Hiding Loan Losses: How to Do It? How to Eliminate It?

Transcription

1 ömföäflsäafaäsflassflassf ffffffffffffffffffffffffffffffffffff Discussion Papers Hiding oan osses: How to Do It? How to Eliinate It? J P. Niiniäki Helsinki School of Econoics and HECER Discussion Paper No. 94 Noveber 007 ISSN HECER Helsinki Center of Econoic search, P.O. Box 7 (Arkadiankatu 7), FI 0004 University of Helsinki, FINAND, Tel , Fax , E ail info hecer@helsinki.fi, Internet

2 HECER Discussion Paper No. 94 Hiding oan osses: How to Do It? How to Eliinate It? Abstract This paper introduces three ethods to hide loan losses and analyzes how they affect bank s loan interest incoe, payents on deposits, liquidity and oral hazard. The analysis reveals that two hiding ethods represent a Ponzi schee. Contrary to classic theory, e.g. Diaond (984), oral hazard ay arise even though bank s loan portfolio is diversified. Alternative instruents to eliinate hiding are investigated. Under specific circustances, a Ponzi schee ay provide a socially optial ethod to create liquidity and prevent the failure of a solvent but illiquid bank. JE Classification: G, G8. Keywords: Banking, Evergreening, Financial Crises, Moral Hazard, Deposit Insurance. Juha Pekka Niiniäki Departent of Econoics Helsinki School of Econoics P.O. Box 0 FI 000 Helsinki FINAND e ail: juha pekka.niiniaki@hse.fi

3 . Introduction A bank s opportunity to hide loan losses has played an iportant part in recent banking crises, ost of all in eerging econoies. This can be confired by abundant evidence. To begin, De Juan (996, p. 9) describes the ethods of hiding as follows..when a loan particularly a large loan becoes questionable or bad because of the borrower s lack of repayent capacity, the bank rolls over the loan so that it does becoe past due. Alternatively, the borrower ay be given a new loan to repay the previous loan. The rolled-over loan does not becoe past due in the books and the new loan is not in arrears, but the actual debt is The hiding ethods a bank rolls over the defaulted loans or refinances the with subsequent loans - are so effective that a bank ay see to be greatly profitable even when it possesses a large burden of hidden proble loans and is de facto insolvent. These types of occurrences are docuented by nuerous researchers. Yet, during the previous banking crises, any of atin Aerica s banking systes have reported positive net incoe to assets, whereas banking systes in industrial countries have reported significant negative net incoe to assets. jas-suarez & Weissbrod (996, p. 3). Iproveents in accounting and transparency, a bank run, a banking crisis or an accurate bank audit finally reveals the bank s true financial condition. In Baltic States, for instance, this is reported by Hansson & Tobak (999, p.7) The ability of banks to roll over proble loans concealed their true solvency and created a false picture of health. Bank profits and thus net worth were overstated. When the hidden probles finally eerged, especially through iproved accounting and auditing, the resulting erosion of profits and

4 capital was unexpected. When large, these changes could transfor a seeingly solvent bank into an apparently insolvent one. Since a bank is often capable of hiding loan losses for a long tie, they accuulate with tie and the agnitude of the surfacing loan losses ay eventually be assive. In Argentina, for exaple, the ratio of non-perforing loans to total loans was over 30% in 986 and in Uruguay it was alost 46%. Even ore draatic, in Bulgaria, the ratio was over 60%. The ratios are uch larger than in the industrialized countries where transparency is relatively good and bank regulators close down or recapitalize insolvent banks. In sharp contrast to eerging econoies, during the savings and loan crisis in the U.S.A, ratio of non-perforing loans to total loans reached a peak value, 4.%, in 987 (Sheng, 996a). For ore evidence on hidden loan losses and banking crises see Kanya & Woo (00), Gunther & Moore (003) and Peek & sengren (005). Given the high frequency of recent banking crises, the crucial role of their hidden loan losses and the coplexity of the hiding ethods, it is iportant to investigate hiding in detail. Few researchers have investigated banking under hidden loan losses: e.g. Aghion & Bolton & Fries (999), Freixas (999), Corbett & Mitchell (000), Mitchell (000, 00) and pullo (004b). With full agreeent with the significance of their contributions, the hiding process is not explored in detail, since they focus on optial bailout policies. The paper ais to fulfil this gap in the literature by investigating alternative ethods to hide loan losses. Do banks loan interest incoe and payents on deposits vary under alternative ethods? What is the ost profitable hiding ethod? Does an opportunity to hide loan losses worsen the oral hazard proble? How can a regulator eliinate this type of oral hazard? Do alternative ethods of hiding require different instruents fro the regulator? The paper explores those two ethods of hiding which are docuented in the literature: the rolling over ethod (a bank extends the aturity of a proble loan and capitalizes unpaid interest in the loan) and the refinancing ethod (a bank grants a subsequent loan to a borrower who cannot repay his original loan. The loan capital of the subsequent loan is

