Is Mark-to-Market Accounting Destabilizing? Analysis and Implications for Policy

Transcription

1 Firt draft: 4/12/2008 I Mark-to-Market Accounting Detabilizing? Analyi and Implication for Policy John Heaton 1, Deborah Luca 2 Robert McDonald 3 Prepared for the Carnegie Rocheter Conference on Public Policy, April 17-18, We are grateful to Robert Magee for helpful dicuion of financial accounting. We emphaize the uual diclaimer that all error are our own. 1 Univerity of Chicago and NBER 2 Northwetern Univerity and NBER 3 Northwetern Univerity 1

2 Abtract Fundamental economic principle provide a rationale for requiring financial intitution to ue mark-to-market, or fair value, accounting for financial reporting. The recent turmoil in financial market, however, ha raied quetion about whether fair value accounting i exacerbating the problem. In thi paper we review the hitory and practice of fair value accounting, and ummarize the literature on the channel through which it can adverely affect the real economy. We propoe a new model to tudy the interaction of accounting rule with regulatory capital requirement, and how that even when market price alway reflect fundamental value, the interaction of fair value accounting rule and a imple capital requirement can create inefficiencie that are abent when capital i meaured by adjuted book value. Thee ditortion can be avoided, however, by redefining capital requirement to be procyclical rather than by abandoning fair value accounting and the other benefit that it provide. 2

3 1. Introduction Fundamental economic principle provide a rationale for requiring financial intitution to ue mark-to-market, or fair value, accounting: (1) Market price are generally the bet available meaure of economic value. They are forward looking and aggregate private information. (2) Market value are eaily inferred from tranaction price, which are hard to manipulate in active financial market. (3) It i not meaningful to draw a ditinction between liquidation value -- a meaured by market price -- and ongoing value, ince liquidation value reflect that aet will be redeployed in their highet value ue. The abrupt and protracted meltdown of world financial market ha brought thee aumption into doubt, and raied quetion about whether mark-to-market accounting i one of the factor exacerbating the ongoing problem. The academic literature ha uggeted everal channel through which mark-to-market accounting could have unintended negative conequence in illiquid market. One i that it can be manipulated. 4 Sham tranaction in thin market could be ued to generate high price, allowing imilar aet to be artificially marked up. A econd concern i that the rule can exacerbate illiquidity. If intitution are unwilling to ell ecuritie at price that force them to mark down other aet, for intance becaue doing o could force aet ale, the requirement could reduce trade. Related to thee effect, there i the poibility of multiple equilibria: When price are high, capital and margin requirement are atified, wherea when price fall, capital requirement are violated, cauing aet ale and a further drop in aet price and capital. In thi paper we focu on one mechanim by which accounting rule can have real macroeconomic conequence: through their interaction with regulatory capital requirement. We develop a general equilibrium model in which to tudy thi interaction, and how that even when market price alway reflect fundamental value, the interaction of fair value accounting rule and a imple capital requirement can create inefficiencie that are abent when capital i 4 We provide a hort urvey of thi literature in ection

4 meaured by adjuted book value, an alternative meaure favored by many banker. Thee problem can be avoided, however, by redefining capital requirement to be procyclical, intead of by abandoning fair value accounting and the other benefit aociated with it. To provide a context for the analyi, we begin in Section 2 with an explanation of the rationale for and a brief hitory of fair value accounting, and explain how accounting rule impact the meaurement of regulatory capital. We alo review the theoretical literature on the channel through which fair value accounting can have negative conequence in illiquid market. In Section 3 we preent a theoretical model in which the accounting definition of bank capital and the regulatory capital requirement ha implication for aggregate outcome, and characterize equilibrium price and quantitie. In Section 4 we examine the model implication for policy, and conider more broadly what it ugget about unregulated financial intitution that are ubject to margin requirement but not capital requirement. Section 5 conclude. 2. Background In thi ection we provide an overview of ome conceptual and practical iue related to fair value accounting, along with ome hitorical context. It i important to recognize that financial accounting tatement can be contructed in a variety of way and are ued for a variety of purpoe. Conumer of accounting tatement include invetor, regulator, cutomer, competitor, and the firm itelf. The choice of accounting rule may depend upon the intended ue of the accounting report, although our view i that there hould be a trong preumption in favor of fair value accounting. It i alo worth noting that much of the dicuion about accounting method and rule preume that for a given firm, the accounting report will emphaize number computed in one particular way. In practice, there i an emphaized et of number and alternative are preented in footnote, and thu at leat for ome purpoe, diminihed in importance. (For example, a firm could elect to report the value of a particular et of aet at hitorical cot with fair value in a footnote.) At leat at a conceptual level, one could imagine requiring firm to report both book 4

5 value and fair value, and then letting report uer make accounting election, rather than having the firm (or the SEC) making thoe election on their behalf. 2.1 Hitorical Cot and Fair Value Accounting: An Economic Perpective Accountant and regulator have long grappled with the problem of whether and how change in the market value of aet hould be incorporated into accounting report. The iue i perhap mot contentiou to the extent that accounting report are ued in the regulatory proce: A reported number may have direct implication for the regulatory uperviion of the firm for intance via a capital requirement or affecting required contribution to penion plan. Many manager alo voice concern about effect of accounting rule on the volatility of earning. Firt, it i helpful to undertand what we mean when we talk about hitorical cot accounting and fair value accounting. 5 Conceptually, accounting for aet at fair value and accounting for them at book are polar extreme. Fair value accounting relie on change in the balance heet to meaure change in the financial condition of a firm, while hitoric cot accounting relie on realization of cah flow to meaure change in financial condition. 6 Suppoe one want to meaure firm reource available to equity holder. One can meaure reource a a flow (the change in available reource per unit time, ideally meaured by the income tatement) or a a tock (the total value of reource at a point in time, ideally meaured by the balance heet). Probably the mot baic accounting notion i that of net income, meaured a the difference between revenue and cot, with both defined baed on current cah flow. (Interet expene i here treated a a cot.) An accounting ytem that emphaize net income meaured in thi way i implicitly baed on hitorical cot becaue it meaure current cah flow ignoring revaluation of aet and liabilitie in reporting the performance of the firm. 5 The SEC report emphaize that the term hitorical cot and fair value are more accurately referred to a pat entry price and exit price, language that i ued by the Financial Accounting Standard Board. 6 In practice the aet of financial intitution are often accounted for at adjuted book value, which i a hybrid meaure baed on hitorical purchae price adjuted for foreeeable but unrealized loe from default. It doe not incorporate the price of market rik aociated with thoe default. 5

