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M E A S U R I NG M I C R O C R E D I T D E L I N Q U E N C Y:R a t i o s C an B e Harm f u l t o Yo ur Hea l t h

Let’s start with the good news. As themicrofinance movement matures, bothmicrocredit practitioners and the donors whofund them are focusing more consistently onthe importance of portfolio quality: how wellare microfinance institutions (MFIs) recover-ing the money they lend? Loan recovery is,after all, the most basic ingredient of long-term sustainability.

Ten years ago a description of an MFI mightsay little about loan recovery, or at least failto quantify it. Today, most write-ups of MFIsinclude a delinquency or repayment rate. Forinstance, “MicroFin has maintained an impres-sive 98 percent loan recovery rate.” But thissimple example also illustrates the bad news—too often, the reader gets a number but noinformation about the measuring rod beingused. MFIs use dozens of ratios to measuredelinquency. Depending on which of them isbeing used, a “98 percent recovery rate” coulddescribe a safe portfolio or one on the brinkof meltdown.

Any delinquency or recovery percentage is aratio—the result of dividing some numeratoron the top of the fraction by some denomi-nator on the bottom. Unless we know exactlywhat goes into the numerator and the denomi-nator, delinquency ratios are more likely toobscure the real situation than to illuminateit. This paper aims to convince the reader ofthis point, and to discuss the uses and mis-uses of some common portfolio quality mea-sures.

Why get so exercised about transparent de-linquency measurement? True, MFIs often

give donors an overly optimistic view of theirportfolio quality—not necessarily intendingto. But the jaded writer of this paper is nei-ther surprised nor particularly horrified bythe prospect of an occasional donor beingmisled. The more serious danger is that amisapplied portfolio quality measure oftenconceals a repayment crisis from MFI man-agers themselves, sometimes to the pointwhere it has become too late to fix the prob-lem.

Delinquency tends to be more volatile inMFIs than in commercial banks. Mostmicroloans are not secured by tangible as-sets that can be seized or sold easily in caseof default. The clients’ main motivation torepay is their expectation that the MFI willcontinue providing them with valued servicesin the future if they pay promptly today. Thismotivation may be reinforced by peer pres-sure, especially in group lending programs.In these circumstances, any serious outbreakof loan delinquency can quickly spin out ofcontrol. As clients watch their peers default,they lose confidence in the MFI’s ability toserve them in the future, and the peer pres-sure to repay can dissipate quickly. Many anMFI has died of a repayment cancer thatcould have been cured if it had been detectedand dealt with earlier. Meaningful delin-quency monitoring is a crucial diagnostictool.

Why are there so many different delinquencymeasures in use? Managing loan collectionposes quite a few different questions, and noindicator answers them all. The most so-phisticated MFIs all track more than one

C G A P

OccasionalPaper

M E A S U R I N G M I C R O C RE D IT D EL I N Q U E N C Y

TWO

measure. And selection of a particular ratio is oftendriven by the availability of information: the MFI hasto settle for a less-than-ideal version of an indicator be-cause its systems cannot produce the information neededfor the ideal indicator it would have preferred.

So delinquency measurement can get complicated. AnMFI needs to choose among the available measures, fig-ure out how to manage irregular transactions like pre-payments or loan renegotiations, and determine whetherits information system can be made to produce the nec-essary numbers. Every time one thinks one has finallysorted out all the issues, an annoying new wrinkle is sureto float into view. In light of such factors, this papercan’t provide definitive guidance about how to measuredelinquency in specific situations. Its aim is less ambi-tious—to sensitize the reader to some of the major dy-namics and pitfalls involved. To keep the paper short,the author has had to sneak past some complications:he cheerfully assumes that the reader who is cleverenough to catch him oversimplifying things will prob-ably be clever enough to handle delinquency measureseffectively without his help.

Most of the discussion will be devoted to three broadtypes of delinquency indicators:

• Collection rates measure amounts actually paidagainst amounts that have fallen due.

• Arrears rates measure overdue amounts againsttotal loan amounts.

• Portfolio at risk rates measure the outstandingbalance of loans that are not being paid on timeagainst the outstanding balance of total loans.

But the reader must be warned that there is no interna-tionally consistent terminology for portfolio quality mea-sures—for instance, what this paper calls a “collectionrate” may be called a “recovery rate,” a “repayment rate,”or “loan recuperation” in other settings. No matter whatname is used, the important point is that we can’t interpretwhat a measure is telling us unless we understand pre-cisely the numerator and the denominator of the fraction.

A . H o w t o Te l l a G o o d R a t i o f r o m a

B a d O n e

Before we line delinquency ratios up against the wall toevaluate them all (and perhaps shoot a few), decency

requires that we first advise them what we’re going toexpect of them. We’ll look at some common ratios inlight of their performance on five tests:

• As a matter of day-to-day portfolio management,an MFI needs a monitoring system that high-lights repayment problems clearly and quickly,so that loan officers and their supervisors canfocus on delinquency before it gets out of hand.Thus we have a red flag test: does the delin-quency ratio support timely response to day-to-day repayment issues?

• When delinquency has reached dangerous lev-els, does the ratio reveal the seriousness of theproblem, or does it tend to camouflage it? Thisis our fire bell test. (Both this and the previoustest focus on problems: red flags are for day-to-day problems, while fire bells signal emergenciesof longer-term consequence.)

• A loan is delinquent when a payment is late. Butthe fact that a payment is late right now doesn’tmean that it will never be paid in the future: de-linquency is not the same thing as loan loss. Wemeasure delinquency because it indicates an in-creased risk of loss. In addition to warning us ofoperational problems, a delinquency measuremay help us predict how much of our portfoliowill eventually be lost because it never gets re-paid. This is our bottom line test: does the mea-sure we’re using give us a reasonable basis forestimating likely loan losses, preferably as a per-centage of our outstanding portfolio? Withoutrealistic provisions for likely loan losses, we willoverestimate our net profit and the real worth ofour portfolio.1 Likewise, we need to know ourloan loss rate in order to factor this cost into theinterest rate we charge.2

1 As used in this paper, “provision” means an extra expense shownas a flow variable in the income statement to reflect probablelosses due to non-repayment of loans. Provisions build up thevalue of a loan loss “reserve,” a stock value on the balance sheetwhich reflects a lessened worth of the active loan portfolio dueto anticipated loan losses. When the probability of collectingan individual loan becomes very low, it is “written off”: that is,it disappears from the lender’s books, as the loan portfolio andthe loan loss reserve are both reduced by the amount of theunrecoverable loan. After the write-off, it may be necessary toprovision further amounts in order to bring loan loss reservesup to a high enough level in relation to the active portfolio.

2 See CGAP, “Microcredit Interest Rates,” Occasional Paper 1(revised), 1996.

O c c a s i o n a l P a p e r N o . 3

THREE

• Can the delinquency measure be made to lookbetter through inappropriate rescheduling orrefinancing of loans, or manipulation of account-ing policies? This is our smoke and mirrors test.

• Finally, does the delinquency measure help uspredict the flow of cash from our portfolio, sothat we can balance sources and uses of funds toavoid running out of cash? Having exhaustedour supply of awkward metaphors, we’ll just callthis our cash-flow test.

The reader who can’t stand suspense, or who wants abird’s-eye view of this paper before plunging into a forestof details, may wish to steal a preliminary glance at sec-tion G, which contains a summary of conclusions and areport card grading several common delinquency measures.