5 used to repay the original loan). In addition, the paper introduces the third ethod to hide loan losses: a copensating balance ethod. A bank grants an oversize loan to a borrower, who ust aintain a part of it in his bank account (=a copensating balance) but the borrower can invest the rest of the loan capital in a project. Since the loan repayents are paid at the beginning fro the copensating balance account, each borrower can then service his loan whether or not his investent project is successful. Therefore, at the beginning the bank bears no loan losses and it generates handsoe profits. Finally, the true condition of the financed projects and of the bank surfaces. The results indicate that the rolling over ethod is the least profitable alternative to hide loan losses. A defaulted loan incurs no losses to a bank (the lost loan capital is not deducted fro the bank s incoe and bank capital) but it yields no repayents either. The refinancing ethod proves to be as profitable as the copensating balance ethod; a defaulted loan incurs no losses to the bank and it yields repayents. Both ethods represent a Ponzi schee. If the share of defaulted loans is large, the bank ay be illiquid under the rolling over ethod, since the defaulted loans yield no loan interest incoe. The illiquidity reveals the hidden loan losses to outsiders. The regulator ay be able to itigate the profitability of the rolling over ethod by forcing banks to diversify their lending or by excluding unpaid loan interest fro retained earnings and thereby fro bank capital. Yet, the regulator s ain instruent against hiding proves to be auditing. Since the paper explores oral hazard under an opportunity to hide loan losses, it is related to rich research on oral hazard in banking: e.g. Merton (977), Matutes & Vives (996, 000), Blu (999, 00), Chiesa (00), Decaps & chet & ger (004), Freixas & chet & Parigi (004) and pullo (004a). The paper differs fro these articles because it investigates how hiding affects oral hazard. In addition, the paper extends fresh research on Ponzi schees, e.g. Bhattacharya (003) and Araujo & Pasoa & Torres-Martinez (00). For an extensive survey regarding this literature, see Freixas & chet (997). 3

6 The paper is organized as follows. Section presents a odel, whereas Section 3 is devoted to banking with onitoring. Banking without onitoring is exained in Section 4, while Section 5 characterizes diversification and Ponzi schees. The copensating balance ethod is studied in Section 6, Section 7 analyses bank supervision and Section 8 concludes.. Econoy The odel includes entrepreneurs (=borrower, banks and a bank regulator. Everyone is risk neutral and the banking sector is fully copetitive. The odel has two periods: period- and period-. Period- begins at tie point 0 and ends at tie point. Period- begins at tie point and ends at tie point.. Project types The total aount of entrepreneurs is in both periods. At the beginning of period-, each entrepreneur can undertake an investent project. When the project is started, its upcoing type is uncertain. The realized project type is learned during period- after the investent. Three alternative project types exist. A fast project lasts for a period. If successful, it produces Y units of output at the end of the period-. A slow project lasts for two periods. It produces no interi output at the end of period-. If successful, it produces Y at the end of period-, is zero at the end of period-. A failed project has no value and the failure is irreversible. Y Y. The liquidation value of the slow project 4

7 If an entrepreneur exerts effort to his project, the project represents a good project variety and it succeeds with certainty. A good project becoes later either the fast project or the slow project. Without effort, a bad project coes true and the project succeeds with probability p, 0 p, in each period and fails with probability p. A bad project becoes later the fast project, the slow project or a failed project. An investent project requires a unit of capital input. An entrepreneur now has capital of his own and he needs to seek for a bank loan. Since the upcoing project type is unknown when the bank grants a loan, the bank lends the funds for a period at the gross loan interest rate i n Ri, R R, R. r denotes the breakeven loan interest rate with bank onitoring while R R n r represents the loan interest rate without onitoring. Here r is the interest rate of the econoy, which is the cost of bank deposits and bank capital, whereas denotes the nononetary costs of onitoring. If the financed project proves to belong to the slow type, it yields no output at the end of period-. Since the slow project has a sall liquidation value, 0, but very large long-ter output at the end of period-, Y, it is optial to reschedule the loan repayents. At the beginning of period-, the bank coits to reschedule the original loan at the fixed loan interest rate, if the financed project proves to be slow. Two alternative ethods for rescheduling exist. lling over: The original loan is rolled over and its extent is interest is capitalized in the loan. During period-, the loan interest rate is again succeeds, the bank receives ( Ri ) at the end of period-. Ri during period- because unpaid R. If the project i finance: At the end of period-, the bank grants a new short-ter loan (= a subsequent loan) to a borrower with a slow project. The extent of the subsequent loan is Ri and its interest rate is R. i 5

8 The borrower repays the original loan, subsequent loan. The repayent of the subsequent loan, Ri, at the end of period- using the funds of the ( i R ), takes place at the end of period-. More precisely, during period- an entrepreneur and his bank recognize the realized project type. The realized type is private inforation and unobservable to outsiders (even if the project output is assued to be publicly observable). The bank reschedules the loan if the financed project proves to be slow. In this way, the interruption of the productive long-ter project can be prevented. A standard effort aversion proble is now constructed. A project has positive NPV only with effort. Yet, given the liited liability of debt finance and the non-onetary costs of effort, e, an entrepreneur will shirk effort exertion without bank onitoring. Effort aversion can be eliinated only through onitoring, which incurs non-onetary costs,, to a bank. The effort aversion proble is detailed as follows. Assuption. With effort, the NPV of the each upcoing project type is clearly positive. i.) Y r e A, ii. ) Y Y. The first inequality states that the NPV of the fast project is clearly positive with effort; the output covers the repayent of the principal and interest, r, the costs of effort exertion, e, the costs of onitoring, and the cost of bank auditing. A denotes the highest auditing cost of the bank regulator and is defined later. The second inequality displays that the slow project is even ore productive than the fast project and thus its NPV is positive. Assuption. Without effort, the NPV of each project type is negative. 6