6 At the other extreme, one could meaure income a net cah flow plu the net change in the market value of aet le liabilitie. Thi i the idea behind fair value accounting. Fair value accounting emphaize the balance heet, while hitorical cot accounting fixe the balance heet, eentially ignoring it. In frictionle market, fair value accounting unquetionably provide the theoretically correct meaure of the change in reource available to hareholder. Aet and liability value reflect future cah flow, and thu profit and loe generated by aet revaluation are imply recognition at one time of future cah flow. If a firm were operating at a lo under hitoric cot accounting but a profit under fair value, it would be poible to borrow or iue equity to fund current operation out of expected gain from future operation. There are at leat four common objection to fair value accounting: Firt, many object that aet valuation under fair value accounting are more manipulable than cah flow under hitorical cot accounting. While there i likely truth in thi, it i poible to manipulate reported earning a well, particularly with accrual accounting. Alo, a we argue below, the hitory of accounting method ha been that hitorical cot accounting eem atifactory until time of economic tre, at which point particular aet clae or indutrie have been witched to fair value accounting. Thi ha reulted in the teady incurion of fair value over the lat 30 year. Second, ome argue that earning are more volatile under fair value accounting than under hitorical cot accounting. Thi eem like an odd objection. If the firm believe that earning hould be le volatile than reported uing fair value, the narration and footnote in accounting report hould provide an opportunity to make the cae that thing have not really changed. If aet value are truly changing rapidly, thi eem like information that would be of interet to owner and other takeholder of a firm. 6

7 Third, the SEC tudy (SEC, 2008) mention an oft-cited concern about fair value: that there i an inconitency between the fair value accounting model and a typical company' buine model a an ongoing entity. (p. 176). Preumably thi objection refer to a firm that i houe rich but cah poor, with valuable aet but temporarily low cah flow. Thi objection ignore the fact, already mentioned, that firm routinely ue financing to fund current operation out of future cah flow. Fourth, valuation may be imperfect. It i true that price of ome aet can be meaured more reliably than other, but it eem odd to object to a ytem on the ground that it may meaure price incorrectly, when the alternative i almot certain to meaure price incorrectly. There are benefit to fair value accounting beide it theoretical appeal. It i poible that firm will behave differently under a fair value accounting regime. An invetor or firm conidering the purchae or etablihment of an aet poition will take into account the propect of future marking to market. In particular, a firm acquiring a riky aet will know that it ha to live with the public conequence of the rik. Firm would no longer have an incentive to ecuritize or otherwie ell aet olely to recognize accounting gain, and there would be no value in trying to boot earning by cherry-picking aet to ell. Under a fair value regime, hedging trategie deigned to mooth earning are better aligned with economic rik avoidance, and compenation contract that depend on accounting earning may provide better incentive for controlling rik. 2.2 Hitory The SEC' 2008 report (SEC, 2008) on fair value accounting provide an excellent dicuion of hitory and the iue, and we draw upon it heavily. Hitorically, a ignificant financial event or crii ha often erved a impetu for a reconideration of the accounting rule governing reported aet valuation. The credit crii of 2008 ha generated call for uch a reconideration of accounting rule, and the SEC report pecifically mention a pat catalyt the Great Depreion, the market decline of 1973 and 1974, and the aving and loan crii of the

8 Prior to the Great Depreion (and thu prior to the etablihment of the SEC), firm had flexibility about reporting aet valuation. In practice, firm revalued aet both up and down. Fabricant (1936) examined a ample of SEC filing (filed when the SEC wa a brand new agency) and found that 75% of the firm in hi ample had written aet value either up or down, with write-down ubtantially exceeding write-up. One of the firt SEC commiioner, Robert Healey, had been general counel of the Federal Trade Commiion, and in that poition had tudied the aet valuation practice of public utility holding companie. He wa incened by write-up that he viewed a manipulative (Zeff, 2007). Stemming from thee concern about accounting manipulation, the SEC eentially forbade upward revaluation of aet, and favored hitorical cot accounting. By 1940, upward revaluation were rare. Zeff (2007) document the SEC' repeated effort to prevent revaluation and to intall hitoric cot accounting a a tandard. The SEC' reitance held firm until the late 1970, by which time the inflation of the 1970 (which affected companie generally) and the large oil price increae (which differentially affected oil and ga producer) made the hortcoming of hitorical cot accounting obviou. 7 In particular, pecial accounting exception were made for oil and ga firm. The aving and loan crii of the 1980' provided another impetu to move away from trict hitorical cot accounting. Bank that had made long-term mortgage loan and borrowed hortterm uffered evere economic loe when interet rate increaed. A fair value accounting ytem would in principal have made thee loe obviou, but with hitorical cot accounting and the reulting emphai on realization, S&L loe took year to be formally recognized. 7 Zeff note that the SEC' tance in favor of hitorical cot accounting wa reflected in CPA exam, and thu a the authoritative literature in the United State move inexorably toward hade of fair value accounting, it qualified accountant are only now learning about a regime of accounting that had been ytematically excluded from their profeional education. Thi circumtance make any tranition from the traditional model to fair value accounting all the more difficult to achieve uccefully and with good effect in the United State. 8