B . M e a s u r i n g t h e U n i v e r s e o f To t a l L o a n s

We need to touch on one more preliminary matter be-fore we start interrogating delinquency ratios. Somemeasure of the MFI’s total loan activity shows up in thedenominator of many delinquency ratios (and all loan lossratios). Great confusion results if we aren’t clear aboutthe differences among various measures of loan activity.

Imagine a loan whose principal of 100 is payable inweekly installments of 10 each. The amount disbursedis 100: at the time of disbursement, this 100 is also theoutstanding (unpaid) balance of the loan. The outstandingbalance on the MFI’s books—that is, the amount theclient still owes—declines as the client makes weekly

payments. Totaling the weekly balances (100 + 90 + …+ 10 = 550) and dividing by 10 weeks gives us an aver-age outstanding balance of 55 over the ten-week life ofthis loan.

Now imagine that we have an active portfolio of 1,000loans just like this one, evenly distributed as to theirage—that is, 10 percent of them are in their first week,10 percent are in their second week, and so on. Thetotal disbursed amount of these loans is 100,000. Butthe portfolio shown on the MFI’s books is not the origi-nal disbursed amount. Rather, book portfolio is onlythe unpaid amounts that clients still owe: 1,000 loanstimes 55 average outstanding balance = 55,000 portfo-lio outstanding.

If each payment contains the same amount of principal(straight-line amortization), the average outstandingbalance on a loan can be calculated with a simple formula:3

original principal + amount of principal in one payment2

Average outstanding balance is usually close to 50 per-cent of original principal amount, except where loansare repaid in a small number of payments.

For 36 payments, the ratio is 51.4 percent (1 + 1/36) ÷ 2 24 52.1 12 54.2 6 58.3 3 66.7

Now we will complicate our case by assuming that theMFI renews its 10-week loans five times a year, with-out changing their amounts or terms. In this case theoutstanding portfolio will continue to be 55,000 at anytime during the year. The original principal of loansoutstanding at any given time will be 100,000. How-ever, the annual amount disbursed jumps to 500,000.Clearly it will make a big difference which of these num-bers we use in the denominator of any delinquency ratio.

3 This formula applies precisely only for straight-line amortiza-tion where each payment contains the same amount of princi-pal. A different “declining balance” amortization scheme isoften found in housing finance, and is used by financial calcu-lators: the total payment is always the same, but the divisionbetween principal and interest changes over the life of theloan. For our purposes here, the difference in average out-standing balance between straight-line amortization and de-clining balance amortization is not substantial, unless the num-ber of payments or the interest rate per period is unusuallyhigh.

B

A

L

A

N

C

E

W E E K S 1 0 t h P a y m e n t1 s t P a y m e n t

8 0

1 0 0

7 0

4 0

5 0

6 0

3 0

2 01 0

9 0

1 3 4 5 6 7 8 9 1 02

S T R A I G H T - L I N E A M O R T I Z A T I O N

M E A S U R I N G M I C R O C RE D IT D EL I N Q U E N C Y

FOU

R

C . C o l l e c t i o n R a t e s

amounts collected amounts fallen due

Many an MFI claims to recover 98 or 99 percent of thefunds it lends. This claim implies an indicator whosenumerator is actual cash collections of principal andwhose denominator is the principal amount that was dueto be paid. We’ll call this kind of ratio a collection rate,but it is also called a repayment rate or a recovery rate.

A collection rate has the advantage of using elementaryinformation that even simple information systems canusually generate. As a result this kind of portfolio qual-ity measure is used by more MFIs than any other.

A collection rate seems to be the complement of a de-linquency rate: if we collected 98 percent of the pay-ments that fell due during a period, then obviously theremaining 2 percent of the payments due were not col-lected. But this apparently simple relationship gives riseto a widespread and dangerous misinterpretation. Thereseems to be a nearly irresistible tendency to assume thata collection rate is the complement of a loan loss rate. 4

An MFI that maintains a consistent 95 percent collec-tion rate may think it is losing only 5 percent of its port-folio each year to default. This kind of assumption isalmost always wrong, sometimes fatally so.

Consider a hypothetical MFI with 1,000 clients whocontinually receive three-month loans of 130, repayablein 13 weekly installments of 10 each. The disbursementdates of these loans are distributed randomly through-out the year, so the outstanding balance of the portfolioremains constant. Suppose that every loan suffers a singlemissed installment that is never recovered.5 An operat-ing grant from a donor permits the MFI to replace theselosses and keep its portfolio at a constant size. Out of130,000 disbursed for a loan cycle, the MFI recovers120,000 and loses 10,000. Thus its collection rate is92.3 percent. This number may not provoke cheers,but neither does it have a disastrous ring to it. The firebell seems silent.

What percentage of its portfolio does this MFI lose everyyear? (Hint: don’t subtract 92.3 from 100 and guess7.7 percent.)

First, we need to recognize that this MFI loses 10,000on every loan cycle. It runs through four three-monthcycles each year, so its annual loss is 40,000. Second,the loans that are active at any point in time have anoriginal amount disbursed of 130,000, but we have toremember that this is not the same as the amount ofportfolio outstanding. Using the formula given in sec-tion B, we calculate the average outstanding balance ona single loan as (130 + 10) / 2 = 70. The portfolio of1,000 loans on the MFI’s books at any point during theyear is not 130,000 but 70,000. This latter number—the outstanding portfolio—is more relevant than theamount disbursed. The outstanding portfolio representsthe actual quantity of funds committed to the lendingoperation; it is this amount, not the amount disbursed,that the MFI really owns and really has to finance. Hav-ing analyzed the situation more closely, we find that ourhypothetical MFI, whose 92.3 percent collection ratedidn’t sound too terrifying, is in fact losing 57 percent(40,000/70,000) of its portfolio every year. Now thefire bell is clanging away.

If we applied the same analysis to an MFI with a 99percent collection rate on two-month loans payableweekly, we would find that it loses about 11 percent ofits portfolio to default each year. These simplified ex-amples are imaginary, but hundreds of real MFIs aredeceived by high-sounding collection rates into think-ing that their portfolios are solid.

4 A loan loss rate tells us what percentage of a lender’s loanportfolio is irrecoverably lost during a period (usually a year).Conceptually at least, the direct calculation of an annualloan loss rate seems straightforward: the amount of loanswritten off as unrecoverable is added to any increase in theloan loss reserve on loans not yet written off, and dividedby the average outstanding portfolio over the course of theyear. In practice, many MFIs can’t directly calculate a mean-ingful annual loss rate, because they haven’t followed sound,consistent policies in writing off loans and in provisioningadequate loss reserves for loans that haven’t been writtenoff, or because of weaknesses in their information system.Such MFIs may be able to use the indirect method pre-sented here, which allows an MFI to estimate its annualloss rate if it is tracking a collection rate.

5 The reader who prefers a slightly more realistic examplecan reach the same conclusion by assuming that 90 percentof the clients pay perfectly, while the remaining 10 percentfail to make any payment on their loans.

O c c a s i o n a l P a p e r N o . 3

about 15 percent of outstanding balance. Our loan cycleis three months, so we lose this 15 percent four times ayear, for a total annual loss rate around 60 percent ofoutstanding balance.