9 i.) py r, ii. ) py r. According to the first inequality, the NPV of the fast project is negative without effort. The second equality expresses the sae results for the slow project, when the project has atured for a period. This ensures that the NPV of the slow project is negative, when the project is started. Assuption 3. In the absence of onitoring, an entrepreneur shirks effort. ( r) Y ( r) e i.) p Y, ( r) Y ( r) e ii.) p Y, ( r) ( ) p Y ( r) Y ( r) e ( ) Y ( r) e iii.) p Y. The first inequality states that an entrepreneur shirks effort if he faces the fast project. The entrepreneur shirks effort also during the second period of the slow project. This is shown by the second inequality. As to the third inequality, it iplies that the entrepreneur shirks effort at the beginning of the period-, when the upcoing type of the project is still unknown, but it will be fast with probability and slow with probability. Consequently, the effort aversion proble appears and it can be eliinated only by onitoring borrowers. The task of onitoring is delegated to banks, which charge breakeven interest, R r, on loans. This does not, however, ensure that the banks onitor their borrowers. Given the liited liability of banks, they ay neglect costly onitoring. A bank 7

10 onitors only if onitoring is at least as profitable as the non-onitoring strategy. This oral hazard proble is investigated in later sections.. Bank s balance sheet In period- the volue of new projects is. The bank finances the projects and funds its operations with the fixed aount of equity capital, E, and deposits. As entioned before, the interest rate of the econoy, r, represents the cost of capital and deposits. With onitoring, a stochastic share s of financed projects proves to be slow. Here s has a support S, S, 0 S S, continuous density g, and distribution G. The rest of the financed projects, s, are fast. Without onitoring, a stochastic share l of financed projects fails. Here l has a support,, 0, continuous density f, and distribution F. garding the rest of the assets, l, a stochastic share s of those will be slow and the rest s will be fast. Thus, the volues of financed projects are: l failed projects, ( l) s slow projects and ( l)( fast projects. Since a few projects are fast and ature at the end of period-, the bank s loan portfolio has roo for fresh loans at the beginning of period-. These funds are invested in fresh projects which are known to be fast and which ature at the end of period-. To clarify connections between sybols, it is useful to note that under shirking a project s expected probability to success eets p ( l) f ( l) dl. (.) The following values, for exaple, satisfy Assuptions -3: r 0.0, e 0.08, 0.03, p Y.5, Y.33, A 0.0, 0.8. Hence, it is known that R

11 Since an average project is unprofitable in the absence of onitoring, loans are on average also unprofitable without onitoring ( l)( R ) f ( l) dl r. (.) call that slow projects as well as failed projects yield no output at the end of period-. In addition, the shares of both project types are stochastic. Furtherore, the loans that are granted for these projects can be rescheduled. Since the realized project type is unobservable to outsiders, they cannot know whether a bank reschedules a loan in order to delay the repayent of a slow project (which is socially valuable) or to hide a loan loss and thereby applying the non-onitoring strategy (which is socially harful). In the bank s loan portfolio, the share of rescheduling loans is saller with onitoring, s, than without onitoring, l ( l) s, since l ( l) s s l( s. The bank regulator (= she) insures deposits and audits banks. She pre-coits to close down banks that neglect onitoring. A closed bank is liquidated and the liquidation proceeds are first and foreost utilized for payents on deposits. The reainder of the proceeds, if any, is paid to the banker. The regulatory instruents are used by the regulator in such a way that banks prefer the onitoring strategy to non-onitoring. Therefore, in equilibriu banks onitor. The regulator cannot directly observe whether a bank onitors or not. Furtherore, at the end of period- loans cannot be liquidated, since it would interrupt slow projects. This is known by the banks that attept to hide their loan losses by rescheduling the defaulted loans. The regulator ais to reveal hidden loan losses by auditing banks at the end of period-. With probability h, she succeeds in revealing a hiding attept and closes down the bank. The quality of the auditing syste can be chosen by the regulator. When a bank anages to hide its loan losses with probability h, 9

12 this incurs costs A( h) to the regulator. 3 It is assued that: A( 0) 0, A' ( h) 0, A' (0) 0, A'' ( h) 0, A() A. Given Assuption, banking is profitable even under the highest quality of auditing, A. The regulator finances the auditing syste by taxing successful entrepreneurs but ais to iniize the costs of auditing subject to the bank s incentive constraint. Even when the regulator cannot uncover a hiding attept, loan losses surface if their realized share is so large that the bank is illiquid. The bank is then closed down. In su, the tie line is the following.. The regulator iposes an equity capital requireent, E, to banks. Banks are established. Each bank aintains the sae aount, E, of capital and attracts the aount E of deposits.. The regulator chooses the quality of the auditing syste. The choice is public inforation..3 Banks grant loans and decide whether or not to onitor..4 Without onitoring, soe projects fail..5 The end of period-: fast projects ature and these loans are repaid. Banks attract deposits for period- and reschedule the loans that are allocated for slow projects. If a bank has neglected onitoring, it reschedules the defaulted loans. Banks fulfil the rest of their loan portfolio with fresh short-ter loans for fast projects..6 The regulator audits banks. If she observes loan losses, she closes down the bank..7 Banks repay the deposits of period-. If a bank is illiquid due to a large burden of loan losses, it cannot repay deposits, the hiding attept surfaces and the regulator closes down the bank. iquid banks repay deposits and the dividends of period-..0 The entrepreneurs invest the loan capital in the fresh fast projects for period-.. The bank decides whether or not to onitor during period-. 3 Here h either because the regulator does not audit each bank of the auditing syste is iperfect. 0

