Insurance Company Capital Structure Swaps and Shareholder Wealth

Transcription

1 Insurance Company Capital Structure Swaps and Shareholder Wealth James I. Hilliard, Linda Schmid Klein, Thomas J. O Brien October 18, 2007 Abstract We review the literature related to capital structure swaps and create a new model of capital structure swaps for insurance companies. We then test the validity of our theory by comparing long-run stock market returns for insurance companies that issue equity and increase reinsurance in the same year. Using long-run event study methodology, we test for value-enhancing capital structure swaps. Finding evidence of value creation resulting from swaps, we demonstrate that insurance company managers may be able to expropriate wealth from reinsurers and new equity investors when the reinsurance markets have mispriced loss reserves. Contact Author, Finance Doctoral Candidate, University of Connecticut, 78 Birchwood Heights, Storrs, Connecticut james.hilliard@uconn.edu (860) Professor of Finance, University of Connecticut Professor of Finance, University of Connecticut 1

2 1 Introduction There is limited and contradictory evidence regarding the valuation effects of capital structure swaps in the insurance industry. While the seminal literature on capital structure (Modigliani and Miller, 1958, 1963) suggests that in absence of frictions, capital structure does not affect firm valuation, and further that the tax-deductibility of interest payments causes debt to have a positive effect on post-tax earnings, there has been little work extending the theory to capital structure swaps in the presence of information asymmetry and other frictions. Reinsurance purchase is one example of a capital structure swap that insurance companies can undertake without disclosing them immediately to the public (i.e. using slack cash to purchase bargain-priced reinsurance rather than paying a dividend) or disclosing only one side of the swap immediately (i.e. issuing stock and using the proceeds to purchase bargain-priced reinsurance.) Further, there is conflicting evidence regarding the valuation effects of seasoned equity offerings in the insurance industry. In two different studies over similar periods, researchers have reached opposite conclusions. First, Akhigbe et al. (1997) find that valuation effects of insurer equity offerings are not as severely negative as those of industrial comparison firms. In contrast, Polonchek and Miller (1995) find that insurance company equity offerings underperform those of both banks and non-financial companies. This essay updates the findings of these papers using both methodologies and explains the differences resulting from the methodologies. We examine capital structure decisions of insurance companies, developing a model by which managers may decide whether they can enhance shareholder value by disposing or acquiring policies. Consistent with prior capital structure work, we show that if either the equities market or the reinsurance market have misestimated the probability distribution of the firm s loss reserves (i.e. the risk inherent in the claims), the manager may be able to enhance the wealth of controlling shareholders by retiring or issuing equity. The process and model are similar to that suggested for the general case by O Brien et al. (2007), except that instead of viewing equity value as a European call option held by the firm s shareholders, equity is an option to exchange the assets of the firm for the policy reserves assets held by the policyholders and reflected as liabilities on the firm s balance sheet. 2

3 2 Motivation When the market value of equity is defined as the difference between the market value of the firm s assets and the market value of its liabilities, O Brien et al. (2007) show that, in some cases, issuing equity can enhance shareholder value. Insurance companies provide a unique forum to explore this finding, since their liabilities can be sold in a marketplace with asymmetric information and limited signaling effects. The chief liability on an insurance company s balance sheet is policy reserves, the accumulation of premiums paid by customers and set aside to satisfy policyholder claims when they arrive. Babbel and Merrill (2005) show that if we regard the market value of the firm s assets as the sum of its franchise value and the market value of its tangible assets and the market value of its liabilities as the expected present value of the firm s liabilities, then the value of equity is the value of an exchange option: the exchange of the firm s assets for the loss outcomes. The firm s franchise value in this model is the net present value of the fixtures that allow the firm to extract economic quasi-rents, including the firm s ability to generate business through its distribution network, charters, licenses, and reputation. Since a change in value resulting from a capital structure swap should not be affected by the presence or absence of the additional fixtures, I can exclude them from my analysis without loss of generality. Babbel and Merrill (2005) model the value of the exchange option, but consider the present value of liabilities to be the present value of promised liability cash flows discounted at the risk-free rate. We follow this convention as well, but further model the market value of liabilities as the difference between the market value of the firm and the value of the exchange option held by the firm s shareholders. Finally, we assume that a reinsurance market exists which would allow the firm to lay off these risks in exchange for a payment equal to the market value of the liabilities (a function of the market estimate of the risk and expected loss of the premium reserve). Using this model, we will consider how the market value of the firm will change if the managers exploit apparent differences in volatility and expected exercise price. We can look to prior research for guidance in this process. Fischer (1978) develops an extension to the Black-Scholes Option Pricing Model, in which the risk-free rate is replaced by the difference between the expected return on a hedge asset and the expected rate of increase of the exercise price of the option. However, it may be difficult to find an appropriate hedge asset for loss liabilities, limiting the usefulness of the Fischer model for this application. Merton (1973); Margrabe (1978) suggest a model 3

