This article studies the connection between risk taking and executive compensation in financial institutions. A model of shareholders, debtholders, depositors, and an executive demonstrates that (i) excess risk taking can be addressed by basing compensation on both stock price and the credit default swaps (CDS) spread, (ii) shareholders may not be able to commit to design such contracts, and (iii) they may not want to due to distortions from deposit insurance or unobservable tail risk. The advantage of using the CDS spread rather than deferred compensation or debt is due to the fact that it is a market price and reduces agency costs.
It is well known that structuring chief executiver officer (CEO) incentives to maximize shareholder value in a levered firm tends to encourage excess risk taking. Indeed, the value of the stock for the levered firm is like the value of a call option and is increasing in the volatility (riskiness) of the assets held by the firm. This issue is particularly troublesome for banks. Although the average non-financial firm has about 35% debt,1 financial institutions have about 90% debt.2 At the same time, “banks can alter the risk composition of their assets more quickly than most nonfinancial industries, and … readily hide problems” (Levine, 2004, p. 4). Excess risk taking at financial institutions affects more than just creditors; it affects depositors, taxpayers, and potentially the financial system as a whole.
The academic literature has recognized this issue over the years and made several proposals to reduce risk taking, none of which have been adopted in the real world (we summarize these proposals below). Moreover, the link between compensation and risk remained strong throughout recent events, as evidenced by several recent empirical studies, which are listed in Figure 1.3 Along with a recent article by Edmans and Liu (2011),4 our goal is to revive the discussion on how to operationalize CEO incentive compensation toward reduced risky behavior by taking advantage of one of the most significant recent financial innovations: credit default swaps (CDS). Thus, we propose tying a CEO’s compensation in part to the financial firm’s CDS spread, which provides a market estimate of the default risk of the bank. In our proposed pay structure for bank CEOs, a high and increasing CDS spread would result in lower compensation, and vice-versa.5
Our model considers a fairly general formulation of the agency problem for banks where the bank CEO faces a multi-task problem: she chooses both the risk level of the bank and an effort level that increases mean returns. Although it may be in shareholders’ interests to commit to induce a CEO to take less risk as a way of lowering the cost of debt, we show that if the CEO’s actions are unobservable, she will be induced to undertake excessive risk in equilibrium. In addition, shareholders face a commitment problem, as they can always renegotiate the CEO compensation contract after the bank has issued its term debt. Also, as many commentators have pointed out, even if shareholders were able to commit to an incentive scheme, they would not want to due to the distortions in debt markets arising from deposit insurance and from unobservable tail risk.
A bank regulator, however, can align the CEO’s and social objectives in terms of risk choice by requiring that the CEO’s compensation be sufficiently exposed to the bank’s CDS spread. Alternatively, we show that better bank governance (or monitoring of the CEO) reduces the reliance on pay incentives, thus lowering both equity and CDS compensation. If labor market competition for CEOs increases, however, incentive pay must go up, increasing both types of variable compensation.
We further show why it is preferable to have CDS-based compensation rather than deferred cash or inside debt compensation to correct CEO risk-taking incentives. As in Holmstrom and Tirole (1993), it is preferable to build incentives around an ex-ante market measure of risk (the CDS spread) rather than just rely on ex-post performance pay. The added information contained in the CDS spread reduces agency costs for shareholders by reducing the overall risk exposure needed to discipline the CEO.
1.1 RELATED LITERATURE
We are by no means the first to consider risk-shifting by a CEO of a levered firm who is only compensated with equity. Several other papers, beginning with Jensen and Meckling (1976) have highlighted the risk-shifting problem for levered firms. Green (1984) proposes that firms issue warrants to eliminate excess risk-taking incentives. Hennessy and Tserlukevich (2008) show that callable bonds with call premia can discipline risk-shifting incentives and that convertible bonds can only discipline the most extreme forms of risk shifting. John and John (1993) suggest a default cost for the manager,6 whereas Brander and Poitevin (1992) propose a bonus contract (without equity compensation). John, Saunders, and Senbet (2000) specifically focus on banks and show that well-priced deposit insurance can possibly eliminate risk shifting. Most recently, Edmans and Liu (2011) demonstrate in a multi-task setting that giving the manager debt (either straight debt or deferred compensation) can solve the risk-shifting problem. We further this insight by demonstrating that using an instrument tied to market prices is cheaper, and analyze the incentives of banks to adopt this type of compensation structure. We explore the effects of governance and labor market competition on these components of the pay package. Bebchuk and Spamann (2010) also advocate linking pay to debt-like instruments.
In sum, our analysis advances this literature in the following main directions. First, Following Holmström and Tirole (1993), we rely on a market-based approach to correct risk-shifting incentives by exposing CEO compensation directly to the market’s assessment of the bank’s risk taking. Several recent papers suggest incorporating CDS spreads into other forms of regulation. Hart and Zingales (2010) suggest CDS spreads as a trigger for when financial firms should be asked to increase capital. Greenlaw et al. (2011) also propose CDS spreads as a macroprudential tool. Flannery, Houston, and Partnoy (2010) suggest replacing credit ratings with CDS spreads for both regulatory and private purposes.