13 . At the end of period-, all loans ature and banks are closed down. They repay deposits and the banker receives the reaining returns. Finally, few siplifying assuptions are ade. Assuption 4. If a bank chooses the non-onitoring strategy in period-, it follows the nononitoring strategy also during period-. Under soe paraeter values, the following strategy is possible. A bank neglects onitoring during period- and thereafter observes the realized share of loan losses. If the share of losses is sall, the bank ay optially turn to the onitoring strategy during period-. This kind of strategy is, however, unrealistic and thus we have rejected it by aking Assuption 4. Assuption 5. The fixed aount of equity capital satisfies: 0 E. Assuption 5 siplifies the analysis. Furtherore, under soe paraeter values, it is possible that the bank neglects onitoring in period- and checks the realized share of loan losses. Thereafter, the banker ay optially reveal loan losses to the regulator although the banker knows that the regulator closes down the bank. In practise, this strategy is highly unlikely, since liquidation rarely yields any returns to the bank s owners. This unrealistic strategy is rejected with Assuption iquidation at the end of period- can be ade unprofitable in several ways. For exaple, it is possible to assue that the share of slow projects is always so large that liquidation is unprofitable. We have chosen Assuption 5.

14 Assuption 6. Under the non-onitoring strategy, the axiu share of rolled over loans or refinanced loans satisfies ( ) S ( R ) and ( ) S R ( E) r. Assuption 6 ensures that the loan portfolio has enough roo to hide loan losses even when the bank does not grow. That is, the bank s inability to grow does not reveal the hiding strategy. 5 The second inequality akes it possible to explore the illiquidity of the bank. This option enriches the analysis. Assuption 7. Under the rolling over ethod, ( ) S R ( E) r. Assuption 7 states that the iniu share of rolled over loans that is, the total share of loans that are channelled either for slow projects or for defaulted projects is so sall that a bank can hide its loan losses by rolling over these loans (the bank is not illiquid with certainty under the rolling over ethod). If Assuption 7 is not satisfied, the rolling over ethod cannot be used to hide loan losses but the refinance ethod can be used. This alternative is, of course, possible but not as interesting. 6 5 By denying the growth of the bank, we deny a coplex proble whether or not the banker will inject fresh capital in the bank with hidden loan losses at the beginning of period-. This proble is already explored in Niiniaki (007). 6 In addition to footnote, suppose that 0.05, 0.45, S 0, S 0.4, E Then, Assuptions 5-7 are also satisfied.

15 3. Monitoring bank This section sheds light on the operations of a onitoring bank under both rescheduling ethods. In Subsection 3. a bank reschedules the loans of slow projects by rolling over these loans. In Subsection 3. the bank refinances these loans. Since the bank has no hidden loan losses, audits by the regulator have no effect on banking. 3. lling over call that with onitoring, a stochastic share s of projects is slow, whereas the rest are fast. At the end of period-, a onitoring bank rolls over the loans that are channelled for slow projects. Those s loans, which are allocated for fast projects, ature yielding loan repayents ( R ). ( The bank attracts fresh deposits, E, for period- and pays back the deposits of period-, ( r)( E). The banker s earnings during period- that is, the profit of the bank fro which the cost of onitoring and the cost of injected bank capital are deducted aounts to S ( R ( E) r g( ds E( r). (3.) S If ŝ denotes the realized share of the rolled over loans, the banker s earnings are ( sˆ) R r E or sˆ R E. Here ŝ R represents bank s interest receivables fro the rolled over loans. The interest receivables belong to the returns fro period- although they are paid out fro the bank at the end of period-. Because the receivables are not paid out at the end of period-, they 3

16 increase the retained earnings of the bank and thus raise its capital. For the sae reason, the need for deposits for period- is E sr ˆ. 7 During period-, the loan portfolio includes the rolled over loans for slow projects, s R ). The rest of the loan portfolio, s( R ), is reinvested at the beginning of period-, ( since a share s of loans atured at the end of period-. Thus, the bank can grant s( R ) loans for fresh, fast projects. At the end of period-, the loans ature. The loans for slow projects yield s( R ), while the loans for fresh fast projects yield s( R ) ( R ). The loan repayents total R. After payents on deposits, ( E sr )( r), the banker s earnings during period- aount to S S R ( E sr )( r) g( ds. (3.) Given s sˆ, this siplifies to ˆR ( r) E( r). The earnings are positive during period-, but s equal to the present value of the losses fro period-. The life-tie earnings fro the onitoring strategy are zero. 3. finance Again, at the end of period- those s borrowers who face a fast project can repay their loans in total. The borrowers, who encounter a slow project, have no funds for repayent and the bank grants a subsequent loan, R, to each of the. Iediately, the borrowers use the subsequent loans to repay their original loans. Since each borrower can repay his original loan, the bank obtains 7 The aount of deposits is positive, thanks to Assuptions 5 and 6. 4

