The Economic Value from the Use of Reinsurance

Transcription

1 The Economic Value from the Use of Reinsurance Nicos Scordis and James Barrese Abstract Whether corporate risk management activities benefit shareholders has received little direct empirical analysis because of the difficulty in obtaining data. This study examines one industry with available risk management data on one area of operations. Property-liability insurance firms report their reinsurance purchases. Reinsurance, for a price, transfers operating risk from the underwriting operations of one insurance firm to another. We use a sample consisting of observations on forty-seven publicly traded insurance firms over the years 1994 through This study examines whether the management of underwriting risk through reinsurance enhances the wealth of stockholders. We measure wealth as the holding period return, as market value and as cash dividends. We relate these measures of wealth to a set of explanatory variables that include a measure of reinsurance usage. We find a statistically strong positive relationship between reinsurance usage and stockholder wealth but the economic significance of the resulting wealth increase is weak. Introduction The pointed-hair boss in the Dilbert cartoon strip (United Feature Syndicates, August 8, 1992) refuses a pay-raise to a subordinate because the raise would induce volatility in the firm s earnings, and volatility upsets stock market analysts, especially the lazy ones. Theorists in the academic literature have also advanced, with less humor, explanations for corporate risk management. These explanations fit in two categories. The one category explains risk management as an attempt to increase the returns (or value, or wealth) of shareholders, the other as an attempt to maximize managers private utility. Unfortunately, lack of data hinders the testing of how well these theories describe the practice of risk management. Data availability forces empirical studies to limit their examination to a single risk management tool (such as derivatives or insurance), analyze individual firms (such as Delta Airlines or Cephalon Inc.), or rely on singe industry samples (such as the oil industry, gold-mining industry or the insurance industry). This study also uses a single industry sample from the insurance industry. The risk management practices in the insurance industry have been the subject of several theoretical and empirical studies. Many of these studies seek to explain why insurance firms

2 2 manage the risk from their underwriting operations through the purchase and sale of risk reinsurance. In a risk reinsurance transaction the reinsurer (the insurance firm that assumes the risk) shares in the losses of the cedant (the insurance firm that surrenders the risk) for a payment of a fixed premium or for a share of the cedant s premium revenue. The reinsurer then reimburses the cedant for the costs of acquiring the business representing the ceded premium. It is often the case that the reinsurer negotiates in advance the size of the premium and of the reimbursement. Thus, it is the net of the present value of these two cash flows that determine the effective price of reinsurance. None of the reinsurance studies, however, has investigated whether the purchase of reinsurance increases the return of the firm s shareholders. Underwriting is a core risk for insurance firms, and the purchase of reinsurance hedges this core risk. 1 As Schrand and Unal (1998) explain, core risks create economic value while noncore risks do not. Thus value maximizing firms should seek to increase core risk and decrease non-core risk. But, Froot and Stein (1998) posit that financial institutions create value by hedging risk regardless if it is core or non-core, as long as the hedge is priced to be of zero net present value. The reinsurance industry uses Froot and Stein (1998) to argue that while the hedge is of zero net present value for the ceding insurance firm, to the reinsurer it is of positive net present value. 2 Thus, according to the wisdom of insurance practitioners, the hedging transaction creates higher returns both for the shareholders of the reinsurer and for the shareholders of the ceding insurers. Regardless of what the belief about the value of reinsurance is, hedging underwriting risk through the purchase of reinsurance is a trade-off between its costs and its benefits. Borch (1961, p.35) was the first to observe that when an insurance company reinsures a part of its 1 Core risk stems from activities for which a firm has some informational advantage. For example, an insurance firm expects to profit from the ability to appropriately accept/reject applicants for an insurance policy, from the ability to invest the premiums policyholders pay and from the ability to administer the reimbursement of losses to policyholders. Acting on these core risks, however, the insurer creates interest rate risk. Now, if the managers of a firm consider themselves as having a comparative advantage in predicting interest rates, then interest rate risk will also be a core-risk for these managers. For example, many insurance firms outsource the process of asset allocation in their portfolio, while others decide their own asset allocation and outsource only the physical process of investing their assets. 2 According to reinsurance marketing literature, the hedging transaction is zero net present value to the ceding insurer because of the competitiveness of the reinsurance market, while it is of positive net value to the reinsurer because reinsurers have superior diversification of their asset and underwriting portfolios. Examples of this literature are page 2 of The Economic Value of Reinsurance, a Converium Reinsurance publication at or page 9 of Sigma No5/2003, a Swiss Reinsurance publication available at

