WP 15-8 april Testing the Modigliani-Miller Theorem of Capital Structure Irrelevance for Banks. Abstract

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1 Workg Paper Series WP 15-8 april 2015 Testg Modigliani-Miller Theorem Capital Structure Irrelevance for Banks William R. Cle Abstract Some advocates far higher requirements for banks voke Modigliani-Miller orem as grounds for judgg associated s would be mimal. The M&M orem holds firm is dependent structure, because any reduction from switchg higher leverage usg lower is exactly fset by an duced crease unit higher- equity as a consequence associated rise risk. Statistical tests for large US banks fd less than half this M&M fset attas practice. Higher requirements would thus impose creases lendg s, with associated output s from lower formation. These s economy would need be compared with benefits from lower risk bankg crises arrive at optimal levels requirements. JEL Codes: E44, G21, G28, G32 Keywords: Fancial Regulation, Bank Capital Requirements, Capital Structure William R. Cle, senior fellow, has been associated with Peterson Institute for International Economics sce its ception His numerous publications clude Managg Euro Area Debt Crisis (2014), Fancial Globalization, Economic Growth, Crisis (2010), The United States as a Debr Nation (2005). Author s Note: I thank Abir Varma for research assistance. For comments on an earlier draft, I thank without implicatg Barry Bosworth, Morris Goldste, Ángel Ubide, Lawrence White. Copyright 2015 by Peterson Institute for International Economics. All rights reserved. No part this workg paper may be reproduced or utilized any form or by any means, electronic or mechanical, cludg phocopyg, recordg, or by formation srage or retrieval system, without permission from Institute. This publication has been subjected a prepublication peer review tended ensure analytical quality. The views expressed are those author. This publication is part overall program Peterson Institute for International Economics, as endorsed by its Board Direcrs, but it does not necessarily reflect views dividual members Board or Institute's staff or management. The Institute is a private, nonprit stitution for rigorous, tellectually open, depth study discussion ternational economic policy. Its purpose is identify analyze important issues make globalization beneficial sustaable for people United States world, n develop communicate practical new approaches for dealg with m. The Institute is widely viewed as nonpartisan. Its work is funded by a highly diverse group philanthropic foundations, private corporations, terested dividuals, as well as come on its fund. About 35 percent Institute s resources its latest fiscal year were provided by contriburs from outside United States. A list all fancial supporters for precedg four years is posted at Massachusetts Avenue, NW Washgn, DC Tel: (202) Fax: (202)

2 Introduction The fancial crisis Great Recession , like bankg crisis Great Depression 1930s, have provoked regulary reform fancial secr. Internationally, new Basel III rules approximately double mimum requirements for most banks triple m (or more) for systemically important fancial stitutions (SIFIs). 1 The new requirements also troduce a mimum leverage ratio ization 3 percent tal (as opposed risk-weighted) assets Basel rules 4 percent United States (BCBS 2014; Federal Reserve 2013). 2 A separate issue is wher shift from risk-weighted assets tal assets as base for applyg requirements. Thomas Hoenig (2013) argues metric risk-weighted assets is illusory should largely be replaced by tal assets regulary emphasis shifted leverage ratio. Some economists have called for far higher requirements. Anat Admati Mart Hellwig (2013) propose a leverage ratio requirg equity percent tal assets (p.179). Considerg risk-weighted assets are typically only about half as large as tal assets (Hoenig 2013), this target would correspond a requirement percent risk-weighted assets, about five times as high as risk-weighted target for SIFIs Basel III. The empirical tests this study are motivated considerable part by apparent wide divergence expert opion about desirable requirements for banks. A key oretical element arguments favorg far higher ratios is structure irrelevance proposition Franco Modigliani Mern Miller (1958). This M&M hyposis matas re is no optimal relationship equity fance fance for a firm, because any crease pritability through greater leverage will be fset by an crease unit remag equity as a consequence greater risk. On this premise, some argue re should prciple be no reason for banks oppose far higher equity requirements because resultg reduction ir leverage would result a fully compensatg reduction equity In change from Basel II Basel III, common equity is rise from 2 percent risk-weighted assets (RWA) 4.5 percent. Total tier 1 (which cludes common equity) is rise from 4 percent RWA 6 percent. There is an additional conservation buffer 2.5 percent, brgg tal 8.5 percent (BCBS 2010a, 69). In addition, SIFIs are mata extra, set at 2.5 percent RWA Basel rules up 4.5 percent United States (Yalman Onaran, Jesse Hamiln, Ian Katz, Big US Banks Face Capital Requirements Up 4.5% on Top Global Mimum, Bloomberg, December 9, 2014). 2. In United States, for banks with assets over $700 billion requirement will be 5 percent (Forbes, Steep Leverage Ratio Requirements Will Force Banks Rethk Their Capital Plans, April 9, 2014). Moreover, United States, Volcker Rule Dodd-Frank legislation additionally seeks constra tradg (as opposed lendg) activity banks are allowed pursue. 3. Admati Hellwig (2013, chapter 5) emphasize Modigliani-Miller orem, although y recognize subsidized fundg through guaranteed bank deposits creates an centive for banks rely less on equity. 2