9 Finally, the introduction of financial derivative in the 1970 and 1980 required change in accounting rule. Financial future allowed firm to take zero-invetment poition that could quickly accrue large gain or loe and there were no accounting tandard recognizing the novel character of thee contract. In repone, SFAS 52 and 80 required fair value accounting for foreign exchange contract and future contract not ued in hedging. In the mid-1980', the FASB initiated a wide-ranging project on financial intrument, intended to addre derivative, debt-equity ditinction, and the like. The reult ha been a wide-ranging overhaul of accounting tandard preented in a number of tatement, including mot recently SFAS 157 and 159. We will provide a brief overview of the evolution of fair value accounting for invetment in ecuritie. There ha been a parallel et of tandard for derivative that we will not dicu. Financial reporting tandard addre two ditinct iue related to fair value: whether to dicloe the fair value of aet and liabilitie, and whether to incorporate change in fair value into reported earning. The reporting tandard alo pecify which kind of aet are covered by that tandard. At the time the FASB began the project on financial intrument mark-to-market accounting wa commonplace for aet held in trading account. The problem the FASB faced wa whether and how to generalize the trading account treatment to aet held for other purpoe. SFAS 107 (1991) required all entitie to dicloe the fair value of financial intrument, both aet and liabilitie recognized and not recognized in the tatement of financial poition, for which it i practicable to etimate fair value (p. 4). At the ame time, the FASB provided ubtantial leeway: practicable mean that an etimate of fair value can be made without incurring exceive cot. It i a dynamic concept: what i practicable for one entity might not be for another; what i not practicable in one year might be in another. Fair value computed under thi tandard had no implication for earning. SFAS 115 (1993) created the baic accounting tructure for debt and equity ecuritie (but explicitly not for unecuritized loan) that i till in ue today. Specifically, SFAS 115 tate 9

10 Debt ecuritie that the enterprie ha the poitive intent and ability to hold to maturity are claified a held-to-maturity ecuritie and reported at amortized cot. Debt and equity ecuritie that are bought and held principally for the purpoe of elling them in the near term are claified a trading ecuritie and reported at fair value, with unrealized gain and loe included in earning. Debt and equity ecuritie not claified a either held-to-maturity ecuritie or trading ecuritie are claified a available-for-ale ecuritie and reported at fair value, with unrealized gain and loe excluded from earning and reported in a eparate component of hareholder' equity. The eparate component of hareholder equity i reported on balance heet under other comprehenive income (OCI). The category wa deigned to reconcile tock and flow but at the ame time keep certain flow eparate from earning. The unrealized gain and loe in OCI are reported in earning if the aet i old. There i alo another circumtance in which OCI i realized and incorporated into earning: For individual ecuritie claified a either availablefor-ale or held-to-maturity, an enterprie hall determine whether a decline in fair value below the amortized cot bai i other than temporary. If the decline in fair value i judged to be other than temporary, the cot bai of the individual ecurity hall be written down to fair value a a new cot bai and the amount of the write-down hall be included in earning (that i, accounted for a a realized lo). (emphai added) Thu, under SFAS 115, debt ecuritie that utain a permanent lo are required to be marked to market, with the lo flowing through the income tatement. Notably, thi impart a conervative bia to earning ince aet that ubequently recover cannot be marked back up. SFAS 157 (2006) defined fair value a the price that would be received to ell an aet or paid to tranfer a liability in an orderly tranaction between market participant at the meaurement date. The tatement created a hierarchy of valuation: Level 1, 2, and 3, defined a price oberved in the market (level 1), baed upon input oberved in the market (level 2), and with unobervable input (level 3). Thi i ometime decribed a mark-to-market, mark-to-matrix, and mark-to-model. Important in the definition of fair value i the notion of an orderly 10

11 tranaction. Forced liquidation and ditreed ale are mentioned a example of non-orderly tranaction. Finally, SFAS 159 (2007) expanded the range of aet that could receive fair value treatment. For example, under 159, it i poible to ue fair value for available-for-ale aet, and gain and loe on thee aet would then flow through the income tatement. SFAS 159 alo permitted firm to market their own liabilitie to market, a omewhat controverial proviion that would permit a firm with bond price falling due to deteriorating credit, to realize a gain. The tatement allowed the firm to elect fair value treatment on individual clae of option. 2.3 Financial Accounting and Regulatory Capital Regulatory accounting, including the calculation of capital, i baed upon tandard financial accounting. Regulator define capital by adding up variou accounting categorie, but the baic accounting principle ued to contruct thoe categorie apply. One intereting iue i the treatment of other comprehenive income, which i excluded from capital calculation. The current accounting controvery hinge in large part on the phrae other than temporary in SFAS 115. CMO and their variant are held by financial intitution in the available for ale or poibly the held to maturity category. In either cae, if a decline in fair value i other than temporary, intitution are required to mark to market with the reulting lo flowing through the income tatement. Since regulator rely on accounting meaure of capital adjuted for change that flow into earning, if bank are required to recognize loe for accounting purpoe, they will be in trouble for regulatory capital purpoe. Following congreional preure, the FASB on April 2, 2009, voted to revie SFAS 157 to account for fair value calculation when a market i inactive. The FASB aid that the forthcoming rule will Affirm that the objective of fair value when the market for an aet i not active i the price that would be received to ell the aet in an orderly tranaction (that i, not a forced liquidation or ditreed ale) between market participant at the meaurement date under current market condition (that i, in the inactive market). The Board alo aid that it would 11

