Where does the Information in Mark-to-Market. Come from?

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1 Where does the Information in Mark-to-Market Come from? Alexander Bleck Pingyang ao Chicago Booth October 2011 Abstract We study how accounting measurement interacts with banks loan origination and retention decisions in the originate-to-distribute (OTD) model and evaluate the overall efficiency of mark-to-market accounting (MTM) relative to historical cost accounting (HC) in this context. On the one hand, MTM exploits the information in the loan price. As such, it improves the accuracy of loan valuation and ex-ante incentives. On the other hand, we show that MTM, by exploiting the information in the loan price, affects the banks incentives to both retain and originate loans. This change in the banks incentives could alter the very information in loan price MTM attempts to exploit. The overall efficiency of MTM is a trade-off of these two forces. We thank Anne Beatty, Sel Becker, Jeremy Bertomeu, Qi Chen, Doug Diamond, Richard Frankel, Andrei Kovrijnykh, Eva Labro, Christian Laux, Christian Leuz, Brian Mittendorf, Raghu Rajan, Korok Ray, Stephen Ryan, Haresh Sapra, Katherine Schipper, Cathy Schrand, Amit Seru, Doug Skinner, Phil Stocken, Lars Stole and participants at the NBER-Sloan Project on Market Institutions and Financial Market Risk, the Carnegie Mellon Accounting Theory Conference, the SUERF and Bank of Spain Conference on Disclosure and Market Discipline, the EIASM Workshop on Accounting and Economics, and workshops at the Bank for International Settlements, the Federal Reserve Banks of Chicago and Philadelphia, UNC, Wharton, Washington University, Duke University, Chicago Booth, Tilburg, CUHK, UST and Ohio State University for valuable discussions and acknowledge financial support from Chicago Booth.

2 The measurement of position necessarily disturbs momentum, and vice versa - Heisenberg (1929) 1 Introduction Conventional wisdom holds that MTM makes asset valuation more accurate by exploiting the information in asset prices. The enhanced accuracy then influences firm behavior and results in various benefits. But where does the information in asset prices come from? In a market with frictions, the information in price is sensitive to the very firm behavior MTM intends to influence. As a result, MTM exploits and affects the information in asset price at the same time, and its efficiency should be evaluated in this context. Consider the following setting in which assets on the balance sheet arise endogenously. Banks follow the originate-to-distribute (OTD) model: they have expertise in originating loans but seek to sell their loans after origination to avoid the regulatory cost of retaining loans on their own books. In distributing (selling) their loans, banks face a lemons market problem due to the natural information advantage they derive from originating the loans. One classic solution for the good bank (the bank with a good loan) is to retain a portion of its loan to convince the market of its high quality. In the resulting signaling equilibrium, the bad bank sells its entire loan at a low price, while the good bank s loan is divided into two portions that are of identical quality: the retained portion and the sold portion. The retained loan on the bank s balance sheet arises endogenously as a response to the informational friction in the market. In this context, the market price of the sold loan is informative about the quality of the retained loan on the bank s balance sheet, but this informativeness of the loan price is sustained by the good bank s costly retention. How should we value the retained loan? What are the economic consequences of measuring the retention at the price of the sold 2

3 loan? To study the effects of MTM, we contrast it against the benchmark of HC. HC records the retained portion at its prior (adjusted) book value and thus does not exploit the information conveyed by the price of the sold loan. In contrast, MTM marks the retained loan up to the high price of the sold loan. In other words, MTM, unlike HC, allows the bank to recognize the expected economic profit on the retained loan before the loan actually pays off. How does this early recognition of the economic profit on the retained loan affect the bank s behavior in its retention and origination decisions? Holding the retention decisions constant (the good bank retaining a critical portion and the bad bank not retaining anything), MTM benefits the good bank by allowing the early recognition of the expected economic profit on the retention. This benefit increases the valuation accuracy of the retention, which in turn increases the value of a good loan to the bank and improves its ex-ante incentive to originate good loans. Therefore, holding the retention decisions constant, MTM improves ex-ante efficiency by enhancing the accuracy of valuation, consistent with the conventional wisdom about MTM. However, the retention decisions are affected by the early recognition under MTM. The additional benefit of early profit recognition on the retention makes retention more valuable and thus holding retention more attractive for a bank. The key observation is that MTM extends the benefit of early recognition to any bank that retains a critical portion of the loan. As a result, while MTM increases the payoff to the good bank that retains on the equilibrium path, MTM also increases the payoff to the bad bank on the off-equilibrium path when it contemplates deviating from the separating equilibrium to mimic the good bank through retention. This increased payoff for the bad bank on the off-equilibrium path increases the bad bank s incentive to mimic and makes it more difficult for the good bank to differentiate itself. As a result, the good bank has to raise the level of costly retention in order to deter the bad bank from mimicking and restore the separating equilibrium. Thus, moving to MTM changes the retention decisions. 3

