather than in the capital markets, by selling insurance policies priced at the risk free rate of interest and investing the premiums received. Premiums from policyholders, and investment income from the premiums, are collected into a dedicated, tax deductible account, which the insurer uses to pay losses back to the policyholders. Insurers call this liability account the loss reserve. Ferrari (1968) explains that disbursements to policyholders from this loss reserve are the implicit interest policyholders, as a group, receive. The limiting factor on how many policies the insurer can issue, and thus how much capital it can channel to investments, is the amount of unencumbered capital it holds beyond its loss reserve. Insurers hold their unencumbered funds in a surplus account. Regulators and rating agencies monitor the adequacy of the loss reserves and impose minimum surplus levels according to the overall risk of an insurer. Thus, as an insurer issues more policies, or the perceived risk of its policies increases, the insurer transfers funds from its surplus account to its loss reserve account (which is tax deductible) if it wants to avoid regulatory scrutiny and/or a rating downgrade. The more surplus insurers hold, however, the less money they can pay out to their shareholders. The purchase of reinsurance lessens the need for surplus. Highly volatile cash flows, at times, result in insufficient cash to fund the operations of a firm. Even if cash shortfalls from a volatile cash flow do not result in bankruptcy, as Mayers and Smith (1982) explain, stakeholders will demand low prices to contract with a firm facing an increased probability of default. In the particular case of insurance firms, Doherty and Tinic (1981) posit that the purchase of reinsurance may in fact increase the price policyholders are willing to pay to contract with the insurance firm, as the use of reinsurance lowers the cedent s probability of default. This supposition is consistent with the empirical results of Sommer (1996) and of

4 VALUE FROM HEDGING RISK WITH REINSURANCE 213 Phillips et al. (1998), who conclude that insurance prices are high when the insurer s likelihood of default is low. Outsiders need information in sufficient detail in order to calculate the true value of the firm; otherwise, they tend to undervalue the firm. An observable decision, such as the purchase of reinsurance, which smooths some aspects of the firm s cash flow, allows outsiders to more easily infer the firm s true value. It may also be that reinsurance is purchased when information asymmetry is low rather than in order to reduce information asymmetry. The greater the information asymmetry between the insurer and outsiders, the higher is the effective price imposed by the reinsurer on the ceding insurer. Jean Baptiste and Santomero (2000) explain that eliminating the information asymmetry premium results in a lower effective reinsurance price, which then results in higher reinsurance purchases. Thus, as Garven and Lamm Tennant (2002) point out, high use of reinsurance may be indicative of low information asymmetry. Scordis et al. (2008) explain that if there is a lot of noise in an insurer s performance, investors do not know whether managers are capable, or just benefit from a favorable loss experience; by purchasing reinsurance and thus removing the effect of extreme losses, they effectively end up with much less noisy performance measures. Furthermore, Doherty and Smetters (2005) provide evidence that reinsurers impose controls on their clients that mitigate underwriting moral hazard. Mitigating moral hazard enhances information symmetry. It seems, therefore, that reinsurance purchases may convey information to outsiders about the propensity of the firm to manage risk, as the findings of Colquitt and Hoyt (1997) suggest. While the purchase of reinsurance can create value by reducing the frictional costs associated with taxes, volatile cash flow, and information asymmetries, managers also may purchase reinsurance simply out of selfinterest. The purchase of reinsurance allows managers to enhance the accounting ratios they report to regulators and access the expert services reinsurance firms bundle with the reinsurance contract. Also, by reducing the insurer s likelihood of default through the purchase of reinsurance, poor managers safeguard their own jobs. The conceptual model of Blazenko (1986), for example, posits that the demand for reinsurance increases as the relative risk aversion of managers increases. Managers also may purchase reinsurance because it is an accepted, usual, and expected business practice. Managers may simply mimic the decisions of their peers, even when they disagree, because they fear that behavior contrary to that of their peers may damage their own reputations (Keynes, 1936, pp ; Scharfstein and Stein, 1990).