3 In contrast, few analytical attempts at identifyg optimal requirements from society s viewpot tend acknowledge higher requirements will make banks less pritable, reduce lendg economic activity somewhat as a consequence. In se studies such reductions are set agast correspondg reductions probabilities fancial crises, thus expected damages avoided, arrive at optimal creases requirements. 4 The purpose this paper is exame empirical evidence on M&M proposition as applied bankg secr. The central question is wher more highly ized banks do deed enjoy lower s equity. The actual extent such a relationship can n be used as an put a broader analysis optimal bank requirements from stpot society, takg account risks fancial crises from sufficient bank ization. Is Bankg Special? At outset it is useful address qualitative terms question, Why is bankg different? For nonfancial secr, shareholder equity typically accounts for about one-third tal assets, whereas or liabilities amount about two-thirds (see, e.g., Rajan Zgales 1995, 1428). In contrast, postwar period US commercial banks have had equity--asset ratios (book value basis) only 4 6 percent up 1970s, risg 6 percent late 1980s 9 percent by 2007 (Berl 2011, 5). Leverage on order 10 1 (or higher) stead 3 1 has meant literature this area has tended treat fancial secr as different, typically excludg it from empirical tests. It seems tuitively appealg secr fancial termediation should rely more heavily on fancg than nonfancial secrs. The tensity puts a secr should depend on nature output secr. One would not expect oil refg have same ratio crude oil tal output as, say, computer dustry. Fancial termediation is a secr by defition volves as its ma put form deposits by households corporations. The ma product provided by bank is a sre value has a high degree safety liquidity: bank checkg savg accounts. The secr also is based on actg as termediary transforms short-term claims (deposits) long-term claims (e.g., mortgages). Deposits are fancial liabilities. Replacg m entirely with equity would require public be ld henceforth bank deposits are not available stead households corporations must hold liquid assets form equity shares (e.g., 4. Thus, Miles, Yang, Marcheggiano (2012, 18) apply an M&M fset only about one-half ir calculations, based on UK bank data. The Basel Committee on Bankg Supervision (BCBS 2010b, 23) makes no allowance at all for an M&M fset, although it does so apparently spirit concludg its calculation optimal requirements may correspondgly be conservative, it cites Kashyap, Ste, Hanson (2010) as supportg M&M relationship equity leverage. 3

4 mutual funds). 5 Considerg deposits amount about one-half assets for large banks much more for smaller banks, deposit-takg nature bankg secr herently means ratio (cludg deposirs) assets will tend be higher than most secrs. There is a considerable tradition literature /equity characteristics bankg are likely be different from those or firms. Thus, ir analysis equity returns Eugene Fama Kenneth French (1992, 429) exclude fancial firms because high leverage is normal for se firms probably does not have same meang as for nonfancial firms, where high leverage more likely dicates distress. In a recent survey, Mitchell Berl (2011, 8) essentially adopts proposition fancial termediation is herently levered when he states: Sce liquid liabilities are a primary output bankg firm, we should expect banks be highly levered. Similarly, Richard Herrg (2011, 9) observes Sce some liabilities are really a product supplied by bank rar than simply a means fundg bank, we know a 100% equity--asset ratio cannot be correct answer. Although Miller (1995) himself formally discussed wher M&M applies bankg, his answer was an ambivalent Yes No. 6 One key reason has been given for observed high leverage bankg is deposits are subsidized by publicly provided deposit surance (e.g., Admati Hellwig 2013). However, it turns out nonbank fancial firms do not enjoy deposit surance also have high leverage. Thus, , median ratio tal assets shareholder funds was 19.1 for banks, 12.1 for nonbank fancial firms, but only 3.0 for nonfancial secrs (Herrg 2011, 17). Once aga implication is somethg is different about leverage for fancial secr even after removg fluence deposit surance. Perhaps most explicit analysis fdg bankg is different is by Harry DeAngelo René Stulz (2013, 1, 3), who conclude MM s leverage irrelevance orem is simply applicable banks. given a material market dem for liquidity, termediaries will emerge meet dem with high leverage structures (made possible by asset structures optimized produce liquidity). In ir model, with bank choosg a portfolio assets is not risky at optimum (p. 8), as a share plus equity turns out be ratio 1/[1+q +φz]. Here q is liquidity spread those purchasg liquidity from banks accept for assured future access, φ is loan spread paid on bank loans by those with limited access markets. With reasonable values for q 5. As proposed by Kotlikf (2010). 6. This was three-word abstract his article. In article he also acknowledged taken literally, y [ M&M Propositions] would not apply anywhere else eir. Much research focus fance last 30 years has been precisely on those departures from strict M&M assumptions thgs like taxes agency s will give a push or a tilt wards more or less leverage. No very simple or coherent set tiltg prciples has yet emerged, however, nor, for matter, has any clear pattern structures been observed across firms (p. 487). 4

5 φ, this ratio will be high, relatively close unity. Moreover, contrast with lower bank leverage earlier hisrical times can be explaed by biddg down q over time as fancial markets developed. Similarly analogy suggested above oil refg, DeAngelo Stulz (2013, 9) state Banks are different because fancial flows are puts outputs y utilize generate value for ir shareholders. Charles Calomiris Richard Herrg (2011) also take issue with notion equity can be creased defitely without s banks. They cite Anil Kashyap, Raghuram Rajan, Jeremy Ste (2008) regardg adverse fluence o much equity on agency problems, as reduced leverage could sulate bank managers from market disciple if leverage is low sck ownership is more fragmented than borrowg. Calomiris Herrg believe although an crease is necessary, we recognize re are negative, not just dimishg, social returns achievg higher amount solely by raisg equity requirements beyond some pot (p. 14). Their solution stead is supplement equity requirement with required contgent (CoCo) form would convert common equity upon a trigger (based on 90-day bank sck prices). Their objective is make conversion so unattractive banks managers would have an extreme centive issue more equity early an emergg deterioration rar than wait o late. They propose a (book value) leverage ratio 10 percent equity relative assets, supplemented by required CoCo fundg 10 percent book assets (Calomiris Herrg 2011, 29). Their equity requirement would thus be only one-third one-half level proposed by Admati Hellwig (2013), although it would be about twice Basel III level for SIFIs (9.5 percent RWA, correspondg about 5 percent tal assets). CAPM Betas versus Direct EstIMAtion It is important emphasize unlike few existg empirical estimates M&M effect for banks, tests this study do not use direct route identifyg sck price beta for banks with framework Sharpe-Ltner-Black asset pricg model (CAPM). In framework, riskess a given sck relative a diversified equity portfolio is measured by parameter beta, which tells percent by which sck price rises when overall market rises by one percent, or falls when overall market falls by one percent. Given CAPM ory, equity yield a sck should equal risk-free return plus sck s beta multiplied by excess diversified market yield over risk-free rate ( equity premium ). For example, if beta is 1.5, risk-free return is 4 percent, general diversified sck market premium is an additional 4 percent (placg equity return at 8 percent), n return on sck question would be expected be 10 percent. 7 The leadg 7. That is: x (8 4) = 10. 5