3 3 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. The Possible Value of Reinsurance If the economy were frictionless, it would have been pointless for managers to act to reduce the risk of the firm as the firm s shareholders could easily adjust the risk of their diversified portfolios. But the economy has friction, and this friction creates costs. Established theory suggests that by reducing the risk of the firm managers can also reduce these frictional costs. If the benefits from reducing frictional costs accrue to shareholders, then shareholders should enjoy higher returns. Frictional costs stem from concerns that a volatile cash flow increases the probability of financial distress, from convex tax schedules and from information asymmetries. Even if cash shortfalls from a volatile cash flow do not result in default, Mayers and Smith (1982) explain that stakeholders will demand low prices contract with the firm. 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 Phillips, Cummins and Allen (1998). They conclude that insurance prices are high when the insurer s likelihood of default is low. Of course higher prices do not always translate to higher returns for shareholders. Reducing the likelihood of default may also allow the insurer to take on more debt which benefits shareholders because it creates tax shields for the firm (Leland, 1998; Graham and Rogers, 2002). In the case of insurance firms, debt often takes the form of selling more insurance policies. The insurance firm accounts for the future net liabilities associated with these policies on its statutory accounting balance sheet as a loss reserve. Insurance firms take an income-tax deduction for this loss reserve under Title 26, Subchapter L of the United States Internal Revenue Code. But insurance firms can overstate their reserves, within certain bounds. It is also unclear if the mechanics of the reinsurance transaction itself confer tax advantages to the ceding insurer. The Code treats the cash flows from a reinsurance transaction symmetrically. It does not

4 4 tax the premium ceded but it taxes the cash received from the reinsurer. It also disallows reinsurance contracts that have significant tax avoidance effects. 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 smoothes some aspect of the firm s cash flow allows outsiders to more easily infer the firm s true value. But it may 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, a high level of ceded insurance business may be indicative of low information asymmetry. In fact, Doherty and Smetters (2005) provide evidence that reinsures impose controls on the ceding insurer to mitigate underwriting moral hazard. Mitigating moral hazard enhances information symmetry. It seems, therefore, that even if reinsurance purchases do not eliminate information asymmetry, they may still convey information to outsiders. Perhaps managers manage underwriting risk by purchasing reinsurance 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. Of course managing underwriting risk through the purchase of reinsurance reduces the firm s likelihood of default which benefits policyholders and also allows poor managers to safeguard their own jobs. The model for reinsurance demand of Blazenko (1986), for example, posits that the demand for reinsurance increases as the relative risk aversion of managers increases. Managers may also 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 their peers may damage their own reputations (Keynes, 1936, p ; Scharfstein and Stein, 1990). We do not know whether the purchase of reinsurance creates higher returns for shareholders because existing empirical studies examine only why insurance firms purchase

5 5 reinsurance not whether reinsurance enhances shareholder value. 3 Mayers and Smith (1990), Adams (1996), Garven and Lamm Tennant (2003) as well as Shortridge and Avila (2004) find that large insurance firms reinsure less, but Hoerger, Sloan and Hassan (1990) and Adiel (1996) are unable to verify this finding. Mayers and Smith (1990) and Garven and Lamm Tennant (2003) are not able to establish a relationship between an insurance firm s product concentration, geographic concentration and its reinsurance purchases. But Shortridge and Avila (2004) find an inverse relationship between an insurance firm s product concentration and its reinsurance purchases, and a positive relationship between its geographic concentration and reinsurance purchases. Mayers and Smith (1990), Adiel (1996) and Shortridge and Avila (2004) find that insurance firms facing a low likelihood of default reinsure less but Hoerger, Sloan and Hassan (1990) are unable to verify this relationship. Mayers and Smith (1990) find that stock insurance firms reinsure less, but Adams (1996) and Garven and Lamm Tennant (2003) find that stock insurance firms reinsurance more. Hoerger, Sloan and Hassan (1990) are unable to link the ownership structure of an insurance firm with its reinsurance purchases. Shortridge and Avila (2004), however, find that as institutional and insider ownership of an insurance firm increases its reinsurance purchases decline. Adiel (1996) is not able to verify that insurance firms under regulatory scrutiny are more likely to purchase risk reinsurance. Adiel (1996) and Garven and Lamm Tennant (2003) are not able to verify that insurance firms adjust their reinsurance purchases as a function of their tax rates. Nevertheless, all authors interpret their empirical findings as favoring the conclusion that insurance firms with a higher likelihood of insolvency purchase more reinsurance. But preventing insolvency, which directly benefits policyholders and managers, is not the same as increasing shareholder returns. There is only one study that examines whether specific risk management activities increase shareholder value. Tufano (1996) examines gold price hedging by the North American gold mining industry and concludes against the proposition that gold price hedging creates value for shareholders. There are three additional studies that say that they examine the impact of risk 3 These empirical studies investigate how changes in variables that reflect the magnitude of an insurer s reinsurance transactions affect the magnitude of other variables that reflect an insurer s bankruptcy risk and its need for expert services. In general the studies capture the magnitude of an insurer s reinsurance transactions by the ratio of premiums ceded to gross premiums written. The studies represent an insurer s bankruptcy risk with financial strength ratings and variables that proxy for the insurer s size, its concentration of products and markets, its financial strength, its ability to pay claims, and its organizational form. Shortridge and Avila (2004) also accept that insurers purchase reinsurance to reduce their likelihood of default and obtain expert services.