Using the same simplified formula, Table 1 shows howdangerous the widespread misinterpretation of collec-tion rates is, especially for MFIs that use short loan cycles.The assumption that the loan loss rate is equal to 100percent minus the collection rate holds only for two-year loans.

Now we can pause for a quick overview of how collec-tion rates, taken as a group, stand up to our five tests.We’ve seen that collection rates, if not understood cor-rectly, fail our fire bell test miserably. However, after asuitable algebraic massage a collection rate not only servesas an effective alarm, but also meets our bottom linetest, because it lets us estimate an annual loan loss rate.(Alas, life is never simple. Our algebraic manipulationworks only for collection rates whose numerators countall amounts paid, and whose denominators count—butdo not double-count—all amounts falling due. Readersconfused by this cryptic statement need not despair, be-cause it will be illustrated when we discuss specific vari-ants of the collection rate.)

FIVE

COLLECTION RATE: PERCENT OF AVERAGE PORTFOLIO LOST ANNUALLY ON LOANS OF

(percent) 2 months 3 months 6 months 9 months 1 year 2 years

99 12 8 4 3 2 198 24 16 8 5 4 297 36 24 12 8 6 395 60 40 20 13 10 590 120 80 40 27 20 1080 240 160 80 53 40 2070 360 240 120 80 60 30

ALR =

x 20.616 =

x 2

T a b l e 1 : C o n v e r t i n g a c o l l e c t i o n r a t e i n t o a n a p p r o x i m a t e a n n u a l

l o a n l o s s r a t e

Readers who like equations can find general formulasfor converting a collection rate into an annual loan lossrate in an annex at the end of this paper. At this stage ofthe discussion we’ll use a simplified formula that is ac-curate enough for most practical purposes:

1 - CR T

where ALR is the annual loss rate, CR is the collection rate,and T is the loan term expressed in years. (The annexshows how to treat a portfolio with a variety of loan terms.)

In the example a few paragraphs earlier, the collectionrate was 92.3 percent, and the average loan term was0.25 years. Our simple formula yields an annual lossrate of 62 percent, acceptably close to the 57 percentwe calculated directly in that example.

1 – 0.923 0.25

This formula and its result make intuitive sense. If ourcollection rate is 92.3 percent, we lose 7.7 percent ofthe amount disbursed each loan cycle. Because the out-standing balance is roughly half of the amount origi-nally disbursed, 7.7 percent of the disbursed amount is

M E A S U R I N G M I C R O C RE D IT D EL I N Q U E N C Y

SIX

Certain collection rates can be star performers on ourcash-flow test. Most MFIs can keep track of how muchclients are due to pay in future periods. Armed with acollection rate summarizing the percentage of paymentsfalling due that have actually been collected in past peri-ods, an MFI can approximate its future cash receiptsfrom loans by simply multiplying the historical collec-tion rate by the amount that will be falling due.

As we will see below, whether a particular collection ratedoes well on our red flag (day-to-day portfolio manage-ment) test depends on what is in the numerator of therate. Performance on the smoke and mirrors test alsovaries among versions of the collection rate.

After that overview, we can refine our analysis by focus-ing on four distinct types of collection rates:

• The best day-to-day red flag performer is an on-time collection rate that tracks success in collectingpayments when they first become due. (This mea-sure needs to be supplemented by a clean-up re-port that tracks collection of late payments.)

• A common Asian collection rate divides all pay-ments received during a period by all amounts dueduring that period, including past-due amountsfrom prior periods.

• A version that we will call the current collectionrate divides cash received during a period by cashthat first fell due during that same period.

• The cumulative collection rate is similar, except thatit covers payments received and payments due overthe entire life of the MFI.

The last two of these collection rates can be algebra-ically manipulated to estimate loan loss rates.

On-time collection rate. In the microfinance programof Chile’s Banco del Estado, the principal tool for day-to-day portfolio management is an on-time collectionrate. For each period, the denominator is amounts fallingdue for the first time during the period, and the numera-tor is amounts that have been paid on time (and in cash).

This measure provides a responsive red flag for loan of-ficers and their supervisors: it gives instant and unam-biguous feedback about the timeliness of client payments.Unlike other collection rates, the on-time collection rateexcludes overdue payments from both the numeratorand the denominator. Inclusion of overdue paymentscan introduce confusing “noise” into the short-terminformation circuit. Suppose client payments of 100,000

fell due this past week, and we collected that sameamount during the week. If our numerator combineson-time payments with late payments of past-dueamounts, we can’t tell whether the 100,000 we collectedreflects all of our clients paying on time, or whether20,000 came from payment of old past-due installmentsand only 80,000 came from on-time payment of cur-rent maturities. The latter situation would demand animmediate operational response.

The manager tracks an on-time collection rate on amonthly, weekly, or even daily basis for branch officesand individual loan officers. When this rate shows acollection deficit, field staff follow up immediately. Themain advantage of this indicator is its ability to focusfield staff’s attention in the short term on the most im-portant practical job at hand—to go out and collect thepayments that didn’t come in on time yesterday.

For the sake of clear focus on what’s happening in theshort term, the on-time collection rate excludes past dueamounts from the denominator and late payments fromthe numerator. Nonetheless, performance in collectingoverdue amounts needs attention, so if an on-time col-lection rate is the primary day-to-day delinquency mea-sure it should be supplemented with some kind of clean-up report. For instance, such a report might show thatlast month the MFI (or the branch or the loan officer)collected

75 percent of payments that were overdue 1-30 days,40 percent 31-90 days,15 percent 91-180 days, and5 percent past 180 days.

Close observation of the on-time collection rate togetherwith a clean-up report can educate management aboutimportant seasonal patterns in clients’ behavior.

Because it excludes late payments, the on-time collec-tion rate cannot be algebraically manipulated to estimatea longer-term annualized loss rate: loss rates reflect, notpayments that aren’t made on time, but rather paymentsthat aren’t made at all. A loss rate might be estimatedby combining on-time collection information with in-formation on late payments from the clean-up report,but this will probably be cumbersome; if estimating aloss rate is the main objective, it may be easier to use thecurrent collection rate described below.

Because cash flow consists not just of on-time paymentsbut also of late payments and prepayments, the on-timecollection rate alone is not a good measure for estimat-ing future cash flow.

O c c a s i o n a l P a p e r N o . 3

SEVEN

Asian collection rate. Some Asian lenders rely on a col-lection rate whose numerator is all cash collected duringa period (including prepayments as well as late paymentsthat first fell due in prior periods) and whose denomina-tor is everything that was due during that period (in-cluding past-due amounts from prior periods). The wideuse of this measure is odd, given how poorly it works.

The argument for including past due amounts from ear-lier periods in the denominator sounds straightforward:since we should be trying to collect these amounts eachperiod, they ought to be included in the performanceindicator for the period. But as noted above, we can geta better day-to-day red flag indicator by using an on-time collection rate together with a clean-up report.From an operational perspective, we want to be able todistinguish amounts that have just fallen due from past-due amounts. Lumping old arrears and current maturi-ties together is especially problematic when the lender isnot writing off bad loans aggressively. In such a case,ancient arrears that are never going to be collected canpile up in the denominator of the collection rate and berepeated indefinitely. This makes it impossible to seewhat is happening to the recent portfolio, which shouldnormally be the main concern. If an institution haschanged its lending or collection practices following adelinquency outbreak, the Asian collection rate doesn’tpresent a sharp enough picture of whether the new prac-tices are working.