12 require an entity to dicloe a change in valuation technique (and the related input) reulting from the application of the FSP and to quantify it effect, if practicable. (FSP=FASB Staff Poition). A a practical matter, auditor, and to a leer extent the SEC, are the arbiter of what i reaonable in pecific intance. The uphot eem to be that if the market i deemed inactive, bank have leeway to ue their own judgment to determine if an aet ha uffered a decline in fair value. Opponent to the change worry that thi will caue aet value, and hence regulatory capital, to be artificially elevated. 2.4 Literature Review 8 Much of the theoretical literature focue on the interaction between market liquidity and balance heet contraint. The liquidity of the market for the aet held by financial intitution can have important conequence for firm following market-to-market accounting while facing capital requirement or contractual retriction. In an illiquid market, price diplay hort-run fluctuation that may have little to do with the fundamental or long-run value. Thee hort-run fluctuation can then force firm to raie capital in a cotly manner by, for example, iuing equity or elling aet at temporarily depreed price. Since price in an illiquid market are expected to mean-revert, marking aet or liabilitie to hort-run price movement can lead to ubtantial cot for intitution. Beide influencing the cot directly faced by firm adhering to capital requirement, market illiquidity can be the ource of an important general equilibrium feedback between market price and intitutional behavior. For example Brunnermeier and Pederen (2008) conider the piral than can occur when trader face capital and margin requirement while trading in market where they provide liquidity. After an initial lo, trader face funding problem due to margin or capital requirement. A they attempt to reduce their poition price are driven down further reulting in additional margin call and hence a downward piral in price. Thi mechanim i 8 Incomplete review of the literature. More to be added. Apologie to thoe not cited properly at thi point! 12

13 related to the credit cycle model of Kiyotaki and Moore (1997) and other. Adrian and Shin (2009) provide ome evidence for thee cycle in the behavior of invetment bank. Plantin, Sapra and Shin (2008) conider an equilibrium etting where intitution make deciion about whether to ecuritize their portfolio and face either mark-to-market valuation or hitorical cot valuation. Relative to hitorical-cot valuation, market-to-market valuation induce intitution to ecuritize their aet more efficiently. When market for the aet are relatively illiquid thi reult i overturned. The illiquidity of market in future period induce intitution to trade more aggreively earlier. The reult i inefficient ecuritization and more price volatility. At the level of an intitution, the cot of adhering to capital contraint in illiquid market will be anticipated and affect intitutional behavior. For example banker will repond to illiquidity in one market by holding buffer of liquid ecuritie. In addition they may ue the latitude they have within the accounting rule to affect their expoure to market-to-market requirement. Milbradt (2008) develop the optimal repone of a firm to liquidity concern when it i poible for an intitution to hield itelf from market-to-market requirement by halting trading in overthe-counter market. The reult i that aet are carried at value above market price. Invetor repond to the halt in trading by dicounting the price of the intitution. Beide the feedback through liquidity, balance heet contraint influence the identity of the marginal trader in market and can therefore influence the amount of rik preent in a market. For example Danielon, Shin and Zigrand (2009) conider a etting where trader face Value-at- Rik (VaR) contraint and fluctuating aet value. The VaR contraint influence their willingne to take rik. In repone price fluctuate more than would be predicted by fundamental. 9 9 Fluctuation of thi type alo occur if trader wealth influence their willingne to take rik. Thi i conider, for example, by Xiong (2001), Pavlova and Rigobon (2008) and other. 13

14 3. The Model In thi ection we propoe a model that allow u to analyze how the accounting definition of bank capital can affect the ocial cot aociated with a banking ytem that relie on capital requirement to dicourage exceive rik-taking. 10 Unlike the literature urveyed above, we aume that price fluctuation are driven by time variation in fundamental rather than by liquidity hock. Even in thi etting the interaction of fair value accounting rule and imple capital contraint are hown to lead to inefficient outcome that can be avoided by either changing the accounting regime or by modifying the capital requirement. The economy lat for three period, time 0, 1 and 2. It i populated by a repreentative conumer, firm, bank, and the government. 3.1 Agent and Their Contraint Conumer. At time 0, a repreentative conumer i endowed with one unit of productive capital of which x (0) i inveted in a portfolio of riky bank equity, x d (0) in inured bank depoit, and x b (0) in a rik-free torage technology with unlimited capacity. Utility i defined over time 2 conumption. The equity portfolio ha a tochatic payoff at time 2, which i decribed below. The torage technology produce one unit of time 2 output for each unit of time 0 input. We aume parameter are uch that in equilibrium depoit do not atify the demand for rik-free aet at time 0, o that a poitive quantity i inveted in the rik-free torage technology. Taking claim to rik-free time 2 conumption a the numeraire, the price of rik-free ecuritie i fixed at Note that we do not provide a reaon for bank to add value to the economy, nor do we include any benefit from depoit inurance. However, one can imagine that bank enhance the productive capacity of the firm through monitoring ervice, and that the mechanim of depoit inurance and capital requirement erve to reduce the cot of monitoring the bank. In any cae, we take the aumed tructure a reflecting alient apect of the current financial ytem and make no claim about global efficiency. 14