5 214 SCORDIS AND STEINORTH RISK MANAGEMENT AND VALUE An exhaustive analysis of empirical results regarding why firms choose to manage risk, by Aretz and Bartram (2010:318), concludes that existing theoretical explanations have little to no explanatory power for determining which firms use derivatives. In empirical studies, the use of derivatives is a surrogate for a risk management program, as we cannot observe the entire panoply of procedures a firm employs to manage risk. Surprisingly, there are only four published papers that directly investigate the relation between hedging and value: Allayanis and Weston (2001), Carter et al. (2006), Jin and Jorion (2006), and MacKay and Moeller (2007). Allayanis and Weston (2001) examine the value of hedging foreign exhange risk with a data set of 4320 annual observations from a crosssection of 720 firms; they mitigate endogeneity in their multi industry data by explicitly controlling for industry. The other three studies use singleindustry data. Carter et al. (2006) use 229 annual observations from 28 airlines, such as United Airlines and Delta Airlines, to examine the value of hedging the cost of jet fuel. Jin and Jorion (2006) use 330 annual observations from 119 oil and gas explorers, such as Anadarko Petroleum and Occidental Petroleum, to examine the value of hedging the price of oil. MacKay and Moeller (2007) use 2145 quarterly observations from 34 petroleum refiners, such as Exxon Mobil and Chevron Texaco, to examine the value of hedging the price of oil as well as hedging interest rate and foreigh exhange risk. These four papers (as well as a manuscript by Perez Gomzales and Yun) use Tobin s q as their measure of shareholder value. This is problematic because it is not clear from the literature whether Tobin s q measures market power, growth expectations, or profitability. Tobin (1969:21) introduces q as a theoretical construct for the value of capital relative to its replacement cost in his examination of the relationship between monetary policy and investment. Over time, authors have diverged in their measurement and use of q. Lindenberg and Ross (1981), the first to calculate q, employ it as a measure of a firm s market power, while Smirlock et al. (1984) arque for the use of q as a measure of a firm s ability to extract rents. Stevens (1986), however, argues that it is the use of current earnings for future growth that underlies high q ratios, rather than market power, and suggests that q is a measure of a firm s future growth opportunities (which is how Lang et al. (1996), for example, are using q). Meanwhile, Wernerfelt and Montgomery (1988) and McFarland (1988), within a different stream of literature, establish q as a measure of a firm s current profitability. So today, researchers are using q to measure a firm s market power, or to measure a firm s growth expectations, or to measure relative profitability.

6 VALUE FROM HEDGING RISK WITH REINSURANCE 215 The data sets used by the four studies of the relation between hedging and q happen to have a progressively larger ratio of assets to growth opportunities from study to study. Looking at these four studies collectively, we find that as the ratio of assets to growth opportunities increases in the data they use, the impact of hedging on q decreases. MacKay and Moeller (2007) find that on average, hedging increases q by 3 percent. The firms in their sample have assets averaging $12,088 million and a ratio of capital expenditures to assets (the study s measure of growth opportunities) of 0.05; this study s data, therefore have the most assets in relation to growth opportunities. The data of Carter et al. (2003) have the least assets in relation to growth opportunities (average assets are $937 million and the ratio of capital expenditures to assets is 0.27); they find that, on average, hedging increases q by 14%. The data in Allayanis and Weston (2001) fall between those two studies, as the average firm in this sample has assets of $7,701 million and a ratio of capital expenditures to assets of 0.10; on average, hedging increases q by 5%. Jin and Jorion (2006), whose average firm seems to have the same amount of assets relative to growth opportunities (if proven oil reserves can serve as a rough proxy of growth prospects), find no relation between hedging and q. It may be a coincidence that the impact of hedging on q increases as the ratio of assets to growth opportunities decreases. It may also suggest that q is sensitive to a firm s ability to capture rents (either monopoly rents or economic rents). Thus, the available empirical evidence may be showing the impact of hedging on the growth opportunities of the firm rather than on its current profitability. In fact, Geczy et al. (1997) show that firms with better growth opportunities (i.e., a small assets to growth opportunities ratio, all other things being equal) hedge more with currency derivatives than do other firms. Due to such ambiguity in the use of Tobin s q as a proxy for value, we instead rely on the stock s excess return. Excess return is an unambiguous measure of shareholder value; it is the return shareholders receive beyond what they require as compensation for systematic risk. At the end of the day, higher excess return means wealthier shareholders. Accordingly, excess return is an easily understandable measure of shareholder value. DATA In this study we use data from 67 publicly traded holding insurance firms for the years 1999 through 2010, for a total of 680 firm year observations. Table 1 provides selected measures of central tendency and correlations for our data. We explain the variables we use in our Analysis section.