6 empirical studies M&M for banks conduct statistical tests calculate beta as a function bank leverage ratio ( relative assets). 8 Considerg analytical objective for policy purposes is calculate extent which a reduction unit equity can be expected fset shift from low- high- equity process creasg regulary requirements, prciple CAPM framework can provide a means accomplishg this objective. However, it is much more direct apply estimation form implied by origal M&M article (as set forth 1 below) than fer M&M fluence through bank beta CAPM framework. Such a test provides direct evidence on how much equity yield can be expected decle when ratio equity is reduced. Because CAPM has been found provide poor explanation equity prices with regard beta coefficient, it is problematical rely on use beta as direct means identify M&M fluence. 9 Fama French (2004) fd response equity return changes sck s beta is only about one-third size what is predicted by CAPM, such scks with low betas have higher than expected return scks with high betas have lower than expected returns. 10 On this basis, those who apply a bank beta estimated relationship leverage calculate reduction required equity yields response higher should presumably shrk ir raw estimates by two-thirds. At a broader level, it is curious accept CAPM beta framework estimate how much additional bank would reduce equity without recognizg bankg secr already has an beta about unity. 11 If bank scks are already about as safe as equity market as a whole, what are grounds for argug secr is unduly risky needs deeper ization comparison with or secrs? Arbitrage versus Optimization A fal troducry remark concerns framework M&M its relationship or frameworks optimization. At its core, M&M is based on an arbitrage proposition. It is a logical syllogism holds: (a) any -equity configuration chosen by firm can be unwound by vesrs, who can sell shares 8. Kg (2009); Kashyap, Ste, Hanson (2010); Yang Tsatsaronis (2012); Miles, Yang, Marcheggiano (2012). 9. Fama French (1992) state Our botm le results are: (a) β [beta] does not seem help expla cross-section sck returns, (b) combation size book--market equity seems absorb roles leverage E/P sck returns. (p. 428). 10. The authors report for , monthly returns are what CAPM would predict for a beta 1.25, but for a beta 1.8 predicted return is considerably higher (at 17 percent) than actual observed (14 percent), whereas for a beta 0.6 predicted return (8 percent) is considerably lower than actual observed (11 percent). The ratio actual difference between two ends spectrum CAPM-predicted is thus [14 11]/[17 8] = 0.33 (Fama French 2004, 33). 11. Kg (2009, 71) estimates bankg secrs Canada, France, Germany, Japan, United Kgdom, United States had an beta

7 additional bank would reduce equity without recognizg bankg secr already has an beta about unity. 11 If bank scks are already about as safe as equity market as a whole, what are grounds for argug secr is unduly risky needs deeper ization comparison with or secrs? Arbitrage versus Optimization A fal a highly troducry leveraged remark firm concerns purchase shares framework unleveraged M&M firms usg its relationship proceeds plus or borrowed frameworks funds, optimization. biddg down At its core, share M&M price is based leveraged on an arbitrage firm proposition. biddg up It is share a logical price syllogism unleveraged holds: (a) any firm. equity (b) Market configuration arbitrage will chosen elimate by any firm pritability can be unwound advantage by a vesrs, more highly who leveraged can sell shares a highly leveraged firm purchase shares unleveraged firms usg proceeds plus borrowed funds, firm. (c) biddg Therefore down share structure price (ratio leveraged equity firm ) is biddg irrelevant. up The share authors price do not formally unleveraged troduce risk. firm. It is (b) tellg Market arbitrage ir s will elimate do not clude any pritability an vesr advantage utility function, a more y highly do leveraged not posit a firm. typical (c) degree Therefore risk aversion. Nor structure do ir (ratio s equity set forth ) a probabilistic is irrelevant. prile The authors returns do not formally troduce risk. It is tellg ir s do not clude an vesr utility function, relationship y do not posit -equity a typical degree ratio, nor risk any aversion. hyposized Nor distribution do ir s function set for forth returns. a probabilistic With such prile a function returns it would be relationship possible explore equity optimal ratio, -equity nor any ratio hyposized as a function distribution risk aversion function for returns. With such a function it would be possible explore optimal equity ratio as a function characterizg fancial markets. Instead authors appeal risk only qualitatively by implication risk aversion characterizg fancial markets. Instead authors appeal risk only qualitatively mata any by risk implication aversion whatsoever mata will suffice any risk aversion drive ir whatsoever arbitrage process will suffice rule drive out any ir arbitrage superiority process one -equity rule out ratio any over superiority any or. one equity ratio over any or. Specifyg Tests Specifyg Tests As set forth appendix A, A, M&M proposition leads a a straightforward specification specification for for an empirical an empirical test. The orem yields result : test. The orem yields result : where i is equity as measured by ratio earngs per share price per share ( 9 6 earngs Fama yield French or verse (1992) state price/earngs Our botm ratio); le results ρ is are: ization (a) β [beta] does rate not at seem which expected help expla cross section streams future earngs sck are returns, ized (discounted) (b) combation for class size (by book market implication, secr) equity seems firms absorb roles leverage E/P sck returns. (p. 428). 10 where The question; authors i is r report is rate equity for terest , at as which measured both monthly by firm ratio returns earngs vesrs are what can per CAPM borrow; share would D price predict is per firm s for share a beta ( 1.25, earngs, but for yield S is a beta shareholder or verse 1.8 equity predicted price/earngs return firm. is Subscript considerably ratio); j ρ refers is higher ization (at firm 17 percent) observed. rate than Because at which actual expected observed ization (14 percent), streams whereas future for earngs a beta are 0.6 ized predicted (discounted) return (8 percent) for is class considerably (by implication, lower than secr) actual observed (11 percent). rate exceeds The ratio terest actual rate difference (ρ > r), reducg between two relative ends equity spectrum will reduce CAPM predicted earngs firms question; r is rate terest at which both firm vesrs can borrow; D is firm s is thus, yield [14 demed 11]/[17 S is shareholder by 8] = market, 0.33 equity (Fama thanks French firm. reduction 2004, Subscript 33). perceived j refers risk. The firm formulation observed. turns Because out cause 11 ization Kg (2009, 71) estimates bankg secrs Canada, France, Germany, Japan, United Kgdom, exactly amount rate exceeds reduction terest earngs rate (ρ yield > r), reducg is needed relative have equity will reduce earngs United yield States demed had by beta market, 0.95 thanks reduction 0.74 perceived risk. The formulation turns out rema cause constant. exactly Moreover, amount this reduction earngs must yield equal ization is needed have rate ρ (appendix A, rema A4). constant. Moreover, this must equal ization rate ρ (appendix The A, A4). will be weighted equity terest The will be weighted equity terest rate rate. Defg. V Defg as value V as value firm, settg firm, this settg value as this beg value equal as beg equal plus equity plus (V = equity D + S), (V = D defg + S), defg fancg share fancg y as share fraction y as tal fraction value attributable tal value attributable rar than rar equity than (such equity (such y = D/V), y it = follows D/V), it : follows : As demonstrated appendix B, given (1), derivative ACC ( ) (2) with respect ratio equity is zero. Capital structure (i.e., decision fance through as opposed equity) refore has no fluence on M&M framework. For purposes empirical implementation, 7 (1) can be estimated as:

8 (appendix A, A4). The will be weighted equity terest rate. Defg V as value firm, settg this value as beg equal plus equity (V = D + S), defg fancg share y as fraction tal value attributable rar than equity (such y = D/V), it follows : As demonstrated appendix B, given (1), derivative ACC ( ) As demonstrated (2) with respect appendix B, given ratio (1), equity is derivative zero. Capital ACC structure ( (i.e., decision ) fance through (2) with respect as opposed ratio equity) refore equity has no is zero. fluence Capital on structure (i.e., decision fance through as opposed equity) refore has no fluence on M&M M&M framework. framework. For purposes For purposes empirical empirical implementation, (1) can (1) be can estimated be estimated as: as: where z is is defed as as equity equity ratio ratio (z = (z D/S), = D/S), a = a ρ, = ρ, b = b = (ρ (ρ r). r). To To support M&M M&M hyposis, constant a should be found have a value plausibly represents return hyposis, constant a should be found have a value plausibly represents return bankg secr (ρ), coefficient b should be such a b yields a plausible value for bankg difference secr between (ρ), this rate coefficient b terest should be rate such r. a b yields a plausible value for difference between this rate terest rate r. Data Data The database developed for tests this study is drawn from annual filgs form 10 K with Securities The database developed Exchange for Commission tests this for study 54 is largest drawn US from banks, annual for filgs period form 10-K 12 with These banks range size from assets $2.4 trillion at end 2013 for JP Morgan Chase $6.5 billion for Securities Exchange Commission for 54 largest US banks, for period PacWest Bancorp (Los Angeles, California). They accounted for tal assets $13.2 trillion 12 These at end 2013, banks range representg size from 82.7 assets percent $2.4 tal trillion assets at US end deposiry 2013 for stitutions JP Morgan (Federal Chase Reserve $6.5 billion 2014, for 77). PacWest The Bancorp 10 K (Los data Angeles, report tal California). assets, tal They liabilities, accounted for tal shareholder assets equity $13.2 trillion ( difference). at end Total liabilities are used as estimate (D 1), shareholder equity as estimate 2013, representg 82.7 percent tal assets US deposiry stitutions (Federal Reserve 2014, 77). equity (S). The dependent variable i, equity, is estimated as verse price/ earngs The 10-K ratio data for report year tal question, assets, tal usg liabilities, fourth quarter shareholder equity sck ( difference). price trailg Total 12 liabilities are used as estimate (D 1), shareholder equity as estimate equity (S). The dependent variable i, equity, is estimated as verse price/ earngs ratio for year question, usg fourth-quarter sck price trailg 12-month 12 For most banks, corporate website provides 10 K filgs on its vesr portal (see, for example, earngs. 13 These data are also from 10-K Note filgs for four most large banks, banks or from data Bloomberg end 2007 orwise. because subsequently It is a stard durg prciple fancial corporate crisis y fance were eir taken earngs over by or yield, banks or verse (Washgn price/ Mutual by JP Morgan Chase, Countrywide by Bank America, Wachovia by Wells Fargo) or failed (IndyMac). earngs ratio, should be higher when riskess asset is greater. 14 There should be no ambiguity whatsoever expected earngs yield should be higher for higher risk, or thgs beg equal. Ambiguity does arise, however, measurg what vesrs expect future returns be, because recently observed actual returns may or may not reflect those expectations. The price a sck should be 12. For most banks, corporate website provides 10-K filgs on its vesr portal (see, for example, com/citi/vesr/sec.htm). Note for four large banks data end 2007 because subsequently durg fancial crisis y were eir taken over by or banks (Washgn Mutual by JP Morgan Chase, Countrywide by Bank America, Wachovia by Wells Fargo) or failed (IndyMac). 13. Modigliani Miller (1958, 271) identify i as verse price/earngs ratio statg market price any share sck is given by izg its expected return at contuously variable rate i j. 14. See, for example, Damodaran (2007, chapter 2). Or, for stard analysis for general vestg public, see Malkiel (2015, 125). 8