15 At time 1 there are no further phyical invetment opportunitie, but the demand for aet change in repone to new information, cauing the price of equity to adjut to clear market. Inveted quantitie x (t), x d (t), and x b (t), t=0,1, are choen to maximize expected utility over time 2 conumption, C. 11 Conumption equal the total return on invetment net of taxe, η, groed up by the deadweight cot of taxation, λ. More formally, at t =0,1 the conumer maximize: E t C 2 2 C (1) At time 0 thi i ubject to the budget contraint: d b x ( 0) x (0) x (0) 1. (2) At time 1 the conumer re-optimize ubject to the wealth contraint: d b 2 d b x (1) x (1) 1 P ( 1) x (1) W (3) where C e x (0) x (0) (1 ), e 2 i the value of bank equity in time 2 conumption unit, and W t i time t wealth. Firm. There are N firm that are ex ante identical. Each invet depoit and equity capital raied from bank in a contant-return-to-cale technology to produce the homogeneou conumption good. To capture the idea that equity capital i more cotly than debt capital without modeling a pecific friction that caue thi to be true, we aume that only a fraction, ψ, of inveted equity i productive. 12 At time 0, firm i invet capital, technology that ha a tochatic payoff at time 2, X i,2, where B 0 x (0) x N d (0), in a X, 2 r i i i i p m ) ( B (4) 0 11 For implicity we aume utility i quadratic, but the qualitative reult hold for more general utility pecification. 12 Without ome cot to equity or ome benefit to depoit, it would be optimal in thi model to require all-equity financing. 15

16 The average return on invetment i the um of four component, the unconditional mean, r>1, plu three hock: i i a normally ditributed idioyncratic hock that i privately obervable to the firm and it bank at time 1; i p i a normally ditributed mean 0 idioyncratic hock that i publicly obervable at time 1, and independent of the privately oberved hock; and i m i a normally ditributed mean 0 hock that i independent of the firt two hock but that i correlated acro firm. The tandard deviation of a type j hock i ζ j. The correlated hock i the ource of aggregate output rik. The correlation of output acro firm, ρ, i tochatic, with {ρ L, ρ H } and an equal probability of each outcome. At time 1, all agent learn the realization of ρ, which trigger a revaluation of equity. Since N i large, 0 for j = ι, p. At time 2 the firm i liquidated and output delivered to it bank. 13 Bank. All firm, and hence all bank, are identical at time 0. Each bank invet it hare of the d aggregate upply of capital x ( 0) x (0) / N in a ingle firm. 14 It on-balance-heet aet conit entirely of thi invetment. Bank liabilitie include government-inured depoit, x d ( 0) / N, and publicly held equity valued at x e ( 0) / N. Bank equity holder receive the reidual value of aet at time 2 when the bank i liquidated. Bank are managed in the interet of equity holder. At time 1, after learning the idioyncratic realization of firm output i and i p and the correlation of aggregate rik acro firm ρ, bank that atify the capital requirement have the opportunity to invet in a rik-generating technology (e.g., off-balance-heet derivative contract) that generate a mean zero hock paying ε = {x, x} at time 2, in exchange for paying a fixed cot f. N i1 i j More realitically, bank would make riky loan to firm and the repreentative agent would own firm equity a well a bank equity and depoit. Incorporating thi more complicated ecurity tructure into the model would not change the baic concluion of the analyi. 14 The i ubcript may be uppreed when a quantity i identical acro firm or bank. 15 The cot can be interpreted a reputation lo for the bank manager who may be eventually found out to have gambled, where the likelihood of detection i increaing in the amount of rik taken. With thi interpretation, the cot would affect the amount of rik taken but would not conume real reource. Whether or not the cot i taken to reduce real output, however, ha no effect on the qualitative reult. 16

17 Whether or not the bank chooe to take rik i not revealed to conumer or regulator until time 2. To reduce the incentive for cotly rik-taking, bank are ubject to a regulatory capital requirement. It tipulate that the ratio of bank equity to bank aet, E t,i /A,t,i, mut exceed a minimum level κ. At time 0 the contraint i alway atified by the initial choice of depoit and equity. If at time 1 the re-pricing of bank equity caue the contraint to be violated, the bank i forced to reorganize and incur a fixed cot ξ. Bank that are reorganized are aumed to be unable to invet in the rik-taking technology, for intance becaue they are more heavily crutinized by regulator. We aume f prevent a bank from certain rik-taking., o it i worthwhile to incur reorganization cot to At time 2, the bank ha total aet X, 2 I g, i i Ir, i I i g, i f, where I r i an indicator function equal to 1 if reorganization ha occurred and 0 otherwie, I g i an indicator function equal to 1 if additional rik wa taken and zero otherwie, and ε i the realization of the additional rik. The bank pay depoitor: d min X i, 2 I g, i i Ir, i I g, i f, x (0) / N (5) and any reidual bank value i paid out to equity holder. When aet fall hort of promied payment to depoitor, the inurer make the bank depoitor whole. The information tructure and timing of cah flow i ummarized in Figure 1 (to be added). Government. The government run the depoit inurance ytem, determine the taxe and tranfer that balance the ytem, and et capital requirement. The depoit inurance ytem enure that depoit are paid off in full. Tax collection equal the um of thee expene multiplied by a factor λ 1, where λ-1 i the deadweight cot of taxation. 3.2 Equilibrium Price and Quantitie The time 0 aet allocation i found by olving the conumer maximization problem. Differentiating (1) with repect to the hare of the endowment inveted in the tock portfolio and impoing the budget contraint (2) yield the firt order condition: 17

