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|کد مقاله||سال انتشار||تعداد صفحات مقاله انگلیسی||ترجمه فارسی|
|694||2004||22 صفحه PDF||سفارش دهید|
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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Banking & Finance, Volume 28, Issue 2, February 2004, Pages 331–352
We analyze optimal risk management strategies of a bank financed with deposits and equity in a one period model. The bank’s motivation for risk management comes from deposits which can lead to bank runs. In the event of such a run, liquidation costs arise. The hedging strategy that maximizes the value of equity is derived. We identify conditions under which well known results such as complete hedging, maximal speculation or irrelevance of the hedging decision are obtained. The initial debt ratio, the size of the liquidation costs, regulatory restrictions, the volatility of the risky asset and the spread between the riskless interest rate and the deposit rate are shown to be the important parameters that drive the bank’s hedging decision. We further extend this basic model to include counterparty risk constraints on the forward contract used for hedging.
The focus of this paper is to study the rationale for banks’ risk management strategies where risk management is defined as set of hedging strategies to alter the probability distribution of the future value of the banks’ assets. There is a broad literature on these decisions for firms in general, beginning with Modigliani and Miller (1959): Their famous theorem states that in a world of perfect and complete markets, financial decisions are irrelevant as they do not alter the value of the shareholder’s stake in the firm. The only way to increase shareholder’s wealth is to increase value of the firm’s assets. Neither the capital structure nor the risk management decisions have an impact on shareholder’s wealth. Some important deviations from the perfect capital markets in the Modigliani–Miller setting have been identified, giving motivations for firms to care about risk management, such as taxes, bankruptcy costs, agency costs and others (Froot et al., 1993; Froot and Stein, 1998; Smith and Stulz, 1985; DeMarzo and Duffie, 1995; Stulz, 1996; Shapiro and Titman, 1986). When these reasons for risk management are incorporated into the firm’s objective function, one finds the following basic result: When all risks are perfectly tradeable the firm maximizes shareholder value by hedging completely (Froot and Stein, 1998; Broll and Jaenicke, 2000; Mozumdar, 2001).1 However, the Modigliani–Miller-theorem as well as the aforementioned hedging motives are ex ante propositions: Once debt is in place, ex post financial decisions can alter the equity value by expropriating debt holders. This strategy is known as asset substitution (Jensen and Meckling, 1976). Because of limited liability, the position of equity holders can be considered as a call option on the firm value (Black and Scholes, 1973). This implies that taking on as much risk as possible is the optimal ex post risk management strategy. In summary, theory is inconclusive regarding the question of the optimal hedging strategy of firms. Turning to the question of optimal hedging and capital structure decisions of banks, a first finding is that the analysis within the neoclassical context of the Modigliani–Miller-theorem would be logically inconsistent. Banks are redundant institutions in this case and would simply not exist (Freixas and Rochet, 1998, p. 8). The keys to the understanding of the role of banks and their financial decisions are transaction costs and asymmetric information. These features have been dealt with extensively in the banking literature, departing from the neoclassical framework (Baltensperger and Milde, 1987; Freixas and Rochet, 1998; Merton, 1995; Schrand and Unal, 1998; Bhattacharya and Thakor, 1993; Diamond, 1984 and Diamond, 1996; Kashyap et al., 2002; Allen and Santomero, 1998 and Allen and Santomero, 2001): • Banks have illiquid or even nontradeable long term assets because of the transformation services they provide. • Part of the illiquidity of banks’ assets can be explained by their information sensitivity; banks can have comparative informational advantages due to their role as delegated monitors. Examples include information about bankruptcy probabilities and recovery rates in their credit portfolio. This proprietary information can be further improved through long term relationships with creditors (Boot, 2000; Diamond and Rajan, 2000). • In contrast to other firms, banks’ liabilities are not only a source of financing but rather an essential part of their business: Depositors pay implicit or explicit fees for deposit-related services (i.e. liquidity insurance, payment services, storage). The leverage in banks’ balance sheets is thus many times higher. • Bank deposits can be withdrawn at any time. The sequential service constraint on these contracts and uncertainty about the bank’s ability to repay can lead to a “bank run” situation: All depositors rush to the bank at the same time to withdraw their money, trying to avoid being the last one in the waiting queue. This threat of bank runs creates an inherent instability for the bank’s business (Diamond and Dybvig, 1983; Jacklin and Bhattacharya, 1988). These characteristics highlight the major differences between banks and other firms: Banks, in contrast to other corporations, are financed by deposits. Their ongoing operating value would be lost to a large extent in case of bankruptcy; depositors can immediately call their claims and run whereas illiquid and information sensitive assets have to be liquidated by fire sales at significant costs (Diamond and Rajan, 2000 and Diamond and Rajan, 2001; Shrieves and Dahl (1992); the size of bankruptcy costs of banks was estimated in James (1991)). However, these features of a bank are ignored by most of the literature on capital structure and hedging decisions, which usually deals with nonfinancial firms. In a recent contribution, Froot and Stein (1998) developed a framework to analyze a bank’s optimal capital allocation, capital budgeting and risk management decisions. Their motivation for