6 6 management activities on shareholder value. But the ratio these studies use to measure market value can also be used as a measure of future opportunities. 4 Allayannis and Weston (2001) examine the foreign exchange hedging practices of United States industrial firms while Carter, Rogers and Simmins (2003) examine the hedging of fuel prices by the United States airline industry. Both of these studies find in favor of the proposition that risk management enhances a firm s investment opportunities. Jin and Jorion (2006) examine the management of market risk for United States oil and gas producers and find against the proposition that risk management enhances a firm s investment opportunities. Empirical Design This paper investigates whether managing underwriting risk through the purchase of risk reinsurance creates higher returns for shareholders. The sample contains observations both overtime and across individual insurers. An observation is a datum from each of forty-seven firms at the end of a particular year from 1994 through There are a total of 455 observations. The sample consists of cross-sectional, time-series observations of United States (US) insurance firms with primary standard industrial classification (SIC) code 6331: property-liability insurance firms. To construct the sample, we first identified the filings of Form 10-K for firms with the primary SIC code 6331 on the Electronic Data Gathering and Retrieval (EDGAR) service of the US Securities and Exchange Commission (SEC). The earliest year electronic filings are available is the data year 1991 but for the majority of the firms available data begins with the 1994 data year. Thus to balance our sample as much as possible we limit our sample to the data years 1994 through There are 161 firms with SIC code 6331 that filed Form 10-K during the period 1994 through Only 114 of these firms are reported on the daily database of the University of Chicago s Center for Research on Security Prices (CRSP). From these 114 firms only ninety-five firms primarily engage in activities that are indeed consistent with the SIC 4 These three studies use Tobin s q as a measure of firm value. We find it conceptually difficult, however, to accept the use of Tobin s q as a measure of firm value. We prefer to think of Tobin s q as a measure of a firm s investment opportunities as used, for example by Chung and Charoenwong (1991), Opler and Titman (1993), Nance, Smith Smithson (1993), Collins, Blackwell and Sinkey (1994), Lang, Ofek and Stulz (1996) and Alti (2003). Tobin (1969, p.21) uses q as a theoretical construct which he defines as the value of capital relative to its replacement cost. Lindenberg and Ross (1981) who first calculated Tobin s q redefined it as the market value of the firm divided by the replacement cost of the firm s assets and used it as a measure of firm market power. On page 29 they conclude that the sectors of the economy that have q ratios at the high end of the spectrum are often those with relatively unique products, unique factors of production and so forth, all of which contribute to monopoly. Uniqueness, as Oster (1999) explains, creates profitable investment opportunities.

7 7 code 6331 according to their description of business in Form 10-K or are not wholly-owned subsidiaries of other insurance firms or have not merged. Out of these ninety-five (95) firms only fifty-nine (59) are included on the North American Compustat databases of Standard and Poor. We are fortunate that all of these fifty-nine firms have reported stock trades in at least half of the available annual trading days. Out of these fifty-nine firms we eliminate ten firms that exclusively engage in selling reinsurance, one firm that has less than three years of data and American International Group (AIG). We eliminate AIG because it has announced, during sample collection, its intention to restate its financial statements from several past years. We hand-collect data from Form 10-K and extracted data from the CRSP daily database, from the Compustat annual and quarterly databases. In some cases we also extracted individual items from the annual ISIS database of Bureau Van Djick. We report the firms in our sample and their corresponding data years in Appendix A. There are hundreds of insurance companies registered to transact insurance business in the US. Almost all of these individual insurance companies are downstream subsidiaries of a relatively small number of firms organized as holding companies. These holding companies fall into four categories: (a) Publicly traded US insurance firms such as Progressive or AIG, (b) Publicly traded non-us insurance firms such as Zurich or Allianz, (c) Publicly traded US conglomerates such as Berkshire Hathaway or GE, and (d) privately held insurance firms such as State Farm or Nationwide. It is firms from the first category that the sample can draw from. We test our models using a fixed effects estimator and a random effects estimator. We report all results for comparison. We use the Hausman (1978) test to decide whether we should favor the fixed effects estimator or the random effects estimator. The fixed effects estimator is a least squares procedure and assumes that the effect of omitted variables captured by a series of firm-specific and year-specific binary variables is constant across firms and years. To estimate the least squares we add to each of our models a series of binary variables to represent each but one of the firms in our sample and each but one of the years in our sample. We do not report the estimated coefficients of the binary variables to conserve space. We test for autocorrelation using the Durbin-Watson test and, when necessary, we correct using the Prais and Winsten (1954) procedure. We also test for heteroskedasticity using the Breusch-Pagan test and correct the associated bias in the standard errors using the White (1980) procedure. To estimate random effects we first calculate variance components using the residuals from an ordinary least squares