18 (1 C)( R 1) 0 E (6) 0 where R i the total return on a unit of capital inveted in the tock portfolio. A relatively imple expreion for R can be found by noting that in equilibrium the total return equal total firm output net of aggregate reorganization and rik-taking cot, minu firm payment to depoitor. Since total taxe cover what bank owe to depoitor but are unable to pay, taxe are effectively a tranfer to equity holder. Then total payoff on equity per unit of invetment can be written a: R N ( i i i d r p m ) B0 L( ) f F( ) x (0) ( ) / x (0) (7) i1 L(. ) i the number of bank that experience a cotly reorganization, and F(. ) i the number of bank that utilize the rik-taking technology. In equilibrium thee cot and taxe will depend on the way in which capital i meaured, a dicued below. Notice that B x (0) x (0). Denote the um of the correlated hock by. Since the publicly and privately oberved idioyncratic hock um to zero, (7) can be rewritten a: m 0 d R d d ( r )( x (0) x (0)) L( ) f F( ) x (0) ( ) / x (0). (8) m Conumption i the um of the return on equity, depoit, and the torage technology, minu the cot of taxe: d d d b C ( r m )( x (0) x (0)) L( ) f F( ) x (0) ( ) x (0) x (0) ( )(1 ) d b ( r m )( x (0) x (0)) L( ) f F( ) x (0) ( ) Subtituting (8) and (9) into (6), d b (1 ( r m )( x (0) x (0)) L( ) f F( ) x (0) ( ) 0 E0 d d ( r )( (0) (0)) ( ) ( ) (0) ( ) / (0) 1 m x x L f F x x (9) (10) The amount of rik-free invetment in the torage technology, x (0), i determined by the total demand for rik-free aet. A i verified below, to maximize the value of depoit inurance b 18

19 bank et initial depoit and equity o that the capital contraint jut bind. In equilibrium thi implie that: x (0). x (0) x d (0) (11) Equation (2), (10), and (11) determine the time 0 allocation to equity, depoit, and the torage technology. The time 1 price of the tock portfolio i found from combining firt order condition from the conumer time 1 optimization problem with market clearing condition. Optimization implie: E1 R (1 C) P (1) (12a) and (1 ) E (12b) 1 C where μ i the Lagrangian multiplier on (3). Taking the ratio, of (12a) and (12b), and impoing the market clearing condition that j j j x 0) x (1) x ( for j=, d, b, determine the price of the tock portfolio at time 1: E 1 P (1) (13) d d d b ( r m )( x x ) L f F x / x 1 ( r m )( x x ) L f F x d b E 1 ( r )( x x ) L f F x 1 m The price of the equity portfolio i affected by the realization of the correlation between firm hock, ρ. Whether the effect of higher correlation on equity price i poitive or negative depend on parameter value. 2 m 2 Firt, holding fixed cot and taxe contant, the term E (1 x (0)) / x (0) in the numerator of (13) decreae in ρ becaue the variance of the 1 b market hock per unit of invetment i ecuritie fall when conumption volatility increae. 2 m 2 m N. Thi i the uual effect that the price of riky 19

20 It i poible, however, to chooe parameter to obtain the unintuitive reult that the equity price increae with aggregate rik becaue of the interaction between depoit inurance, liquidation rate and taxe. An increae in ρ increae expected payout from the depoit inurance ytem ince it increae the proportion of firm with output realization that are too low to repay depoitor in full. Thi ha a poitive effect on expected tax liabilitie. Both the numerator and denominator of (13) increae in expected taxe, with taxe having a negative effect on conumption through the deadweight lo of taxation, and taxe having a poitive effect on equity value becaue the ubidy value of depoit inurance accrue to equity holder. The direct effect of the liquidation rate on the numerator of (13) i indeterminate; it increae the marginal utility of conumption but decreae the value of equity. The liquidation rate alo ha an indirect effect on equity price through taxe, ince taxe increae in the liquidation rate. Finally, we will how that when the bank objective i to maximize the time 2 payout new information about ρ doe not affect rik-taking at time 1, o f F i invariant to ρ Bank Optimization Problem The value of bank equity depend on the two choice of bank manager: (1) the initial capital ratio, and (2) whether the bank take on additional rik at time 1. We aume that the bank objective i to maximize the time 2 payout to equity holder. Auming that reorganization cot and the value of acce to the rik-generating technology are not too large, the initial capital ratio that accomplihe thi i κ, ince thi maximize the ubidy value of depoit inurance which i provided for free, and minimize the equity financing cot (1 ) x (0). The time 1 deciion whether or not to invet in the rik-taking technology maximize: 16 d e d E1 max ( r i i i p m )( x (0) x (0)) I g, i I g, i f x (0) / N,0 (14) The deciion i conditional on the bank oberving the realization of it firm public and private idioyncratic hock, and the realization of ρ. Holding all ele fixed, there i a critical value ω* of idioyncratic output uch that for i i p < ω*the bank weakly prefer to invet in the riky 16 Maximizing the future value of equity alo maximize the preent value, ince adding idioyncratic rik by inveting in the rik-generating technology doe not affect the dicount rate. 20

21 technology, and otherwie chooe not to. The cutoff ω*decreae in κ, ince a higher κ increae the probability that the firm output will exceed the promied payment to depoitor. The time 1 price of an individual bank i then the um of three component: 1/N of the price of the diverified equity portfolio P (1), the obervable idioyncratic hock i p, and the expected cot of rik taking conditional on i p. Denoting the conditional expected cot of riktaking ( i p ) f, we have, i P (1) P (1) / N i i p ( p ) f (15) 4. Policy Analyi The ocial cot aociated with regulating the banking ytem i the um of the deadweight cot of taxation, bank reorganization cot, equity financing cot, and the cot of rik-taking. We conider how the choice of κ and the definition of bank equity and aet affect thi total cot, and derive the cot-minimizing policy with regard to the definition of κ and bank capital. We begin by conidering the optimal policy when the capital requirement i a contant value that i conditional only on public information at time 0. That i, policymaker chooe a capital requirement κ* to minimize: E 0 ( ) f F( ) (1 ) x (0) L( ) (16) Holding aet price and the initial invetment in riky firm fixed, the cot of taxation and rik-taking decreae in κ. 17 Taxe decline becaue bank are more likely to be able to repay depoitor, and rik-taking decreae becaue bank equity i le like a call option and becaue thoe bank mot likely to take exceive rik are reorganized. 18 On the other hand, the cot of equity financing increae with the capital requirement, ince a larger fraction of inveted aet 17 We aume that the general equilibrium effect of varying κ over the relevant range are mall, and do not affect quantitie enough to make the effect non-monotonic. 18 Notice that we aume the regulator i rik neutral, and therefore we do not have to take into account the cyclicality of cot and the effect on the conumer utility, which we expect would be econd order. 21