Second, we show why optimal risk-taking incentives will not be implemented by shareholders: Shareholders suffer from a commitment problem in the model, which will be exacerbated by either the renegotiation of compensation contracts, deposit insurance, or the unobservability of tail risk to debt markets. Consequently, regulation may be necessary for implementation. Our analysis of deposit insurance highlights the richness of our model; we are able to incorporate shareholders, an executive, debtholders, depositors, and a regulator in a tractable framework.
Several recent empirical studies suggest that inside debt decreases risk taking. Wei and Yermack (2011) study non-financial firms and find that the revelation of more CEO inside debt compensation increases debt prices, decreases equity prices, and lowers the CDS spread for these firms.7Sundaram and Yermack (2007) find a significant positive effect of CEO inside debt compensation on the distance to default measure for a sample of 237 of the Fortune 500 firms from 1996 to 2002. Cassell et al. (2012) find a negative relationship between CEO inside debt compensation and the volatility of future firm stock returns, research and development expenditures, financial leverage, and a positive relationship with diversification and asset liquidity. Srivastav, Armitage, and Hagendorff (2013) find that CEOs at Troubled Asset Relief Program (TARP) banks with more CEO inside debt compensation are more likely to cut dividends and cut dividends by a larger amount. Bennett, Guntay, and Unal (2012) find that for Bank Holding Company CEO compensation there is a negative relationship between CEO inside debt compensation and default risk and a positive relationship with performance during the crisis.
The article is organized as follows: In Section 2, we write down the model. In Section 3, we analyze the optimal risk choice for a firm under concentrated ownership. Section 4 considers CEO risk choice under separation of ownership and control. Section 5 demonstrates that CDS-based compensation costs less than deferred compensation and debt. Section 6 characterizes optimal CDS-based compensation and why shareholders are unlikely to implement the first best. Section 7 discusses how CDS-based compensation could be implemented by regulators. Finally, Section 8 concludes. All proofs are in the Appendix.
2. The Model
We consider a bank that is run by a manager hired by shareholders under an incentive package designed to align the manager’s objectives with shareholders. The manager chooses: (i) the underlying riskiness of the bank’s investments and (ii) an effort level that affects the bank’s returns. We consider a classical incentive contract, where the manager receives a fixed wage and a payment that depends on the price of the bank’s stock, augmented by a payment that depends on the price of a CDS. In the benchmark model, we do not allow for deposit insurance, though in Section 6.2 we add deposit insurance to examine how the implicit subsidy in deposit insurance toward risk-taking affects the bank’s choice of risk.
2.1 INVESTMENT CHARACTERISTICS
The bank has access to an investment technology with the following characteristics. By investing an amount I the bank can get a gross return per unit invested, where can take the following values:
a high return with probability q,
a medium return x with probability , and
a low return with probability q.
The low return can take two possible values:
1. with probability γ, conditional on being in the low return state; the unconditional probability is and
2. 0 with probability
The variable q represents the risk of the investment, and will be a choice variable for the manager. This risk choice will be unobservable to the bond market. We restrict q to be in the interval . An increase in q thus increases the likelihood of both the high and low return outcomes. Having more than two outcomes makes it possible for q to be a direct measure of risk, that is, the variance of the outcomes is strictly increasing in q for all .
The manager can increase q at a cost c(q) per unit of investment. We will demonstrate below that the optimal amount of risk q is positive. We assume for simplicity that c(q) takes the quadratic form , where α is a parameter that shifts the variable cost. In contrast to the standard principal-agent model, we take the cost c(q) to be a cost borne by the bank. A natural interpretation is that c(q) is the cost of originating assets with risk characteristics q.
The variable ei, where is an observable but unverifiable effort choice by the manager that influences the high return. We set the high effort eH = 1 and the low effort . Effort i has a utility cost Ki for the manager. The cost of high effort KH is and the cost of low effort KL is normalized to 0.
The parameter γ is outside the influence of the manager. We simply treat it as an exogenous probability. It represents the likelihood that the low return will not be a tail event that completely wipes out the bank.