9 discounted present value its future stream earngs. Expected future earngs depend on base period earngs expected rate growth earngs future. The appropriate discount rate apply equals risk-free rate return plus a premium reflect riskess firm. In M&M framework, this riskess varies directly with ratio equity. The discount rate will thus be higher for a more leveraged firm. Accordgly, for a specific class firms (such as banks) which growth rate future earngs is expected be similar among firms question, earngs yield is expected be higher for firms with greater risk. Application a higher risk premium discount rate will translate future stream earngs a lower present value (sck price) relative earngs. Although sck valuation is based on expected future earngs, empirical estimates require use actual observed earngs as proxy for expected future earngs. However, use observed earngs yield as measure equity raises problem terpretg data for a year losses. The problem is such years actual net earngs will not be a meangful proxy for expected stream future earngs, relevant concept M&M. Invesrs would not supply if y believed future earngs would be negative, so by defition a year losses does not provide a meangful proxy future expected earngs. Negative net earngs occur about 8 percent bank-year observations, with heavy concentration (83 percent negative stances) Great Recession years The solution adopted here is constra earngs yield observation be no lower than real return on US Treasury flation-protected (TIP) five-year bonds, plus a risk spread 100 basis pots, as lowest meangful rate at which vesrs might be prepared provide equity. 15 Choice real rate reflects fact when flation is expected nomal stream earngs will be expected rise over time, aumatically providg flation protection, such clusion flation rate for year question would be double-countg expected flation. As an alternative measure equity, a second test uses ratio net come year question book value equity at end previous year. The same imposed floor replaces observations for years with negative come. Figure 1 shows trends simple s se ratios for 54 large US banks The earngs yield (EY) refers verse price/earngs ratio usg trailg earngs fourth-quarter sck price, percentage terms. (Flankg confidence tervals for two stard deviations, or 5 percent level, for each year are also shown.) Net come relative equity (NI/Eq) refers net come for year shown as a percent equity (assets mus liabilities) at end previous year, aga percentage terms. Both series are constraed observations, overridg negative observations as just discussed. The unconstraed series are shown appendix D, figure D.1. They 15. The five-year TIP rate d 1.27 percent , 1.91 percent , but fell an 0.23 percent (Federal Reserve 2015a). 9

10 dicate losses for earngs yield measure near zero s for net come relative equity measure. Figure 1 also shows ratio equity (lagged one year), this time as a pure number. It turns out re has already been significant deleveragg for US banks sce 2007 (i.e., 2008 figure with respect /equity ratio). The ratio equity has fallen from an (unweighted) about 10.5 about 8. Based on same 10-K filgs data, tier 1 is persistently an about 83 percent book equity. By implication, ratio tier 1 tal assets has already risen from about 7.2 percent assets about 9.2 percent assets. 16 The (constraed) earngs yield, contrast, has remaed relatively steady with a range 6 8 percent durg this period, with exception a dip as low as about 4 percent 2009 Great Recession. However, (constraed) ratio net come book equity has substantially decled, from about 16 percent a range 8 10 percent. The contrast between come-book equity ratio earngs yield is a manifestation decle ratio market ization book value equity, which fell from an It is formative consider distribution net come for se large banks over 12-year period Figure 2 is a hisgram showg distribution net come as a percent tal assets at end previous year. The left panel shows full distribution. The right panel shows distribution for just cases losses. The right-h bucket 0 refers percent bank-year observations with net come between 1 percent zero. A tal 8.3 percent bank-year cases had negative come this period (which cluded worst recession sce 1930s). Only 1.1 percent had losses exceedg 3 percent assets; only 0.7 percent had losses exceedg 5 percent assets, respectively new Basel III US largest-bank leverage stards. Critics low Basel ratio ten seem consider it self-evident 3 percent level is far o low given what might be expected losses, but it turns out frequency larger losses is relatively low. Of course, a major caveat is book come may be overstated ( losses understated) by failg capture erosion market value assets periods stress. 18 Noneless, distribution come results figure 2 suggests 16. For a given ratio equity (D/E), correspondg ratio assets equity (A/E) is higher by unity. That is: A/E = (D+E)/E = (D/E) + 1. With tier 1 at 83 percent equity, a reduction /equity ratio from represents an crease (verse) leverage ratio tier 1 assets from 7.2 percent (= 1/(11.5/0.83)) 9.2 percent (= 1/(9/0.83)). 17. Market ization data are from Bloomberg. 18. Thus, IndyMac consistently had positive earngs , its losses 2007 were only 2.1 percent end-2006 assets. Those losses amounted only 30 percent book equity at end 2006, so technically bank does not seem have been solvent when it was closed down. 10

11 settg leverage ratio far higher than US level would amount addressg a small fraction cases based on most recent decade s experience. Test Results The tests here estimate (3) usg a pool 12 years observations on largest US banks. 19 Because unusual conditions durg Great Recession, tests clude a dummy variable for years For earngs yield variant unit equity, results are: 20 4) ey t = z t D 0810 ; Adj. R 2 = (19.5) (1.62) ( 7.2) where ey is earngs yield (percent), or verse price/earngs ratio; z is ratio equity (with equity defed as excess book assets over book liability); D is a dummy variable with value 1 for orwise. T-statistics are parenses. The coefficient on leverage ratio is not significant. Importantly, size coefficient is relatively small, about 5 basis pots for each unit change leverage ratio. Instead, M&M value for coefficient should be ρ r. It seems unlikely terest rate r would be so close bank class rate return on difference would be this small. When net come/equity variant is applied stead as measure unit equity, re is a considerably stronger relationship: 5) NI t /E t 1 = z t D 0810 ; Adj. R 2 =0.268 (10.0) (9.4) ( 10.5) where NI t /E t 1 is ratio book net come equity at end previous year (percent). This time coefficient on leverage ratio is highly significant. Moreover, its size is substantial, at about 60 basis pots for each crement by unity ratio equity. Noneless, even this magnitude is small as a likely gauge excess bankg secr return on mus terest rate. 19. The tests exclude three p 54 banks: Ally Fancial (which was not publicly listed durg most this period), UnionBanCal (which was acquired by Mitsubishi UFJ 2008),, as an outlier, Synovus Fancial (which had extreme swgs earngs yield from 164 percent percent 2011). 20. Tests on earngs yield variant apply 564 bank-year observations; tests on net come relative equity apply 579 bank-year observations. 11