4 Another way to see why MTM makes it more difficult for the good bank to differentiate itself is as follows. MTM does not reveal the bank s private information about the quality of the retained loan directly. If MTM could grant the mark-up only to the good bank and force the bad bank to mark its retention down, or equivalently if the information MTM exploits were exogenous, MTM would improve the valuation accuracy without inducing a strategic response. However, the MTM rule stipulates that the retention be marked to the market price of the loan the bank has sold. To exploit the information in the loan price, MTM has to rely on the banks retention behavior to generate the information. Thus, the information in the loan price MTM exploits is endogenous to the banks retention decisions. Because the bad bank could also hold retention on the off-equilibrium path, the early recognition benefit under MTM is also available to the bad bank on the off-equilibrium path. This increase in the payoff for the bad bank on the off-equilibrium path, induced by MTM, increases the equilibrium retention by the good bank and makes signaling more costly. In this sense, the attempt to exploit the information in the loan price via MTM makes producing the information in the loan price more costly. Compared with HC, MTM thus creates a trade-off: MTM reduces the unit cost of retention but at the same time raises the equilibrium level of retention. The net effect of this trade-off determines the value of a good loan to the bank and its ex-ante incentive to generate good loans. In particular, we demonstrate three consequences of MTM. First, the higher level of retention under MTM (relative to HC) to sustain the informativeness of the loan price means that banks retain more exposure to the risk of the loans they originated. Second, as the equilibrium level of retention increases, separation becomes infeasible at some point. In any resulting non-separating equilibrium, the loan prices are less informative about the quality of both the sold and the retained loans. Finally, the above trade-off of MTM could be such that MTM reduces the value of originating good loans, resulting in banks lower ex-ante incentive to originate good loans and a lower overall quality of loans in the economy. The most important contribution of our paper is to highlight the reverse causality 4

5 between accounting measurement and the liquidity (information) of asset markets, liquidity broadly defined as the sensitivity of the loan price to banks trading. It is commonly perceived that illiquidity of asset markets is the main implementation obstacle for MTM. For example, the three levels of inputs for fair value measurement in FAS 157 are based on the (il)liquidity of the asset market. Our analysis emphasizes a conceptual obstacle for MTM. MTM does not directly reveal the quality of assets and improve the valuation accuracy; rather, MTM attempts to exploit the informativeness of asset price to influence a firm s behavior. Because the informativeness of asset price is influenced by the firm s behavior, we show that MTM could make it either more costly or prohibitively costly to sustain the informativeness of asset price. It is this feedback from MTM to the informativeness of asset price that compromises the efficiency of MTM. The benefit of MTM in the form of the improvement in valuation accuracy should be balanced with the endogenous cost arising from the change in the firm s real decisions that adversely affect the informativeness of the asset price MTM attempts to exploit. The logic that how we measure a firm s balance sheet changes the firm s balance sheet seems to be a general feature of accounting measurement beyond our particular model (e.g. Kanodia (1980)). It is reminiscent of the Lucas Critique that policies derived from the observed empirical relation could change the underlying relation. It is also consistent with Demski s call for providing micro-foundations for equilibrium expectations (Demski (2004)). In a separating equilibrium, the price of the sold loan is informative about the retained loan but HC ignores this information. Attempting to exploit this observed link by switching to MTM, however, changes the banks behavior and therefore alters the previously observed link. In general, attempting to resolve accounting measurement problems via a market-based solution could lead to unintended and sometimes undesirable consequences. A firm s business model is viable only if it has some competitive advantage over the market in conducting its activities. As a result, the core assets and liabilities on a firm s balance sheet, dictated by its business model, are often subject to the same market frictions that sustain 5

6 the business model. Market prices in these markets are thus endogenously linked to the firm s activities that are guided partially by accounting measurement. The optimal design of an accounting measurement rule thus requires an understanding of the firm s business model to efficiently support the business model. The inefficiency of MTM in the OTD model, where retention serves as a costly signal to overcome the information asymmetry in the market, is that MTM treats retention as if it was sold, directly contradicting the bank s purpose (business model) of holding retention. Even though there has been a growing theoretical literature examining the costs and benefits of MTM, the relation between MTM and liquidity has not been examined until recently. Allen and Carletti (2008) and Plantin, Shin, and Sapra (2008) are the first to show how MTM could exacerbate illiquidity in asset markets. Firms sales caused by an initial shock affect the market price and MTM feeds the price impact back into firms sales, resulting in a loop that amplifies the initial shock in the market. We extend their work by endogenizing the illiquidity from the primitive friction of information asymmetry. The information in the loan price and the liquidity in the loan market are sustained by the privately costly signaling. As soon as one attempts to exploit them by marking the retained loan to the market price, the private cost to sustain price discovery increases and the liquidity could deteriorate. The point that the overall efficiency of MTM should take into account the endogenous nature of the information is also shared by Reis and Stocken (2007) and orton, He, and Huang (2008). Reis and Stocken (2007) study the production and price setting behavior of firms in a duopoly. They show that it is difficult to implement fair value measurements because they are endogenous to the strategic interactions between firms. orton, He, and Huang (2008) study the optimal use of information gleaned from market prices of securities in solving the agency problem between a principal-investor and an agent-trader. They show that the inclusion of market prices in the compensation contract induces traders to collude and manipulate market prices when they are able to do so. 6

7 The rest of the paper is organized as follows. Section 2 describes the model, Section 3 presents the equilibria, Section 4 states our main results, Section 5 provides details on additional results, Section 6 considers various extensions to the basic model, and Section 7 concludes. Appendix A includes the proofs that are not in the text. 2 Model The model has two elements. The first element is a setting in which the bank retains its loans endogenously and the retention decision affects its origination decision. For this part we adopt a "skin-in-the-game" component to endogenize the bank s retention decision and a moral hazard component to link the retention decision to the origination decision. The second element, which is our main contribution, is to link accounting measurement to the bank s retention and origination decisions. 2.1 Overview There are three dates, t = 0, 1, 2, and a continuum of ex-ante identical banks of unit mass. A representative bank follows the originate-to-distribute (OTD) model, which implies two features. First, the bank has expertise in originating loans. Second, it is costly for the bank to retain the loan to maturity. A loan portfolio originated at t = 0 generates a random cash flow θ + x at t = 2. 1 θ, the realization of θ, is privately observed by the bank at t = 1. θ can take two values: either good () or bad (B), > B. The ex-ante probability distribution of θ depends on the origination effort at t = 0 in a way that will be specified in the next paragraph. In 1 We will henceforth simply refer to the origination as a single loan. The single loan is a stand-in for a large portfolio of loans, each with cash flow θ + x + ε n, where θ + x and ε n are the systematic and the idiosyncratic components) respectively. Thus, the aggregate cash flow of the loan portfolio is 1 θ + x = lim ( θ + x + εn. N N N n=1 7