7 216 SCORDIS AND STEINORTH Table 1. Measures of Central Tendency and Correlations a Measures of central Tendency Correlations Median Mean Std. Dev. A B C D E F G H A: Excess Return B: Total Return C: Price to Book D: Reinsurance Use E: Current Profitability F: Growth Expectations G: Total Risk H: Total Downside Risk a The table shows selected descriptive statistics for the aggregate of the data. The data are from 67 publicly traded holding insurance firms for the years 1999 through 2010, for a total of 680 firm year observations. We explain the variables we use in our Analysis section. The firms in our data represent the universe of publicly traded insurers with a Standard Industrial Classification (SIC) code 6311 (life insurance) or 6331 (fire, marine, and casualty insurance) that file Form 10K with the Securities and Exchange Commission (SEC) and are listed in the Center for Research in Security Prices (CRSP) database. Publicly traded insurers are generally structured as holding firms of wholly owned insurance companies licensed by individual states to sell either property/casualty or life insurance products. For example, The Travelers Companies has 103 insurance companies on record. It is often the case that empirical research on the United States insurance industry relies on data these individual insurance companies, rather than data the publicly traded holding firms, report. Individual insurance comanies report their data under statutory rules to

8 VALUE FROM HEDGING RISK WITH REINSURANCE 217 their state regulators. This statutory data is rich in detail. It thus allows researchers to carry out measurements that are not possible with any other publicly available data on firms. For our paper, however, it is inappropriate to use statutory data, for two reasons. First, the task of state insurance regulators does not include the protection of shareholders and other investors. This task falls to the SEC. Thus, since we are investigating how the use of reinsurance affects shareholders, we need to look at the data intended for monitoring the welfare of shareholders. This data is reported in Form 10K, which publicly traded firms file with the SEC. An alternative source of data would have been an aggregation of the data individual insurance companies file with their state regulators up to the insurance holding company level. We do not have confidence, however, in the accuracy of aggregating statutory data up to the holding firm level. For example, in 2010, the Form 10K filed by Progressive Corporation reports consolidated total assets and liabilities of $21,150 million and $15,101 million, respectively. By comparison, for the same year, aggregating what all of Progressive s individual insurance companies reported to state regulators into the Progressive Group (NAIC Group Code 115) results in total assets and liabilities of $17,286 million and $12,213 million, respectively. Progressive operates exclusively in the United States. Second, the statutory data individual insurance companies file with their state regulators does not capture the global scope and scale of the publicly traded insurance holding firms under which the individual insurance companies reside. Since statutory data reflect only the insurance business the individual companies underwrite, it is either life or non life, and reflects mainly insurance business underwritten in the United States. There are, however, publicly traded insurance holding firms that own both life and non life insurance companies both in the U.S. and abroad. For example, in 2010, Horace Mann Educators Corporation, a non life insurer, according to its SIC code, derived 47.0 percent of its insurance premiums from life related insurance products, while Metropolitan Life, a life insurer, according to its SIC code, derived 8.7 percent of its insurance premiums from non life insurance products. And then there are insurers with international operations, such as Aflac Insurance, a life insurer domiciled in the state of Georgia, which in 2010 derived 75.6 percent of its premiums from outside the United States. Our use of data from a single industry is consistent with the convention of using single industry data in risk management research. Empirical study of corporate risk management practice presents an endogeneity challenge. When corporate risk becomes the focus of management, even if management takes no specific action, the dynamics between the corporation and its risk change. For example, a better understanding of the firm s