The Asian collection rate falls apart on our bottom linetest. Including past-due amounts in the denominatorresults in double-counting. A payment due shows upduring the period when it first falls due, and in everysubsequent period until it is collected or written off. Buta payment collected only shows up once. Table 2 mod-

els an extreme illustration of this dynamic. A hypotheti-cal loan portfolio runs for 100 successive periods, withregular payments of 1,000 falling due each period. Dur-ing the first period nothing is recovered. In each subse-quent period 1,000 is recovered. The collection ratewould be zero percent for the first period. In the sec-ond period, receipts of 1,000 would be divided by de-mand of 2,000 (1,000 overdue from the first periodand 1,000 coming due during the second period), pro-ducing a collection rate of 50 percent. The same 50percent collection rate would prevail in all subsequentperiods. But in fact, by the end of 100 periods the insti-tution will have recovered 99 percent of the loanamounts it disbursed—even though its collection ratenever rose above 50 percent.

Because overdue amounts are counted more than oncein the denominator of the Asian collection rate, the sumof the denominators (line 3 of Table 2) will exceed thetotal due under the loan (line 1) whenever there is anynet delinquency. Thus the average value of the collec-tion rate over the life of the loan (line 5) will be lowerthan the actual long-term collection performance (line6). The amount of this gap depends on the amountand length of delinquency, and appears impossible toestimate analytically. As noted, the gap will be espe-cially problematic in an MFI that is not writing off oldloans aggressively. Because of this gap, the Asian col-lection rate doesn’t provide a meaningful bottom-lineapproximation of how much of the portfolio is likely tobe lost, either intuitively or after algebraic manipula-tion. The same gap makes this indicator useless for cashflow projection. Nor does the indicator work well as afire bell—it is too prone to false alarms.

T a b l e 2 : T h e A s i a n c o l l e c t i o n r a t e v s . a c t u a l l o n g - t e r m c o l l e c t i o n

PERIOD 1 2 3 4 5 6 7 ... 100 Total

(1) Current due 1,000 1,000 1,000 1,000 1,000 1,000 1,000 ... 1,000 100,000(2) Collected 0 1,000 1,000 1,000 1,000 1,000 1,000 ... 1,000 99,000(3) Current + past due 1,000 2,000 2,000 2,000 2,000 2,000 2,000 ... 2,000 199,000(4) Asian collection rate [(2)/(3)] 0% 50% 50% 50% 50% 50% 50% ... 50%(5) Cumulative average of (4) 0% 25% 33% 38% 40% 42% 43% ... 49%(6) Cumulative collected / Cumulative due [∑(2)/ ∑(1)] 0% 50% 67% 75% 80% 83% 86% ... 99%

M E A S U R I N G M I C R O C RE D IT D EL I N Q U E N C Y

EIG

HT

Finally, the Asian collection rate fails the smoke and mir-rors test. It can create an incentive to “evergreen” loans.Suppose a certain past-due loan is really uncollectable.If the MFI reschedules or refinances it, its accumulatedoverdue amount will disappear from the next period’sdenominator, thus raising the ratio’s value. Of course,this apparent improvement in the collection rate will beonly temporary, and will have nothing to do with thereal collection performance of the portfolio. A relateddynamic is worth mentioning: a large accounting write-off will produce a major improvement in the Asian col-lection rate. When a substantial quantity of past-dueamounts disappears from the denominator of the frac-tion, its value rises even though there has been no realchange in the underlying collection performance. Theevolution of an Asian collection rate over time will cre-ate a misleading impression unless write-offs are factoredinto the picture—something that is hard to do in anysystematic mathematical way.

Current collection rate. The numerator of the currentcollection rate is all cash received in payment of loansduring the period, whether this cash represents currentpayments, prepayments, or late payments of amountsoverdue from previous periods. The denominator is all

amounts that fall due for the first time during the pe-riod. Normally, the numerator and denominator includeprincipal only, excluding interest. But a lender whoseinformation system has trouble sorting payments intoprincipal and interest can use a current collection ratebased on total payment amounts without seriously dis-torting the results. (The same is true, incidentally, ofthe on-time collection rate.)

The current collection rate is not a stellar performer onour red flag test. Its numerator lumps together prepay-ments, payments of current maturities, and late pay-ments. The failure to distinguish among these types ofpayments can obscure a manager’s picture of what ishappening to her portfolio in the short term. The in-clusion of prepayments and late payments in the numera-tor can cause the current collection rate to fluctuate con-siderably from one period to the next even though therehas been no significant change in the overall risk profileof the portfolio. To take the simplest case, a loan pay-ment that is delayed for one period will lower the cur-rent collection rate for that period and then raise it forthe next. Table 3 illustrates how prepayments and latepayments can produce volatility, and suggests four ap-proaches for smoothing it out.

MONTH 1 2 3 4 5 6 7 8 9 10 11 12

1. Current am’t due in period 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,0002. Current payments collected 900 800 1,000 950 850 900 900 850 800 850 950 8503. Late payments collected 0 0 0 50 0 200 0 0 50 0 150 504. Prepayments collected 50 0 100 0 0 0 0 0 150 0 0 05. Total payments collected 950 800 1,100 1,000 850 1,100 900 850 1,000 850 1,100 900

COLLECTION RATES (percent)

6. Current collection rate: monthly 95 80 110 100 85 110 90 85 100 85 110 907. Current collection rate: quarterly 95 98.3 91.7 958. Current collection rate: by semester 96.7 93.39. Current collection rate: 6-month moving average* 96.7 95.8 96.7 95 92.5 96.7 93.310. Cumulative collection rate [ ∑(5) / ∑(1) ] 95 87.5 95 96.3 94 96.7 95.7 94.4 95 94 95.5 95

*Average of the six months ending w ith the current month

T a b l e 3 : S m o o t h i n g c u r r e n t c o l l e c t i o n r a t e v o l a t i l i t y

O c c a s i o n a l P a p e r N o . 3

NIN

E

Over the span of a year the hypothetical MFI in Table 3is recovering 95 percent of the amounts due. Measuredeach month, the current collection rate jumps around alot, from a low of 80 percent to a high of 110 percent.But this volatility probably reflects random or seasonalvariation in the timing of prepayments and late payments,rather than significant changes in the underlying risk ofthe portfolio. Measuring on a quarterly basis smoothesmuch of the volatility. Measuring by semester or with asix-month moving average smoothes the current collec-tion rate even more. So does the use of a cumulativecollection rate, at least after the first few months. Theonly way to be sure of eliminating seasonal fluctuationis to measure the collection rate on an annual basis.

There is a tradeoff here. Using a broad measuring span,such as a year, eliminates seasonal or other short-termsources of volatility and leaves an indicator that betterreflects the long-term underlying risk of the portfolio.But the longer the measuring span, the less responsivethe current collection rate will be to real short-termchanges in borrower behavior and the less useful it is as ared flag. The on-time collection rate discussed earlier is amore responsive indicator of day-to-day portfolio per-formance, and is thus a better guide for day-to-day op-erations, especially if it is supplemented by a clean-up report.