22 i in the form of equity. Becaue return are proportional to inveted capital, when the initial capital requirement bind it i traightforward to how that the forecloure rate i not directly enitive to the choice of κ. We now turn to the central quetion, which i whether meauring capital in market value term minimize the ocial cot given by (16), or whether there i an alternative definition of capital, alo baed on public information, that dominate? Recall that the price of bank equity at time 0 depend on the expectation of ρ, wherea at time 1 it depend on it realization, which by aumption i binomial with {ρ L, ρ H }. When the dominant effect of higher correlation i via rik averion, the effect will be for price to fall when ρ H i realized ince aggregate conumption rik increae, but a dicued above it i poible for the effect to go in the other direction becaue of the effect of depoit inurance. In either cae, market price are enitive to information about the aggregate tate. However, the payoff on individual bank equity depend on the total volatility aociated with the firm invetment, but not the correlation between payoff acro firm. Hence the realization of ρ i irrelevant to the deciion of banker maximizing (14) on whether or not to take additional rik. Since the purpoe of impoing a capital requirement i to dicourage rik-taking, but the realization of ρ doe not affect the propenity of bank to take rik, meauring capital in a way that depend on the expected value of ρ rather than the realized value provide better incentive and i welfare improving. Alternatively, pecifying a tate dependent capital requirement to be ued in conjunction with a market-value definition of capital improve welfare relative to a policy that evaluate market capital relative to a fixed ratio. Thi intuition i etablihed formally in propoition 1. Propoition 1: Let κ* be the capital requirement that minimize (16) when bank capital i evaluated in market value term, and aume that the ditortionary tax cot, λ, i zero. (a) Holding κ* fixed, there exit an alternative definition of bank capital, baed on the publicly oberved idioyncratic hock i p but independent of the realization of ρ, that reduce ocial cot relative to meauring bank capital at market price. 22

23 (b) There exit a tate-dependent capital requirement that, when capital i meaured in market value term, reduce the ocial cot relative to a capital requirement fixed at κ*. Specifically, a * procyclical ( ) that increae with the price of the bank equity portfolio i welfare improving relative to a fixed capital ratio. Proof of (a): With a market value capital requirement, a bank will be reorganized if:, i P (1) x (0) *., P i (1) x (0) x d (0) (17) The price of the bank i given by (15). It i linear in the price of the bank equity portfolio P (1), which varie with the realization of ρ. Examining the bank optimization problem (14) and the regulator objective function (16), the optimal capital requirement clearly depend on the conditional volatility of output at time 1, 2 m / N, and on the realization of the publicly oberved idioyncratic hock, i p, ince both 2 affect the probability that the bank will chooe to take on cotly rik. For intance, if i p i very negative it i better to reorganize the bank and prevent certain rik-taking ince we aume f. Equation (14) doe not depend on ρ, and equation (16) depend on ρ only through the ditortionary cot of taxation, which increae in ρ. Here we aume that λ i zero, o the optimal incentive mut be independent of ρ. Since κ* i choen at time 0 to balance average reorganization cot with average rik-taking cot, the realized reorganization rate (amount of rik-taking) i lower (higher) than i optimal when P (1) i high, and converely when P (1) i low. Let P (1, ) be an alternative meaure of firm value baed on the book value of the equity portfolio (which i equal to 1) plu a fixed adjutment δ, where: P, i, i 1 (1, ) ( ) i i p ( p ) f (18) N 23

24 , i If P (1, ), which we will refer to a adjuted book value, i ued in (17) intead of a bank market value, the reorganization rate will be independent of ρ, and by continuity there exit a δ that et the reorganization rate to a contant value that optimize the tatic tradeoff between the cot of rik-taking, reorganization, and equity finance. Proof of (b): Let, i P (1, ) x (0) 0, where the adjuted book value of bank tock i, i d P (1, ) x (0) x (0) given by (18). From the proof of (a), it i clear that welfare i increaed by etting a tatedependent, market value capital requirement uch that: P, i, i P (1) x (0) * d (1) x (0) x (0) P, i, i P (1) x (0) 0 ( ). (19) d (1) x (0) x (0) Thi i welfare improving becaue it i identical in effect to the capital requirement decribed in part (a). It i procyclical becaue, i P (1) x (0) increae in the time 1 tock price., i d P (1) x (0) x (0) 4.1 Dicuion The above reult illutrate everal important point about the interaction between fair value accounting and capital requirement that we believe are likely to be carry over to le retrictive etting. The incentive for a bank to gamble depend on it capital, and on the rik aociated with it aet and liabilitie, broadly defined. Some factor that affect market price, uch a the price of aggregate rik, may have little effect on the incentive to gamble. In other word, incentive may be motly a function of actual or p-meaure rik facing the bank, wherea market price depend on rik-adjuted or q-meaure rik to conumption. For intance in the model here, becaue of time variation in perceived aggregate rik that leave individual bank rik unchanged, there i a potentially ignificant component of market price fluctuation that i unrelated to bank incentive for rik-taking. A a reult, a contant, market-value-baed, minimum capital requirement i inefficient, and can caue an inefficiently high a rate of bank reorganization (or contraction in lending) in downturn. 24