12 Application fixed-effects tests for an unbalanced panel yields results are very close those s (4) (5). 21 Because ir simplicity transparency, results s (4) (5) are applied impact estimates below. Implications for Average Cost capital Table 1 considers implications a sharp crease bank requirements on for banks. The table uses estimates s (4) (5) assess effects raisg bank from a benchmark 10 percent tal assets 25 percent ( midpot range suggested by Admati Hellwig 2013). This crease is equivalent reducg /equity ratio from The equity is obtaed usg (4) or (5) (with no dummy variable) as applied first z = 9 next z = The table considers two cases: one (A) with terest rate at 3 percent or (B) at 2 percent. The table n shows before reform (0) after (1), for each two alternative terest rate assumptions. The table also shows correspondg changes. Surprisgly, two models show identical changes : an crease 54 basis pots if real terest rate is 3 percent, 69 basis pots if real terest rate is 2 percent. Essentially larger coefficient b NI/E model higher base level equity provide a substantially larger absolute reduction equity, but because equity (both before after) is substantially higher NI/E model than equity yield model, re is a fully fsettg effect from a more powerful impact shiftg from low- high- equity. The table next shows change would occur if re were no M&M effect at all (namely, unit equity after reform is identical before reform). Fally, table reports correspondg percent tal potential crease is fset by duced reduction equity as a consequence M&M effect. As expected from small size coefficient b ey model large size this coefficient NI/E model, percentage fset is much smaller earngs yield model (only about 10 percent) than net-come model (about 60 percent). Takg s over two models two alternative terest rates, expected change from higher requirement would amount 61.5 basis pots. In 21. Usg fixed effects, which is equivalent havg dividual dummy variables for each bank each year, yields followg coefficients on /equity ratio z t-1 : (1.31) for earngs yield (stead , 4) (8.12) for net come relative equity (stead 0.636, 5), with t-statistics parenses. 22. That is, with shares D E, respectively, at , D/E = 0.9/0.1 = 9. With se shares stead at , D/E = 0.75/0.25 = The value for b estimated (4) is applied even though it is not significantly different from zero. 12

13 absence any M&M fset crease would be basis pots. So on, M&M fset amounts 45 percent potential crease weighted. 24 Banks could be expected pass along net crease household corporate borrowers. Permanently higher real terest rates would reduce amount formation thus reduce future GDP from levels orwise reached. The central estimate, an crease approximately 62 basis pots for a 15 percent tal assets crease, is considerably more modest than would be implied by fdgs Benjam Cohen Michela Scatigna (2014) for actual behavior lendg rates so far durg phase- Basel III. They estimate for a sample 94 banks both advanced emergg-market economies, common equity rose from 11.4 percent risk-weighted assets percent 2012 (p. 12). Net terest come rose from 1.37 percent tal assets 1.67 percent. The authors state 30 basis pot crease translates 12 basis pots per percentage pot crease (risk-weighted) /asset ratio. Considerg risk-weighted assets would likely be no more than 50 percent tal assets gog forward ( 2012 ratio was only 0.42; p. 11), each percentage pot tal assets crease would impose at least 24 basis pots crease lendg based on Cohen-Scatigna results. In exercise this study, 15 percentage pot crease relative tal assets would thus boost bank lendg s by 360 basis pots. So estimates here can be seen as substantially on conservative side comparison with actual experience under creased requirements Similarly, crease 62 basis pots estimated here is more modest than correspondg crease implied by estimates David Miles, Jg Yang, Gilber Marcheggiano (2012), which would amount 81 basis pots for same crease. As discussed appendix C, y estimate raisg by 3.33 percent tal assets (reducg asset/ leverage ratio from 30 15) would crease weighted by 18 basis pots after takg account M&M fset (duced reduction equity ). Applyg an crement 15 percentage pots assets would thus imply an crease 81 basis pots (= 18 x [15/3.33]). Anor study discussed appendix C, by Jg Yang Kostas Tsatsaronis (2012), obtas results imply a 15 percentage pot crease ratio tal assets would boost weighted by 120 basis pots. The fdgs se two studies thus also imply estimates present study for impact on lendg rates from a 15 percentage pot crease relative assets may be understated rar than overstated, although not by as wide a marg as implied by comparison fdgs Cohen Scatigna (2014) for creases have already occurred from much smaller creases already curred itial phase- Basel III. 24. Note this turns out be same fset as identified by Miles, Yang, Marcheggiano (2012). See appendix C. 13

14 Impact on Economy Miles, Yang, Marcheggiano (2012, 15 16) provide a methodology for calculatg impact higher s on economy. As pot departure, share national come (defe it as α) is benchmark for elasticity output with respect sck. Output will thus fall by a percentage equal α % K, where fal term is percent reduction sck. This reduction turn will depend on sensitivity used price, which depends on degree ease substitutg for labor change price relative price labor. The substitution effect depends on elasticity substitution, σ, which authors place at 0.5 on basis literature. The change price relative price labor turns out be greater than just itial crease price, because with less cooperate with, margal product labor will fall so will its price. This fal relative price term turns out be a facr 1/(1 α). The combed effect a v percent rise will n be reduce output by v α σ (1/[1 α]) percent. With α = 0.33 σ = 0.5, change output will be a decle by 0.25 v percent. 25 How much would crease requirements exercise above crease economy? Aga followg Miles, Yang, Marcheggiano (2012), assume one-third fancg nonbank economy comes from banks. Considerg one-third comes from equity (Rajan Zgales 1995, as cited earlier), by implication nonbank firms secure one-third fancg from nonbank borrowg (for example, corporate bond market). 26 The equity United States can be gauged by earngs yield. This yield has been an 6.8 percent from 1960 through 2014 (Damodaran 2015). As for, proper concept is a real terest rate on say 5-year obligations. Assumg normal flation-protected Treasury bond this maturity would be 1.5 percent, assumg an credit risk spread 200 basis pots, a reasonable benchmark for United States would be 3.5 percent. So benchmark would st at: 1/3 6.8% (for equity) + 2/3 3.5% (for ) = 4.6 percent. If central estimate crease bank lendg rates caused by rise banks requirements from 10 percent tal assets 25 percent is 62 basis pots ( result above), if banks provide one-third tal fancg, n crease economy will be 1/3 62 basis pots 20 basis pots ( absence any spillover higher lendg rates by nonbank fancial termediaries). This crease would constitute an crease 25. That is: (1/0.67) = This share would likely be considerably lower euro area than United States United Kgdom ( country considered Miles, Yang, Marcheggiano 2012). 14