4 extension of the Black-Scholes model that models the value of an option to exchange one asset for another, when the value of each asset is a random variable. Margrabe specifically suggests that this model is appropriate for valuing margin accounts, which accurately describes any firm with financial or operating leverage, including insurance companies. We will refer to this model as the Merton-Margrabe model. While most reinsurance literature assumes that the baseline price for reinsurance is actuarially fair, We suggest that there may be times when reinsurance is a bargain for the ceding company. For example, if the ceded losses have a low correlation with the reinsurer s loss pool, reinsuring these losses may reduce the volatility of the reinsurance firm, allowing the reinsurer to assume these risks at a lower premium than charged to the policyholder. This may be especially true for excess reinsurance, in which the cedant typically transfers only the tails of the claim to the reinsurer. Alternatively, the cedant may benefit from information asymmetry, since the ceding manager knows the underwriting experience for the losses while the reinsurer does not. In such cases, the cedant may have a different estimate of either the ceded pool s expected loss, or a different estimate of the pool s volatility, or both. Finally, frictions in the reinsurance market may cause the reinsurance market underwriting cycle to lag the primary insurance underwriting cycle, creating market timing opportunities. Any of these cases may create capital structure arbitrage opportunities similar to those suggested by O Brien et al. (2007). Furthermore, unlike the signaling equilibrium problems in executing otherwise optimal publicly-traded security transactions, reinsurance purchases are not announced immediately but revealed ex post in accounting and statutory reports. The absence of signaling effects relative to other capital structure transactions could intensify the incentives to purchase reinsurance. 3 Literature Review Any discussion of capital structure changes must begin with a review of the seminal work of Modigliani and Miller (1958, 1963), which showed that in a frictionless environment, firm performance was invariant to capital structure. It also showed that the cost of equity capital was a linear increasing function of the debt/equity ratio. Thus, in equilibrium, capital structure swaps should not affect shareholder wealth. Specifically, says Miller (1988), the sum of the values of all the claims is independent of the number and the shapes of the separate partitions. 4

5 In later reviews of their work, Miller (1988) and Modigliani (1988) examine the potential of information content in dividend announcements and by extension, capital structure swaps. As Miller said in his review paper, management-initiated actions on dividends or other financial transactions might then serve, by implication, to convey to the outside market information not yet incorporated in the price of the firm s securities. Indeed, the work of Modigliani and Miller shows that in the presence of both corporate and personal taxes, it is theoretically feasible for firms to carry extremely high leverage ratios in order to maximize shareholder wealth. While banks and insurers are generally highly leveraged, the ability for such firms to keep leverage unsustainably high is mitigated by regulatory pressure. Garven (1987) applies the earlier work on capital structure to the insurance industry. He suggests that reinsurance is one way to adjust the insurance firm s capital structure, and consistent with Modigliani and Miller (1958), shows that reinsurance is irrelevant when there are no frictions. He then models the impact of default risk and taxes on reinsurance purchase and finds, consistent with Modigliani and Miller (1963) that ceding insurers will purchase reinsurance to the extent that they can take advantage of tax shields. Later work by Garven and Lamm-Tennant (2003) find empirical support for most of Garven s theoretical predictions. Rendleman (1980) and Myers and Majluf (1984) show how managers can exploit information asymmetry to transfer wealth from debtholders to shareholders in project selection, when debt is risky. Doherty and Tinic (1981) show that in many ways policyholders are similar to holders of risky corporate debt. Indeed, if policyholders are willing to pay a higher price for insurance when the probability of insurer ruin is lower, then insurers have an incentive to buy reinsurance. Similarly, Scordis and Barrese (2006) demonstrate a number of operational (i.e. non-tax) benefits of reinsurance purchases, including but not limited to, reduction of information asymmetry, reduction of default probability or managers rent-seeking behavior. However, there appears to be little research into the optimal capital structure changes for insurance companies when managers have information that investors and reinsurers do not have. Here, then, we extend the work of Myers and Majluf (1984) and Rendleman (1980) to the specific project of reinsurance purchase by insurance companies. 5