8 8 regression and then the estimated variances are used to compute the feasible generalized least squares. The random effects estimator assumes that the effect of omitted variables differs across firms and years. Specification and Estimation of a Returns Model Practitioners and academic economists have long relied on the capital assets pricing model (CAPM) of Shapre (1964) to estimate a stock s return. There is considerable debate, however, on whether the CAPM and its use of just the stock s beta is a sufficient estimator of returns. Perhaps, the most recent, widely known analyses of factors that might be influencing average returns is that of Fama and MacBeth (1973) and Fama and French (1992; 1993). Fama and MacBeth (1973) find that the stock s systematic risk, which they measure by the stock s beta, explain shareholder returns. Fama and French (1993), however, have proposed two additional risk factors to explain stock returns. One of these additional risk factors is the difference between the return on a portfolio of small market capitalization stocks less the return from a portfolio of large market capitalization stocks. The other additional risk factor is the difference between the return on a portfolio of high book to market stocks less the return from a portfolio of low book to market stocks. (Returns for these factors are at There is also a discussion in the literature on whether non-systematic risk is an explanatory variables of return (Goyal and Santa-Clara, 2003; Bali et. al., 2005; Guo and Savickas, 2006). We do not take a stance on which model correctly describes returns. If in fact returns are explained by variables other than systematic risk, not including such variables in our model will bias our estimated coefficients. No bias results, however if, we erroneously include additional explanatory variables in our model (Schmidt, 2005, p. 190). We thus investigate whether the returns to shareholders are influenced by the usage of reinsurance using the specification of Fama and French (1993) with additional variables for reinsurance usage and a variable for the net-of-reinsurance idiosyncratic risk of the firm. We also use a series of binary variables to denote all but one of the individual firms (firm effects) as a further control for firm-specific omitted variables. We estimate our model using a fixed effects estimator and a random effects estimator:

9 9 (HPR) it = γ o + γ 1 (ReU) it + γ 2 (SRSK) it + γ 3 (IRSK) it + γ 4 (SMB) t + γ 5 (HML) t + B i + ε it (1) The subscripts (i) and (t) define the insurer and the year of the observation, (HPR) represents the annual holding period return the insurer generates for its shareholders, (ReU) measure reinsurance usage, (SRSK) measures the systematic risk of the insurer s stock, (IRSK) represents the idiosyncratic risk of the insurer not eliminated by reinsurance, (SMB) is the difference between a portfolio of small market capitalization stocks and a portfolio of large market capitalization stocks, (HML) is the difference between a portfolio of high market to book ratio stocks and a portfolio of low market to book ratio stocks, (B i ) is a series of binary variable to denote all but one of the individual firms and (ε) is the error term. The binary variables control for additional factors that may influence (HPR). We report descriptive statistics for these variables and their correlation coefficients in Appendix B. We report estimated results for relationship (1) in Table 1. We report the elasticity of our estimated coefficient evaluated at absolute mean sample values, and discuss our results in Table 5. We measure holding period return (HPR) as the change in market value of the firm during the year plus dividends paid to stockholders, all divided by the market value of the firm at the beginning of the year. We measure market value as the product of the annual Compustat items 24 (closing stock price) and 25 (common shares outstanding). We use the firm s market capitalization (closing stock price multiplied by common shares outstanding) rather than individual stock price in order to capture events such as stock-splits, share sales or share repurchases. Such events impact both the number of shares outstanding and stock price. We measure total cash dividends paid by the firm as the annual Compustat item 127. We measure reinsurance as the ratio of ceded premiums to gross premiums written (ReU). This ratio is the most popular measure of reinsurance usage. It is used by Mayers and Smith (1990), Adams (1996), Adiel (1996) Garven and Lamm Tennant (2003) and Shortridge and Avila (2004). We hand collect premiums from SEC Form 10-K available on EDGAR. We measure systematic risk (SRSK) as the estimated coefficient (βˆ) of the ordinary least squares regression (SRET) ij = α + β(mret) ij + δ ij. The subscripts (i) and (j) define individual stocks and days, (SRET) is the daily stock return and (MRET) is the daily value-weighted market return. We measure stock return as the daily CRSP variable RET and the value-weighted market return as the daily CRSP variable VWRETD.

10 10 We measure idiosyncratic risk net-of-reinsurance (IRSK) as the error term in the regression model σ(δ ij ) it = α + θ (ReU) it + κ it. Recall that for each firm in our sample, we have daily values for the error term (δ ij ) as we explain in the earlier paragraph. We use the daily values for each firm to compute the standard deviation of these daily value over the corresponding annual period (σ(δ ij ) it ). This standard deviation, however, is a measure of the overall idiosyncratic risk of the firm. Since the reinsurance transaction is seen as reallocation of the insurer s idiosyncratic risk to the reinsurer we need to strip away from the overall idiosyncratic risk the portion of the reinsurance-specific idiosyncratic risk. We do this by estimating using ordinary least squares regression model σ(δ ij ) it = α + θ (ReU1) it + κ it. This procedure is commonly employed in the literature to isolate idiosyncratic risk. See for example Goyal and Santa-Clara (2003); Guo and Savickas, It is not possible to estimate relationship (1) using time effects because variables (SMB) and (HML) are year-specific which in conjunction with the addition of time effects create perfect linearity in these variables. In relationship (2) below, we drop the year-specific variables (SMB) and (HML) and use instead both firm effects and time effects. (HPR) it = γ o + γ 1 (ReU) it + γ 2 (SRSK) it + γ 3 (IRSK) it + B i + B t + ε it (2) The subscripts (i) and (t) define the insurer and the year of the observation, (HPR) represents the annual holding period return the insurer generates for its shareholders, (ReU) measures reinsurance usage, (SRSK) measures the systematic risk of the insurer s stock, (IRSK) represents the idiosyncratic risk of the insurer not eliminated by reinsurance, (B i ) is a series of binary variables to denote all but one of the individual firms and (B t ) is a series of binary variables to denote all but one of the individual years and (ε) is the error term. We report estimated results for relationship (2) in Table 1. We report the elasticity of our estimated coefficient evaluated at absolute mean sample values, and discuss our results in Table 5. The Hausman test favors the use of the random effects estimator over the fixed effects estimator. We reject the hypothesis that there is no relationship between holding period returns and reinsurance usage in the random effects estimator of relationship (1). The p-value suggests a 90.1 percent probability that the estimated coefficient of (ReU) is significantly different from zero and positive. We fail to reject the hypothesis that there is no relationship between holding