2.1.b The market
The bank raises funds through deposits and subordinated debt.8 For a total amount I of deposits and subordinated debt, it promises a return of . We assume that all lenders to the bank have an outside option of investing their money in an alternative that yields a safe gross return of , say treasury bills. We exogenously fix I and assume that the bank is able to raise sufficient funds given that the expected rate of return R weakly exceeds the safe return. We later endogenize the amount of funds invested in the section on deposit insurance.9
A key constraint for the bank is that risk-neutral depositors obtain a return equal to or larger than the safe return 1. If the bank were to default only when investment returns are low, this constraint would be:10
The most interesting case is the one where risk taking by the bank may lead to a default on its debt only when the low return occurs. For default to be restricted to the situation when the returns are low, two conditions must hold. First, when the low return occurs, the amount recovered is not sufficient to avoid default:
The left-hand side (LHS) is the promised return for a unit of investment (given by Equation (2)) and the right-hand side (RHS) is the highest return possible in the low state per unit invested. Since R(q) is strictly increasing in q, we ensure that this inequality holds for all q, by setting q = 0. This gives us assumption A1a:
2.2 THE MANAGER
To simplify the algebra and notation, we assume that the discount rate is zero and all agents aside from the manager are risk-neutral. Given the manager’s compensation Wi, the manager’s utility over consumption is given by a constant absolute risk aversion (CARA) utility function:
The manager faces two choices (i) the risk level of the bank q and (ii) the effort level ei. We restrict compensation to a classic linear incentive contract, where is the base pay, sE is the shares of equity, and sD is the loading on the CDSs of the bank. The price of equity is represented by and the CDS spread is represented by , where the superscript i reflects the fact that these prices will depend on the manager’s effort choice :11
Since the CDS spread is increasing in the probability of default, it is judged relative to a high benchmark in order to align the manager’s incentives. The only requirement for this benchmark is that it be large enough to ensure that the manager receives a positive payment from the CDS compensation component.12 Paying the manager in equity- or CDS-based compensation costs the shareholders dollars, where z > 0 is a small transaction cost.
The timing of our model is as follows:
Incumbent shareholders hire a manager under a linear incentive contract .
The manager chooses the bank’s risk q and effort ei.
The bank raises I to fund the asset from bondholders or depositors, with a promised return of .
The equity of the firm is priced at and the CDS spread at . The manager gets paid Wi.
The returns on the asset are realized. Depositors and bondholders get paid first. If there are returns left the shareholders get the residual value.
In other words, as long as there is upside there are gains to exposing the bank to some risk.
3. Ownership Concentration
We consider next the case where incumbent shareholders manage the firm with one voice. Shareholders choose q to maximize shareholder value net of the cost of debt. The cost of debt will reflect the market’s assessment of the risk the bank is taking. The debt market may or may not be able to observe the true risk q the bank is taking. Accordingly, we distinguish between two subcases. We first allow bond prices to reflect the perfectly observed risk q, and then we consider the case where q is not observed and where the debt market has rational expectations about the amount of risk chosen by the bank. In both, we will assume that there is no effort problem and high effort is implemented.
3.1 OBSERVABLE RISK
In equilibrium, the promised repayment R(q) is set so that this constraint binds, given by Equation (2). Substituting for R(q) in the shareholders’ maximization problem, we obtain the unconstrained problem:
As one would expect, the observability of q induces shareholders to limit their risk taking. Shareholders fully internalize the cost of greater risk taking, as it is immediately reflected in the cost of debt, so much so that the optimal solution for shareholders under observable q coincides exactly with the first-best solution: .13
3.2 UNOBSERVABLE RISK
Consider next the more realistic case where the choice of risk q is not observable to bondholders. In this case, the best bondholders can do is to form rational expectations about the bank’s optimal choice of q. This means, in particular, that if the bank changes its risk exposure at the margin, this change will not be reflected in the price of debt. As a result, the bank may be induced to take excessive risk when risk is unobservable.
In the following proposition, we prove that shareholders choose an excessive amount of risk: .
If a rational expectations equilibrium exists, the amount of risk chosen () is larger than the optimal amount (qo).
See the Appendix. □
In fact, two possible solutions to the shareholders’ problem may exist, both of which satisfy the property that . Only the smaller solution, however, is stable.14 Unobservable choices, although rationally expected, are thus riskier than observable choices, since the pricing of risk cannot respond to changes in unobservable risk choice. The bank’s shareholders are worse off with the riskier unobservable choice. This worse outcome is due to an inability of the bank’s shareholders to commit to a lower risk exposure. We will see in the next section that under separation of ownership and control the incentive contracting problem between the bank’s shareholders and the manager involves both the classical problem of aligning the shareholders’ and manager objectives and a commitment problem with respect to the bank’s bondholders. This joint contracting problem for a levered financial institution is an important conceptual difference with respect to the classical moral hazard incentive contracting problem of Mirrlees (1975) and Holmstrom (1979).
4. Separation of Ownership and Control and the Choice of Unobservable Risk
Suppose next that the bank CEO decides on the level of risk. The manager’s contract, as we stated before, is composed of three components: a fixed wage, a loading on equity, as well as a loading on the CDS spread. The equity part is standard and represents shares given to the manager as compensation. The CDS part is the innovation. In this section, we show that it can restore optimal risk-taking incentives. In Section 5, we discuss the advantages of using the CDS spread over other forms of debt and deferred compensation.
As in Holmstrom and Tirole (1993), we assume here that both equity and the CDSs are being traded by informed traders who observe signals that are perfectly correlated with the bank’s actual risk exposure q. Thus, although the bank’s actual risk choice is not observable ex-ante when the bank issues bonds it becomes effectively observable to analysts ex-post.15 In Section 6.3, we will analyze the case where tail risk is also unobservable to the market.
In order to analyze the optimal compensation contract we must first characterize equilibrium securities prices. The price of equity is given by the present discounted value of equity cash-flows, net of origination costs and expected debt repayments , where qT represents the risk level that bondholders believe the bank will implement through the compensation contract. Note that in the low return state the bank defaults and shareholders get nothing, so that the price of equity is given by:
Note that the price (and risk choice) depends on whether the manager exerted effort or not.
