Retention Requirements and Incentives for Controlling Inefficient Risk-Taking Bridging Banking, Securitization and Capital Requirements

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1 Retention Requirements and Incentives for Controlling Inefficient Risk-Taking Bridging Banking, Securitization and Capital Requirements Rose Neng Lai University of Macau Robert Van Order George Washington University November 20, 2014 Abstract This paper models incentives for risk-taking by managers of banks or securitization deals. Of particular interest are risk-retention rules for producers of structured securitization deals, which have been mandated by the Dodd-Frank Act; the model can also be applied to bank managers. We show how incentives can be set up so that problems of asymmetric information can co-exist with socially optimal risk-taking. The role of holding an equity piece as an incentive tool has been over-emphasized; the best skin in the game incentive structure for management is to hold securities of all levels of risk, including the safest piece. As a device for protecting against bank runs, the best incentive tools require tilting the incentive structure toward the safest pieces, but not by much. Keywords: Financial Institutions, Contingent Convertible Bonds, Management Incentives, Risk-Taking, Dodd-Frank Act JEL Code: G2 Rose Neng Lai is Professor, Faculty of Business Administration, University of Macau, Taipa, Macau, China. RoseLai@umac.mo. Robert Van Order is Oliver Carr Professor of Real Estate and Professor of Finance and Economics at George Washington University, Washington D.C.. rvo@gwu.edu. 1 Electronic copy available at:

2 1. Introduction It is understandable that the focus on the link between financial institutions (FIs) and the Great Recession has been primarily on risk-taking, bankruptcy and bailout costs. However, economic cost is better measured in terms of misallocated resources, both from mispricing risk and from macroeconomic costs of financial panics. Much of the discussion of regulating risk-taking by banks has focused on capital requirements as a way of preventing bankruptcy. Similarly, the Dodd-Frank Wall Street Reform and Consumer Protection Act 1 requires risk retention, in the form of an equity position be held by managers of private securitization deals that have loans with certain observable characteristics, such as low downpayment. A critical problem in the Great Recession was, however, risks that were unobservable to investors and/or regulators. For instance, the so called Alt-A mortgages, which generally had high downpayments and credit scores, but low documentation and unobservable (to investors) risks, were one of the major sources of default losses. Similarly, some pools of loans had higher concentration levels (e.g., more geographic or product concentration) than believed. The focus of this paper is on the role of incentives for controlling unobserved risk for those who manage risk, and on deriving the optimal risk structure for management compensation. The problem is similar to the well-known problems of conflicts of interest between shareholders and bondholders in corporate finance. This has been well studied in the case of banks and deposit insurance (e.g., Buser et. al., 1981). More recently, Blum (1999), Kim and Santomero (1988), Bris and Cantale (1998), and Mitchener and Richardson (2013) have discussed the roll of capital and risk-taking. As is pointed out in Kupiec (2013), the discussions of incentives for controlling bank risk have not focused much on risk-taking by management, as opposed to CEOs. We propose a structure that can be easily imposed on managers of a financial institution. The economic need for incentives comes from shareholders desire to align management s interests with their own. We begin by assuming that this means paying 1 The Dodd-Frank Act proposed, among other things, improving the process of securitization by requiring securitizers to retain not less than 5% of the credit risk (for some types of pools) and establishing contingent capital requirements to ensure securitizers, loan originators and loan suppliers not take up higher risk than necessary. 2 Electronic copy available at:

3 them in equity shares. One reason for this is to provide incentives to maximize profits by making good business decisions like cutting costs or preserving asset value. It is also well known that managers of information-sensitive financial institutions, such as banks or managers of securitization deals, can make money for shareholders and themselves by structuring portfolios with imbedded options to take on excessive risk before depositors or regulators or investors can catch on to them. The role of capital in limiting costs of risk-taking has become a major part of the ongoing Basel Process as well as the Dodd-Frank Act. 2 Our discussion focuses on how much capital, and against what type of assets, is right. A part of that discussion is contingent capital. Calomiris and Herring (2011), for instance, propose Contingent Convertible Bonds (or CoCo bonds) as a tool that can incentivize financial institutions to control risk and raise additional capital in times of trouble. Sundaresan and Wang (2013), Hilscher and Raviv (2012), Flannery (2009) and Lai and Van Order (2013b) also provide discussions of incentives. Squam Lake Group (2010, 2013) develops a proposal for CoCo requirement and shows that CoCos can play a role alongside a standard minimum book-value-of-equity-ratio requirement. A much discussed resolution is to put CoCo bonds and similar contingent claims into remuneration packages as a way of unraveling risk-taking incentives. For securitization the discussion has been about risk retention requiring deal-makers to hold an equity interest, but not other tranches in the deal. The problem of risk-taking incentives is analyzed recently in Kupiec (2013) and Chemla, G. and C.R. Hennessy (2014), both of which look at risk-taking in the context of a model where effort is unobservable and the question is setting up incentives for efficient effort. We develop a simple model of risk-taking under asymmetric information. In particular, we assume that the deal maker or manager of structured deal or financial institution (FI) has inside information that comes for free as a part of putting the deal or FI together. This induces a range of risk that the deal maker can choose, and the model allows us to propose first-best solutions, which restores a Modigiani-Miller type equilibrium (indferent among alternative capital structures), but which might be lost due to asymmetric information. Because the 2 The online version of the original document can be found from 3

4 Modigiani-Miller type solution is optimal, any structure that favors one type of asset over another will distort asset selection and pricing, and the first best solution is to restore indference. A result is that while CoCo bonds can be helpful in controlling excessive risk-taking, neither they nor equity pieces in structured deals provide the best incentives. Rather managers have optimal incentives to control risk they are required to hold a portfolio that reflects the overall liability composition of the structure, because holding only equity provides incentives to maximize volatility. Furthermore, the best strategy to control risk-taking beyond the neutral level, for instance in order to control macro costs of bank runs, is to overweight the safer pieces of the deal, but not by much. 2. Risk-Taking We assume a simple form of deal, which we call a financial institution (FI), such as a one period structured securitization deal or a bank with assets and liabilities that last one period, which is made up of risky loans that are zero coupon bonds that promise to pay off one dollar at maturity time, which is of unit length. The loans are funded by a (tranched) structure containing an equity piece plus a debt piece. They enter the deal with value V 0 (to be discussed below), and are worth V at maturity; equity is positive and equal to E. Debt is paid off V equals or exceeds D. If we assume the same information by all agents, then absent guarantees or subsidies, there is no reason for FI management or investors to care about choices of either assets or liabilities because the Modigliani-Modigliani Theorem holds. We assume that there is an elastic supply of loans available that FIs can purchase at a price equal to the expected present value of their cash flows. They know the details of the cash flows, loan by loan, at zero marginal cost, but have to go to the market to raise money for the loans. Investors in the FIs debt, on the other hand, do not have loan level information; so there is an information asymmetry problem. In our model, anything that causes one type of asset structure to be preferred over another will raise its price and is therefore a distortion. The first best policy is to return managers to indference among structures. 4