6 4 Theoretical Development and Hypotheses 4.1 Firm Description and Basic Valuation Consider an insurance company with one customer. The assets of the firm are risk-free marketable securities and the liabilities of the firm are the loss reserves. The manager s objective is to maximize the wealth of controlling shareholders and he will undertake a capital structure adjustment when market conditions are favorable to achieve this end. The model has three time points, t = 0, referring to a time prior to the capital swap when market values of equity and liabilities are observed, t = 1, referring to the time of the capital swap and t = 2, referring to the future point at which the actual losses are known and paid. Any assets remaining at t = 2 are distributed to the shareholders and the firm ceases to exist. t = 0 t = 1 t = 2 Observe Expected Losses Execute Swap Pay Claims E M E I E M = E I Figure 1: Model Timeline The firm s controlling shareholders are those who own shares at t = 0 and hold them to t = 2. Other shareholders may exist at t = 0 and t = 2, but the manager is not constrained to consider their wealth objectives in the capital swap (this suggests that the controlling shareholders may benefit at the expense of intermediate or future noise traders). Nor is the manager constrained to consider the wealth objectives of policyholders, except to honor their contractual obligations and maintain regulatory compliance. At t = 0, the manager knows the true probability distribution of claims, and therefore, the volatility of the loss reserves and determines whether an opportunity exists to increase the wealth of controlling shareholders by issuing or retiring equity and either purchasing reinsurance (i.e. laying off the risk at the cost of a certain payment and reducing liabilities) or issuing more policies (i.e. increasing liabilities). The manager also observes market values for the company s equity and loss reserves (i.e. the cost of purchasing reinsurance on all or part of its book of business). At t = 1, the capital restructuring occurs and at t = 2, all policies expire, claims are paid and any remaining loss reserves and other assets are distributed to the t = 2 6

7 equity holders. We begin with an assumption that the intrinsic value of the firm is the value of its assets, remaining constant over all time periods. Therefore, a change in the value of liabilities (brought about by either issuing more policies or reinsuring some portion of the book) will require an equal and opposite change in the value of the equity. Note the difference between the intrinsic value of the firm s equity (reflecting the true probability distribution of the loss pool and assets) and the market value of the firm s equity (reflecting the market s implied probability distribution of the loss pool and assets). When these values differ, the manager may have an opportunity to engage in a capital swap that will enrich the controlling shareholders. E j = A j L j (1) In Equation 1, E is value of equity, A is value of tangible assets and L is the present value of expected claims. The subscript j is either M (market value) or I (intrinsic value). If the assets of the firm are investments in the market portfolio, they can be readily valued without dispute and market values equal intrinsic values. We are left with E j sensitive to only L j. Suppose the manager knows the true probability distribution of claims, while the market assumes a different probability distribution. Thus, when the expected losses differ, the intrinsic value of the firm s equity is defined by Equation 2: And the market value is defined by Equation 3: E I = A L I (2) E M = A L M (3) In a competitive market regulated both by state insurance departments and the Securities and Exchange Commission, some might argue that differences between the intrinsic value and the market value of expected losses should rarely exist. However, a recent exception is the 2003 restatement of reserves for asbestos exposure. As the true exposures became clear, firms analyzed their books and re-stated the true expected loss related to asbestos. Prior to the completion of these reserve analyses, the market had estimated the value of the losses higher than the firm had estimated them. Differences between the intrinsic variability of losses and the market estimation of variability may exist in other instances if the manager observes the details of the policy and true probability distribution of losses for the customer, while 7

8 the market can only estimate the policy characteristics under limited access to the underwriting files, prior loss experience, regulatory filings and ratings agency estimates. Doherty and Garven (1986), Babbel and Merrill (2005) and O Brien (2004) show that when asset returns are risk-free and loss distributions are uncertain, the value of the firm s equity is the value of an option to exchange the firm s assets for the policyholders losses, with the strike price being the future value of the assets and the option can be valued using the standard Black-Scholes option pricing model. When asset returns are risky (such as the market portfolio or a firm-specific risky investment portfolio), the option can be valued using the Merton-Margrabe exchange option pricing model. In cases where either the market s estimation of expected loss or asset return volatility differs from the manager s estimation (the intrinsic value), the manager may consider making a capital structure swap to enhance the wealth of t = 0 shareholders who will hold their shares until t = Valuation When Assets and Liabilities are Risky If the insurer is investing its assets in at least some risky securities, the strike price for the exchange option is also a random variable and can be valued using a Merton-Margrabe exchange option pricing model. The models of Merton (1973); Margrabe (1978) show that an option to exchange one risky asset for another can be valued according to the following formula: E j = A j N (d 1 ) L j N (d 2 ) (4) E j is value of equity, A j is current value of assets and L j is expected value of loss liabilities. N ( ) is a draw from the standard normal distribution function. ( ) Aj ln L j + 0.5Vj 2t d 1 =, d 2 = d 1 V j t V j t V 2 j = σ 2 ja + σ 2 jl 2ρ jal σ ja σ jl j takes the value of M when for market value of equity and I for intrinsic value of equity, σ jk is the standard deviation of the variable k under j with k=a for assets and L for losses. t is time to policy expiration. Note that is the instantaneous variance of the portfolio of long assets and short liabilities. Two examples follow in which expected managers estimates of loss (policy face value) and volatility differ from market estimates. Vj 2 8