The main advantage of the current collection rate (andof the cumulative version of it discussed below) is itsperformance on the bottom line test: even a simple in-formation system can use this measure to estimate theannual loan loss rate, applying the formulas given earlierin this section and in the annex. With this algebraicadjustment, the current collection rate provides an ex-cellent fire bell. But as noted, the measure can be disas-trously misleading without such an adjustment.

A current or a cumulative collection rate can be a pow-erful tool for cash-flow planning: an MFI can estimateactual cash receipts from loan payments during a futureperiod by simply multiplying the total of payments fall-ing due during the period by the historical collectionrate.

Cumulative collection rate. Many institutions, such asthe huge Unit Desa system of Bank Rakyat Indonesia,report a cumulative collection rate. The numerator re-flects all principal payments received since the inceptionof the program. The denominator is all repayments ofprincipal that have fallen due as of the date of measure-ment (or in other cases, all disbursements). Because itsmoothes out the random or seasonal volatility causedby the timing of prepayments and late payments, thecumulative collection rate can provide a clear bottomline picture of long-term portfolio quality—but only ifit is accompanied by information on the average loanterm. Table 1, which converted collection rates intoannual loan loss rates, showed that a cumulative collec-tion rate of 98 percent would be excellent for an MFImaking two-year loans (only about 2 percent of the port-folio is lost each year), but disastrous for an institutionmaking two-month loans (nearly a quarter of portfoliois lost each year).

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TEN

Not surprisingly, this cumulative historical measure doesn’t work well as a red flag for early warning purposes. Asimple example illustrates this problem:

A m o u n t s d u e A m o u n t s c o l l e c t e d C o l l e c t i o n r a t e

Cumulative through June 30, 19xx 2,000,000 1,980,000 99.0% (cumulative collection rate)July, 19xx 10,000 5,000 50.0% (current collection rate)Cumulative through July 31, 19xx 2,010,000 1,985,000 98.8% (cumulative collection rate)

An MFI tracking only a cumulative measure might barelynotice the drop from 99 percent to 98.8 percent, eventhough it reflects a serious current repayment problem.The cumulative collection rate is a meaningful long-termmeasure of bottom line portfolio performance, but forday-to-day analysis and management it needs to be ac-companied by some other measure more sensitive torecent repayment performance.

Renegotiated loans. When a borrower runs into repay-ment problems, an MFI will often renegotiate the loan,either rescheduling it (that is, stretching out its originalpayment terms) or refinancing it (that is, replacing it—even though the client hasn’t really repaid it—with anew loan to the same client). These practices compli-cate the process of using a collection rate to estimate anannual loan loss rate. Before exploring those complica-tions and suggesting alternative solutions for dealing withthem, the author needs to issue a warning: any readerlooking for a perfect solution will be disappointed. Thesuggested approaches all have drawbacks. It is impor-tant to recognize that heavy use of rescheduling or refi-nancing can cloud the MFI’s ability to judge its loanloss rate. This is one of many reasons why renegotiationof problem loans should be kept to a minimum—someMFIs simply prohibit the practice. And renegotiatedloans should always be flagged and reported separatelyfrom the rest of the portfolio, as discussed in a later sec-tion.

To illustrate the complications and solutions, we willassume that a client has missed the first three monthlypayments of a six-month loan. After the third missedpayment, the loan is rescheduled by changing the termsof the original loan, or refinanced by replacing the origi-nal loan with a new one. Either way, the client is nowexpected to make six payments beginning in the fourth

month. The client complies with this new obligation.If each month we make an entry recording the paymentexpected that month, our collection register will pro-duce a strange result:

Month Amount due Amount collected1 100 02 100 03 100 0(renegotiation)4 100 1005 100 1006 100 1007 100 1008 100 1009 100 100Total 900 600

Even though the MFI has completely recovered its loan,its collection rate for the nine months seems to be only67 percent (600/900). This anomaly stems from thedouble-counting of amounts due.

There would seem to be three ways to avoid this double-counting. Under the first approach, at the time of rene-gotiation we would retroactively eliminate the missedpayments from the register of payments due (thus chang-ing the collection rate for the first three months). Thefinal treatment of the loan would then be as follows,showing a 100 percent collection rate for the ninemonths. The drawback of this method is that goingback to change our record for the earlier period may beproblematic.

O c c a s i o n a l P a p e r N o . 3

ELEVEN

Month Amount due Amount collected 1 0 0 2 0 0 3 0 0 (renegotiation) 4 100 100 5 100 100 6 100 100 7 100 100 8 100 100 9 100 100 Total 600 600

A second approach would be to treat the renegotiationas a payoff of the missed payments under the originalloan. This treatment also produces a 100 percent col-lection rate, corresponding to the complete repaymentof the amount lent to the client:

Month Amount due Amount collected 1 100 0 2 100 0 3 100 0 (renegotiation) 3006

4 100 100 5 100 100 6 100 100 7 100 100 8 100 100 9 100 100 Total 900 900

Treating our renegotiated loan this way adds an extra300 to both the numerator and the denominator of ourcollection rate, thereby inflating the value of the ratiofor our overall portfolio. If we are renegotiating a sub-stantial percentage of our loans, this distortion could bematerial.

A third approach is mentioned in a hushed voice and isnot necessarily recommended, because the author hasnot seen it used in practice, and two expert reviewers ofthis paper recoiled in horror at its unorthodox nature.This approach would tie the denominator of the cur-rent collection rate to the terms of the original loan con-tract. At the time a loan is made, the information sys-tem would schedule all the loan’s payments accordingto the periods when they’re expected. As each periodoccurs, the collection rate register uses the paymentamount scheduled for that period. When a loan is rene-gotiated, the denominator continues to use the paymentamounts and times provided in the original agreement.

(If the renegotiated loan adds unpaid interest to the prin-cipal amount, or otherwise increases the principal pay-ments due, then the amount of the increase is spreadout over the future periods when it is due to be paid.)

Month Amount due Amount collected1 100 02 100 03 100 0(renegotiation)4 100 1005 100 1006 100 1007 0 1008 0 1009 0 0 100Total 600 600

Likewise, if an accounting decision is made to write offthe loan, nothing changes in the current collection ratedenominator. This technique passes our bottom linetest, because it introduces no algebraic distortion intoour estimation of a loan loss rate. It also scores well onthe smoke and mirrors test: when a portfolio is mea-sured this way, there is no incentive to engage in inap-propriate write-off, rescheduling, or refinancing, becausenone of those actions affects the ratio. The substantialdrawback is that this approach requires maintaining aparallel payments-due register that does not always cor-respond to the actual payments that are legally due andcollectable. For instance, the register illustrated aboveshows no payments due in months seven, eight, and nine,even though renegotiated payments do in fact fall duein each of them. Thus, this presentation of renegoti-ated loans could not be used in a report intended toguide day-to-day operations. (As noted earlier, the cur-rent collection rate is not a good red-flag performer, nomatter how renegotiated loans are treated: for opera-tional management, the better choice is an on-time col-lection rate supplemented by a clean-up report for over-due amounts.)

6 This entry in the register that calculates the collection ratedoes not correspond to the accounting treatment of the trans-action. Rescheduling the original loan (simply extending itsterm) would usually produce no accounting entry. Refinanc-ing the loan (replacing it with a new one) would be accountedfor by showing a complete payoff of the old loan, not by cash,but by the new loan.