15 by 4.3 percent. 27 Based on share substitution elasticity relationships just discussed, 12 consequence would be reduce level future path GDP by 1.08 percentage pot. 28 Consider significance this reduction over a tangible time horizon such as 30 years. Assumg basele GDP discussed, consequence would be reduce level future path GDP by 1.08 percentage pot. growth 28 Consider at 2 percent, significance discountg this reduction by a social over rate a tangible time preference time horizon such 1.5 percent, as 30 years. present Assumg discounted basele value GDP growth loss at output 2 percent, over this discountg horizon would by a social amount rate 35 time percent preference base 1.5 year s percent, present discounted value loss output over this horizon would amount 35 percent GDP. 29 base year s GDP. 29 Furr Considerations Furr Considerations Social Social versus versus Private Private Returns. Returns. Admati Admati et al. et (2011, al. (2011, 22 23) 22 23) argue argue even if even higher if bank higher bank requirements cause an crease bank lendg rates, result is likely be welfare enhancg from requirements viewpot cause society an crease opposed bank private lendg shareholders rates, result borrowers. is likely Their be reason welfare-enhancg is existg from government viewpot guarantees society as deposit, opposed as well private as implicit shareholders guarantees borrowers. o big fail, Their give reason a disrted is existg centive banks take excessive risks can damage economy a fancial crisis. These disrted government centives guarantees are additive deposit, as general well as disrtion implicit guarantees from tax favoritism o-big--fail, relative give a disrted equity. centive Identifyg banks socially take optimal excessive creases risks bank can damage, however, economy would require a fancial takg crisis. These account a realistic evaluation s economy from raisg bank lendg rates as a consequence disrted centives reducg are additive formation. It general may well disrtion be from correspondg tax favoritism reduction relative expected equity. social Identifyg losses from socially fancial optimal crises would creases warrant bank substantial, s however, from lower would require formation. takg But account a prciple re is likely be some optimal limit socially beneficial crease if operational realistic evaluation effect is some s loss output economy because from raisg M&M fset bank is lendg fact rates far from complete. as a consequence It is reducg furr worth formation. notg It may social well benefits are associated correspondg with reduction service expected providg social bank deposits, losses from fancial because y constitute money performg its three basic functions: liquidity, sre value, medium crises would exchange. warrant It substantial is not clear s from social lower subsidy formation. banks from But government prciple deposit re guarantee is likely be is some greatly optimal larger than limit social socially externality beneficial provided crease by banks if form operational providg money effect is some form loss deposits. output In because short, although M&M recognition fset is fact need far from take complete. societal It externalities is furr worth account notg could social benefits deed are associated lead identification with service optimal providg bank requirements deposits, because are significantly y constitute higher money than performg past, calibration appropriate policy is considerably more complicated than implied by a general proposition higher requirements are less existg arrangements subsidize banks 27. That is: encourage 20/460 = m Note take Miles, risks at Yang, expense Marcheggiano public. (2012, 16) get a much smaller proportionate crease : only 0.6 percent, for a halvg leverage. The much lower figure results from a lower estimate impact Monetary bank lendg Policy rates Offset? (18 basis Anor pots central stead policy 62) question a substantially is wher higher estimate be concerned at equity all about (10 percent possible stead creases 6.8 percent) bank borrowg lendg s rates (5 as percent a consequence stead 3.5 percent). higher The lower requirements, impact part on reflects grounds fact ir halvg any such leverage crease is less aggressive terest than rates could two-thirds be fset reduction by a relaxation leverage (from monetary 9:1 3:1) policy. examed A here major implied by problem preferred with range this monetary Admati policy Hellwig fset (2013). argument The lower is estimates monetary Miles, policy Yang, should Marcheggiano be reserved (2012) for translate a task present achievg value loss equal a balanced 6 percent macroeconomic one year s GDP, outcome much smaller regardg than flation 35 percent unemployment. estimate here (despite It is ir discountg over an fite horizon rar than just 30 years) That That is: is: It should It be be emphasized 1.08 percent reduction refers level level GDP at at each each future pot future time, not pot time, annual not growth annual rate over growth period. rate over period. 29 See Cle (1992, 255) for derivation a long term rate social time preference 1.5 percent. This parameter 29. See Cle (1992, 255) for derivation a long-term rate social time preference 1.5 percent. This parameter is based on is based on an elasticity margal utility 1.5, combed with a long term growth rate per capita come an elasticity margal utility 1.5, combed with a long-term growth rate per capita come 1 percent. (The social 1 percent. (The social rate time preference equals rate pure time preference, for myopia, plus elasticity rate time margal preference utility equals multiplied rate by pure time growth preference, rate per for myopia, capita consumption; plus elasticity see Ramsey margal utility I have multiplied by argued, growth followg rate per Ramsey, capita consumption; re is see no Ramsey justification for I have pure argued, time preference followg Ramsey, from stpot re is no justification society.) for pure Defe time preference g =0.02 as from basele stpot growth rate, society.) =0.015 Defe as g =0.02 social as rate basele time growth preference, rate, δ =0.015 = as social as rate time fraction preference, output λ = lost because as fraction lower output lost sck. because The stream lower output lost sck. is n The ( stream year t): output Q 0 e gt lost. is n ( When year t): this λ Qstream 0 e gt. When is discounted this stream at is, discounted present at δ, value present stream value losses stream over losses first over 30 years first is years percent is 35 percent base year base-year GDP. That is: = 0.35 Q 0. 15

16 its three basic functions: liquidity, sre value, medium exchange. It is not clear social subsidy banks from government deposit guarantee is greatly larger than social externality provided by banks form providg money form deposits. In short, although recognition need take societal externalities account could deed lead identification optimal requirements are significantly higher than past, calibration appropriate policy is considerably more complicated than implied by a general proposition higher requirements are less existg arrangements subsidize banks encourage m take risks at expense public. Monetary Policy Offset? Anor central policy question is wher be concerned at all about possible creases bank lendg rates as a consequence higher requirements, on grounds any such crease terest rates could be fset by a relaxation monetary policy. A major problem with this monetary policy fset argument is monetary policy should be reserved for task achievg a balanced macroeconomic outcome regardg flation unemployment. It is unlikely any crease private secr borrowg s resultg from higher bank requirements could be exactly fset by precisely same reduction terest rates would be optimal from stpot addressg duced changes flation unemployment. This task would course be even more difficult if risk-free terest rate were already at zero bound (as United States followg Great Recession). Moreover, extent over a period years a higher bank lendg rate had consequence reducg potential supply because less formation, central bank could have less scope for reducg terest rates without flationary consequences because more constraed supply. Conclusion Higher requirements may still be socially beneficial, but y are not free, by implication it is desirable compare social benefits higher requirements agast social s associated with higher lower formation. If rough calculations here are dicative, implication would be sum fancial crisis losses avoided over next 30 years as a consequence a much higher requirement (benchmarked at an additional 15 percent tal assets) would need be on order one-third one-year s GDP warrant output s additional bank. These s would arise because, on basis statistical estimates for large US banks, less than half M&M fset (reduction unit equity response reduction leverage thus risk) would be likely occur. 16