17 incoe R. It attracts deposits, E, for period- and pays back the deposits of period-, ( r)( E). Hence, the bank profits in period- aount to ( E) r Er. If we deduct R the cost of onitoring and the cost of bank capital, ( r) E, fro Er, we obtain the banker s returns E. During period- the loan portfolio consists of the subsequent loans that are allocated for slow projects, s R ), and of fresh loans, s( R ), that are channelled at the beginning ( of period- to fresh fast projects. At the end of period-, the fast projects ature, yielding loan repayents s( R ) ( R ), whereas the subsequent loans yield s( R ). Therefore, the loan repayents total R, which is spent to repay interest on deposits, ( r)( E). The bank enjoys profit ( r)( E) or ( r) E. When the non-onetary costs of onitoring R are subtracted fro this, we obtain the banker s profits during period-, ( r) E. Under the lifetie of the bank, the NPV of the banker s returns is E ( r) E Discussion I It is interesting to note that even though the two ethods of rescheduling loan repayents provide the sae returns, 0, to the banker during the life-tie of the bank, the banker s returns differ between period- and period-. Under the rolling over ethod the returns are sr units saller than under the refinance ethod during period-, but sr ( r) units larger during period-. Iportantly, in subsection 3. it is iplicitly assued that under the rolling over ethod the bank can always pay interest on deposits after period-, ( S) R ( E) r 0. Yet, it is possible that ( S) R ( E) r 0. Then, the bank is illiquid; its loan interest incoe does not 5

18 cover interest payents on deposits. This is true if the axiu share of slow projects (and thereby the axiu share of the rolled over loan, S, is sufficiently high. The proble is avoided under the refinancing ethod. Then, each loan is repaid and the bank is liquid. Under the rolling over ethod, the illiquidity effect depends crucially on whether or not the interest receivables can be incorporated into the regulator s capital requireent, E. To see this, recall that the unpaid loan interest of the rolled over loans, sr in all, represents bank s interest receivables. Because the receivables cannot be paid out fro the bank at the end of period-, they boost the retained earnings of the bank and thus raise its capital. call the capital requireent, E. Given the retained earnings, the total aount of capital, E sr, exceeds the requireent, E. If the retained earnings can be incorporated into the regulator s capital requireent, the bank can release excessive capital, E Min E sr sr Min, sr, at the end of period-. If,, the bank s funds consist of loan interest incoe, ( R, and released capital, sr, R in all, which cover interest payents on deposits, ( E) r. During period- the capital aounts to E which consists of retained earnings, capital, sr, and reaining initially injected E sr. Hence, illiquidity is avoided and the bank obtains in both periods the very sae returns as under the refinance ethod! If MinE sr E,, the bank s incoe totals ( R E, which can be saller than ( E) r. It is possible that the bank is illiquid and fails at the end of period-. To avoid this, the bank can optially follow the refinance ethod that avoids the proble of illiquidity. We will see later that the refinance ethod represents a Ponzi schee. Consequently, it ay be socially optial to obey a Ponzi schee and thus avoid the failure of the solvent bank due to teporary illiquidity. A suary follows. 6

19 Proposition. When a bank onitors borrowers and reschedules the loans that are channelled for the slow projects, both rescheduling ethods yield equal returns to the bank during its life-tie. If the retained earnings cannot be incorporated into the regulator s capital requireent, the refinance ethod is ore profitable during period- but the rolling over ethod is ore profitable during period-. If the retained earnings can be incorporated into the regulator s capital requireent and if the aount of the rolled over loans is sufficiently sall ( E yield equal returns in both periods. sr ), the ethods 7

20 4. In the absence of onitoring This section investigates bank returns in the absence of onitoring when a bank hides its loan losses either by rolling over defaulted loans (subsection 4.) or by refinancing failed projects (subsection 4.). Thereafter the profitability of the ethods is copared in subsection lling over Consider a representative bank that neglects onitoring during period- and a stochastic share l of loans default (subscript stresses that the realized loan losses ste fro period-). The expected bank returns can be found out by aggregating returns under four situations. period- expected returns With probability h the bank anages to hide its loan losses and generates during s l l )( R ( E) r f ( l ) dl g( ds, (4.) S ( which can be paid out as dividends to the banker at the end of period-. Here ( l )( R arks the total loan interest incoe fro the fast projects. The bank rolls over l defaulted loans and ( l )s loans, which are allocated for slow projects. The outsiders do not observe whether the loans have been rolled over in order to finance slow projects or to hide loan losses. The second ter ( E)r indicates interest payents on deposits. Only if the loan interest incoe is adequate to pay interest on deposits, hiding is possible. In (4.) l represents the highest possible share of loan losses which satisfies ( l )( S) R E) r (, where l, (recall that E is fixed). Thus, l is the highest possible share of loan losses such so the bank is still liquid when the realized share 8

21 of slow projects is at the inial level, S. We ay have l. In addition, s ˆ l ) denotes the ( highest realized share of slow projects so that the bank is liquid, when the realized share of defaulted loans is given, ˆl, s (ˆ l ) R ( E) r 0, s S S lˆ ),. (4.) ( It ay be possible that not satisfied even when s S, if ˆl is sufficiently sall. On the other hand, if the constraint (4.) is s S then s S. The probability that the realized share of slow projects is so low that the bank is liquid, sˆ s, is s l S f ( l) g( dl ds. (4.3) The optiality of hiding copared with the revelation of loan losses is shown in Appendix A. With probability h the audit reveals hidden loan losses, the regulator closes down the bank, liquidates it and repays the deposits. The banker receives the rest of the liquidation proceeds s S l l )( ( R ( E)( r) f ( l ) dl ( ) g( ds, (4.4) where l is the highest share of loan losses which satisfies ( l )( S)( R ) ( E)( r), l,. If the constraint is not satisfied even when the realized share of loan losses is at the iniu level, l ˆ, it is known that l. If the constraint is satisfied even when the realized 9