Note also the key simplification in our model that the risk choice qi is incorporated into the equity price and the CDS price through the valuations of informed traders. This implies that the risk-averse manager is not affected by risk with respect to these prices when her compensation is based on these prices (i.e., after the choice of qi and ei the variance: .17
We begin by demonstrating that shareholders will choose a contract such that the manager’s participation and incentive constraints bind.
In the shareholders’ optimal contract, the manager’s participation and effort-incentive constraint bind.
See the Appendix.
When the manager’s compensation package only contains stock, so that , the manager’s and shareholders’ objectives with respect to the choice of risk q are perfectly aligned, so that the manager chooses the socially excessive level of risk . If instead, we allow the compensation package to be based also on CDS spreads, then first-best incentives can be restored with the proper loading factors on equity and the CDS spread. We show this in the following proposition:
Assuming that the solution has the property , the first-best level of risk can be induced by setting , , and such that:
the participation constraint (4), and
the effort constraint (3) bind.
See the Appendix.
The number of shares to grant, the loading on the CDS component, and the fixed payment are jointly determined by the participation and effort constraints and the manager’s prescribed choice of risk. The ratio of the equity and CDS loadings should be set equal to the rate of return promised to bondholders at the first-best risk level. This relationship is directly derived from: (i) the manager’s optimal risk choice and (ii) by implementing the first-best level of risk.
Although the first-best risk level may be difficult to calculate, this provides a simple framework for thinking about how to balance incentives. Opening up the black box by substituting for qo provides further understanding:
The right-hand side (RHS) of this equation is increasing in the return on the safe investment (when the safe return is increased from 1). As the need to satisfy depositors with higher returns increases and depositors themselves are less sensitive to local change in risk, the manager will take on more risk. This is then reined in by pushing up the loading on the CDS portion of the manager’s contract. The term is the marginal return on a unit increase of risk, where the term represents the expected default recovery amount. Assuming this is positive (otherwise ), an increase in the marginal return increases this term. With higher returns to risk taking, the manager is controlled by exposing her more to the downside risk of default. Finally, the RHS of Equation (9) is decreasing in α, the marginal origination cost of q. If it is more costly to increase risk, there will be a reduced need for incentives to correct risk taking.
Although we cannot provide explicit solutions for , , and , they are pinned down by the binding effort and participation constraints and the first-order condition of the manager’s maximization problem (written out in the Appendix as Equation (16)). We can thus study implicitly how they depend on the fundamental parameters of the environment. In the next proposition, we look at how they vary with the level of competition and the quality of bank governance.
Implementing the first best level of risk, the optimal compensation package has the following properties:
Increased labor market competition (higher ) increases the amount of shares granted sEand the loading on the CDS component sD.
Stronger governance (lower ψ) decreases the amount of shares granted sEand the loading on the CDS component sD. It increases the fixed part of compensation .
See the Appendix.
Increased labor market competition for managers is reflected in a higher outside option . An increase in the value of outside offers induces shareholders to offer the manager higher compensation and higher-powered compensation through increased weightings on equity and the CDS component. We also observe in the proof that the direction of change of the fixed part of compensation is ambiguous. Thus, raising compensation is cheaper to do through the equity and CDS components because it incentivizes effort and reduces the tightness of the effort constraint.
Following Holmstrom and Tirole (1997), we proxy for improved governance through a lower cost of exerting effort for the manger. Better governance thus makes it less likely that the manager will choose to enjoy her private benefit instead of increasing the profitability of the bank. Then, the lower the cost of high effort the lower the performance-based weightings in the manager’s compensation. As the total compensation remains the same (determined by the participation constraint), the fixed amount then goes up. These predictions are consistent with Fahlenbrach (2009), who finds a substitution between stronger governance (as measured by several variables relating to board quality, the ease of launching a proxy fight, and monitoring by outside large stakeholders) and pay for performance. Chung (2008) and Acharya and Volpin (2010) also find this substitution effect.18
5. Advantages of CDS-based Compensation
Our model demonstrates the efficacy of CDS-based compensation in reducing risk taking. It is, of course, possible that other instruments exposing the manager to default risk would reduce risk taking as well. One instrument often used in practice is deferred compensation. We now show that such deferred compensation, including inside debt itself, is less efficient than CDS-based compensation in controlling CEO risk taking.
Deferred compensation is a debt-like instrument since it is unsecured and therefore is vulnerable to the risk of default. To be able to model the effects of deferred compensation we slightly extend the model by allowing for two periods (t = 1, 2) of consumption for the manager. The first period is subsequent to market pricing of equity and CDS but before the realization of the state of nature. The second period follows the realization of the state. We continue to assume that there is no discounting so as not to artificially bias the results against deferred compensation.