11 11 period returns and reinsurance usage in the random effects estimator of relationship (2) as the p- value suggests only a 85.6 percent probability that the estimated coefficient for reinsurance usage is significantly different from zero. Systematic risk and idiosyncratic risk are positively related to holding period returns in relationships (1) and (2) as their p-values suggest at least a 95 percent probability that the random effects estimated coefficients of (SRSK) and (IRSK) are significantly different from zero and positive. This positive relationship between systematic risk and return is well established in the literature. Table 1 Fixed Effects and Random Effects Estimator of the Holding Period Returns Model The fixed effects estimator is a least squares procedure and assumes that the effect of omitted variables captured by the series of firm-specific and year-specific binary variables is constant across firms and years. The random effects estimator is a feasible generalized least squares procedure and assumes that the firm and year effects differ across firms and years. Fixed Effects Random Effects Estimated Estimated Coefficient p-value Coefficient p-value (HPR) it = γ o + γ 1 (ReU1) it + γ 2 (SRSK) it + γ 3 (IRSK1) it + γ 4 (SMB) t + γ 5 (HML) t + B i + ε it There are 403 degrees of freedom. The adjusted R² from the least squares estimator is percent. The Hausman test value of 5.04 favors the random effects estimator over the fixed effects estimator. Constant ReU SRSK IRSK SMB HML (HPR) it = γ o + γ 1 (ReU1) it + γ 2 (SRSK) it + γ 3 (IRSK1) it + B i + B t + ε it There are 395 degrees of freedom. The adjusted R² from the least squares estimator is percent. The Hausman test value of 3.73 favors the random effects estimator over the fixed effects estimator. Constant ReU SRSK IRSK

12 12 The positive relationship between idiosyncratic risk and return is consistent with an environment where shareholders are not well diversified so background risk creates risk aversion. The positive relationship between risk and return is also consistent with viewing stock as a combination of cash flow from assets-in-place and cash flow from real options. An increase in total risk will make the option component of a stock more valuable. Our holding period return (HPR) variable combines the cash dividends the insurer pays as well as its market value. If indeed the use of reinsurance confirms wealth benefits to stockholders, then we should also observe a positive relationship between the use of reinsurance and the payments of dividends or between the use of reinsurance and stock price. We investigate further how reinsurance usage impacts these cash dividends and market value. Specification and Estimation of a Dividends Model The literature advances several reasons as to why firms pay dividends. Unfortunately, there is not a single generally accepted model for the dividend decision of firms as the reviews by Frankfurter and Wood (2002) as well as Baker, Powell and Veit (2002) reveal. In fact, Benartzi, Michaely and Thaler (1997, p.1032), conclude that Lintner s model of dividends remains the best description of the dividend setting process available. The Lintner (1956) model is an inductive model where the dividends a firm pays are a function of the firm s current earnings and past dividends. Lee and Forbes (1982) extend Lintner s dividend model to propertyliability insurance firms. We estimate the Lee and Forbes (1982) model with an added term for reinsurance usage as well as firm- and year-effects to provide further control for omitted variables. We use a fixed effects estimator and a random effects estimator: (DIV)) it = γ o + γ 1 (ReU) it + γ 2 (NI) it + γ 3 (DIV) it-1 + γ 4 (CR) it + B i + B t + ε it (3) The subscripts (i) and (t) define the insurer and the year of the observation, (DIV) is the firm s cash dividends, (ReU) measures reinsurance usage, (NI) is the net income of the insurers, (CR) represents the capacity ratio of the insurer, (B i ) is a series of binary variables to denote all but one of the individual firms and (B t ) is a series of binary variables to denote all but one of the individual years and (ε) is the error term. We report descriptive statistics for these variables and