9 218 SCORDIS AND STEINORTH risk can change the risk appetite of managers, which in turn changes the firm s risk. Jin and Jorion (2006, pp. 894 and 895) argue that endogeneity is best controlled by using single, industry data. The use of a single industry also alleviates the exogeneity problem identified by Froot et al. (1993) as well as by Adam et al. (2007), who explain that the risk management strategy for a given firm further depends on the nature of competition in the firm s market and on the risk strategies of its competitors. Our use of insurance firms confers an additional advantage to our study. When insurers hedge their underwriting risk, they do so using reinsurance; the use of the same hedging instrument by firms in the study removes the need to control for the payout characteristics of the hedging instrument, as the work of Gay et al. (2003) and others suggests. Econometric Specification ANALYSIS We investigate the relation between the use of reinsurance and value using time series, cross sectional data, or panel data. In drawing inferences from time series, cross sectional data we can assume that the effect of omitted variables captured by the panel design is either fixed or random. We present analysis results from all the data under both of these assumptions. The Hausman (1978) test, however, favors the fixed effects assumption. This test and models of panel data analysis are an econometrics standard and are well documented in relevant textbooks, such as Judge et al. (1982, Ch. 11) or Green (2012, Ch. 11). We make a decision to use time effects to control for systematic events, since our data, which span the years 1999 to 2010, reflect the effect of economic cycles as well as years of high losses associated with man made catastrophes and natural disasters. For example, it is often mentioned in the literature that the price and/or availability of reinsurance follows a cycle; Meier and Outreville (2010) conclude that periods of high prices and of little availability of reinsurance are usually followed by periods of low prices and of much availability. We also use firm effects to mitigate misspecification resulting from omitting control variables we cannot accurately measure. Consistent with standard econometric practice, we look at varianceinflation factors to analyze multicollinearity, we plot standardized residuals and compute their degree of fit to analyze influential observations, and we plot the cumulative sum (cusum) of residuals to test the stability over time of the coefficients of our regression model, as suggested by Brown et al. (1975). We compute robust estimators for the model s covariance matrix

10 VALUE FROM HEDGING RISK WITH REINSURANCE 219 using feasible generalized least squares. We report in each table of results adjusted R 2 values and F statistics from an ordinary least squares estimation of the corresponding model. These goodness of fit metrics suggest a strong fit to the data and well specified models. Dependent Variable: Value We measure the dependent variable as Excess Return. Return over the return shareholders require as compensation for the firm s systematic risk is an unambiguous measure of shareholder value. At the end of the day, higher excess return means wealthier shareholders. Practitioners favor the Sharpe Lintner capital asset pricing model (CAPM) when estimating the return shareholders require, while an increasing number of empirical studies are using the Fama and French three factor model. There is considerable debate, however, on whether the CAPM, with market risk as the only factor, or the Fama and French model, with its three factors, is the appropriate estimator of returns. Since there is no consensus in the literature as to what is a suitable measure of risk (see, for example, Levy, 2010), and consequently how to best measure it, the debate on the validity of the CAPM remains to be resolved. The Fama and French three factor asset pricing model says that the return of a stock over the risk free rate is a linear function of market risk, relative firm size, and relative firm growth. The implication of their results is that reliance on the CAPM to estimate Excess Return leads to measurement error. Without a robust theory to explain the results of Fama and French (1996), however, we have to assume that deviations from the true value of the dependent variable are random across firms and over time. Such measurement error, therefore, only increases the variance of the error term; it does not affect the consistency of the estimated coefficients. We thus estimate the return shareholders require using the more theoretically robust and computationally less intensive asset pricing model. We use the CAPM in conjunction with daily data from CRSP and from the Federal Reserve Economic Database (FRED). In addition to Excess Return as a measure of value, we also use Total Return and the popular ratio of Price to Book value of the stock. We think of Excess Return and Total Return as measures of realized value, while we think of the Price to Book ratio as a measure of anticipated value. Total Return is the actual return shareholders receive each year from holding the stock of a firm. It includes stock price appreciation and cash payments to shareholders, all adjusted for any stock splits or other such events but not for risk. We get Total Return from the CRSP database. The Price to Book ratio is the market price of the stock divided by its book value, which is a popular metric for gauging a stockʹs relative value. In an efficient market, the share price (in the numerator of the ratio) should reflect a firm s future value