Thus, consider deferred cash compensation C given in addition to (non-deferred) equity compensation. It is important to note that giving cash that can be consumed at period t = 1 would not affect risk taking at all. The key here is that it is deferred, so that the manager will lose some of it if there is a default. Deferred cash compensation could be in the form of actual compensation or pension benefits (i.e., inside debt). Assume that if the low return occurs, the manager gets a return of ηC (where and represents the haircut on the manager’s claim), and when the low return of zero occurs, the manager gets nothing. Compensation for the manager then takes the form:
As we noted before, exposure to the price of equity and CDS is less risky (in fact it is riskless in the model, as market analysts are assumed to be able to perfectly infer qi and ei). We show in the next proposition that as result of this reduced risk, using CDS spread exposure is more efficient than using deferred compensation:
As , deferred cash compensation is more costly than CDS-based compensation.
See the Appendix.
In the proof we begin by showing that the participation constraint binds in the deferred cash compensation case, and then show that deferred cash compensation is more costly due to risk aversion. Notice that this argument holds irrespective of what risk choice of the manager is implemented. We also note that the condition on z is sufficient, but not necessary; in fact deferred cash compensation may also be more costly when .
Proposition 5 discusses the differing costs of compensation. In order for shareholders to prefer one type of compensation over another, we must take into account the returns shareholders get as well as the cost. We examine this in the following corollary:
As , shareholders prefer CDS-based compensation to deferred cash compensation when both implement the same level of risk q.
See the Appendix.
In Section 6, we give several reasons why optimal compensation may not be implemented. These reasons may also explain why we observe deferred cash and pension benefits as part of the compensation package in the real world and do not observe CDS-based compensation.
In principle, deferred cash compensation is very similar to compensation with a debt component, implying that CDS-based compensation should be better than debt as well. And given that debt is relatively illiquid it would be more costly to use than cash, so that CDS-based compensation dominates debt compensation even more.
One might imagine tying compensation to the price of debt rather giving the manager actual debt that they must hold. This would certainly be better for the arguments given above for CDS-based compensation. However, depending on the type of debt used, it may be difficult and/or costly to value the debt instrument at issuance and on an on-going basis. Individual debt issues vary by maturity, seniority, and specific covenants. Actual debt credit spreads may reflect liquidity and taxes (see Longstaff, Mithal, and Neis, 2005) and may lag CDS spreads (see Blanco, Brennan, and Marsh, 2005; Forte and Peña, 2009; Norden and Weber, 2009).
6. Optimal and Equilibrium CDS-based Compensation
Although it is in principle possible to make use of CDS price exposure to induce a levered bank’s manager to choose a socially optimal level of risk, it is far from obvious that a levered bank’s shareholders will want to align the manager’s risk-taking objectives. There are at least three reasons why we should not expect shareholders to offer socially optimal incentive contracts to their managers: renegotiation, deposit insurance, and unobservable tail risk.19 We explore these below.
The next two reasons why shareholders may not offer the socially optimal contract to their manager are valid even if contracts can have full commitment power.
6.2 DEPOSIT INSURANCE
Suppose now, as is true in practice, that the bank funds its investments partly with deposits that are fully insured. Concretely, consider the liability structure where funds raised through debt issues are given by B and funds raised through insured deposits are given by L. The premium charged by the deposit insurance authority is π. Therefore, the total amount of funds other than equity capital available for investment is .21 The premium set by the deposit insurance authority is set fairly and covers expected losses. It is given by:
We assume in this formulation that the amount recovered in default goes only to depositors, but is not enough to cover their obligations, which is equivalent to assuming that the premium is positive. Formally, it amounts to the following condition, which supersedes assumption A1a:22
The timing with deposit insurance is now:
Incumbent shareholders hire a manager under a linear incentive contract , where is the base pay, sE is the shares of equity, and sD is the loading on the CDSs of the bank.
The deposit insurance authority sets π.
The manager chooses the bank’s risk q for the asset.
The bank raises B and L to fund the assets from debtholders and depositors, respectively, with a promised return and 1, respectively. It pays the deposit insurance premium π.
The equity of the firm is priced at PE and the CDS spread on the firm is priced at PD.
Returns are realized. Depositors and debtholders get paid first. In the case of bank failure, the recovery amount is distributed to depositors. The deposit insurance authority compensates depositors for any shortfall below 1.
Our first benchmark is the situation where q is perfectly observed by debtholders and the deposit insurance authority can set its fees after perfectly observing q.
When q is observable to debtholders and the deposit insurance authority, there is a unique optimum qoDI. Furthermore,.
See the Appendix.
The bank takes less risk when there is deposit insurance because the deposit insurance premium increases with risk and therefore reduces the bank’s returns.
In our second benchmark, we maintain the observability of q to debtholders, but suppose that the deposit insurance authority set its premium in advance (i.e., the authority revises premia infrequently). The bank thus takes the premium π as fixed, but the deposit insurance authority rationally foresees the level q and sets the premium fairly. We then obtain the following result:
When q is observable to debtholders but not to the deposit insurance authority the optimum satisfies the property .
See the Appendix.
The level of risk is larger than qo and qoDI. When the bank is not sensitive to the cost it pays for deposit insurance it increases the level of risk q.