13 13 their correlation coefficients in Appendix B. We report estimated results for relationship (3) in Table 2. We report the elasticity of our estimated coefficient evaluated at absolute mean sample values, and discuss our results in Table 5. The Hausman test favors the use of the fixed effects estimator over the random effects estimator. We reject the hypothesis that there is no relationship between cash dividends and reinsurance usage. The p-value for the fixed effects estimator suggests a 96.6 percent probability that the estimated coefficient of (ReU) is significantly different from zero and positive. Lagged dividends and net income are positively related to cash dividends in relationship (3) as their p- values suggest at least a 99.8 percent probability that the estimated fixed effects coefficients of (DIV t-1 ) and (NI) are significantly different from zero and positive. The capacity ratio of the insurer is positively related to cash dividends in relationship (3) as its p-value suggest a 89.6 percent probability that the estimated fixed effects coefficient of (CR) is significantly different from zero and positive. The positive relationship between lagged dividends, net income, capacity ratio and cash dividends is consistent with the findings of Lee and Forbes (1982). Table 2 Fixed Effects and Random Effects Estimator of the Dividends Model The fixed effects estimator is a least squares procedure and assumes that the effect of omitted variables captured by the series of firm-specific and year-specific binary variables is constant across firms and years. The random effects estimator is a feasible generalized least squares procedure and assumes that the firm and year effects differ across firms and years. (DIV)) it = γ o + γ 1 (ReU) it + γ 2 (NI) it + γ 3 (DIV) it-1 + γ 4 (CR) it + B i + B t + ε it There are 391 degrees of freedom. The adjusted R² from the least squares estimator is percent. The Hausman test value of favors the fixed effects estimator over the random effects estimator. Fixed Effects Random Effects Estimated Estimated Coefficient p-value Coefficient p-value Constant ReU DIV t NI CR

14 14 Akhigbe, Borde and Madura (1993) as well as Zhong (1999) find that the stock price of a property-liability insurance firm increases when cash dividends increase. It is possible, however, that the relationship between dividends and stock price is moderated by the volatility of the market. Lee and Forbes (1980, Table 1) conclude that in years of low market volatility the payment of dividends either increases insurance stock price or leaves it unaffected, but in years of high market volatility the payment of dividends either decreases stock price or leaves it unaffected. Thus, since we find that reinsurance usage is positively related to cash dividends, we further investigate the relationship between reinsurance usage, dividend payments and market value. Specification and Estimation of a Market Value Model There are several broad drivers to insurance firm value. These drivers are the current cash flow to stockholders, the growth opportunities of the firm (which hopefully will translate to more future cash flow for stockholders), and the relative size of the firm s liabilities to policyholders and bondholders (see for example Cummins and Lamm-Tennant, 1994; Babbel and Merrill, 2005, Sigma 3/2005). 5 We first estimate the following model using a fixed effects estimator and a random effects estimator using our entire sample: (MV) it = γ o + γ 1 (ReU) it + γ 2 (CFO) it + γ 3 (CFI) it + γ 4 (DIV) it + γ 5 (REP) it + γ 6 (GO) it + γ 7 (TDRA) it + B i + B t + ε it (4) The subscripts (i) and (t) define the insurer and the year of the observation, (MV) represents the firm s market, (ReU) measures reinsurance usage, (CFO) represents the net cash flow from operating activities, (CFI) represents the cash flow from investing activities, (DIV) measures the cash paid to stockholders in the form of dividends, (REP) measures the cash paid to stockholders in the form of stock repurchases, (GO) represents the growth opportunities, (TDRA) measures the total debt of the insurer relative to its assets, (B) is a binary variable to denote individual firms or individual years and (ε) is the traditional error term. We report descriptive 5 Sigma No3/2005 is available at 4V9GUY

15 15 statistics for these variables and their correlation coefficients in Appendix B. We report estimated results for relationship (4) in Table 3. We report the elasticity of our estimated coefficient evaluated at absolute mean sample values, and discuss our results in Table 5. Table 3 Fixed Effects and Random Effects Estimator of the Market Value Model The fixed effects estimator is a least squares procedure and assumes that the effect of omitted variables captured by the series of firm-specific and year-specific binary variables is constant across firms and years. The random effects estimator is a feasible generalized least squares procedure and assumes that the firm and year effects differ across firms and years. (MV) it = γ o + γ 1 (ReU) it + γ 2 (CFO) it + γ 3 (CFI) it + γ 4 (DIV) it + γ 5 (REP) it + γ 6 (GO) it + γ 7 (TDRA) it + B i + B t + ε it There are 391 degrees of freedom. The adjusted R² from the least squares estimator is percent. The Hausman test value of favors the fixed effects estimator over the random effects estimator. Fixed Effects Random Effects Estimated Estimated Coefficient p-value Coefficient p-value Constant ReU CFO CFI DIV REP GO TDRA In relationship (4) we do not directly control for the size of the insurer because the insurer s size is highly correlated with the other explanatory variables. For example, the correlation coefficient between the insurer s assets and (CFO) is 73.2 percent while the correlation coefficient between assets and (DIV) is 75.4 percent. The correlation coefficient between the insurer s premiums and (CFO) is 74.1 percent while the correlation coefficient between premiums and (DIV) is 74.5 percent. These correlation coefficients by themselves are not a problem, but in conjunction with the correlation coefficients of 89.3 percent between (CFI) and (CFO) and of 72.5 percent between (DIV) and (CFO) create problems in the estimated coefficients associated with multicollinerity. Thus, the impact size may have on the market value