11 220 SCORDIS AND STEINORTH creation potential, while the book value of equity (in the denominator of the ratio) should reflect the firm s theoretical liquidation value. Thus, in a well functioning market, a higher ratio represents investors higher expectations of future gains. Independent Variables: Reinsurance and Controls Reinsurance Use is the amount of reinsurance premium ceded by an insurance holding firm in a given year divided by total insurance premiums collected by the firm during the year. The ratio measures how much of the core operating business of an insurance company, namely underwriting, is hedged by purchasing reinsurance. Our measure of reinsurance is the consensus measure in the literature. We collect this information from Form 10K, filed with the SEC by each insurance holding firm. The information reported is consolidated across the entire firm regardless of where in the world the firm conducts operations. Borch (1961) and Scordis et al. (2008) point out that when the firm buys reinsurance, it pays others to take on its own risk. Therefore, shareholder value is affected at the point wealth is transferred outside the firm s economic family. In the language of Powell and Sommer (2007), this is net external reinsurance; it is this external hedging of risk that affects shareholder value, rather than internal reinsurance arrangements that simply allocate risk within operating units. Current Profitability and Growth Expectations are, respectively, the accounting return on equity (ROE the ratio of net income to shareholders equity) and Tobin s q, which we calculate according to Chung and Pruitt (1994). It is well argued in the literature, beginning with Miller and Modigliani (1961), that the value of a firm s equity is driven by the firm s assets in place and the firm s growth opportunities. Thus, more profitable firms (which we measure as ROE) and firms with more growth opportunities (which we measure as Tobin s q) are likely to trade at a premium relative to other firms. Total Risk and Total Downside Risk control for the firm s risk as it is reflected in the volatility of the stock s return. Neoclassical finance assumes that shareholders hold well diversified portfolios and thus are indifferent to all but systematic risk. Studies, however, find mixed results in terms of the direction and significance of the relation between risk and returns. Thus, we control for risk as shareholders may perceive it. We use daily returns over a period of one year to calculate these measures of risk. We define Total Risk as the standard deviation of each stock s return for each year. The standard deviation is the square root of 1 N ( R n R) 2, where N n = 1

12 VALUE FROM HEDGING RISK WITH REINSURANCE 221 (N) is the number of individual returns (R n ) during the year and ( R ) is the mean return during the year. Harry Markowitz, in his 1959 book on portfolio selection, was the first to make the point that from a general perspective, standard deviation as a measure of risk may miss the link with an investor s preferences and presented semivariance as a more plausible measure of a stock s risk. Thus we define Total Downside Risk as the semideviation (the square root of semivariance) of each stock s return for each year with respect to the mean return. Semideviation with respect to the mean return is the square root of 1 N [ Min( R n R, 0) ] 2. N n = 1 RESULTS The use of reinsurance increases value. The results we report in the following tables support this statement. Table 2 shows results from estimating fixed effects regressions where the measures of value are Excess Return, Total Return, and the Price to Book ratio. We also estimated the same models we show in Table 2 using random effects regressions. The large values of the Hausman test (which we report in Table 2) favor the use of fixed effects over random effects regressions. Table 2 shows that there is a positive and significant relation between the independent variable Reinsurance Use and each of the dependent variables we use to measure value. For the fixed effects regression, where excess return is the measure of value, at mean sample values, a 1 percent increase in Reinsurance Use increases Excess Return by percent. In the analysis that follows, we continue to report results for the fixed effects regression where the measure of value is Excess Return. We do this because we believe that Excess Return is the conceptually appropriate measure of value. Anticipated market volatility as well as volatile firm revenue may be obscuring the relation between the use of reinsurance and value. Both market and revenue volatility create noise in the performance of a firm, which makes it difficult for shareholders to decide the true value of the firm. We thus stratify the data according to anticipated market volatility and according to how robust the firm s revenue is during a year. We measure anticipated market volatility according to the Chicago Board of Trade s volatility index (VIX) averaged over a period of one year. The VIX has often been dubbed the investor fear gauge. It is a measure of anticipated market volatility. When investors are concerned about a potential drop in the stock market, they can insure the value of their