Now consider the case where q is unobservable to the deposit insurance authority and debtholders. Here, the bank takes both R(q) and the deposit insurance premium π as fixed.23 We then obtain:
When q is unobservable to both debtholders and the deposit insurance authority the optimum satisfies the property .
See the Appendix.
As the proof highlights the optimum may not be unique. Any solution, however, has the property that it is larger than the first benchmark and at least as large as the second benchmark . Thus, when q is unobservable shareholders prefer to increase the level of risk.
It is possible to incentivize the manager to implement qoDI by exposing the manager’s compensation to the CDS spread. The formula for the ratio of the share of CDS to the share of equity is now more complicated:
Importantly, however, shareholders will not want to implement qoDI and implement the CDS contract. When the deposit insurance authority cannot observe risk directly it is only in the interest of shareholders to implement . Consequently, regulatory intervention is required in the presence of deposit insurance to be able to implement the socially desirable level of risk.
6.3 UNOBSERVABLE TAIL RISK
Although CDS spreads were fairly accurate as the crisis began in the second quarter of 2007, particularly for distinguishing risk across banks, they did not seem to reflect the underlying risks being taken leading up to the crisis.24 The CDS market therefore may not be as efficient as we assume in the text, particularly in terms of observing tail risk. We now look at the implications of this inefficiency for the model. We use the model of “local thinking” of Gennaioli and Shleifer (2010) to capture this effect.25
We assume that both bondholders and the CDS market are not aware of the lowest possible outcome (where the bank’s investment returns zero). The probabilities, from their point of view, for the remaining states are then conditional on the zero return state not occurring: the high return occurs with probability , the medium return occurs with probability , and the low positive return occurs with probability . We maintain all other parts of the model. Bondholders still do not observe q but have “rational local expectations,” and the CDS market still observes q. The shareholders of the bank and manager are not assumed to be “local thinkers” and understand the risk being generated by the bank’s choices. All non-local thinkers, however, take into account that some agents think locally.
Not surprisingly, this is strictly larger than the original choice qo since the bondholders do not need to be compensated as much for the risk. When the manager is only compensated with equity she chooses the risk level , where:
If a rational expectations equilibrium exists, .
See the Appendix.
As in the main model, there is excessive risk taking as the interest rate the bondholders demand is not sensitive to small changes in risk. In the proof of Proposition 6, we show that if both and exist and we apply the notion of stability that we used in Proposition 1, then . In other words, local thinking may lead to less risk () than in the main model when bondholders do not observe q. The reason is that local thinking results in lower interest payments to bondholders, so that shareholders are less keen to avoid these states. From a social surplus perspective, it is thus better to have debtholders who think locally rather than fully rational debtholders. This logic, however, only goes so far. From the perspective of shareholders and the manager, local thinking in debt markets increases returns, but the increase in returns comes from two sources—an increase in actual expected returns and a transfer of expected returns from debtholders to shareholders. Debtholders expect (incorrectly) that their returns will be equal to 1, when in fact their expected returns will be less because of risk taking by the manager. So although returns are higher, debtholders are worse off in this scenario.
We now examine whether excess risk taking can be corrected by modifying the compensation package. Again, it is not in shareholders’ interest to implement such a correction. Even if they wanted to implement a correction, they would correct to rather than qo. Regulatory intervention is required to achieve this reduction in risk taking.
As the equity market is not affected by the low state, the price of shares is the same as in Equation (7) save for the fact that the local thinking interest rate is used.
We now solve for the compensation contract that implements the first-best risk level qo. Although it is conceivable that the social planner/regulator is also a local thinker, implementing qo remains the appropriate benchmark to see how compensation must be structured optimally. The following proposition shows that the weighting given to the CDS component relative to the equity component in the local thinking model may be more or less than that in the main model, depending on the parameters.
A compensation contract under local thinking can implement the first best risk level qo. Such a contract may have a larger or smaller weighting on the CDS component relative to the equity component than the compensation contract from Proposition 3, depending on the parameters.
See the Appendix.
Even though bondholders and the CDS market ignore tail risk, including CDS in compensation contracts will improve incentives. Indeed, it is still the case that all-equity contracts cannot implement the first best and that contracts with some CDS-based compensation will implement the first best. There still needs to be a part of compensation that deals with default risk, even if it does not deal directly with tail risk. There is a tradeoff in determining how much to weight the CDS component. As local thinking leads to lower interest payments to bondholders, there is less risk taking (as shown in Proposition 6), making the CDS component less important. However, local thinking in the CDS market means that CDS spreads do not reflect risk sufficiently, so that they need to be overweighted. This implies that the parameters will determine which effect is larger in determining optimal compensation.