8 contrast, x cannot be influenced by anyone and its realization is not revealed to anyone, including the bank, until t = 2. x has density f(x) and distribution F (x) in [x, x], with x < x, f(x) > 0, and E[ x] = 0. Thus, the expected cash flow of a loan conditional on the bank s private information at t = 1 is E[ θ + x θ] = θ. We call θ the quality (type) of a loan or interchangeably the quality (type) of the bank. The timeline of the model is as follows. At t = 0, the banker exerts an uncontractible effort m, at a private cost of s (m), to originate one unit of a loan. The effort m determines the ex-ante distribution of θ. ) Specifically, Pr ( θ (m) = = m. That is, a bank with origination effort m receives a good loan (θ = ) with probability m and a bad loan (θ = B) with probability 1 m. This assumption operationalizes the first part of the OTD model that the bank has expertise in loan origination and could improve loan quality with uncontractible efforts. At t = 1, after the bank originates the loan and learns its quality θ, the bank decides what portion of the loan portfolio to sell or retain. There are three factors that affect the retention decision. First, the bank incurs a cost c for every unit of the risky loan it carries on its books from t = 1 to t = 2. We discuss the various interpretations of cost c in Section 6 and will stick to the interpretation of c as a regulatory cost for the ease of reference in the rest of the paper. This assumption operationalizes the second part of the OTD model that it is costly for the bank to retain the loan. Second, the bank faces the lemons problem in the loan market as a result of its private knowledge of its loan quality θ, which in turn results from its expertise in loan origination (the first part of the OTD model). To overcome the lemons problem (Akerlof (1970)), the bank adopts a standard skin in the game solution. It retains k portion of the loan on its own books and investors respond with a per-unit price p(k), k [ 0, k ], for the 1 k portion of the loan it sells. k < 1 as otherwise the sold portion degenerates to 0. As a result, the bank endogenously holds a non-cash asset, i.e. the retained loan, on its balance sheet. 2 Finally, the accounting 2 In Section 6.4, we show that using a more general contract to solve the lemons market problem does 8

9 measurement of this endogenous asset on the bank s balance sheet affects the incentive in the retention decision in a way to be specified in the next Subsection. At t = 2, the loan payoff realizes and the bank is liquidated after all claim holders are paid off. There is no discounting and all parties are risk-neutral. The timing of the model is summarized in Figure 1. t = 0 t = 1 t = 2 Origination decision: Retention decision: Cash flow realization: Bank exerts effort m Bank learns loan quality θ; The loan pays off; to originate a loan decides fraction k to retain Bank liquidates and and 1 k to sell; distributes to all claim holders Market prices the sold loan at p (k) Figure 1: Timeline 2.2 Accounting measurement and the bank s objective function at t = 1 In this Subsection, we link accounting measurement to the bank s objective function at t = 1 when the bank makes the retention decision. We assume that the bank, which is financed by equity and debt and maximizes its equity holders value, is protected by limited liability. iven the retention decision k, bank type θ and any accounting regime A, we denote the dividends distributed at t = 1 and t = 2 by d A 1 (k; θ) and d A 2 (k; θ), respectively. At t = 1, the bank maximizes the equity value not affect the main results qualitatively provided that the bank s regulatory cost is proportional to the bank s risk exposure to the loan that results from the contract. 9

10 by solving the following program [ ] max U A (k; θ) = d A 1 (k; θ) + E 1 da 2 (k; θ) k,d 1,d 2 (Program 1) The limited liability together with the risk in future cash flow x induces the bank to distribute dividends at t = 1 as much as possible. In response to the bank s opportunism, accounting measurement is used to restrict the bank s dividend distribution. We formalize this restriction on the bank s decision problem above in the following assumption. Assumption 1. The amount of dividends a bank is allowed to distribute at t = 1 cannot exceed its retained earnings at t = 1 (before dividend distribution). iven the retention decision k, bank type θ and any accounting regime A, we define e A 1 (k) and ẽa 2 (k; θ) as the bank s earnings at t = 1 and t = 2, respectively.3 Because the retention decision is made at t = 1, e A 1 (k) is a constant and ẽa 2 (k; θ) is a random variable due to the randomness in the cash flow x at t = 2. Further, θ appears in ẽ A 2 (k; θ) but not in e A 1 (k), because it is private information of the bank at t = 1 and cannot be directly used in any accounting measurement. This highlights the critical observation that accounting measurement A at t = 1 does not directly reveal the bank s private information about the quality of the retained loan. The fundamental property of any accounting measurement regime is that, fixing a firm s real decisions, the sum of earnings is equal to the sum of net cash flow over the firm s entire life. That is, e A 1 (k) + ẽa 2 (k; θ) is independent of accounting measurement A. An accounting measurement regime thus shifts earnings across the two periods without affecting the bank s net cash flow. This inter-temporal allocation of earnings would be economically irrelevant without additional assumptions. We prove that limited liability 3 Even though we have not specified how earnings are determined under any particular accounting regime A, proceeding without such a specification is inconsequential as the results in this Subsection apply to any accounting regime A. 10