22 share of loan losses exceeds, that is of slow projects that satisfies is given. l ˆ, then l.in addition, s ( ˆ ) l is the highest share l ˆ )( s(ˆ l ))( R ) ( E)( r) ( when s lˆ ) S, S ( and ˆl With probability h the audit does not reveal loan losses, but the true financial condition of the bank surfaces due to illiquidity. The burden of rolled over loans, which yield no loan interest payents at the end of period-, is so large that the bank is illiquid; the realized loan interest incoe, ( l ˆ )( sˆ ) R, is insufficient for the interest on deposits, ( E) r. This reveals the hiding attept and the bank is closed down. The banker receives the reainder of the liquidation proceeds Max 0,( lˆ)( sˆ)( R ) ( E)( r), (4.5) where ˆl and ŝ are the realized shares of loan losses and slow projects. Soe anipulation gives ( lˆ)( sˆ) R ( E) r ( lˆ)( sˆ) ( E) Max 0,. (4.6) Here the ter in the first brackets is negative due to the illiquidity and the ter in the second brackets is negative because the ter in the first brackets is negative and R r. Thus, it is known that Max.. 0. When the loan losses surface due to illiquidity and the bank is closed down, the banker receives no returns. 8 8 De Juan (996, p. 93) highlights the iportant signalling effect of illiquidity: In the id 980s, Argentina suffered a very serious banking crisis that affected ostly new banks and banks run by new bankers. Soe two to three hundred banks experienced interventions and/or were liquidated. Practically all were insolvent, but intervention was triggered by illiquidity. Only through illiquidity was the insolvency discovered. 0

23 With probability h the bank anages to hide loan losses during period- and reaches period-. Then, the loan portfolio includes the rolled over loans. In addition, since a part of the loans is allocated for fast projects during period-, these loans ature at the end of period- and the funds can be used to finance fresh, fast projects during period-. At the end of period- the loans ature. The bank s expected returns fro period- are (the ex ante point of view, when the share of period- loan losses has not been realized) l s l ( ) ( )( ) ( )( ) ( ) ( ) ( ), R l R l E R r f l dl g s ds f l dl (4.7) S where l l ) s represents the total aount of the rolled over loans. Given Assuptions 5 ( and 6, it known that the aount of deposits is positive, E R 0. In addition, l ˆ ) ( l is the highest realized share of loan losses during period- so that the bank can repay deposits ( R )ˆ l ( R )( l ) ( E R )( r) 0, l,. (4.8) If the bank akes a profit even when the realized share of loan losses is at the upper liit, l ˆ, we have l. On the other hand, if the bank cannot repay deposits even when the realized share of loan losses is at the lower liit, l ˆ, we have l and 0. In (4.8) the loan repayents, ( R ) l ( R )( ) l, consist of two parts. The first part includes the loan repayents fro the successful loans that are granted by the bank at the beginning of period- for

24 fresh fast projects, ( R ) ( R )( l ). The second part represents loan repayents fro the loans that were channelled for slow projects, l ) s ( R ) ( ). 9 ( l The banker s total earnings fro the non-onitoring strategy consist of expected bank returns fro which the costs of injected bank equity are subtracted ( E; h) h ( h) h ( r) E. (4.9) We are iplicitly assuing that ( E;0) 0. The aount of bank capital is so sall that the rolling over strategy yields a profit to the banker if the quality of the auditing syste is zero. 0 9 Sheng (996b, p. 5) docuents how the rolling over ethod was used during the Chilean banking crisis at the beginning of 980s. Auditors for Banco Espanol qualified their report for 979 by stating that 37% of loans could not be evaluated because of lack of inforation on the debtors ability to pay even through the loans had been rolled over repeatedly. 0 call the nueric exaple in Footnotes and 5. Under these values, it is known that 0. Fro (4.) it is possible to observe that the axiu share of rolled over loans,, such that a non-onitoring bank is liquid, is Inserting this to (4.8) indicates that the payents on deposits are at least Since the loan repayents are at ost ) 0.95, the bank fails with certainty at the end of period-, 0. The banker s expected earnings fro the nononitoring strategy, (4.9), are h ( r E. et us extend the nueric exaple by assuing that both the share of defaulted loans and the share of slow projects have a continuous unifor distribution. It is possible to find out that Hence, it is known that h * If h, the non-onitoring strategy yields profits and it is the optial to neglect onitoring. To ake the non-onitoring strategy unprofitable, the regulator needs to invest in auditing so that h or saller.

25 4.3 finance The bank neglects onitoring, learns the realized share of loan losses and the realized share of slow projects. Each fast project yields repayent, R units. The bank refinances the failed projects and slow projects by granting subsequent loans to these borrowers. The subsequent loans are used to repay the original ones. Consequently, the bank receives loan interest incoe R. It attracts deposits for period-, E, and repays the deposits of period-, ( E)( r). In period-, the bank enjoys profit R ( E) r, (4.0) which can be paid out to the banker. This represents returns in the case that the hiding attept is successful. Since the loan interest incoe exceeds the payents on deposits, losses never surface due to the illiquidity, as with the rolling over ethod. R ( E) r, loan With probability The returns are the sae as with the rolling over ethod, h, the audit reveals hidden loan losses and the bank is closed.. With probability h, the bank anages to hide and keeps on operating during period-. Then, the loan portfolio includes l ( R ) subsequent loans, which are used to hide loan losses and l ) s( R ) subsequent loans that are allocated for slow projects. The rest of the loan ( portfolio, l ( R ) l ) s( R ), consists of short-ter loans to finance fresh, fast projects. ( At the end of period-, each project and loan atures. The slow projects yield loan interest payents s l )( R ) ( ). The loans for fresh, fast projects yield repayents, ( l l ( R ) s( l )( R ) ( l )( R ). Given these, the loan interest incoe 3