25 Interetingly, the olution to reduce inefficiency uggeted in propoition 1(a), which i to define bank capital baed on book value adjuted for verifiable realization of idioyncratic rik, i in keeping with call for capital meaured by book value adjuted for expected loe by banker. The equivalent olution uggeted in propoition 1(b), which i to et procyclical capital requirement, i conitent with recent regulatory propoal that call for higher capital requirement in good time. 19 The analyi i not intended to ugget that market price are irrelevant to determining appropriate capital reerve; in fact we believe that in mot intance they are likely to be the mot accurate meaure of value. In the context of our model, if time-varying market price volatility were introduced by auming time variation in the common component of output hock ζ m rather than through time variation in ρ, lower market price would coincide with tate of the world where banker would have a greater incentive to take rik, and an optimal capital requirement would be enitive to the common component of market price a well a to the idioyncratic component. 4.2 Fundamental Shock v. Liquidity Shock Mot critique of fair value accounting have emphaized the effect of illiquidity on market price, wherea the mechanim in our model arie from fundamental economic rik. To the extent that one i keptical that liquidity rather than deteriorating fundamental explain the recent harp decline in aet value, thi analyi make clear that ditortion can arie even when all hock to value are fundamental. It eem that the idea that the interaction of illiquidity and capital requirement generate ocial cot could be incorporated into thi framework by adding an aggregate liquidity hock that i realized at time 1, and interpreting reorganization cot a ariing from inefficient bank liquidation reulting from thee liquidity hock in the preence of a tatic capital requirement. 19 For intance, in a peech delivered on March 20, 2009 to community banker, Federal Reerve Chairman Ben Bernanke aid, Capital rule, accounting policie, and other regulatory tandard hould not make thi job even more difficult by encouraging exceively procyclical behavior by financial intitution--that i, behavior that caue financial intitution to tighten credit in downturn and eae credit in boom more than i jutified by change in the creditworthine of borrower. 25

26 By analogy to the analyi here, if the interaction of liquidity hock and capital requirement lead to inefficiency, modifying the form of the capital requirement may be a better way to addre the ditortion than by changing accounting rule. Some banker have argued that if an invetment i intended to be held to maturity, then if it price drop due to liquidity condition it hould not affect required capital. 20 Thi preume that manager incentive to take rik i inenitive to the liquidation value of illiquid aet. While thi i conitent with our imple etup where banker are only concerned with the value of aet at maturity, in a more general etting we expect the effect of temporary price change on incentive to be more complicated, and hence we do not interpret our reult a upporting thi contention. 4.3 Fair Value Accounting and Private Contract An intereting quetion i whether the adoption of fair value accounting rule caue imilar problem for financial firm that are not ubject to capital requirement. In a frictionle market where the interet rate on outtanding debt adjut continuouly with the rik of the underlying aet and there i a fair depoit inurance premium that alo adjut continuouly, neither debt holder nor inurer require protection uch a capital requirement or retrictive covenant, and manager acting in the interet of equity holder have no incentive to take uncompenated rik. However, when financial intitution iue debt only infrequently or when depoit inurance i incompletely rik-baed, equity take on the characteritic of a call option, and it value i enhanced at the expene of unecured debt holder and the depoit inurer by the ubtitution of rikier aet for afer one. For commercial bank, capital requirement mitigate thi incentive to take rik, ince they prevent the call option from moving too far out-of-the-money and into a region where the value of rik-taking i high. 20 Some ympathy to thi tory, and coniderable political preure, may account for the recent change by SFAS 157 to allow more dicretion in the ue of market value when market are judged to be illiquid, a decribed in ection

27 Protective covenant uch a margin requirement provide imilar protection to the creditor of le regulated financial intitution. Margin requirement require borrower to pot additional collateral or cah when the value of pecified aet decline below a contractually et trigger. Both capital requirement and counterparty margin call can force firm to raie capital quickly in illiquid market, and may reult in inefficient reorganization. An important difference i that capital requirement are impoed by regulator, wherea margin requirement arie by mutual conent in private contract. 21 Preumably, private contract are conditioned on the meaure of aet value that minimize expected ex pot ditortion, o a witch to fair value accounting hould only have unintended conequence for contract already in effect at the time of the witch. Although we do not have data on a large ample of uch agreement, it i our impreion from converation with practitioner that margin requirement are generally conditioned on market value. A detailed analyi of the effect of fair value accounting on private contracting and it equilibrium implication i beyond the cope of thi paper, but an intereting quetion for future reearch. 4. Concluion In thi paper we have provided a brief account of the hitory and motivation behind fair value accounting for financial ecuritie, and a new model that we ue to examine the interaction between fair value accounting and capital requirement, and it implication for ocial welfare. Our analyi make clear that ome of the problem that arie with the introduction of fair value accounting are not due to the accounting rule in itelf, but rather from the interaction of fair value accounting and the definition of capital requirement. 27 Over time capital requirement are periodically revied by bank regulator, a i the FASB definition of capital, but the two type of regulatory action i not coordinated. In fact the recent trend toward more comprehenive fair value accounting doe not eem to have been accompanied by a rethinking of capital requirement and how they hould be harmonized with a fair value accounting regime. A 21 Private margin requirement can alo be renegotiated ex pot, which in ome intance may avoid inefficient liquidation. However, conflict of interet between variou claimant ugget that uch negotiation need not reult in ocially efficient outcome.

28 illutrated by propoition 1, for any change in the FASB definition of capital it hould be poible to pecify an offetting change in the definition of the capital requirement that make the accounting change neutral with repect to economic outcome. If fair value accounting ha advantage in other context, which we believe it doe, then a enible olution to the problem caued by the interaction of volatile capital meaure and a tatic capital requirement i to redefine the capital requirement rather than to back away from a fair value accounting tandard. 28

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