11 and the accounting-based restriction on the dividend distribution are sufficient to establish the economic relevance of accounting measurement. Lemma 1. With the assumptions of (i) limited liability and (ii) Assumption 1, Program 1 is equivalent to Program 2 max k U A (k; θ) = e A 1 (k) + E 1 [ max {ẽa 2 (k; θ), 0 }] θ {, B} (Program 2) Intuitively, the link between the dividend distribution and retained earnings (Assumption 1) transforms the dividend distribution problem to an accounting earnings problem, and the limited liability is responsible for the max function. The formal derivation involves some detailed accounting techniques. Readers who are not interested in these details could skip the rest of the proof and jump to Lemma 2 without affecting the understanding of the rest of the paper. Because the proof applies to any given values of A, k and θ, we omit these arguments or indices for simplicity. Assume that the bank at t = 0 starts with a cash balance C, one unit of a loan B 0, a debt (deposits) D that pays an interest rate normalized to zero, an initial equity r, and no retained earnings. The accounting identity at t = 0 requires that C + B 0 = D + r. At t = 1, we assume that there are no new accruals except for the potential revaluation of the retained loan. Thus, the bank receives (1 k) p (k) cash for the sale of 1 k portion of the loan and pays the regulatory cost kc and dividend d 1 with cash. We also assume that the bank receives cash for the earnings from sources other than the loan e 0. e 0 is assumed to be so large that e 1 is positive regardless of the retention choice k and accounting regime A. 4 At t = 2, the cash flow of the retained portion of the loan k (θ + x) realizes. We also include in d 2 the liquidation of initial equity at t = 2. Therefore, the net cash flow of the bank over the two periods is (1 k) p (k) kc + e 0 + k (θ + x) B 0. 4 This assumption eliminates the uninteresting case in which the game ends at t = 1 because of a binding limited liability constraint at t = 1. A sufficient condition is e 0 > kc + B 0 B. 11

12 The original book value B 0, which reflects the original cost of the loan, is subtracted to arrive at net cash flow. At t = 2, the bank starts with a cash balance of C + e 0 + (1 k) p (k) kc d 1, receives k (θ + x) cash from the loan, and pays cash D to debt holders. The residual cash is C + e 0 + (1 k) p (k) kc d 1 + k (θ + x) D and is distributed back to the equity holders subject to limited liability. Thus the distribution to the equity holders at t = 2 could be summarized as follows d 2 max { C + e 0 + (1 k) p (k) kc d 1 + k (θ + x) D, 0 } = max{e 1 + ẽ 2 d 1 + r, 0} The equality follows from the fundamental property of accounting measurement and the accounting identity at t = 0. In equilibrium, this constraint must bind as the bank would otherwise leave resources in the firm upon liquidation. Therefore, d 2 = max {e 1 + ẽ 2 d 1 + r, 0} At t = 1, the bank sells a fraction 1 k of its loan, revalues the retained fraction k based on the accounting regime in place, recognizes earnings e 1 accordingly, and distributes dividend d 1. The decision problem can be summarized as follows max k,d 1 U (k; θ) d 1 + E 1 [ d 2 ] s.t. d 1 0 (2) d 1 e 1 (3) d 2 = max {e 1 + ẽ 2 d 1 + r, 0} (4) (1) 12

13 Constraint (2) captures the bank s limited liability: the dividend distribution cannot be negative. Constraint (3) states that the dividend at t = 1, d 1, cannot exceed the retained earnings at t = 1 before dividends (the initial retained earnings are assumed to be zero). As discussed in footnote 4, we have assumed that e 1 > 0 to avoid the uninteresting case in which the game ends at t = 1. Thus, constraints (2) and (3) could be written as 0 d 1 e 1. Constraint (4) is the dividend distribution at t = 2. Substituting (4) into the objective function max k,d 1 U (k; θ) d 1 + E 1 [max {e 1 + ẽ 2 d 1 + r, 0}] s.t. 0 d 1 e 1 The objective function is increasing in d 1. 5 Therefore, d 1 = e 1. Further, d 2 = max {e 1 + ẽ 2 d 1 + r, 0} = max {ẽ 2 + r, 0}. Plugging both d 1 and d 2 into the objective function (1), we could rewrite the bank s objective function as max k U (k; θ) = e 1 + E 1 [max {ẽ 2 + r, 0}] Since r only scales the payoff, we set r = 0. This completes the proof of the equivalence between the earnings-based and the dividend-based objective functions at t = U(k;θ) d 1 = 1 F (e 1 + ẽ 2 d 1 + r > 0) > 0. 6 The assumption of the accounting-based restriction of the dividend distribution captures real-world intuition reasonably well. A prototype bank in our model is an insured-deposit bank. The bank issues insured debt (deposits), makes risky loans, pays the FDIC insurance premium based on its risky balance sheet, and is subject to limited liability. In the event of non-performance of the loans on the bank s balance sheet, the equity of the bank is first in line to absorb losses. However, the equity holders are not obliged to contribute new capital or disgorge dividends previously received. As a result, the bank has an incentive to pay dividends as early as possible. To curtail such abuse of limited liability, the bank s dividend distribution is restricted by, among other things, a capital requirement. Since the capital requirement is mainly based on accounting numbers, the amount of dividend the bank could distribute without violating the capital requirement is linked to such accounting numbers as earnings. All else equal, the higher the earnings the more freedom the bank has to distribute dividends. To the extent that the regulator could be viewed as a representative of the debt holders of the bank, the example could also be extended to other uninsured financial institutions where the capital requirement is replaced by other forms of payout restrictions, such as debt covenants. Smith and Warner (1979) discuss the prevalence 13