5 We use a simplied version of models that have been used to evaluate credit risk and risks of pools of loans (see Kupiec (2007)). The terminal value, V, of the bonds is the face value (set equal to unity) minus the number of loans underlying the deal, n, that default times average loss severity rates, l. We assume that pools are made up of one- unit loans with known, and equal, unconditional default rates, p, so that expected loss per loan is pl. As in Merton (1977), we assume the model runs for one period. If V D at the end, the debt is paid, and shareholders get the residual. To this we adjust the option for FI managers to control the distribution of future values of V via the distribution of default probabilities, for instance by controlling geographic diversication. We do not model interest rate risk, assuming rates to be zero. The model suggests a binomial distribution of outcomes (success or failure) for a pool of loans. A binomial distribution can be approximated by several continuous distributions, such as normal. We assume that the number of defaults, n, is stochastic, and that the outcomes of defaults in the pool are generated from a distribution function F(n), density function f(n) and volatility. All the loans have initial value of (1 - pl), which is known to everyone. The only thing known by the managers, but not investors, is, which comes from the underlying diversication across products or location Information and Volatility Level We take it as given that managers of the FI need to have some sort of equity stake in order to manage costs in the interest of equity-holders, independent of the risk of the portfolio. We assume that the best that investors can do is to determine a range within which lies. Formally, the FI owns a portfolio of loans with par value equal to one and initial value V0 1 pl. The manager chooses subject to the limits between minimum and maximum levels of possible risk given by and, respectively. We normalize all values by V. The equity investment in the deal becomes e = E/V. The par value of the pool is unity. We assume risk neutrality throughout and, again, interest rates are zero. The expected value of the pool untranched is 3 l v h v 3 We are assuming that the probability of having zero losses or 100% losses is sufficiently small that we can take integration limited from negative infinity to positive infinity rather than from 0 to 1. 5

6 v p 1 1 f ( n) nldn 1 pl 0 (1) The value of the equity piece is given by v e e pl 1 e f ( n) nldn (2) That is, the equity holder gets back its investment minus losses, which are limited to its equity position. The third term in (2) represents the optionality in the deal. It is the expected value over the truncated distribution and can be thought of a call option on n. Hence, the equity owner has limited liability, but because the assets are bonds, it does not have the upside of a stock option; the most the equity can get back is the equity investment. The value of the debt piece is v d 1 1 e f ( n) nldn. (3) e We can model 1 e f ( n) nldn as it were a call option on n. We choose to approximate F(n) with a normal distribution, which is the case there is a large number of loans in the pool, because it yields a convenient closed form solution. A key assumption is that the possibility of n being less than zero or greater than one can be ignored. Then the value of the call on n is given by 4 c d f d ( pl e) F (4) where d pl e, F() is cumulative normal and is the volatility of n at the end of the period; and we have set the length of the period equal to one. Then 4 See Dawson et al (2007) for a derivation of properties of options on underlying normally distributed assets. 6

7 v e e pl c. (5) Note that c / f ( d) 0. (6) In the model so far, risk choice for management (and shareholders) is to maximize volatility because v e is increasing in σ via the call option. This implies putting together the least diversied deal. 3. Risk-Taking with Skin in the Game A way of controlling the cost of risk-taking is to require more capital from the FI. It is clear that this will lower the value of the call on n. However, it will not change the managers incentive to take as much risk as possible, which suggests misallocated resources. Given that there is something desirable about paying management with shares, or other financial instruments with the same payoff structure, we analyze strategies that can unwind the excess risk incentives and move equilibrium to one where capital structure is irrelevant. We show that by incorporating CoCo bonds into the model of risk-taking, the management does have the incentive to reduce extensive risk taking, thereby reducing the probability of default. Risk can be mitigated there is some benefit to surviving. A possibility of benefit is the franchise value (see Lai and Van Order (2013)). Another is for the regulators to create it. CoCo bonds create such incentives depending on the details of their conversion. We choose a simple form of virtual CoCo bond. Managers are given both shares, equal in amount to k% of existing shares, and CoCo bonds with face value B, which will be converted into (worthless) equity at the end of the period the firm is insolvent (nl > e). Because interest rates are zero, risk free debt trades at par. The only stochastic variable is n. The position of the management at the beginning of the period is like a call on its assets. The advantage of this call is that the management gets B plus its share of profit the call on n is not exercised. Then the payoffs to management at the end of the first period, are 7