9 4.3 The Swap If managers believe that the liabilities of the firm are undervalued, they may be able to enrich controlling shareholders by issuing equity and retiring liabilities. In the case of an insurance company, the liabilities may be retired by purchasing reinsurance, sending cash along with the liabilities to the reinsurer. In our example, the firm will raise cash by issuing equity. However, if the firm uses slack cash for this purpose it may accomplish the desired capital structure adjustments without incurring flotation costs. In the reverse, if the managers believe that equity is undervalued, they may be able to enrich controlling shareholders selling more policies, increasing liabilities, and using the cash raised to retire equity. Efficient market theory, especially Ross (1977), suggests that announcement of an equity issue or equity repurchase should signal the manager s private information to the market and prices should immediately adjust to reflect that new information. However, empirical evidence (See, for example, Lakonishok and Vermaelen (1990); Ikenberry et al. (1995); Loughran and Ritter (1995); Spiess and Affleck-Graves (1995)) suggests that market responses are not as swift as theory would suggest. In order to test the impacts of such capital structure shifts, we assume that the manager will undertake these transactions without singalling frictions (certainly reasonable under the action of purchasing reinsurance or issuing new policies) and that the market becomes aware of the true probability distributions at t = 2. Of course, benefits accruing to controlling shareholders will decline in the presence of signaling frictions. At t = 0, the market value and the intrinsic value are equal, E M,t=2 = E I,t=2, so we will suppress the j subscript for values at t = 2. To motivate our signaling friction restrictions, consider a firm whose controlling shareholders have superior information, perhaps by virtue of board seats or managers with significant equity stakes 1. The managers of such a firm, whose compensation is tied to changes in the intrinsic value of shares held by these controlling shareholders, may seek to expropriate wealth from less informed noise and liquidity traders. They will do so by issuing or retiring equity when they believe the information asymmetry situation and market conditions are best suited to maximizing controlling shareholder wealth. Furthermore, insurance companies typically hold cash and marketable securities in sufficient quantity that equity market transactions need not be contemporaneous with cash flow shocks within the firm. The definition of terminal controlling shareholder wealth depends on the 1 We recognize the contribution of Josè Manuel Campo for this illustration. 9

10 type of swap. First, where there is no swap, there is no wealth change. Second, when the firm issues equity and uses the proceeds to buy reinsurance, the t = 2 wealth of controlling shareholders (W t=2 ) is the ratio of market value of equity at t = 0 to market value of equity at t = 1, multiplied by the value of the firm s equity at t = 2. W t=2 = E M,t=0 E M,t=1 E t=2 (5) Where W t=2 is the shareholder wealth at t = 2 and E jt is the j value of equity at time t. Equation 5 represents the proportion of total equity market value before the swap (held by the controlling shareholders) to total equity market value after the swap (held by both controlling shareholders and noise traders), reflecting the smaller proportion of total equity market value held by the controlling shareholders after the swap has occurred. This ratio is then multiplied by the total t = 2 equity value to represent the terminal wealth of the controlling shareholders. New shareholders have been added, and the controlling shareholders now hold a smaller portion of the total equity than they held before the swap occurred. Managers will engage in the swap only when the optimal t = 2 wealth exceeds the t = 0 wealth. When the firm issues new policies and uses the proceeds to retire equity, the initial wealth of controlling shareholders is the ratio of market value of equity at t = 2 to the market value of equity at t = 0, multiplied by the t = 0 intrinsic value of the firm s equity: W t=0 = E M,t=1 E M,t=0 E I,t=0 (6) Equation 6 represents the proportion of total equity market value after the swap to total equity market value held before the swap, reflecting the increased proportion of total equity held by the controlling shareholders. This ratio is then multiplied by the total t = 0 intrinsic equity value to represent the wealth of the controlling shareholders prior to the swap. The controlling shareholders hold a larger portion of the equity after the swap than they held before the swap occurred. Again, managers will engage in the swap only when the the t = 2 wealth exceeds the t = 0 wealth. For firms issuing equity and using proceeds to purchase reinsurance, noting that only the t = 1 and t = 2 equity values are functions of the final liability value, the change in controlling shareholder wealth as a function of expected losses is: 10