14 With Lemma 1, the bank s preference for the early distribution of dividends becomes its preference for the early recognition of earnings. Lemma 2. iven accounting regime A, bank type θ and its retention decision k, the equity value U A (k; θ) increases in e A 1. Lemma 2 indicates that the bank benefits from the early recognition of profit even though the total earnings over the two periods are the same under any accounting regime. To see this, suppose one dollar is shifted from ẽ 2 to e 1 while keeping their sum unchanged. 7 The bank is then allowed to distribute one more dollar of dividend at t = 1 as e 1 increases by one dollar. The cost of this additional dollar in early dividend is that the expected earnings at t = 2, E 1 [ẽ 2 ] = E 1 [e 1 + ẽ 2 ] e 1, are reduced by one dollar, which reduces the expected dividend at t = 2. The key observation is that the reduction in the expected dividend at t = 2 is smaller than one dollar because the bank receives a dividend at t = 2 only if ẽ 2 is positive, which occurs with probability F (ẽ 2 > 0). As a result, the shift of one dollar from ẽ 2 to e 1 increases the equity value of the bank by 1 F (ẽ 2 > 0). 8 For the bank with limited liability, a bird in the hand (one more dollar of e 1 ) is worth more than one in the bush (one more dollar of E 1 [ẽ 2 ]). Lemma 2 describes how accounting measurement per se affects the equity value. This creates the interaction between accounting measurement and the bank s retention decision and provides us with a setting to compare the effects of different accounting measurement and rationale for restricting dividend payouts to retained earnings. Alternatively, we could also interpret the assumption more broadly. What is required for our model is that accounting measurement affects the payoffs of the decision maker, being the equity holders or the manager of the bank. If there is a conflict of interest between the manager and the rest of the stakeholders of the bank as a whole and the manager of the bank has to be the decision maker (of the origination and retention decisions), then we should interpret the dividend distribution as compensation to the manager and the accounting-based restriction on the dividend distribution as an accounting-based component of compensation. In this sense, our payoff structure is also similar to that in Bleck and Liu (2007) and Plantin, Shin, and Sapra (2008). 7 We drop the arguments and superscripts of the variables in this paragraph for simplicity. 8 For limited liability to bind at t = 2 with an interior probability, the distribution of x has to be sufficiently risky. Specifically, we assume that 0 < F (ẽ 2 > 0) < 1 or x < B 0 < B < x. 14

15 regimes on the bank s retention decisions. We consider two polar accounting regimes: HC and MTM. The only non-cash asset on the balance sheet of our bank is the retention k. Thus, the key accounting measurement issue is how we measure the value of this retained loan. Under HC, the k portion of the retained loan is recorded at its initial book value B 0. Under MTM, the retained loan is revalued to the market price of the sold loan p (k). 9 Before developing the details of HC and MTM, we link the retention decision at t = 1 to the origination decision at t = 0, which then links accounting measurement indirectly to the origination decision. 2.3 Origination decision at t = 0 Denote by V A θ U A ( kθ A ; θ) the equilibrium equity value of the bank of type θ under accounting regime A, where k A θ denotes the equilibrium retention decision as the solution to Program 2. Because of limited liability, the equity value of a loan V A θ differs from the net cash flow of the loan θ + x. Anticipating that a loan of type θ will receive an equilibrium equity value of Vθ A, the bank chooses how much effort m to exert to originate a good loan at t = 0 max m mv A + (1 m) V A B s (m) A {H, M} (5) Recall that s (m) is the private origination cost to the bank. The more effort the bank exerts, the higher the chance it originates a good loan. The optimal level of origination 9 In practice, for example in FAS 157, MTM reflects the extent to which market prices for the same or similar assets influence the valuation of an asset. For example, under MTM retained interests could be directly marked to the market prices of the homogeneous portion that has been sold. Alternatively, if there are no homogeneous assets for the retention, retention could be valued by valuation models that use inputs implied from the market prices of the sold assets that derive from the same loan pools. 15

16 effort is determined by the first-order condition 10 s ( m A ) = V A V A B A {H, M} (6) The condition is intuitive. The left-hand side is the marginal cost of effort. The right-hand side is the marginal benefit of effort, which equals the difference of the equity value of a good and a bad loan at t = 1. The higher the equity value of a good loan relative to a bad loan at t = 1, the greater the incentive the bank has to originate a good loan at t = 0. Since the equity value differential of the good and the bad loan is determined by the signaling game at t = 1, the price discovery via the signaling game is related to the ex-ante origination incentives. Accounting measurement affects the cost of price discovery and thus ex-ante incentives. Now we turn to the details of accounting measurement HC and MTM. 3 The retention decisions under HC and MTM In this Section, we study the banks retention decisions at t = 1 under HC and MTM respectively. In a separating equilibrium, the price of the sold loan is perfectly informative about the quality of the retained loan, which provides the strongest motivation for using MTM to exploit the informativeness of the loan price. Thus, we focus on separating equilibria in this Section. For completeness, we also discuss in Section 5 the non-separating equilibria where separating equilibria do not exist. We use the equilibrium concept of Perfect Bayesian Equilibrium (PBE) with the Intuitive Criterion by Cho and Kreps (1987) as the refinement to select a unique equilibrium. To keep the focus on the economic discussion in the text, we refer the interested reader to Appendix A for the standard technical details. 10 The condition has a unique interior solution if s (m) satisfies the standard properties: s (0) = 0, s (0) = 0, s (1) = S, s > 0, where S is a large positive number. 16