7. Regulatory Aspects of CDS-based Compensation
Our analysis suggests that regulatory intervention is needed to correct the bias in executive pay in favor of shareholder interests. The incentives provided induce managers to take excessive risks at the expense of financial stability. Bank regulators can enhance financial stability and increase expected social surplus by requiring that there be a debt component in bank CEO compensation; in particular, by requiring that bank CEOs be exposed to their own bank’s CDS spread. Although initial compensation regulations following the financial crisis did not focus on debt components for bank CEO compensation,26 more recently the issue of risk taking and bankers’ compensation has received renewed attention from bank regulators. Thus, the Federal Reserve, mandated by the Dodd–Frank act, recently released final rules27 on “Enhanced Prudential Standards,” which provided the Federal Reserve with the scope to regulate compensation and risk management at Bank Holding Companies28 in their annual bank examinations.29 Furthermore, Daniel Tarullo, the governor of the Federal Reserve System charged with prudential regulation, noted in remarks on June 9, 2014, that while compensation packages based on equity have “succeeded in better aligning the interests of shareholders and employees, they intensify the conflict between shareholder and regulatory interests” and concluded by saying that it is key to adopt measures that adjust “incentives so as to promote prudential objectives across the many risk decisions made within the firm.”30
The new regulatory framework in the USA permits compensation based on CDSs. We believe that the implementation of CDS-based compensation for bank CEOs, other executives, and traders making risk-taking decisions most compatible with current practice and regulations is to simply introduce a formula reducing the deferred bonuses set aside by the bank when the bank’s CDS spread increases.31 The higher the spread, indicating more risk, the bigger the cut in deferred bonuses. The undistributed bonuses could then also be added to bank reserves.
Nevertheless, given the reasons discussed in Section 6, boards (as representatives of shareholders) are unlikely to implement CDS-based compensation without persuasion. Therefore, incorporating it directly into regulation is important. Firms are also unlikely to introduce other forms of compensation if there is not a regulatory standard and guidance for that form of compensation.
Note that, by linking deferred compensation to changes in CDS spreads it is possible to partially correct for myopia in the CDS market. Of course, as we point out in Section 6.3, the precise formula and the weighting of CDS spreads in bankers’ compensation will no doubt require careful calibration. No matter how complex the determination of the exact weighting of CDS price risk exposure is in practice, it is safe to say based on our analysis that the optimal weight on CDS spreads is unlikely to be zero.
In this article, we propose using a recent innovation in financial markets, the CDS, to reduce risk taking of executives at highly levered financial firms. The CDS provides a market price for risk, which, when weighted correctly in a compensation contract that includes an equity component, can provide first-best risk incentives. We demonstrate that while in their interest, shareholders would be reluctant to adopt this type of contract due to a commitment problem that may be exacerbated by renegotiation, deposit insurance, and/or unobservable tail risk. Although other debt-like instruments are available, basing compensation on the CDS spread reduces agency costs and is thus cheaper for shareholders.
One side-benefit of our approach is that it creates a built-in stabilizer using compensation that would have been useful in the crisis. When banks’ performance deteriorates and their credit quality weakens (and they experience an increase in their CDS spread), the banks will be forced to conserve capital through the automatic adjustment of bonuses. Our approach is thus in a sense analogous to cutting dividends to protect the bank and its creditors. Although cutting dividends imposes a cost on all shareholders, our approach imposes a direct cost on risk-taking managers as well.
A.1 PROOF OF PROPOSITION 1
Taking the first-order condition of the shareholders objective function (Equation (6)) gives:
In a rational expectations equilibrium, the choice of risk by the bank must be the same as depositors’ expectations, so that . This implies that the equilibrium choice of risk is determined by the intersection of the depositors’ and the banks optimal responses:
The solution is implicitly given by Equation (A.1). For a solution, we can show that Indeed, recall that
Using the quadratic formula on Equation (A.1), we find that the solution exists as long as
There can be two solutions to Equation (A.1), as depicted in Figure 2. If we define as the price of the supply of risky debt and as the price of the demand for risky debt, the smallest solution can be seen to be as stable. For this solution, if risk (q) were to be slightly larger, then the price of supply would be larger than the price that debtholders would be willing to accept, pushing risk lower. If risk (q) were to be slightly smaller, the price that debtholders would be willing to accept would be larger than the price at which risk is supplied, pushing risk higher.
A.2 PROOF OF PROPOSITION 2
The shareholders face the participation constraint (Equation (4)) and the effort constraint (Equation (3)). We denote the Lagrange multipliers on those constraints and λK, respectively. In addition, the manager maximizes his compensation by choosing q, giving us the following simplified first-order condition (given that ):
Notice that the second-order condition is negative. This choice represents additional constraints for the shareholders, with the multiplier . We must examine this for both effort levels even though we have assumed the shareholders prefer to implement high effort. That is because we must define what happens off-the-equilibrium path, which will be important for implementing high effort using the effort constraint (Equation (3)).
The shareholders maximize Equation (A.3), choosing the components of the wage , sE, and sD and taking into account the participation constraint, the effort constraint, and the manager’s risk choice (Equation (A.4)). The first-order conditions are, respectively:
Given that z > 0 and , this implies that and the effort constraint binds.
A.3 PROOF OF PROPOSITION 3
Setting and simplifying yields Equation (9) in the proposition.
A.4 PROOF OF PROPOSITION 4
We examine the solution where . Note that is defined in the text as a function of parameters by Equation (9).
Note that we will use the envelope theorem for the subsequent calculations (and thus do not have to look at the effect on qi).