M E A S U R I N G M I C R O C RE D IT D EL I N Q U E N C Y

Prepayments. A similar but less bothersome issue is cre-ated by prepayments. If the client in our previous ex-ample makes her first two payments on time and thenpays off the rest of her six-month loan on the third pay-ment date, what happens in our register of paymentsdue? One approach is to accelerate all the remainingpayments due into the period when the loan is paid off.This treatment would seem best where the full outstand-ing loan balance is prepaid, because the loan disappearsfrom the portfolio after that point.

Month Amount due Amount collected1 100 1002 100 1003 400 400Total 600 600

The alternative is to use the unorthodox rule mentionedabove—tying the entries in the amounts-due register tothe terms of the original loan contract:

Month Amount due Amount collected1 100 1002 100 1003 100 4004 100 05 100 06 100 0Total 600 600

A reader with masochistic inclinations can find more discussion of col-lection rates in Richard Rosenberg, “Portfolio Quality Measurementin India’s Regional Rural Banks” (1997). That paper proposes a manual(non-computerized) system for tracking a current collection rate. Itcan be found on CGAP’s home page (http:/ /www.worldbank.org/html/cgap/ cgap.html) or requested as an e-mail attachment fromRRosenberg@worldbank.org.

D . A r r e a r s R a t e s

late payments total loans

Arrears rates are the second most common measure ofmicrofinance delinquency. These rates focus on theamount of late payments, dividing this number by somemeasure of total loan activity—typically outstandingportfolio. Arrears rates tend to create an overoptimisticimpression of portfolio quality.

In a sense, arrears rates compare apples with oranges:missed payments are compared not with payments due,but with total loan amounts. The problem is that pay-ments that have fallen due may be small relative to totalloan amounts. Thus an arrears rate is usually a smallnumber, allowing managers and loan officers to remaincomplacent even when portfolio quality is deterioratingrapidly. Poor repayment can continue for a long timebefore the arrears rate becomes large enough to causeconcern. Where an arrears rate is the only delinquencymeasure, problems often go unnoticed until it is toolate to correct them.

The same point can be made from another perspective.When a client misses a payment on a loan, the MFI’srisk increases. The arrears rate captures the increasedrisk that the payment in question will never be collected.But there is also an increased risk that the MFI will loseall the subsequent payments—the outstanding loan bal-ance—as well. It is this latter risk, usually much larger,that the arrears rate fails to capture.

A stylized example illustrates how an arrears rate failsboth our fire bell and bottom line tests. Suppose thaton January 1 our MFI disburses a portfolio of 1,000eight-year housing loans. The principal amount of eachloan is 100. The loans are to be repaid in 96 monthlypayments. In theory the loans are secured by the bor-rowers’ houses, but in practice legal collection proce-dures are unreliable.

Now suppose that February 1 rolls by, and not a singleone of the 1,000 borrowers makes a payment. The samething happens again on March 1 and yet again on April 1.Our portfolio is clearly in desperate trouble: our cli-ents’ behavior on the first 3 payments casts strong doubtson our ability to recover the remaining 93. Yet the ar-rears rate on this portfolio would be only about 3 per-cent: on each loan, only 3 payments out of 96 are late—so far at least. (As this example illustrates, the distortiveeffect of an arrears rate is greater for loans with a largenumber of scheduled payments.)

For an MFI that wants to report really low delinquency,the arrears rate can be made even tamer by the simpleexpedient of defining “late” payments in the numeratorvery gently: some MFIs do not include a payment inthe calculation until it is 30, 90, or 180 days late. Otherprograms don’t count any payment as late until the en-tire term of the original loan has expired. By some ofthose measures, our stylized portfolio would appear100 percent current.

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longer treated as performing, and it has to be reportedin a way that reflects that the full outstanding balance isat risk.

In microfinance, delinquency is more delicate. Amorti-zation is more frequent. Loans become nonperformingmore quickly, and most are uncollateralized. Once cli-ents fall significantly behind, they often never becomecurrent again. An arrears rate simply does not reflectthe true risk level of a microloan portfolio with substan-tial numbers of late payments, or one where a signifi-cant portion of loans have several missed payments.

Thus arrears rates almost always paint too rosy a pictureof portfolio quality. This is not meant to imply thatevery MFI using an arrears rate is deliberately camou-flaging its portfolio. In fact, the more common—anddangerous—occurrence is that the MFI is acting in goodfaith, with the result that the MFI is as much in the darkabout its true portfolio quality as is the outside readerof its reports.

E . P o r t f o l i o a t R i s k

outstanding balance of loans with overdue payment(s)

total outstanding balance

The international standard for measuring bank loan de-linquency is portfolio at risk (PAR). This measure com-pares apples with apples. Both the numerator and thedenominator of the ratio are outstanding balances. Thenumerator is the unpaid balance of loans with late pay-ments, while the denominator is the unpaid balance onall loans.7 The PAR uses the same kind of denominatoras an arrears rate, but its numerator captures all theamounts that are placed at increased risk by the delin-quency.

A PAR can be pegged to any degree of lateness. PAR ,a common measure among banks, captures the outstand-ing balance of all loans with a payment more than 90days late. BancoSol in Bolivia reports PAR , recogniz-ing a loan as delinquent the very next day after a pay-ment is missed.

The distortive potential of arrears rates is importantenough to reiterate with a less extreme example. Con-sider the case of two clients who have each missed threepayments. The first has a short-term working capitalloan of 300, payable in 3 equal monthly installments.The second has an equipment loan of 3,600, payable in36 monthly installments. Both clients have been un-willing or unable to make any payment so far. Thusboth loans would be considered “nonperforming.”

Measured against total portfolio, the three-month de-linquency of the first client will have the same effect onthe MFI’s overall arrears rate as the three-month delin-quency of the second client. But the outstanding bal-ance at risk with the second client is 12 times the out-standing balance at risk with the first client. Creditmanagers need to discriminate between these two loans,because the second loan is much more worrisome thanthe first one. The arrears rate doesn’t help them.

When delinquent loans are rescheduled or refinanced,most MFIs then treat the loan as being on time, withthe result that the arrears accumulated under the origi-nal loan disappear from the arrears rate calculation. Thissituation can create an incentive for inappropriate re-scheduling or refinancing, so the arrears rate does notdo well on our smoke and mirrors test.

The longer a loan goes without payment, the less likelyit is to generate income for the MFI, and the more likelyit is to produce the extra expense associated with collec-tions procedures. This is why loans eventually must beclassified as nonperforming, even though they remainon the MFI’s books throughout the collections period.Both managers and analysts need to know what per-centage of the loan portfolio is producing normal in-come and expenses, and what percentage is generatingminimal income and exceptional expenses. Arrears ratesdo not capture this information, and therefore fail ourcash-flow test.

Occasionally someone defends arrears rates by pointingout that commercial banks use them. In the world ofcommercial banking, large long-term loans are usuallysupported by physical collateral or other security thatprovides an alternative source of loan recovery if theborrower fails to make the agreed payments. Thus com-mercial banks tend to be more relaxed than MFIs abouton-time repayment. In fact, most banks don’t even be-gin collection procedures until multiple payments havebeen missed. As a result, banks in many countries areallowed to use an arrears rate to report on loans that areup to 90 days late. Past 90 days, however, the loan is no

7 As discussed later in this section, it may be technically moreprecise to exclude from the PAR denominator loans for whichthe first payment has not yet fallen due.