17 3.1 The retention decision under HC iven retention k and price p (k), the earnings for the first and second period under HC are e H 1 (k) (1 k) (p (k) B 0 ) kc + e 0 (7) ẽ H 2 (k; θ) k ((θ + x) B 0 ) θ {, B} (8) At t = 1, the bank recognizes a profit for the portion of the loan that was sold (1 k) (p (k) B 0 ). kc is the regulatory cost charge against earnings. e 0 is the bank s net cash earnings from all other sources (see footnote 4). The key is that there is no revaluation of the retained loan under HC. At t = 2, when the cash flow θ + x from the loan is realized, earnings are recognized as the difference between the cash flow of the retention and its book value. Since the book value of the retention remains at B 0 at t = 1, i.e. B H 1 = B 0, the earnings at t = 2 equal k ((θ + x) B 0 ). HC thus defers the recognition of the expected profit on the retained loan until its maturity at t = 2. Substituting the earnings expressions (equations (7) and (8)) into Program 2 and rearranging terms, we have the equity value for the bank of type θ under HC U H (k; θ) = (1 k) (p (k) B 0 ) kc + e 0 + ke 1 [max { x + θ B 0, 0}] (9) The first term of the bank s equity value is the proceeds from the sale of the 1 k portion of the loan at the per-unit price p (k). Because the market does not observe the loan s true quality, the retention serves as a signal of the loan quality based on which the market prices the loan. The second term of U H (k; θ) is the regulatory cost kc the bank pays for the retention. The max function in the last term means that the bank expects to 17

18 receive only the profit from the retention at t = 2 due to its limited liability. To illustrate the intuition of signaling, we construct a separating equilibrium in which the good bank retains k H > 0 and the bad bank retains kh B = 0. The market then sets prices accordingly: it pays price p (k) = to any bank that holds k k H and p (k) = B otherwise. This constitutes an equilibrium if neither the bad bank nor the good bank has an incentive to deviate. Let us first consider the incentive of the bad bank. iven the market s beliefs that only the good bank retains k k H, the bad bank s payoff from playing the equilibrium strategy of k H B = 0 is U H ( k H B holds k H, its off-equilibrium payoff is = 0; B) = B + e 0 B 0. In contrast, if the bad bank deviates and U H ( k H ; B ) = ( 1 k H ) ( B0 ) k H c + e 0 + k H E 1 [max { x + B B 0, 0}] Thus, in making its retention decision, the bad bank compares the payoffs of the two options U H ( k H ; B ) U H (0; B) = ( 1 k H ) ( B) + k H H B k H c where H B E 1 [max { x + B B 0, 0} (B B 0 )] = ˆ B0 B x (B 0 B x) df (x) (10) The tradeoff in the bad bank s decision is clear. On the one hand, the benefit of mimicking by holding k H ( 1 k H is two-fold. First, the bad bank could sell part of the loan ) at a higher price ( instead of B because with retention k H be treated as a good bank in the loan sale). Second, by retaining k H the bad bank would instead of selling the entire loan, the bad bank could exploit its limited liability. This benefit is captured 18

19 by k H H B. H B is the per-unit option value of retention k H for the bad bank on the off-equilibrium path. On the other hand, the cost of mimicking is that the bad bank needs to pay the regulatory cost k H c. Similarly, we could derive the good bank s incentive to retain. Following the same procedure, the good bank compares the payoffs of the two options where U H ( k H ; ) U H (0; ) = ( 1 k H ) ( B) + k H H k H c H E 1 [max { x + B 0, 0} ( B 0 )] = ˆ B0 x (B 0 x) df (x) (11) Retention k H costs the bank the regulatory charge but at the same time enables the good bank to sell the remainder at a higher price and receive the option value of the retention. Therefore, any pair ( k H > 0, kh B = 0) is an equilibrium strategy profile if U H ( k H ; B) U H (0; B) 0 (the bad bank does not have incentive to deviate) and U H ( k H ; ) U H (0; ) 0 (the good bank does not have an incentive to deviate), vindicating the market s belief. The lowest retention level for the good bank that could sustain the separating equilibrium is determined by setting U H ( k H ; B) U H (0; B) = 0, or equivalently k H = B B+c H B. Because k H k, the separating ) ( B). In Appendix A, we show = B B+c H B ( equilibrium exists only for c c 1 H B + 1 k k ( ) that k H = B B+c H B, kb H = 0 is the unique equilibrium that survives the Intuitive Criterion. Proposition 1. For c c 1, the unique (separating) equilibrium under HC is as follows 19

20 B 1. the retention decisions are kθ H B+c H B if θ = = ; 0 if θ = B 2. the per-unit prices of the loans conditional on retention are p (k) = B 3. the banks equity values are V H θ = B 0 + e 0 k H (c H ) if θ =. B B 0 + e 0 if θ = B if k k H otherwise ; The salient feature of the equilibrium is the informativeness of the price of the sold loan about the retention. The quality of the retained loan on the bank s balance sheet is perfectly revealed by the equilibrium price of the sold portion. However, this informativeness of the loan price is sustained only by the costly retention of the good bank that deters the bad bank from mimicking. The retention costs the good bank k H (c H ), the product of the equilibrium retention level and the net unit cost of retention. The latter is equal to the regulatory cost c offset by the option value the bank derives from the retention. HC does not recognize the expected profit on the retained loan even though its quality is perfectly revealed by the market price. This seems to be inefficient and motivates the use of MTM. 3.2 The retention decision under MTM The analysis of MTM parallels that of HC and we thus focus mainly on their difference. The central idea behind MTM is to exploit the informativeness of the loan price about the retained loan by marking the retained loan from its original book value B 0 to the loan price p (k) for any bank that retains k. iven bank type θ and retention k (and thus p (k)), 20