16 16 of the firm is captured by the size of the firm s cash flow from operating and investing activities as well as from the series of binary variables we include to denote individual firms. We measure market value of the firm during the year (MV) as the product of the annual Compustat items 24 (closing stock price) and 25 (common shares outstanding). We measure reinsurance as the ratio of ceded premiums to gross premiums written (ReU) which we hand collect from SEC Form 10-K available on EDGAR. We measure net cash flow from operating activities (CFO) as annual Compustat item 308 and we measure net cash flow from investing activities as annual Compustat item 311. We measure cash dividends (DIV) as annual Compustat variables 127. We measure cash paid to stock repurchases as annual Compustat variable 115. We measure growth opportunities (GO) as annual Compustat item 24 (stock closing price) divided by the annual item BKV (book value per share of stock ) from the Compustat Price, Dividends, and Earnings database. 6 We measure total debt relative to assets (TDRA) as net (of reinsurance) reserves from annual ISIS item 7100 or from Form 10-K on EDGAR, plus total long-term debt from annual Compustat item 9, all divided by assets. We measure assets as annual Compustat item 6. The Hausman test favors the use of the fixed effects estimator over the random effects estimator. We fail to reject the hypothesis that there is no relationship between market value and reinsurance usage. The p-value for the fixed effects estimator suggests a 80.8 percent probability that the estimated coefficient of (ReU) is significantly different from zero and positive. Cash flow from operating activities, dividends, stock repurchases and growth opportunities are positively related to market value in relationship (4) as their p-values suggest at least a 93.4 percent probability that the estimated fixed effects coefficients of (CFO), (DIV), (REP) and (GO) are significantly different from zero and positive. The liabilities of the insurer relative to its assets are negatively related to market value as its p-value suggests a 99.9 percent probability that the estimated fixed effects coefficients of (TDRA) is significantly different from zero and negative. These results are consistent with the findings in the literature that higher actual or 6 It is not possible to observe the value of a firm s options, but as an aid to analysis, the market to book ratio is a commonly used measure for this purpose (see for example, Chung and Charoenwong (1991), Smith and Watts (1992) or footnote 4). The book value of equity represents how much of the insurer s assets-in-place would be left over for shareholders if the insurer went out of business immediately. Firms are generally expected to grow, retrench and adapt in response to strategic opportunities in an effort to generate economic profits for their shareholders far into the future. When shareholders believe in the ability of the insurer s managers to convert these future choices into value (or expressed alternatively, from exercising the insurer s in-the money options) shareholders are willing to pay more than the residual value of the assets-in-place. Thus the firm s market to book ratio exceeds one.

17 17 anticipated cash flow to stockholders results in higher market valuations. The negative estimated coefficient of (TDRA) is consistent with the residual nature of stock. As the liabilities of the insurer to its policyholders and bondholders increase in relation to its assets, the stockholders who are residual claimants of the firm see their share of the cash flow generated by the assets of the firm decline. We re-estimate relationship (4) using each of two sub-samples. One sub-sample consists only of observations from years where the market volatility is high. The other sub-sample consists only of observations from years where the market volatility is low. We report descriptive statistics for the variables in relationship (4) for the high market volatility and low market volatility sub-samples and their correlation coefficients in Appendix B. We report estimated results for the re-estimated relationship (4) in Table 4. We report the elasticity of our estimated coefficient evaluated at absolute mean sample values, and discuss our results in Table 5. We use the Chicago Board of Trade s volatility index (VIX) to separate our sample into years of high and low market volatility. There is a strong sense among traders that the index s long-term average value is around 22. Thus we consider years with an average volatility index value above 22 to be high volatility years and we consider years with an average volatility index value below 22 to be low volatility years. High volatility years are years 1997, 1998, 1999, 2000, 2001 and Low volatility years are years 1994, 1995, 1996, 2003 and The Hausman test favors the use of the fixed effects estimator over the random effects estimator. As with the entire sample we again fail to reject the hypothesis that there is no relationship between market value and reinsurance usage. The p-value for the fixed effects estimator for the high market volatility sub-sample suggests a 76.8 percent probability that the estimated coefficient of (ReU) is significantly different from zero while the fixed effects estimator for the low market value volatility sub-sample suggests a 75.7 percent probability. Dividends are negatively related to market value when market volatility is high but dividends are positively related to market value when market volatility is low. When market volatility is high, the p-value suggests a 99.0 percent probability that the estimated fixed effects coefficient of (DIV) is significantly different from zero and negative. When market volatility is low, the p-value suggests a 99.9 percent probability that the estimated fixed effects coefficient of (DIV) is significantly different from zero and positive. These results confirm the findings of Lee and Forbes (1980). Cash flow from operating activities and cash flow from financing activities