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Compared to conventional banks, MFIs should argu-ably use a tighter definition of delinquency because theirloans tend to be shorter term, their payments more fre-quent, and their delinquency more volatile. Recall ourearlier stylized portfolio of housing loans, all of whichhad gone unpaid on the first three monthly due dates.PAR would not be a good red flag measure for thisadmittedly odd portfolio, because this measure wouldshow a delinquency of zero. On the other hand, PAR ,PAR , and PAR

would all be 100 percent, delivering

a clear message to management about the urgency of itsproblem. The message is not that 100 percent of theportfolio is going to be lost, but rather that 100 percentof the portfolio is at special risk. Estimating likely lossesis discussed later.

Rather than tracking just one PAR indicator, MFIsshould age their portfolios: that is, they should breakthem into groups by degree of lateness, as in the fol-lowing example.

Payment status Outstanding loan balance (share of total)Current 440,000 (88%)1-7 days late8 30,000 ( 6%)8-14 days late 15,000 ( 3%)15-28 days late 10,000 ( 2%)More than 28 days late 5,000 ( 1%)Total 500,000 (100%)

If the MFI is a licensed financial institution, the publicregulatory authority will probably prescribe the agingintervals to be used, at least for official reporting. Anunregulated MFI can choose its own aging schedule.The period used—weekly, monthly, quarterly—shouldcorrespond to the repayment frequency of the MFI’sloans. The aging schedule should also line up with breakpoints in the MFI’s loan collection process: for instance,if a loan is transferred from the loan officer to a supervi-sor when it becomes 28 days late, then 28 days shouldbe a break point in the aging report.

An aged PAR like the example above works well as a redflag or a fire bell. This measure discriminates betweenloans where a payment is just barely late and much riskierloans that have been overdue a long time. It distin-guishes a late payment that represents the last install-ment of a 24-month loan from one that represents thefirst. It gives proper relative weight to small and largeloans, short- and long-term loans. Managers who re-ceive a daily or weekly aged PAR report can quickly pickout loans that need to be pursued aggressively, whilekeeping a finger on the pulse of overall portfolio qual-ity. No one indicator meets all needs or all situations,

but an aged PAR is generally the single most useful in-dicator. Almost all MFIs should produce and use such areport.

Do PAR ratios meet our bottom line test? That is, dothey generate information that allows us to estimateprobable loan losses, in order to provision and price ourportfolio? Many late loans are eventually paid, so hav-ing 10 percent of our portfolio late as of today doesn’tmean that we’ll ultimately lose all of the late loans. Evenwith PAR information, we still need to estimate whatpercentage of late loans will be lost, but the PAR reportlets us make that estimate in a much more sophisticatedmanner. The longer a loan has been delinquent, the lesslikely we are to recover the unpaid balance. An agedPAR report breaks the portfolio into groups dependingon the length of time loans have stayed delinquent, andallows us to assign different probabilities of loss to eachgroup.

But how do we derive these loss probabilities? For aregulated financial institution, loss reserve percentagesfor external reporting are usually prescribed by the regu-lator. For instance, the Central Bank of Bolivia requiresinstitutions it regulates to provision microcredit loanbalances so as to maintain the following levels of lossreserves:

Payment status Loss reserve percentageCurrent or up to 5 days late 1%6-30 days late 5%31-60 days late 20%61-90 days late 50%More than 90 days 100%

Bolivia is unusual in having separate loss reserve rulesfor microloans. Most countries have a single reserveschedule, which has been set with normal commercialbank loan products in mind. These normative levelsmay be far too lax for microcredit portfolios, which tendto have shorter terms, more frequent payments, and notangible collateral. A commercial bank might reason-ably expect to recover a good percentage of secured loans

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8 The preferred method for time-sorting of overdue amounts isto compare the total amount of payments received with theamortization schedule in the loan contract. For instance, ifprincipal payments of 100 are due each month, and only 200in principal has been received by the tenth month, the loanwould be eight months in arrears, regardless of when the lastpayment was received. See Von Pischke et al., “Measurementof Loan Repayment Performance,” Washington, D.C.: Eco-nomic Development Institute, 1988.

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that are overdue by two quarterly payments; an MFI,on the other hand, could not expect to recover many ofits 12-week uncollateralized loans that had gone 180days without a payment. Thus an MFI, regulated ornot, might need to provision more aggressively than bankregulations or conventional accounting practice wouldrequire.

A large MFI with a good portfolio information systemmay want to base its loss reserve percentages on a his-torical analysis. To do so the MFI would take a cohortof loans that are old enough so that it knows their finalrepayment outcome. It would then divide these loansinto groups according to the degree of lateness they ex-perienced, and determine what percentage of each groupwas ultimately collected. This produces an estimatedpercentage of loss for each interval in the MFI’s agedPAR report. Before adopting these loss reserve percent-ages, the MFI needs to adjust them for circumstances—like seasonality, changes in the loan delivery methodol-ogy, or problems affecting the income of a large num-ber of clients—that bear on the probability of loan re-covery. Table 5 on page 17 illustrates the kind of lossreserve schedule that emerges from this analysis.9

Such historical loss analysis can be time-consuming oreven impossible, especially for MFIs whose informationsystems do not retain old loan data in a usable form.New or small MFIs may choose a more elementary ap-proach, simply estimating a flat percentage to use in pro-visioning all loans. For instance, an MFI might auto-matically provision 1 percent of all loan disbursementswhen they are made, or provision every quarter to keepits loan loss reserves at 2 percent of the outstandingportfolio. But even when such a blanket provisioningrule is used, the information system should support somekind of checking of present reserve levels against actualloss experience on the past portfolio, or at least againsta projected loan loss level derived from a collection rate,as described above in section C.

A full discussion of provisioning is beyond the scope ofthis paper.10 The relevant point here is that while PARmeasures do not predict likely loan losses directly, theydo provide a basis on which sophisticated provisioningfor such losses can be done. In this sense, the PAR passesour bottom line test.

There is a simpler measure that, in MFIs at least, canapproximate a PAR: percentage of active loan accountsoverdue. This measure is the same as the PAR, exceptthat it uses the number of accounts, which some MFIs

can track more easily than the amount of those accounts.Use of this simplified measure is risky unless manage-ment has a good reason to believe that delinquency onlarger loans behaves more or less the same as it does onsmaller loans.

9 For more discussion of historical provisioning, see Robert PeckChristen, Banking Services for the Poor: Managing for Finan-cial Success, Washington, D.C.: ACCION International, 1997,pp. 42-67. This book can be ordered from the ACCION Pub-lications Department, 733 15th Street NW, Suite 700, Wash-ington DC 20005, USA; telephone (01) 202-393-5113, fax(01) 202-393-5115. A useful framework for analysis and pre-sentation of historical delinquency experience and trends canbe found in Jacob Yaron et al., Rural Finance: Issues, Designs,and Best Practices, World Bank Environmentally and SociallySustainable Development Studies and Monographs Series 14,1997, pp. 96-97.

10 To tell the truth, a really full discussion of provisioning wouldbe beyond the scope of the author’s present knowledge as well.

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Table 4 applies arrears rates and two types of PAR measures to a sample loan portfolio. Not surprisingly, what theportfolio looks like depends on the lens we use to view it.