13 222 SCORDIS AND STEINORTH Table 2. Use of Reinsurance Creates Value: Firm and Year Effects a,b Dependent variable: Excess Return Total Return Price to Book Independent variables: Estimated Coefficients (p values) Constant (0.191) (0.793) (0.401) Reinsurance Use (0.098) (0.050) (0.101) Current Profitability (0.133) (0.025) (0.157) Growth Expectations (0.000) (0.002) (0.000) Total Risk (0.000) (0.000) (0.000) Total Downside Risk (0.000) (0.000) (0.000) a The data are from 67 publicly traded holding insurance firms for the years 1999 through 2010, for a total of 680 firm year observations. We consider estimated coefficients to be significant at a confidence level of 90.0 percent or better. b The adjusted R 2, the proportion of variability in the data, explained by the models (left to right) is 0.381, 0441, and Their F tests of joint significance with degrees of freedom [83, 596] are 6.05, 7.44, and 34.87, respectively; they are all significant at a p value of The Hausman test and associated p values (in parentheses) of fixed vs. random effects with 5 degrees of freedom (left to right) are (0.021), (0.020), and (0.000). portfolio by purchasing S&P 500 index puts. The more puts investors demand, the higher the price of portfolio insurance rises. The VIX is an indicator that reflects the price of portfolio insurance. There is a strong sense among investors that the VIX s long term average value is around 22, which happens to also be close to the average for our data. We separate our data according to a year s average VIX value relative to this long term

14 VALUE FROM HEDGING RISK WITH REINSURANCE 223 average value of 22. The VIX was below 22 for the years 2003, 2004, 2005, 2006, and These years of low anticipated market volatility coincide with the last economic expansion, which, according to the National Bureau of Economic Research (NBER), lasted from November 2001 to December The VIX was above 22 for the years 1999, 2000, 2001, 2002, 2008, 2009, and It peaked in 2008 and 2009, which are the years of the Great Recession, according to the NBER. We measure the robustness of a firm s revenue during a year as the firm s coefficient of variation of revenue. We use each firm s quarterly revenue (premiums plus investment income). Volatile revenue in relation to its average size produces a large coefficient of variation, while relatively stable revenue in relation to its average size produces a smaller coefficient of variation. We denote firms with a coefficient of variation of revenue above the median data value of as having less robust revenue, and we denote firms below this median data value as having more robust revenue. On average, the coefficient of variation for firms with more robust revenue is 0.027, and for firms with less robust revenue it is In Table 3 we report the results from stratifying the data according to anticipated market volatility and according to how robust a firm s revenue is during a year. For years of high anticipated market volatility and for firms with less robust revenue we do not find a significant relation between the use of reinsurance and value. Note, however, that while the estimated coefficient of Reinsurance Use for firms with less robust revenue is not significant at the 90.0 percent confidence level, it is positive and significant at the 88.2 percent confidence level. We do find a significant relation for years of low anticipated market volatility and for firms with more robust revenue. For the years of low volatility, at mean sample values, a 1 percent increase in Reinsurance Use increases Excess Return by percent. For firms with more robust revenue, at mean sample values, a 1 percent increase in Reinsurance Use increases Excess Return by percent. The empirical evidence on the demand for reinsurance finds that larger insurers tend to use less reinsurance. We thus stratify the data according to a firm s size to investigate whether the amount of assets an insurer holds moderates the relation between hedging with reinsurance and value. We measure size by the total assets of an insurer, which we scale by its natural logarithm. We report these results in Table 4. We denote firms with assets above the median data value of $10,070 million as large and firms with assets below the median as small. On average, small firms have assets of $4,647 million and large firms have assets of $95,439 million. The average size for all firms is $12,262 million. For large firms we do not find a relation between the use of reinsurance and value, while for small firms we find a strong positive relation. For small firms, at mean sample values,