8 B ke knl w m n 0 n e. (7) e n Then letting is given by: B b, the value of the expected wealth of the management per unit of V V w m e pl c( ) b(1 F( )) ( ) k (8) The last term in (8) is the CoCo bond multiplied by the probability of survival under the normal distribution assumption. Note again that surviving means not exercising the call on defaults, so that the term is 1 F() rather than F(). The CoCo bond will induce less risk-taking pl < e, i.e., expected share that default is less than the equity share; otherwise maximizing variance will maximize survival probability the gambling for resurrection strategy. l h Management chooses to maximize (8) subject to, condition is. Then the first order bf ( d)( e pl) / 2 0 w m ( ) / kf( d) (9) Note also that 2 2 k b( e pl) / ) f ( d) b( ke p) / 2 2 w m ( ) / f '( d) (10) So (9) can have an interior solution: 2 b ( e pl) / k (11) Note that this is only defined e > pl. If e < pl, managers again take as much risk as they can get away with. However, even there is an interior solution it is a minimum. That is, in the neighborhood of the solution to (9) the first term in (10) is zero and the second term is positive. Hence, wealth as a function of risk looks like the U-shaped curve in Figure 1 or is upward sloping. In either case the solution is a corner 8

9 depending on the value of b (which is the value of the coco bonds relative to the shares received by management). Figure 2 presents some intuition by presenting the payoffs for the various arrangements. The horizontal axis shows the value of the assets given by number of loans that survive through the end of the period multiplied by l. The length of the line OV represents par value of loans in the pool, which is the value none default. OD represents debt part of the pool and DV is the equity. ODA shows the end of period payoffs to management it has nothing but equity (multiplied by the fraction, k). It is convex throughout. Clearly, given such payoffs and applying Jensen s Inequality, maximizing expected management wealth implies taking as much risk as possible. Now, given OB as the amount of CoCo bonds, the line ODCB gives the payoff from the CoCo bonds. Therefore, the payoff to management, including the shares and such bonds, is the line ODCE. It is both convex and concave over dferent regions (because the bond provides concave payoffs), which accounts for the ambiguity regarding taking maximum or minimum risk. Hence, the existence of CoCo bonds can deter bank management from taking too much risk by making the low risk strategy more likely. However, it is unclear that this is an optimal strategy. Our analysis suggests that, from a social perspective, banks should be indferent to risk strategy. The CoCo bond model cannot achieve this, but instead still leaves open the possibility of abrupt swings in risk choice. The underlying reason for this is that CoCo bonds still have a limited liability dimension. 4. Perfect Offset Optimal Risk-taking and Guarantees Co-exist CoCo bonds (or mezzanine bonds in securitization deals) have limited liability that is similar to that of shareholders. Because of the convex payoff region still left to management, these bonds only imperfectly discourage risk-taking. A question is whether we can set up a virtual bond that along with the equity piece can make the payoff linear and proportional to 1 nl. A way of doing it is to make the bond conversion into virtual securities that have payoffs based on asset value, so that managers lose as assets fall all the way down to zero. 9

10 To see this, suppose that we set up some incentive similar to the CoCo/mezzanine bond in the sense that the FI pays management a remuneration package that consists k the FI stays alive, and k nl of ( 1 e) 1, which is proportional to the terminal value of the deal (net of default costs), it does not. The payoff from this is: k(1 e) w c k(1 nl) nl e. (12) e nl And the equity piece pays: k( e w s 0 nl) Then the payoff to management is: k(1 nl) w m k(1 nl) nl e e nl nl e e nl As a result, management gets k1 nl no matter what. 5 In Figure 2, w c is given by the line OFL, and the total payoff to management is given by OFG, which is a straight line through the origin i.e., neither convex nor concave, which gives incentives to maximize overall asset value without a bias in risk-taking. 6 (13) (14) For securitization deals, contrary to Dodd-Frank, this means that deal makers should hold securities that reflect performance of all tranches in the deal; holding only the equity pieces increases distortions toward risk-taking, and instruments like CoCo bonds are just like mezzanine pieces. This is still fine for securitizations deals, but probably not for banks default has macro costs, for instance in the case where impending defaults lead to bank runs. 5 Existence of franchise value of the bank will also result in management taking less risk and therefore provides social benefit - management will take less risk now in order to ensure remuneration later by maintaining the franchise value. 6 Note that k can be increased or decreased to adjust the level of compensation so that it is the same as with just equity. 10