21 the earnings for the first and the second period under MTM are e M 1 (k) e H 1 (k) + k ( B M 1 B 0 ) = (1 k) (p (k) B 0 ) kc + e 0 + k (p (k) B 0 ) ẽ M 2 (k; θ) ẽ H 2 (k; θ) k ( B M 1 B 0 ) (12) (13) = k ((θ + x) p (k)) θ {, B} Relative to HC, MTM marks the book value of the retention at t = 1 from B 0 to B1 M = p (k) and recognizes the difference p (k) B 0 as part of the earnings at t = 1. B1 M = p (k) then becomes the new basis on which to calculate the earnings at t = 2 which thereby reverses the revaluation component in the second period, keeping the sum of earnings over the two periods constant. Substituting the earnings expressions (equations (12) and (13)) into Program 2, we have the equity value for the bank of type θ under MTM U M (k; θ) = (1 k) (p (k) B 0 ) kc+e 0 +ke 1 [max { x + θ B 0 (p (k) B 0 ), 0} + p (k) B 0 ] (14) Comparing the bank s equity value under MTM with that under HC (equation (9)), the only difference is in the last term. Relative to HC, for every unit of retention the early recognition under MTM allows the bank to swap an uncertain amount of future dividend (the term (p (k) B 0 ) in the max function) for a certain amount of current dividend (p(k) B 0 ). That is, the early recognition under MTM creates a different per-unit option value for retention. k M We could construct a similar separating equilibrium in which the good bank retains > 0 and the bad bank retains km B p (k) = if k k M = 0. The market then sets prices accordingly: and p (k) = B otherwise. This constitutes an equilibrium if neither 21

22 the bad bank nor the good bank has an incentive to deviate. Following the same procedure of the previous Subsection, the difference in payoffs to the bad bank with and without mimicking is where U M ( k M ; B ) U M (0; B) = ( 1 k M ) ( B) + k M M B k M c (15) M B E 1 [ max { x + B p ( k M = ˆ B x ) } ( ( ))], 0 B p k M = E1 [max { x + B, 0} (B )] ( B x) df (x) (16) The tradeoff for the bad bank under MTM is similar to that under HC except that the per-unit option value of the retention for the bad bank on the off-equilibrium path has changed from H B to M B. That is, the early recognition under MTM also changes the off-equilibrium payoff of the bad bank. The payoff difference for the good bank is calculated similarly where U M ( k M ; ) U M (0; ) = ( 1 k M ) ( B) + k M M k M c [ ( ) } ( ( ))] M E 1 max { x + p k M, 0 p k M = E1 [max { x, 0}] = ˆ 0 x x df (x) (17) The tradeoff for the good bank under MTM is also similar to that under HC except that the per-unit option value of the retention for the good bank on the equilibrium path 22

23 has changed from H to M. Therefore, any pair ( k M > 0, km B = 0) is an equilibrium strategy profile if U M ( k M ; B) U M (0; B) 0 (the bad bank does not have incentive to deviate) and U M ( k M ; ) U M (0; ) 0 (the good bank does not have an incentive to deviate). The lowest retention level for the good bank that could sustain the separating equilibrium is similarly determined by setting U M ( k M ; B) U M (0; B) = 0, or equivalently k M = B B+c M B. Because k M M B + ( 1 k k = B B+c M B ) ( B). k, the separating equilibrium exists only for c c 2 Proposition 2. For c c 2, the unique (separating) equilibrium under MTM is as follows B 1. the retention decisions are kθ M B+c M B if θ = = ; 0 if θ = B 2. the per-unit prices of the loans conditional on retention are p (k) = B 3. the banks equity values are V M θ = if k k M otherwise B 0 + e 0 k M (c M ) if θ =. B B 0 + e 0 if θ = B ; The separating equilibrium under MTM is almost identical to that under HC. The loan price is informative about the quality of the retained loan but its informativeness is sustained only by the costly retention of the good bank, which costs k M (c M ). The only difference is that the per-unit option value of the retention for the bad bank changes from H B to M B and for the good bank from H to M. This reflects the way accounting measurement works. By Lemma 2, accounting measurement, by shifting the earnings across periods, affects the retention decision only through its impact on the option value of retention. iven the importance of the option values of retention, we compare them under HC 23