15 224 SCORDIS AND STEINORTH Table 3. Volatility Moderates the Relation Between Use of Reinsurance and Value a,b Dependent variable: Excess Return. Years with low anticipated market volatility Years with high anticipated market volatility Firms with less robust revenue Firms with more robust revenue Independent variables: Estimated coefficients (p values) Constant (0.000) (0.501) (0.712) (0.033) Reinsurance Use (0.283) (0.118) (0.035) Current Profitability (0.578) (0.398) (0.276) Growth Expectations (0.000) (0.001) (0.008) (0.006) Total Risk (0.000) (0.000) (0.000) (0.000) Total Downside Risk (0.000) (0.000) (0.000) (0.000) a The table shows results from fixed effects regression. We classify firms according to revenue robustness based on whether the coefficient of variation of their revenue is either below or above the 50th percentile of all firms in the data. We classify years according to their anticipated market volatility based on whether the Chicago Board of Trade s volatility index (VIX) is either below or above 22 during a year. We consider estimated coefficients to be significant at a confidence level of 90.0 percent or better. b The adjusted R 2, the proportion of variability in the data, explained by the models (left to right) is 0.693, 0.329, 0.239, and Their associated F tests of joint significance with degrees of freedom [73, 224], [78, 303], [82, 257], and [78, 261], respectively, are 10.17, 3.39, 2.30, and 9.46; they are all statistically significant at a p value of a 1 percent increase in Reinsurance Use increases Excess Return by percent. We confirm the moderating effect of size on the relation between the use of reinsurance and value by using all data to estimate our model, but

16 VALUE FROM HEDGING RISK WITH REINSURANCE 225 Table 4. Size Moderates the Relation Between Use of Reinsurance and Value a,b Dependent variable: Excess Return Small firms Large firms All firms Independent variables: Estimated coefficients (p values) Constant (0.001) (0.382) (0.378) Reinsurance Use (0.003) (0.400) (0.007) Reinsurance Use Size (0.019) Current Profitability (0.605) (0.794) (0.155) Growth Expectations (0.000) (0.026) (0.000) Total Risk (0.000) (0.000) (0.000) Total Downside Risk (0.000) (0.000) (0.000) a The table shows results from fixed effects regression. Small firms have assets that are below the 50th percentile of the assets held by all firms in the data, while large firms have assets that are above it. We consider estimated coefficients to be significant at a confidence level of 90.0 percent or better. b The adjusted R 2, the proportion of variability in the data explained by the models (left to right) is 0.652, and Their associated F tests of joint significance with degrees of freedom [58, 281], [54, 285] and [84, 595], respectively, are 9.11, 3.50 and 6.08; they are all significant at a p value of with the addition of a multiplicative interaction term Reinsurance Use Size, where Size is the natural logarithm of assets. This multiplicative term is significant and negative. Its negative sign suggests that size acts to mitigate the relation between Reinsurance Use and Excess Value. We interpret this interaction variable as in Scordis et al. (2008); at mean sample values, a 1 percent increase in Reinsurance Use increases Excess Return by percent (as compared to percent from Table 2, where assets do not interact with the use of reinsurance).