11 A rule to control the chance of default is underweight the equity piece. This can be done by changing (12) to k' (1 e) w c k' (1 nl) n e e nl (15) with k >k Then payoff to management is k' (1 e) k( e nl) w m k' (1 nl) nl e e nl This is depicted by OHJ in Figure 2, which is concave throughout. Hence, the expected value is decreasing in σ via Jensen s inequality. As a result management has an incentive to minimize risk for any k just above k, while still having incentives to control cost via its stake in the FI. (16) 5. Conclusions We show how simple adjustments to management remuneration can diminish risktaking incentives from guarantees like deposit insurance or asymmetric information in structured securitization deals. A widely discussed vehicle is contingent convertible, or CoCo, bonds. However, while the usually understood CoCo bonds, along with traditional capital requirements, can take the default option further out of the money, they have limited incentive effects toward less risk-taking. If the desire is to keep decisions neutral relative to cases of symmetric information, then management should be required to hold some of all the deal s liabilities. If the desire is to minimize the chance of failure, then management should be required to hold a package that is somewhat overweighed toward the safest pieces. The overweighting need not be large, so that management still has incentives to maximize asset value. 11

12 References Black, F. and M. S. Scholes The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81(3), Blum, J Do Capital Adequacy Requirements Reduce Risks in Banking? Journal of Banking & Finance. 23, Bris, A., and S. Cantale Bank Capital Requirements and Managerial Self- Interest. Working Paper. Buser, S.A., A.H. Chen, and E.J. Kane, 1981, Federal Deposit Insurance, Regulatory Policy and Optimal Bank Capital, Journal of Finance, 36, Calomiris, C. R. Herring Why and How to Design a Contingent Convertible Debt Requirement. Working Paper. Chemla, G. and C.R. Hennessy Skin in the Game and Moral Hazard, Journal of Finance, 69(4), Dawson, P., D. Blake, C. Cairns and K. Dowd Options on Normal Underlyings, Centre for Risk and Insurance Studies, Nottingham University Business School. Flannery, M. J Stabilizing Large Financial Institutions with Contingent Capital Certicates, University of Florida, Working Paper. Hilscher, J., and A. Raviv Bank Stability and Market Discipline: The Effect of Contingent Capital on Risk Taking and Default Probability. Working Paper. Jeitschko, T. D. and D. J. Shin Incentives for Risk-taking in Banking a Unied Approach, Journal of Banking and Finance, 29, Kim, D., and A. Santomero Risk in Banking and Capital Regulation. The Journal of Finance. 43 (5),

13 Kupiec, P A Generalized Single Common Factor Model of Portfolio for Credit Risk.. Kupiec, P Incentive Compensation for Risk Managers When Effort is Unobservable, AEI Economic Policy Working Paper Lai, Rose Neng and Robert A. Van Order Risk-taking, Securitization and the Option to Change Strategy, Real Estate Economics, 42(2), Lai, R. N. and R. A. Van Order (2013b). Conditional, Convertible Bonds Capital Requirements, Working Paper. and Merton, R. C An Analytic Derivation of the Cost of Deposit Insurance and Loan Guarantees, Journal of Banking and Finance, 1, Mitchener, K. J., G. Richardson Does Skin in the Game Reduce Risk Taking? Leverage, Liability and the Long-Run Consequences of New Deal Banking Reforms. National Bureau of Economic Research Working Paper No Squam Lake Group The Squam Lake Report: Fixing the Financial System, Princeton University Press, Princeton, New Jersey, USA. Squam Lake Group Aligning Incentives at Systemically Important Financial Institutions. Memorandum. Willen, P Mandated Risk Retention in Mortgage Securitization: An Economist s View, American Economic Review 104(5),

14 Figure 1 Risk Level that Maximizes Wealth of the Financial Institution W m () C B O σ l σ h σ 14

15 Figure 2 Wealth Manager in Case of CoCo Bonds and Perfect Offset Manager Wealth J H E B B C G F L A O D V Value of Pool 15