11 [ ] EM,t=0 E t=2 E M,t=1 = L t=1 ( EM,t=0 E M,t=1 ) ( Et=2 L t=1 ) ( E t=2 E M,t=0 E 2 M,t=1 ) ( EM,t=1 L t=1 (7) The first term on the right-hand side of equation 7 represents the change in value of the controlling shareholders terminal equity value for each unit change in expected losses. The second term on the right-hand side represents the cost or benefit (dilution or accretion) associated with this change in value. The optimal swap exists when these two terms are equal. For firms selling new policies and using the proceeds to retire equity, the optimizing formula is: E t=2 L t=1 E I,t=0 E M,t=0 E M,t=1 L t=1 (8) In Equation 8, the first term on the right-hand side represents the change in terminal equity value for each unit change in loss reserves. The second term on the right-hand side represents the cost of retiring the shares of noise traders. An optimal equity value exists where these two terms are equal. If equity and liability values are linear functions, the solution to each equation, 7 and 8, will be a corner solution. In other words, consistent with prior research, firms should always issue as much equity as possible when equity is overvalued relative to reinsurance and should always issue as many new policies as possible when new policies are overvalued relative to equity. However, nonlinearity in the valuation model (such as when equity is valued as an option) may suggest an interior solution, in which only some of the losses should be reinsured. To confirm that we have maximized shareholder wealth, we will find the second derivative of the same function with respect to the new value of loss reserves. If this second derivative is negative, we know that shareholder wealth has been maximized. 4.4 Swap Examples We will illustrate the various swaps with a series of numerical examples. We will then show the sensitivity of the most interesting examples with a graph. We begin with a base case where losses are assumed correctly valued by market participants. Next, we consider the case where losses are undervalued and the reverse where losses are overvalued. Finally, we ) 11

12 consider more extreme misvaluations of equity and losses, and disagreements about the correlation between assets and losses. In each case, we assume that the firms assets are invested in the market portfolio, with σ = , and that there is no disagreement about their value Base Case First, we consider a case where managers and traders agree about the risk and value of both the asset and loss pools, and their correlation. To begin, we assume an asset pool (consisting of investments in the market portfolio, σ = 0.19) of $1,500, and a portfolio of insurance policies with expected loss of $1,000 and σ = 0.4. In this case, the managers may issue $500 in equity and use the proceeds to purchase reinsurance, effectively reducing the firm s expected loss portfolio $500, without changing the value of the assets. Alternatively, the firm may sell $200 in new policies and use the cash to retire equity, again without changing the value of assets. Assuming no taxes or market frictions for simplicity, we find, consistent with (Modigliani and Miller, 1958), Table 1 shows that shareholder wealth is not affected by leverage choices Losses Undervalued In table 2, we propose two swaps when managers believe losses are undervalued, and thus, reinsurance actuarially cheap, due to differences in volatility assumptions. This is reasonable since managers know the contents of the underwriting files and are in a better position to judge the diversification benefit of their policies than investors, policyholders and reinsurers are. In the first case, the managers issue $500 of equity and use the proceeds to purchase reinsurance in the same amount. In the second case, the managers sell $200 in new business and use the cash proceeds to retire equity. In either case, the capital structure has changed and shareholder wealth is impacted. Specifically, issuing equity and using proceeds to purchase reinsurance increases the wealth of the controlling shareholders, while issuing new policies and using proceeds to retire equity is wealth diminishing. Since the manager s objective is to maximize wealth for controlling shareholders (defined earlier as the pre-swap shareholders that still hold shares after the swap), the firm will adjust capital structure by issuing equity and 2 A long-run analysis of the standard deviation of annual returns on the market portfolio, obtained from Ken French s website, suggests a standard deviation of

13 Table 1: Expected Loss and Volatility Properly Estimated Changes in intrinsic shareholder wealth following recapitalizations of insurance companies. Calculated using Merton-Margrabe model. Base Case Issue Equity Retire Equity Intrinsic Market Intrinsic Market Intrinsic Market Asset Value Expected Loss Asset Volatility Loss Volatility Time Asset/Loss Correlation Equity Value Loss Value Controlling Portion of Initial Equity Controlling Portion of Post-Swap Equity Change in Controlling Equity Intrinsic Value

14 Table 2: Loss Volatility Overstated Changes in intrinsic shareholder wealth following recapitalizations of insurance companies. Calculated using Merton-Margrabe model. Loss Volatility Overstated Issue Equity Retire Equity Intrinsic Market Intrinsic Market Intrinsic Market Asset Value Expected Loss Asset Volatility Loss Volatility Time Asset/Loss Correlation Equity Value Loss Value Controlling Portion of Initial Equity Controlling Portion of Post-Swap Equity Change in Controlling Equity Intrinsic Value

15 using the proceeds to purchase reinsurance, changing the outstanding loss reserves Losses Overvalued We now reverse the misvaluation and show that losses are overvalued when investors believe that the loss pool is less risky than managers know them to be. This can happen when the managers undertake a more risky line of business or increase their sales effort in a particular line with less diversification benefit. Here, as shown in table 3, if insurers are able to sell higher-priced policies and use the proceeds to retire equity, controlling shareholders will gain wealth Losses Overvalued on Two Variables Until now, we have assumed that managers and investors differed only in their assumptions about volatility of losses. We now introduce another layer of uncertainty: the expected loss of the policy portfolio. Managers have access to claim files and become aware of shifts in loss values before investors and policyholders do. As long as there is a set of uninformed noise traders, managers may be able to expropriate wealth from them to the benefit of controlling shareholders. In table 4, we show two swaps, both destroying shareholder value. We will further explore this interesting finding in the next section Losses Undervalued on Two Variables Now, consider the same swaps when managers believe that the market has overestimated both its expected losses and volatility. Not surprisingly, as shown in table 5, the indicated swaps have the opposite effect from when the market has underestimated the variables of interest Other Scenarios We conclude this numerical analysis by showing the results of swaps when managers believe that market estimates of expected loss and volatility are inaccurate, but in opposite directions, and finally, when estimates of correlation between assets and losses are inaccurate. These results are not surprising. Tables 6 through 9 illustrate various other levels of misvaluation. 15