26 , whereas payents on deposits aount to ( E)( r). The totals l ( R ) ( l )( R ) bank generates expected profits l ) ( R ) l ( R )( l ) ( E)( r) f ( l ) dl f ( l dl, (4.) where ˆ ) l, l, ( l, is the highest share of loan losses during period- which satisfies ( R )ˆ l ( R )( l ) ( E)( r) 0. (4.) Here l if the bank can repay deposits with each realized share of loan losses during period-. In addition, l, if the realized share of loan losses is always so high that the bank cannot pay back deposits. The banker s expected returns during its life tie total h ( h) h ( r) E. (4.3) call the nueric exaple in Footnotes, 6 and 0. Under these values, it is known that 0. During period-, the payents on deposits exceed, whereas the loan repayents are less than Hence, the bank fails with certainty and 0. Under the refinance ethod, the banker s expected earnings fro the non-onitoring strategy siplify to h ( r) E or h * Suppose that h. It is easy to observe that the refinance ethod is uch ore profitable than the rolling over ethod, To ake the refinance ethod unprofitable, the regulator needs to invest in auditing so that h is at ost /3. 4

27 4.3 Discussion II This subsection explores which ethod, the rolling over ethod or the refinance ethod, is ore profitable to a non-onitoring bank. Two cases are exained depending on whether or not interest receivables are allowed to be incorporated in the required aount of bank capital. In the first scenario, this is not possible, but in the second, it is. By deducting the bank returns under the rolling over ethod fro the bank returns with refinance, we obtain difference,, or S s l hr ( E) r f ( l) dl g( ds hr f ( l) dl g( ds h s l S. (4.4) Here l l ) s represents the total aount of rolled over loans. The difference consists of ( three ters in such a way that the first ter and the second ter describe returns in period-. The first, positive ter indicates returns fro refinancing when the realized share of rolled over loans is so large that the rolling over ethod is unprofitable due to the illiquidity. Since the bank is always liquid under the refinance ethod, this ethod yields profits. The second, positive ter expresses the difference in returns when both ethods yield profits. The realized share of the rolled over loans is so sall that the bank is liquid also under the rolling over ethod. Yet, under the refinance ethod each loan yields the loan interest incoe, R, whereas under the rolling over ethod only a share ( l )( of loans yield interest incoe. Obviously, the refinancing ethod is ore profitable. The third ter in (4.4) shows the difference in expected returns during period- and can be detailed as (recall (4.7) and (4.)) 5

28 l ( R ) l ( R )( l ) ( E)( r) f ( l ) dl f ( l ) dl h (4.5) h l s l S ( R ) l ( R )( l ) E R ( r) f ( l ) dl g( ds f ( l ) dl. Both ethods yield an equal loan interest incoe but the payents on deposits are saller under the rolling over ethod, since unpaid loan interest is capitalized in the loan size. This raises bank capital and thereby reduces the need for deposits. The effect akes the rolling over ethod ore profitable than the refinance ethod during period-. Yet, the probability that the bank achieves period- is saller under the rolling over ethod because illiquidity ay reveal hidden loan losses at the end of period-. As a result, we do not know which ethod yields higher expected returns fro period-. Appendix B shows the difference in expected returns during period-, h, is larger than s l h R f ( l ) dl g( ds. (4.6) S Hence, it is known that (4.4) is positive; the refinance ethod is ore profitable than the rolling over ethod. More precisely, the refinance ethod is ore profitable than the rolling over ethod during period- while during period- the reverse is true. The effect of period-, however, doinates for two reasons. To begin, under the rolling over ethod the bank achieves period- only if it is liquid during period-. Thus, the bank does not achieve the relatively high returns of period- with certainty. In addition, during period- the hidden loan losses surface. The burden of loan losses is likely to be so large that the bank fails whether it has rolled over the defaulted loans or refinanced the. The fact that the bank returns are larger under the rolling over ethod is 6

29 eaningless when both ethods yield negative returns and the banker is protected by liited liability. A conclusion can be ade. Proposition. When interest receivables cannot be incorporated into the regulator s capital requireent, the refinancing ethod is ore profitable for a non-onitoring bank than the rolling over ethod. Consider now that the regulator iposes a capital requireent for banks and that interest receivables, which belong to retained earnings, can be incorporated into the required capital. Thus, after period-, bank capital totals excessive capital by Min E R If Min E R R E R. The bank can lower the aount of capital by releasing,. This creates two cases.,, it is possible to lower capital back to the required level, E. During period- bank capital, E, consists of retained earnings, R, and the reaining, initially injected capital, E R. Thus, at the end of period- the bank can release R units of initially injected capital and spend these funds to cover interest payents on deposits. These funds, R, and the loan interest incoe, ( s )( l ) R or R R, together aount to R, which covers interest payents on deposits, ( E) r. In period-, the bank generates returns R ( E) r and in period- it akes returns. In both periods the returns are the sae as under the refinance ethod! If Min E R E,, the bank can drop capital to E for period-. Then, bank capital consists entirely of the retained earnings, R R, and it exceeds E. The bank can release the initially injected capital in total and spend these funds to cover interest payents on deposits at the end of period-. These released funds, E, and the loan interest incoe, R R, together aount 7