the bank to care about risk management stems from convex costs of external financing for a follow-up investment opportunity. This induces the bank’s objective function to be concave (the authors call this internal risk aversion): The more difficult it is for the bank to raise external funds, the more risk averse it behaves. A publicly traded bank in an efficient and complete market does not reduce shareholder value by sacrificing return for a reduction in risk. Thus, risk reduction is always desirable for the risk-averse bank in the Froot and Stein (1998)-setting. Hence, the resulting optimal strategy is to hedge completely. However, the authors omit the equity’s feature of limited liability and the corresponding agency problems between shareholders and debtholders. Furthermore, since in their model, there is no depository debt and thus no bank run possibility, potential effects of defaults on capital structure and risk management decisions are ignored. In this paper, we model the hedging decision of a bank with the aforementioned characteristics. We assume the capital budgeting decision to be fixed. In a one-period-two-states-model, the bank has a given amount of depository debt. The deposit rate contains a discount due to deposit-related services. The present value of this discount constitutes the bank’s franchise value. On the other hand, bank runs can force the bank to sell all of its assets at once, incurring significant liquidation costs. This creates an incentive for not having extraordinary high levels of depository debt. Further, we assume that the bank is restricted in its risk taking behavior by a regulator. We also incorporate limited liability for equity. We assume that the bank’s management acts in the shareholder’s interest and maximizes the present value of the equity. It faces thus conflicting incentives for risk management: Regulatory restrictions and liquidation costs in case of bank runs limit the risk taking on one hand. On the other hand, limited liability creates incentives for risk taking. This setting allows us to identify situations in which well known results from the corporate finance literature are found: We show that for some banks, it is optimal to hedge completely as in Froot and Stein (1998). Other banks will take on as much risk as possible to augment shareholder value by expropriating wealth from depositors, a strategy known as asset substitution (Jensen and Meckling, 1976). For still other banks, the risk management decision is shown to be irrelevant as in Modigliani and Miller (1959). The remainder of this paper is organized as follows. In Section 2, we present the model, discuss the bank’s objective function and derive the optimal hedging strategy. In Section 3, we discuss the impact of forward counterparty restrictions on the hedging positions of the bank: Since depositors have absolute priority because of their possibility to withdraw at any time, the forward counterparty can face additional default risk. It may therefore limit its contract size with the bank. Section 4 concludes the analysis and gives an outlook on further research possibilities.
نتیجه گیری انگلیسی
We have presented a one-period model in which we analyze the bank’s risk management decision. The bank is regulatory restricted, financed by deposits and is subject to liquidation costs in the event of a bank run. We find that the common interpretation of equity as an ordinary call option does not apply: Equity value is not always increased by increasing the asset’s volatility, since this also raises the likelihood of a bank run. Whenever the expected costs of such a run for shareholders cannot be outweighed by an increase of the expected return (because regulatory restrictions limit the maximum achievable risk), it is not optimal to take as much risk as possible. In these cases, safe banks with low debt ratios and asset volatility can still augment their risk exposure to the point where downside loss comes into play. However, for banks with a high debt ratio and a high asset volatility, risk reduction is the optimal strategy. This deterrence of asset substitution however vanishes in the absence of regulatory constraints or with a complete deposit insurance (Calomiris and Kahn, 1991): Without the possible downside loss, the equity payoff would be that of an ordinary call option and it would always be optimal for the bank to take as much risk as possible. Also, without regulatory restrictions, the possible downside loss could always be outweighed by higher expected return through higher risk-exposures. On the other hand, depending on how much risk taking regulatory or other restrictions allow, it may not be optimal for the bank to hedge completely as in Froot and Stein (1998): Because equity features limited liability, risk shifting to depositors is still preferred as long as the higher expected return outweighs the possible downside loss. The less restrictive regulatory restrictions are, the more relevant becomes this strategy of asset substitution. Without any restrictions of regulators or counter parties, asset substitution would always be the optimal strategy. Further, there is one constellation for which the hedging decision is shown to be irrelevant, which coincides with the result of the Modigliani–Miller-theorem. This, however, is only a special situation, where the risk management restrictions, the size of the liquidation costs in case of a bank run and the initial debt ratio are all set such that risk shifting to depositors is impossible and no bank run takes place. Among the open questions remains the analysis of the hedging decision in a multiperiod setting. Bauer and Ryser (2002) have looked at the effect that the bank’s franchise value of deposits then has. It gives an incentive to reduce risk taking since the whole stream of future income from deposit services would be lost in a run situation. Furthermore, it would be interesting to analyze the hedging decision in the presence of a nontradeable proprietary bank asset that generates an extra rent as in Diamond and Rajan (2000). The market completeness breaks down in this case and the determination of a unique objective function for the bank is not trivial anymore.