16 Table 3: Loss Volatility Understated Changes in intrinsic shareholder wealth following recapitalizations of insurance companies. Calculated using Merton-Margrabe model. Loss Volatility Understated Issue Equity Retire Equity Intrinsic Market Intrinsic Market Intrinsic Market Asset Value Expected Loss Asset Volatility Loss Volatility Time Asset/Loss Correlation Equity Value Loss Value Controlling Portion of Initial Equity Controlling Portion of Post-Swap Equity Change in Controlling Equity Intrinsic Value

17 Table 4: Expected Loss and Volatility Overstated Changes in intrinsic shareholder wealth following recapitalizations of insurance companies. Calculated using Merton-Margrabe model. Expected Loss and Volatility Overstated Issue Equity Retire Equity Intrinsic Market Intrinsic Market Intrinsic Market Asset Value Expected Loss Asset Volatility Loss Volatility Time Asset/Loss Correlation Equity Value Loss Value Controlling Portion of Initial Equity Controlling Portion of Post-Swap Equity Change in Controlling Equity Intrinsic Value

18 Table 5: Expected Loss and Volatility Understated Changes in intrinsic shareholder wealth following recapitalizations of insurance companies. Calculated using Merton-Margrabe model. Expected Loss and Volatility Understated Issue Equity Retire Equity Intrinsic Market Intrinsic Market Intrinsic Market Asset Value Expected Loss Asset Volatility Loss Volatility Time Asset/Loss Correlation Equity Value Loss Value Controlling Portion of Initial Equity Controlling Portion of Post-Swap Equity Change in Controlling Equity Intrinsic Value

19 Table 6: Expected Loss Understated and Volatility Overstated Changes in intrinsic shareholder wealth following recapitalizations of insurance companies. Calculated using Merton-Margrabe model. Expected Loss Understated and Volatility Overstated Issue Equity Retire Equity Intrinsic Market Intrinsic Market Intrinsic Market Asset Value Expected Loss Asset Volatility Loss Volatility Time Asset/Loss Correlation Equity Value Loss Value Controlling Portion of Initial Equity Controlling Portion of Post-Swap Equity Change in Controlling Equity Intrinsic Value

20 Table 7: Expected Loss Overstated and Volatility Understated Changes in intrinsic shareholder wealth following recapitalizations of insurance companies. Calculated using Merton-Margrabe model. Expected Loss Overstated and Volatility Understated Issue Equity Retire Equity Intrinsic Market Intrinsic Market Intrinsic Market Asset Value Expected Loss Asset Volatility Loss Volatility Time Asset/Loss Correlation Equity Value Loss Value Controlling Portion of Initial Equity Controlling Portion of Post-Swap Equity Change in Controlling Equity Intrinsic Value

21 Table 8: Asset/Loss Correlation Understated Changes in intrinsic shareholder wealth following recapitalizations of insurance companies. Calculated using Merton-Margrabe model. Correlation Understated Issue Equity Retire Equity Intrinsic Market Intrinsic Market Intrinsic Market Asset Value Expected Loss Asset Volatility Loss Volatility Time Asset/Loss Correlation Equity Value Loss Value Controlling Portion of Initial Equity Controlling Portion of Post-Swap Equity Change in Controlling Equity Intrinsic Value

22 Table 9: Asset/Loss Correlation Overstated Changes in intrinsic shareholder wealth following recapitalizations of insurance companies. Calculated using Merton-Margrabe model. Correlation Overstated Issue Equity Retire Equity Intrinsic Market Intrinsic Market Intrinsic Market Asset Value Expected Loss Asset Volatility Loss Volatility Time Asset/Loss Correlation Equity Value Loss Value Controlling Portion of Initial Equity Controlling Portion of Post-Swap Equity Change in Controlling Equity Intrinsic Value