17 226 SCORDIS AND STEINORTH Since the amount of assets an insurer holds moderates the relation between the use of reinsurance and value, we further investigate how size may interact with anticipated economic uncertainty as well as the robustness of a firm s revenue. We thus estimate regressions for additional subsamples that we stratify according to size, robustness of revenue, and anticipated market volatility. One subsample consists of the union of large firms, firms with less robust revenue and years of high anticipated market volatility. Another subsample consists of the union of large firms and firms with more robust revenue and years of low anticipated market volatility. For these subsamples the estimated coefficient of Reinsurance Use is not significant; we report these results in Table 5. Note that the absence of a relation between the use of reinsurance and value for large firms is consistent with the large firm results we report in Table 4. In Table 5 we also report results for two additional subsamples: the union of small firms and firms with less robust revenue and years of high anticipated market volatility, and the union of small firms and firms with more robust revenue and years of low anticipated market volatility. For small firms with less robust revenue in years of high anticipated market volatility, a 1 percent increase in Reinsurance Use increases Excess Return by percent. By comparison, for small firms with less robust revenue in years of low anticipated market volatility, at mean sample values, a 1 percent increase in Reinsurance Use increases Excess Return by percent. The estimated coefficients of Reinsurance Use of and for these two subsamples are statistically different. SUMMARY AND DISCUSSION We investigate how the use of reinsurance by publicly traded insurers affects value for shareholders. We use time series, cross sectional data. We use different measures of value and different techniques to estimate the reinsurance value relation. We find that small firms with less robust revenue during years of high anticipated market volatility experience a strong positive relation between the use of reinsurance and value. This result suggests that shareholders value hedging for the information it reveals about the firm s true value. Often, a firm knows best the true shape of its loss distribution. Noise, however, creates added volatility in its financial numbers. This volatility makes it difficult for shareholders to decide whether managers are capable, or just benefit from a favorable loss experience; by purchasing reinsurance and thus removing the effect of extreme losses, they effectively end up with much less noisy performance measures. It is much like what happens when a car mechanic takes a car with a

18 VALUE FROM HEDGING RISK WITH REINSURANCE 227 Table 5. The Effect of Size, Robustness of Revenue, and Anticipated Market Volatility a,b Dependent variable: Excess Return Large firms, less robust revenue, years of high anticipated volatility Large firms, more robust revenue, years of low anticipated volatility Small firms, less robust revenue, years of high anticipated volatility Small firms, more robust revenue, years of low anticiapted volatility Independent variables: Estimated coefficients (p values) Constant (0.121) (0.006) (0.035) (0.071) Reinsurance Use (0.897) (0.656) (0.025) (0.015) Current Profitability (0.310) (0.434) (0.842) (0.831) Growth Expectations (0.878) (0.061) (0.001) (0.006) Total Risk (0.033) (0.000) (0.000) (0.015) Total Downside Risk (0.007) (0.000) (0.000) (0.000) a The table shows results from fixed effects regression. We classify firms according to size and revenue robustness based on whether their assets and the coefficient of variation of their revenue are either below or above the 50th percentile of all firms in the data. We classify years according to their anticipated market volatility based on whether the Chicago Board of Trade s volatility index (VIX) is either below or above 22 during a year. We consider estimated coefficients to be significant at a confidence level of 90.0 percent or better. b The adjusted R 2, the proportion of variability in the data, explained by each of the models (left to right) is 0.014, 0.815, 0.498, and Their associated F tests of joint significance with degrees of freedom [47, 47], [44, 62], [51, 76], and [36, 37], respectively, are 0.97, 11.64, 3.47, and The F test of 0.97 is not significant (p value is 0.540); all the others are significant at a p value of defective wheel bearing for a test drive; on a quiet road the mechanic can clearly hear the whoamp whoamp whoamp sound from the defective bearing, but on a busy highway the sound of the defective bearing gets drowned out by all the noise on the highway.

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