Therefore, the denominator is positive.
The first expression, combined with the results above, gives us that . Furthermore, we know that . Finally, the second expression gives us .
A.5 PROOF OF PROPOSITION 5
We will first prove that the participation constraint binds in the case where there is deferred cash compensation. As before, we assume it is optimal to implement high effort. The shareholders’ objective function is
Substituting this into the second and third lines of Equation (A.15) and rewriting, we get:
Given that , it is straightforward to see the expression in the second and third lines in curly brackets is equal to the first-order condition for risk choice in Equation (A.14). Therefore, it is equal to zero. Furthermore, we set z = 0, which is one of the conditions for the proposition. This gives us:
This implies that .
As above, the properties of the CARA function given in Equation (A.16) imply that the second line and third line of Equation (A.18) can be rewritten as equivalent to the first-order conditions for risk choice, making them equal to zero. This gives us:
This implies that and the participation constraint binds.
Given that the participation constraint binds, we can now show that deferred cash compensation is more costly than CDS-based compensation.
In both the CDS-based compensation case and the deferred cash compensation case, the participation constraint binds (Equations (4) and (A.12)). This implies that:
Given that z is equal to zero, the cost of compensation is thus smaller with CDS-based compensation than with deferred cash compensation. It is then straightforward to show that the shareholders are better off: if we implement the first-best level of risk qo and positive effort for both types of compensation, the price of equity is the same in both cases. Therefore, the shareholders’ objective function is larger when there is CDS-based compensation.
A.6 PROOF OF LEMMA 1
Not surprisingly, this expression represents total surplus. The difference with our previous model is that P is present and depends on q.
First note that . We will assume that for all , which says the project has positive NPV for all q. This then implies, from Equation (A.19), that for any solution, .
The expression . Assumption A3 ensures that . As we noted above, the FOC implies that . Remember that qo from our original model satisfied the condition . This implies that . Furthermore, it implies the objective function is strictly concave over the interval . It may not be concave over the interval , but as there is no inflection point in that interval, meaning that qoDI must be the global maximum.
A.7 PROOF OF LEMMA 2
First, examine the LHS. At , it is equal to B + L. As we showed in Lemma 1, it is decreasing and concave, and Assumption A3 assures it is positive.
Next, examine the RHS and for now, take . When , the RHS is negative, decreasing, concave, and approaching negative infinity as approaches . When , the RHS is positive, decreasing, and concave (and approaching positive infinity as approaches ). Therefore, the RHS may intersect the LHS when 0,1, or 2 times. If it does not intersect, that implies the solution is for the manager to choose the maximum as the first-order condition in Equation (A.20) is positive holding fixed the deposit insurance authority expectations at . If it intersects twice, both intersections are rational expectations equilibria, but only the smaller one is stable (using the notion of stability that we use in Proposition 1).
If , the solution would be .
Now we prove that . Clearly, this must be the case if . Otherwise, we can rewrite Equation (A.20) by adding and subtracting :
This implies that , which proves our statement.
A.8 PROOF OF LEMMA 3
We proceed with a similar approach to Lemma 2.
First, examine the LHS. At , it is equal to B + L. As we showed in Lemma 2, it is decreasing and concave, and Assumption A3 assures it is positive.
Next, examine the RHS and take . When , it is negative and approaching negative infinity as approaches . When , it is positive (and coming from positive infinity as approaches ). Furthermore, for any such that , the RHS is strictly larger than the RHS in Equation (A.21). Therefore, if there are zero intersections for Equation (A.21), there are zero for the current equation and . If there is one intersection for Equation (A.21), then the solution is strictly larger than and may be equal to .32 If there are two intersections for Equation (A.21), then the solution is strictly larger than the stable rational expectations equilibria .
If , the solution would be .
A.9 PROOF OF PROPOSITION 6
In a rational expectations equilibrium the choice of risk by the bank must be the same as depositors’ expectations, so that . This implies that the equilibrium choice of risk is determined by the intersection of the depositors’ and the banks optimal responses:
For a solution, we can show that . The LHS of Equation (A.24) is when and is increasing and convex in (given A1). We depict this in Figure 3, which demonstrates that . Furthermore, if we employ the same notion of stability as in Proposition 1 and assume existence both for Proposition 1 and here, the stable solution here is smaller than . This comparison can also be observed in Figure 3.
A.10 PROOF OF PROPOSITION 7
The CDS spread is given by Equation (11).
The benchmark from the non-local thinking case (the main model) can then be written as . Therefore, we analyze whether is larger than, smaller than, or equal to 1.
When γ = 0, . When γ = 1, . The slope of is and its second derivative is , which is positive. The slope of is 1. Since is increasing and convex, its intersection with γ at γ = 1 is either the only intersection or the second intersection. It is the only intersection if the slope of at γ = 1 is less than or equal to 1, and is the second intersection if the slope of at is more than 1. If there is one intersection, then for all . If there are two intersections, there exists some cutoff , such that for , and for .
Finally, the first derivative of at γ = 1 is equal to or which may be larger or smaller than 1 depending on the parameters.