23 4.4.7 Swap Example Charts Figures 2 through 5 illustrate the range of possible controlling shareholder effects from the swaps discussed in the prior section. In these figures, we hold all values constant except the intrinsic and market value of liabilities, preserving the spread between the market and intrinsic values when there is a deviation. The graphs show the change in shareholder wealth resulting from swaps that issue equity and reinsure losses on the left, to swaps that issue new policies and use cash proceeds to retire equity on the right. The most interesting of these figures is figure 3, which provides some intuition for the interesting results in tables 4 and 5. In these graphs, we can see that the arbitrary swaps chosen for the numerical examples resulted either destroying or adding value no matter which swap was executed. From figure 3, we can see the reason for this interesting result: interior extremes. In the case of both expected loss and volatility being overstated, managers can increase controlling shareholder value by issuing equity and purchasing reinsurance, but at some point, the dilution from issuing equity eliminates the gains from buying cheap reinsurance. 4.5 Hypotheses Since we have demonstrated that in the absence of signaling and other frictions, managers can increase the wealth of controlling shareholders by engaging in capital structure swaps, we now test whether these value-enhancing swaps can actually occur in practice. First, given our theory, increasing liabilities to retire undervalued equity will benefit the controlling shareholders at the expense of noise traders, exploiting both information asymmetry and tax effects. This is only possible when insurers are able to charge a relatively high price for insurance policies. Under perfect competition, of course, this would not be possible, but in the face of information asymmetry, regulatory constraints and bankruptcy costs, it may be possible. In fact, Doherty and Garven (1995) and prior literature show that underwriting returns appear to follow a second-order autoregressive process. This creates an underwriting cycle in which prices and profitability rise and fall over time. If information asymmetry, transaction costs and other frictions prevent the capital markets from fully incorporating the increased profitability for firms in the high-profit phase of the cycle, then managers may be able to increase shareholder wealth by issuing more policies and using the proceeds to retire equity. If managers are controlling shareholder value-maximizers, they will undertake these capital 23

24 Figure 2: Volatility Deviations 24

25 Figure 3: Expected Loss and Volatility Deviations Same Direction 25

26 Figure 4: Expected Loss and Volatility Deviations Opposite Direction 26

27 Figure 5: Asset/Loss Correlation Deviations 27

28 structure swaps when appropriate. Thus, our first hypothesis: Hypothesis 1 When managers engage in a capital structure swap that increases liabilities and uses proceeds to retire equity, the firm s long-run market value will increase. To test this hypothesis, we will plot the underwriting cycle for the property-casualty insurance industry. We predict that when the underwriting cycle indicates relatively high premiums, firms will incur higher levels of liability and higher leverage ratios. Firms that increase liabilities during the high-premium period and simultaneously retire equity through special dividends and share buybacks will increase the market value in the long run. This is consistent with the corner solutions indicated by 8. This hypothesis will be fully tested in future research. The second hypothesis suggests that when reinsurance is inexpensive relative to expected losses, issuing equity, even when undervalued, may increase the firm s long-run market value, contrary to most prior equity issue literature. If information asymmetry prevails between primary insurers and reinsurers, and we account for transaction and information costs, it is reasonable to assume that reinsurance prices would also follow an underwriting cycle and that this cycle lags the cycle for primary insurers. In such a case, managers of primary insurance companies may, at times, observe reinsurance policies that are priced lower than the intrinsic value of the loss liabilities on their own balance sheets. When equity is valued as an option, this would create an opportunity to engage in a capital structure swap, issuing equity or using slack cash to buy reinsurance and decrease the leverage of the firm. Again, controlling shareholder value-maximizing managers will undertake these swaps when appropriate. Hypothesis 2 When managers issue equity and use the proceeds to purchase reinsurance, the firm s long-run market value will increase. To test this hypothesis, we will plot the underwriting cycle for the reinsurance industry. We predict that when the reinsurance underwriting cycle lags the property-casualty underwriting cycle, firms will buy more reinsurance, even issuing equity to take advantage of reinsurance mispricing. To evaluate impacts to long-run market value, we will use event study methodology. First, we evaluate investor s initial responses to equity issue and repurchase announcements as related to use of funds. We will then extend the analysis with a long-run event study to evaluate the long-run market performance for companies that change their capital structure. 28

29 5 Data Collection and Sample We collected data about capital structure changes in the insurance industry from 1990 to 2006 (the last year for which market returns and accounting data are available) 3. We have collected data on equity issues, consistent with Akhigbe et al. (1997); Polonchek and Miller (1995), but for this study have omitted the debt issue analysis that both prior studies included. Our analysis extends the prior work by examining more recent announcements, allowing us to determine whether valuation effects have changed over time. We have obtained debt and equity offerings over the sample period from Thomson SDC Platinum for insurance companies (two-digit SIC 63 and 64) and reviewed the Wall Street Journal archives and the Factiva database to determine announcement dates. Our stock price returns from the Center for Research in Security Prices (CRSP) daily database. Premium, reinsurance ceded, distribution method, and other firm characteristics have been obtained from the National Association of Insurance Commissioners InfoPro database 4. 6 Empirical Models We used three models to estimate the effect of security issuance in the insurance industry using event-study methodology. First, following Polonchek and Miller (1995), we estimated abnormal returns for each company as compared with the return on an equally-weighted market portfolio. We estimated results for security issues in the sample period and compare abnormal returns with those of the results reported by Polonchek and Miller (1995). Consistent with Polonchek and Miller (1995), we will estimate the model for each firm over a 120-day estimation period that begins 210 days before the announcement date for the firm s equity. In our first estimate, the event day is the date of the registration of the security with the Securities and Exchange Commission (SEC), while future models will set the event day as the earlier of the day of the announcement publication in the Wall Street Journal registration with the SEC. The market model is: 3 We attempted to replicate the results of Akhigbe et al. (1997); Polonchek and Miller (1995), by beginning with a sample period that coincides with both studies ( ), but due to limitations in data availability, we could not. 4 Data Source: National Association of Insurance Commissioners, by permission. The NAIC does not endorse any analysis or conclusions based upon the use of its data. 29