24 and MTM. Lemma 3. iven the beliefs in the separating equilibria, if a bank retains k k A, A {H, M}, then 1. the per-unit option value of retention is larger under MTM than under HC for both banks. That is, M θ > H θ for θ {, B}; 2. the increase in the per-unit option value of retention from HC to MTM is larger for the bad bank than for the good bank. That is, M B H B > M H. Part 1 of Lemma 3 follows immediately from Lemma 2. Relative to HC, MTM permits the bank that retains k k M to recognize the expected profit on the retained loan (p ( k M ) B0 = B 0 > 0) at t = 1 and thus increases e M 1 (the earnings at t = 1). By Lemma 2, this early recognition of profit increases the equity value of a loan because it allows the banks to pay out more in dividends at t = 1 to exploit limited liability. One key result of the model is that part 1 of Lemma 3 holds for both types. It is easy to see that M > H. For the good bank that retains a positive portion of the loan in the equilibria, the benefit of early profit recognition on the retained loan under MTM makes the per-unit option value of retention higher under MTM than under HC. The reason for M B > H B is more subtle. The bad bank does not retain any loan in the equilibria under either MTM or HC and therefore does not receive an option value of retention in the equilibria. Despite receiving the same payoffs from retention in the equilibria, the bad bank receives a higher value from retention on the off-equilibrium path under MTM than under HC, which is captured by M B > H B. Recall that M B and H B are defined as the per-unit option values for the bad bank on the off-equilibrium path. Thus, M B > H B means that, had the bad bank mimicked the good bank with the critical amount of retention, the bad bank would have also been treated as a good bank and received the extra benefit of the 24

25 early recognition under MTM. This change in the bad bank s off-equilibrium payoff changes the bad bank s incentive to mimic and the good bank s equilibrium retention. This argument highlights the subtle way MTM works. MTM does not directly reveal the quality of the retained loan. Indeed, the accounting regime by itself cannot distinguish between the different bank types θ and thus cannot treat them differently by applying the revaluation benefit only to the good bank that fundamentally deserves it. Rather, to capture and apply the information about θ, the accounting regime has to rely on the costly retention that keeps the bad bank from mimicking and thus makes the loan price informative. Therefore, the benefit of early recognition under MTM not only improves the valuation accuracy for the good bank but also reduces the cost of mimicking for the bad bank. The overall efficiency of MTM needs to be evaluated in this context. Part 2 of Lemma 3 compares the relative increase in the option value the good and the bad banks receive from MTM when they hold retention k k A. Because the bad bank is more likely to produces losses and thus hit the limited liability constraint at t = 2 than the good bank, the early recognition under MTM is more valuable to the bad bank than to the good bank. 4 Comparison of HC and MTM In this Section, we compare the economic consequences of MTM relative to HC for banks and the loan market. By part 1 of Lemma 3, we have c 2 > c 1. That is, the threshold for the existence of a separating equilibrium is higher under MTM than under HC. Thus, we first examine the case of c c 2, in which a separating equilibrium exists under both regimes. We show that MTM makes signaling more costly in the attempt to exploit the information in the separating equilibrium. Indeed, MTM forces banks to retain more risky loans on their own books and could reduce the banks ex-ante incentive to originate good loans. We 25

26 then consider the case of c 2 > c c 1, in which a separating equilibrium exists only under HC. We show that MTM, in an attempt to exploit the information in the loan price, could destroy its informativeness. 4.1 Risk retention Proposition 3. When c c 2, banks retain more loans on their own balance sheets under MTM than they do under HC, that is k M θ k H θ (equality for θ = B). Proposition 3 derives from part 1 of Lemma 3. The early recognition under MTM provides a benefit to the good bank (by increasing the option value of retention for the good bank in equilibrium) but also increases the incentive of the bad bank to hold retention to also capture this benefit (by increasing the option value of retention for the bad bank on the off-equilibrium path). If the good bank still retains k H when switching from HC to MTM, the bad bank will find it attractive to mimic the good bank due to the reduced cost of retention. As a result, the good bank is forced to retain a larger and thus more costly position in order to deter the bad bank from mimicking in the new equilibrium. Proposition 3 helps explain the puzzling observation that banks have maintained excessive exposure to the risk of the loans they originated, contrary to what is suggested by the OTD model. This concentration of risk in the banking sector has been alleged as one of the key factors that turned the subprime mortgage crisis into a full-fledged financial crisis. Banks retain skin in the game to overcome the information asymmetry problem in the loan market. MTM exacerbates the problem by forcing banks to put even more loans on their own balance sheets. 26

27 4.2 Incentive to originate good loans and the average quality of loans Proposition 4. If c is sufficiently large, the equity value of a good loan and thus the incentives of originating good loans are lower under MTM than under HC. Proposition 3 can be understood from the tradeoff created by MTM. On the one hand, the early recognition under MTM exploits the informativeness of the loan price. If we keep the retention level constant, then the early recognition under MTM does improve the accuracy of the valuation of the retained loan. The benefit of valuation accuracy is to increase the option value of retention (part 1 of Lemma 3), which offsets the cost of retention and results in a higher equity value of a good loan. On the other hand, as Proposition 3 points out, the early recognition under MTM also increases the equilibrium retention level, making equilibrium retention more costly. As a result, the net impact of MTM on the value of a good loan is a tradeoff between a lower net unit retention cost and a higher equilibrium retention level. This tradeoff can be expressed by rewriting the difference between V M V H = kh (M H ) ( k M kh ) (c M ). The equilibrium retention level is determined by the bad bank s marginal retention cost c A B, A {H, M}, while the net unit retention cost is determined by the good bank s marginal retention cost c A, A {H, M}. When c is high, the level effect dominates the unit retention effect and MTM reduces the equity value of having good loans. The equity value of a good loan is linked to the incentives to originate good loans by the first-order condition for the origination decision (equation (6)) and the observation that the equity value of a bad loan is the same under HC as under MTM (because the bad bank does not retain any loan in any separating equilibrium). Thus, if c is sufficiently large, banks exert less effort ex ante to originate good loans under MTM than under HC, that is m M < m H. In addition, since there is a continuum of banks, by the law of large numbers, m is also the average quality of loans in the economy. Thus, if c is sufficiently 27