30 to R ( R E). Since E, the incoe is lower during period- than under the refinance R ethod. Hence, during period-, the refinance ethod yields larger returns. During period-, the rolling over ethod is ore profitable thanks to the larger aount of bank capital, R E, and thus saller payents on deposits. Appendix C shows that even when R B E 0 is inial, the refinance ethod is ore profitable than the rolling over ethod during the lifetie of the bank. The intuition is obvious. Since the bank goes into bankruptcy with a positive probability during period-, the expected, relatively high returns fro the rolling over ethod during period- are insufficient to cover its relative losses during period-. Proposition 3. When interest receivables can be incorporated into the regulator s capital requireent, the profitability of the ethods depends on the realized aount of rolled over loans,. If R B E, the refinance ethod and the rolling over ethod yield equal returns for a nononitoring bank. If E, it is ore profitable to refinance than to roll over loans. R B Given Proposition and Proposition 3, the refinancing ethod is always at least as profitable as the rolling over ethod. Obviously, the regulator should not allow banks to incorporate interest receivables into the required bank capital, since this option increases the returns fro hiding under the rolling over ethod. The regulator cannot be sure whether or not the interest receivables are based on perforing loans (slow project or on defaulted loans. Suppose that the bank neglects onitoring, rolls over the defaulted loans and thus obtains interest receivables. If the bank can incorporate the interest receivables into the required bank capital, the receivables raise the capital and the bank can pay out excessive capital at the end of period-. This increases the expected returns fro the nononitoring strategy. At the end of period-, the true financial condition of the bank surfaces; a large share of interest receivables proves to be worthless and the bank is likely to be insolvent. 8

31 5. Diversification and Ponzi In his seinal article, Diaond (984) utilizes the weak law of large nubers as well as an assuption on independent and identically distributed project returns to deonstrate how perfect diversification within the bank eliinates oral hazard. As the nuber of financed projects ultiplies without bound, the risk of project returns is eliinated through diversification. Thus, the bank s incoe is fixed and it cannot gable with deposits. In our odel, suppose first that a bank has no equity capital and it cannot hide loan losses. In addition, the bank neglects onitoring and the realized share of loan losses is at the expected level p ( l) f ( l) dl. (5.) At the end of period-, the regulator observes loan losses, closes down the bank and liquidates it. Given (.), the bank cannot repay deposits even if the liquidation value of the slow projects was one p ( R ) ( r) ( l)( R ) f ( l) dl ( r) 0. (5.) Since the liquidation value of slow projects is, however, zero, the non-onitoring strategy is even ore unprofitable (here the realized share of slow projects is at the iniu level) Diaond (984) analyzes ex post onitoring, whereas this paper investigates interi onitoring. 9

32 p( S)( R ) r. (5.3) Therefore, the oral hazard proble is eliinated when loan losses are observable. et us again assue that loan losses can be hidden. The bank rolls over the defaulted loans and anages to hide the loan losses. At the end of period-, the successful fast projects yield loan interest incoe, p ( S), to the bank that pays interest r on deposits and achieves returns R p ( S ) R r, (5.4) which can be rewritten as p S)( R ) ( r) p ps (. (5.5) Given (5.3), the ter in the first brackets, which expresses bank returns without hiding, is negative. The ter in the second brackets is positive. It indicates the extra returns that a bank can achieve by hiding its loan losses. If the second ter is sall, bank returns (5.5), are negative and the nononitoring strategy is unprofitable even with hiding. More precisely, we have p ( S ) R r ; the bank is illiquid. When the second ter in (5.5) is sufficiently large, the bank returns (5.5), are positive. The bank s chance to hide its loan losses by rolling over the defaulted loans akes the non-onitoring strategy profitable although the loan portfolio is strongly diversified; that is, the realized share of loan losses is at the average level. Consequently, the chance to hide loan losses extends the agnitude of the oral hazard proble. The positive incentive effect of diversification is based on the principle that loan losses are deducted fro the repayents of successful loans and bank capital. The subtracted volue is so large under perfect diversification that the non-onitoring strategy is unprofitable. 30

33 This effect eliinates oral hazard also in our setting when loan losses are observable, (5.3). The effect fades when the bank can hide its loan losses by rolling over defaulted loans. Since no loan losses officially exist, no losses are subtracted. The extra benefit is represented by p in the second brackets of (5.5). The existence of slow projects also itigates the proble of oral hazard when loan losses are observable (see (5.3)). Since these loans have low liquidation value, their existence decreases the bank returns when the auditor observes hidden loan losses at the end of period- and closes down the bank. This effect is thus avoided when the bank can hide its loan losses ( p S in the second brackets of (5.5)). Although the bank can dapen the effects of diversification by rolling over defaulted loans, diversification still influences the bank returns, because the defaulted loans yield no interest incoe. The larger the share of defaulted loans, the saller the bank returns are. As a result, iproved diversification ay ake the rolling over ethod unprofitable. Consider two distributions. The support of the first distribution is, and the second support is, so that. It is possible that ( )( S ) R r, ( )( S ) R r. (5.6) The bank can hide loan losses only if its loan interest incoe is based on distribution,, which is relatively less diversified than,. Under distribution,, a hiding attept surfaces with certainty due to illiquidity. Thus, the regulator ay optially force banks to diversify their lending in order to eliinate oral hazard. This positive effect of diversification exists, however, only when the bank uses the rolling over ethod in hiding. If the bank adopts the refinancing ethod, each loan is repaid at the end of period- and diversification has no effect. 3