18 18 Table 4 Fixed Effects and Random Effects Estimator of the Market Value Model for High Market Volatility Years and Low Market Volatility Years The fixed effects estimator is a least squares procedure and assumes that the effect of omitted variables captured by the series of firm-specific and year-specific binary variables is constant across firms and years. The random effects estimator is a feasible generalized least procedure and assumes that the firm and year effects differ across firms and years. Fixed Effects Random Effects Estimated Estimated Coefficient p-value Coefficient p-value High Market Volatility Years (MV) it = γ o + γ 1 (ReU) it + γ 2 (CFO) it + γ 3 (CFI) it + γ 4 (DIV) it + γ 5 (REP) it + γ 6 (GO) it + γ 7 (TDRA) it + B i + B t + ε it There are 208 degrees of freedom. The adjusted R² from the least squares estimator is percent. The Hausman test value of favors the fixed effects estimator over the random effects estimator. Constant ReU CFO CFI DIV REP GO TDRA Low Market Volatility Years (MV) it = γ o + γ 1 (ReU) it + γ 2 (CFO) it + γ 3 (CFI) it + γ 4 (DIV) it + γ 5 (REP) it + γ 6 (GO) it + γ 7 (TDRA) it + B i + B t + ε it There are 130 degrees of freedom. The adjusted R² from the least squares estimator is percent. The Hausman test value of favors the fixed effects estimator over the random effects estimator Constant ReU CFO CFI DIV REP GO TDRA

19 19 are positively related to market value for both sub-samples as the p-values suggests at least a 97.0 percent probability that the estimated fixed effects coefficients of (CFO) and (CFI) are significantly different from zero and positive. The liabilities of the insurer relative to its assets are negatively related to market value for both sub-samples as its p-value suggests at least a 97.5 percent probability that the estimated fixed effects coefficients of (TDRA) is significantly different from zero and negative. Dividend repurchases are not related to market value when market volatility is high as its p-value suggests a 76.7 percent probability that the estimated fixed effects coefficients of (REP) is significantly different from zero. When market volatility is low dividend repurchases are positively related to market value as its p-value suggests a 99.9 percent probability that the estimated fixed effects coefficients of (REP) is significantly different from zero and positive. Growth opportunities are positively related to market value when market volatility is high but are not related to market value when market volatility is low. Its p-value suggests a 99.9 percent probability that the estimated fixed effects coefficients of (GO) is significantly different from zero and positive when market volatility is high. When market volatility is low, the p-value suggests a 50.3 percent probability that the estimated fixed effects coefficients of (GO) is significantly different from zero. Conclusion This paper addresses a gap in the literature on reinsurance, whether the purchase of reinsurance increases the wealth of the insurance firm s stockholders. The logic of Froot and Stein (1998), accepted by insurance practitioners, supports the notion that a reinsurance transaction yields benefits to stockholders. On the other hand, Schrand and Unal (1998) observe that a firm creates economic value through its core risks. Since reinsurance hedges an insurance company s core risk, the purchase of fairly-priced reinsurance will have a neutral effect on the wealth of stockholders. Table 5 summarizes our results. We consider a variety of model specifications. We relate first holding period returns, then the cash dividends the insurer pays to its stockholders and finally the market value of the insurer s stock to the use of reinsurance and a set of explanatory control variables appropriate for each measure of wealth we use. We also include a set of binary variables to our regression models to denote individual insurers and individual years. We estimate each of our models using

20 20 Table 5 Summary of Results Presented as Elasticity at Absolute Mean Sample Values Random Effects Estimator, Relationship (1) No significant relationship between reinsurance usage and holding period return. A one percent increase in systematic risk increases holding period return by 0.22 percent. A one percent increase in idiosyncratic risk increases holding period return by 0.47 percent. Random Effects Estimator, Relationship (2) No significant relationship between reinsurance usage and holding period return. A one percent increase in systematic risk increases holding period return by 0.31 percent. A one percent increase in idiosyncratic risk increases holding period return by 0.01 percent. Fixed Effects Estimator, Relationship (3) A one percent increase in reinsurance usage increases cash dividends by 0.08 percent. A one percent increase in lagged cash dividends increases cash dividends by 0.94 percent. A one percent increase in net income increases cash dividends by 0.00 percent. A one percent increase in capacity ratio increases cash dividends by 0.10 percent. Fixed Effects Estimator, Relationship (4): Entire Sample No significant relationship between reinsurance usage and market value. A one percent increase in cash flow from operations increases market value by 0.18 percent. A one percent increase in cash flow from investing increases market value by 0.00 percent. A one percent increase in cash dividends increases market value by 0.03 percent. A one percent increase in stock repurchases increases market value by 0.09 percent. A one percent increase in growth opportunities increases market value by 0.14 percent. A one percent increase in total relative liabilities decreases market value by 0.14 percent. Fixed Effects Estimator, Relationship (4): High Market Volatility No significant relationship between reinsurance usage and market value. A one percent increase in cash flow from operations increases market value by 0.08 percent. A one percent increase in cash flow from investing increases market value by 0.06 percent. A one percent increase in cash dividends decreases market value by 0.05 percent. No significant relationship between stock repurchases and market value. A one percent increase in growth opportunities increases market value by 0.18 percent. A one percent increase in total relative liabilities decreases market value by 0.12 percent. Fixed Effects Estimator, Relationship (4): Low Market Volatility No significant relationship between reinsurance usage and market value. A one percent increase in cash flow from operations increases market value by 0.35 percent. A one percent increase in cash flow from investing increases market value by 0.07 percent. A one percent increase in cash dividends increases market value by 0.18 percent. A one percent increase in stock repurchases increases market value by 0.07 percent. No significant relationship between growth opportunities and market value. A one percent increase in total relative liabilities decreases market value by 0.16 percent.