30 R jt = α j + β j R mt + ɛ jt (9) Where R jt is the return on security j on day t in the estimation period and R mt is the return on a market portfolio on day t. Extracting the estimated intercept and coefficient for each firm from equation 9, we then define the firm s abnormal return during the event period as: ( AR jt = R jt ˆα j + ˆβ ) j R mt (10) Where AR jt is the abnormal or unexpected return on security j on day t during the event period, ˆα j is the estimated intercept from the estimation period regression and ˆβ j is the estimated coefficient on the market return from the estimation period regression. Having obtained abnormal returns for each firm for the period beginning one day prior to the announcement and ending on the announcement day, we will find the cumulative average abnormal return over all firms in the sample. Second, following Akhigbe et al. (1997), we selected matching firms from manufacturing firms issuing securities of similar size and characteristics. Firms chosen as control firms are selected from among offerings within 180 days before or after the insurer offering, with announcement dates and relative sizes of its offered security as close as possible. Relative size of offering will be measured as the ratio dollar value of issuance to market capitalization of the firm. We calculated the market capitalization as of the last day of the month preceding the offering. We standardized the number of days between insurance and manufacturing offering by the standard deviation of number of days for each firm, and standardized the difference in relative size by the standard deviation of differences in relative size. For each insurance firm, we chose a matched firm with the smallest sum of standardized day and relative size differences 5. A difference in means test, shown in table 10 indicates no differences between the relative size or days between the insurance firm offerings and the control firm offerings. We estimated abnormal returns relative to an equally-weighted portfolio for the insurance offerings and compared the results with the abnormal returns for the matched-firm security portfolio. We compare our results with those of Akhigbe et al. (1997) for the sample period Finally, we use the three-factor model of Fama and French (1992, 1993) to estimate results from this model for the entire sample period: 5 We recognize the suggestion of Andrew Petersen for this technique. 6 Akhigbe et al. (1997) employ the event parameter approach of Karafiath (1988), which yields the same results as our two-step model. 30

31 Table 10: Descriptive Statistics Descriptive Statistics for Sample Firms. t-statistics for point estimates and z-statistics for difference in means in parenthesis. Insurance Firms Matched Industrial Firms Difference N Relative Offering Size (2.32) (6.53) (0.799) Market Capitalization (000) 1,483, , , (7.02) (8.76) ( ) Offering Size (000) 190, , , (8.42) (8.38) (33.296) Days Between Offerings (0.57) 31

32 R jt = α j + β j R mt + s j SMB t + h j HML t + ɛ jt (11) I will then estimate event window returns using this model: ( AR jt = R jt ˆα j + ˆβ ) j R mt + ŝ j SMB t + ĥjhml t (12) This model accounts for size and growth opportunities, as well as general market movements, in generating expected returns. Fama and French (1992, 1993) show that their model is better supported empirically than the standard market model of equations 9 and 10. After estimating the cumulative average abnormal return from this model for the periods from , and , we extract excess daily returns from each model and use them as the dependent variable in a future cross-sectional regression, testing market reactions to such factors as direct-to-net premium ratio, distribution method, leverage change, and other control variables. Our model follows Sefcik and Thompson (1986): CAAR jk = FB + e jk (13) CAAR jk is the cumulative average abnormal return over the event period obtained from equation 12, F is a vector of firm characteristics such as a constant term and other variables suggested above. B is a vector of coefficients on F. Our cross-sectional analysis may allow us to synthesize the work of Polonchek and Miller (1995) and Akhigbe et al. (1997) and provide additional insight into the valuation effects of capital structure change. Finally, in future research, we extend the event study methodology to evaluate long-run abnormal compoud returns over the two-year period following the announcement of a security issue. 7 Results Our event study results are shown in table 11. The results confirm significant negative event period abnormal returns for the sample of insurance companies, confirming the result of Polonchek and Miller (1995). However, the results are not as strong and convincing as Polonchek and Miller (1995), and in fact, are less negative than the sample of commercial bank equity offerings that they cite. However, the significant abnormal returns for insurance companies negates the result of Akhigbe et al. (1997), as does the lack of significance in the difference between the insurance portfolio and the 32