17 References Admati, Anat, Peter M. DeMarzo, Mart F. Hellwig, Paul Pfleiderer Fallacies, Irrelevant Facts, Myths Discussion Capital Regulation: Why Bank Equity is Not Expensive. Bonn: Max Planck Institute. Admati, Anat, Mart Hellwig The Bankers New Clos: What s Wrong with Bankg What Do About It. Prcen: Prcen University Press. BCBS (Basel Committee on Bankg Supervision). 2010a. Basel III: A Global Regulary Framework for More Resilient Banks Bankg Systems. Basel: Bank for International Settlements, December. BCBS (Basel Committee on Bankg Supervision). 2010b. Basel Committee on Bankg Supervision, An Assessment Long-term Economic Impact Stronger Capital Liquidity Requirements. Basel: Bank for International Settlements, August. BCBS (Basel Committee on Bankg Supervision) Basel Committee on Bankg Supervision, Basel III Leverage Ratio Framework Disclosure Requirements. Basel: Bank for International Settlements, January. Berl, Mitchell Can We Expla Banks Capital Structures? Busess Review Q Philadelphia: Federal Reserve Bank Philadelphia, pp Calomiris, Charles W., Richard J. Herrg Why How Design a Contgent Convertible Debt Requirement. New York: Colombia Busess School, April. Processed. Cle, William R The Economics Global Warmg. Washgn: Institute for International Economics. Cohen, Benjam H., Michela Scatigna Banks Capital Requirements: Channels Adjustment. BIS Workg Papers No Basel: Bank for International Settlements, March. Damodaran, Aswath Valuation Approaches Metrics: A Survey Theory Evidence. Bosn: Now Publishers. Damodaran, Aswath S&P Earngs: 1960-Current. New York: New York University. DeAngelo, Harry, René Stulz Why High Leverage is Optimal for Banks. Los Angeles: University Sourn California, Marshall School Busess, May. ECB (European Central Bank) Bank Interest Rates loans corporations (new busess). Statistical Data Warehouse. Frankfurt. Fama, Eugene F., Kenneth R. French The Cross-Section Expected Sck Returns. Journal Fance 67, no. 2 (June): Fama, Eugene F., Kenneth R. French The Capital Asset Pricg Model: Theory Evidence. Journal Economic Perspectives 18, no. 3 (Summer): Federal Reserve Press Release, July 2. Washgn. Available at: bcreg/ a.htm. Federal Reserve Fancial Accounts United States (Z.1): Third Quarter Washgn. Federal Reserve. 2015a. Selected Interest Rates H.15. Washgn. Federal Reserve. 2015b. Consumer credit G.19. Washgn. Graham, B., D. Dodd Securities Analysis: Prciples Techniques. New York: McGraw-Hill. Herrg, Richard J The Capital Conundrum. International Journal Central Bankg 7, no

18 Hoenig, Thomas M Basel III Capital: A Well-Intentioned Illusion. Paper presented 2013 Research Conference, International Association Deposit Insurers, Basel, April 9. IIF (Institute International Fance) The Cumulative Impact on Global Economy Changes Fancial Regulary Framework. Washgn: IIF, September. Kashyap, Anil K., Raghuram G. Rajan, Jeremy C. Ste Rethkg Capital Regulation. In Matag Stability a Changg Fancial System. Kansas City: Federal Reserve Board Kansas City, pp Kashyap, Anil K., Jeremy C. Ste, Samuel Hanson An Analysis Impact Substantially Heightened Capital Requirements on Large Fancial Institutions. Chicago: University Chicago, Booth School Busess, May. Kg, Michael R The Cost Equity for Global Banks: A CAPM Perspective from BIS Quarterly Review (September): Kotlikf, Laurence J Jimmy Stewart Is Dead: Endg World s Ongog Fancial Plague with Limited Purpose Bankg. Hoboken, NJ: John Wiley & Sons. Malkiel, Burn G A Rom Walk Down Wall Street. New York: W. W. Norn. Miles, David, Jg Yang, Gilber Marcheggiano Optimal Bank Capital. Economic Journal 123 (March): Miller, Mern H., Do M&M Propositions Apply Banks? Journal Bankg Fance 19: Modigliani, Franco, Mern H. Miller The Cost Capital, Corporation Fance Theory Investment. American Economic Review 48, no. 3 (June): Rajan, Raghuram G., Luigi Zgales What Do We Know about Capital Structure: Some Evidence from International Data. Journal Fance 50, no. 5 (December): Ramsey, F. P A Mamatical Theory Savg. Economic Journal 138, no. 152: Yang, Jg, Kostas Tsatsaronis Bank Sck Returns, Leverage Busess Cycle. BIS Quarterly Review (March):

19 Figure 1 Trends net come relative equity, earngs yield, /equity ratio for 54 largest US banks, a NI/Eq % EY % D/E NI/Eq = net come relative equity; EY = earngs yield; D/E 1 = equity (lagged one year) a. For observations with earngs constraed exceed zero; see text. Note: Also shown figure are flankg confidence tervals for two stard deviations, or 5 percent level, for each year. Source: Calculated from annual filgs Form 10-K with Securities Exchange Commission. 19

20 Figure 2 Distribution annual bank net comes relative assets, 54 largest US banks, percent cases 60 All net come as percent assets Loss cases only percent cases net come as percent assets Sources: 10-K filgs with Securities Exchange Commission; Bloomberg. 20