T a b l e 4 : D e l i n q u e n c y a s s e e n t h r o u g h t h r e e l e n s e s

Using an arrears rate and defining payments as late onlyafter expiration of the full loan term, an MFI would re-port this portfolio as having 0.9 percent delinquency—a number that would warm any auditor’s heart. Treat-ing loans as late after 90 days produces an arrears rate of3.8 percent, which still sounds healthy. Even if pay-ments are counted as late the day after a payment ismissed, delinquency under the arrears rate lens shows at15.9 percent, which sounds substantial but not cata-strophic. But all these arrears rates seriously underesti-mate the risk of the portfolio. As the PAR analysis shows,the majority of the money owed to the MFI lies in loansthat are at higher risk because they are late. One eighthof its portfolio is more than 90 days late. This MFI hasa serious delinquency problem. (The policy at one largedonor agency is not to fund any MFI whose PAR isabove 10 percent.) The simplified PAR in Table 4 showssimilar worrisome results. The percentage of accountsat risk is slightly lower than the percentage of amountsat risk, indicating that the MFI’s larger loans are a littlemore likely to be delinquent. A final point illustrated bythe table is that PAR ratios are meaningless unless a timeperiod is specified: the PAR of the sample portfolio is55.6 percent, while its PAR is only 12.6 percent.

Clearly, it is more revealing to report a range of PARsbased on an aging of the portfolio, as in Table 4, ratherthan just a single ratio.

Like many other delinquency measures, the PAR can bedistorted by improper handling of renegotiated loans.MFIs sometimes reschedule—that is, amend the termsof—a problem loan, capitalizing unpaid interest and set-ting a new, longer repayment schedule. Or they mayrefinance a problem loan, issuing the client a new loanwhose proceeds are used to pay off the old one. In bothcases the delinquency is eliminated as a legal matter, butthe resulting loan is clearly at higher risk than a normalloan. Thus a PAR report must age renegotiated loansseparately, and provision such loans more aggressively.If this is not done, the PAR is subject to smoke andmirrors distortion: management can be tempted to giveits portfolio an artificial facelift by inappropriate rene-gotiation. Table 5 illustrates the proper process.

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Overdue Overdue Overdue Total Overdue on loansINDICATORS 1-30 days 31-90 days 91+ days overdue whose full term has expired

Arrears rateValue of late payments 12,904 6,583 6,094 25,581 1,462

As a share of outstandingportfolio ( = 161,119) 8.0% 4.1% 3.8% 15.9% 0.9%

Portfolio at risk (PAR)Value of unpaid balance ofdelinquent loans 39,119 30,095 20,314 89,557

As a share of outstandingportfolio ( = 161,119) 24.3% 18.7% 12.6% 55.6%

Simplified portfolio at riskNumber of late loan accounts 8 7 5 20

As a share of total activeaccounts ( = 40) 20.0% 17.5% 12.5% 50.0%

Adapted from Christen , p . 47; see note 9 .

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T a b l e 5 : S a m p l e P A R r e p o r t a n d l o s s r e s e r v e l e v e l s

A disadvantage of the PAR measure is that it is depen-dent on accounting policy. When a loan is finally writ-ten off because the probability of recovery has becomevery low, the loan balance disappears from both the nu-merator and the denominator of the PAR fraction, low-ering the value of the fraction. Thus failure to write offloans will inflate the PAR. An MFI in Guatemala car-ried all bad debts on its books for years and accumu-lated a PAR of almost 15 percent. Nine out of ten ofthe problem loans were more than 180 days overdue,and therefore very unlikely to be collected. Had theMFI written off such loans each year, it would be show-ing a PAR of less than 2 percent. But the MFI wasunwilling to correct this distortion because the correc-tion would involve a huge one-time loss on its incomestatement. The MFI continued to avoid writing off orprovisioning its bad loans, thus overstating its incomeand assets while making its current portfolio appear worsethan it really was.

Conversely, a crafty manager could generate a PAR mea-sure as low as he wanted by adopting an artificially ag-gressive write-off policy—if he were reporting to a boardor donor more concerned about delinquency than prof-itability. To give a full picture of portfolio quality, PARmeasures must be viewed in conjunction with write-offexperience.

Another potential distortion in PAR measures is worthmentioning. Arguably the PAR denominator shouldinclude only loans on which at least one payment hasfallen due, so that late loans in the numerator are com-pared only to loans that have had a chance to be late.Nevertheless, it is customary to use the total outstand-ing loan balance for the denominator. The distortioninvolved is usually not large for MFIs, because the pe-riod before the first payment is a small fraction of thelife of their loans. For instance, for a stable portfolio ofloans paid in 16 weekly installments with no grace pe-riod, a PAR of 5.0 percent measured with the custom-ary denominator (total outstanding portfolio) would riseonly to 5.3 percent using the more precise denominator(excluding loans on which no payment has yet comedue.) However, if a portfolio is growing very fast, or ifthere is a grace period or other long interval before thefirst payment is due, then the customary PAR denomi-nator can seriously understate risk.

To illustrate this dynamic, imagine a portfolio of 1,000one-year loans payable in quarterly installments, and as-sume that half the clients fail to make their first paymenton time. Intuitively, we might expect such a situationto produce a PAR of about 50 percent. But now sup-pose that the portfolio is growing very fast, so that 500of the loans have been disbursed in the past 90 days.

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OUTSTANDING BALANCE LOSS RESERVEShare of total Amount Percent Amount

Normal loans Current 86.2% 850,924 1% 8,509 1-30 days late 4.1% 40,713 10% 4,071 31-90 days late 2.1% 20,967 25% 5,242 91-180 days late 1.4% 14,026 50% 7,013 More than 180 days late 0.9% 8,645 100% 8,645 Subtotal 94.7% 935,275 33,480

Rescheduled and refinanced loans Current 3.8% 38,002 10% 3,800 1-30 days late 0.8% 8,215 25% 2,054 31-90 days late 0.4% 4,001 50% 2,001 More than 90 days late* 0.2% 1,712 100% 1,712 Subtotal 5.3% 51,930 9,566

Total 100.0% 987,205 43,047

*If a loan has been renegotiated more than once , it should automatically be included in the most delinquent category.

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M E A S U R I N G M I C R O C RE D IT D EL I N Q U E N C Y

For these new loans, the first payment has not yet fallendue, so none of them has had a chance to be late. Ofthe 500 older loans, 250 are overdue. If we use the1,000 total loans as our denominator, the simplifiedPAR is only 25 percent, which substantially understatesthe actual frequency of problem loans in our portfolio.It would be more meaningful to include in the denomi-nator only the 500 loans on which a payment had fallendue, yielding a more realistic PAR of 50 percent.11

The PAR measure works only for loans that are repaidin installments. Consider a portfolio of crop loans thatare to be paid in full at the end of their term. The firstpayment is also the last payment, so the loan disappearsfrom the portfolio, and from the PAR calculation, whenthe payment is made. At any point in time a crop loanportfolio will consist exclusively of two types of loans:loans that have had no payment due, and loans that areoverdue. For such a portfolio, a PAR of 15 percentconveys the irrelevant information that the outstandingbalance of overdue loans is equal to 15 percent of theoutstanding balance of loans not yet due. For such aportfolio, a more meaningful indicator would be a col-lection rate comparing amounts paid with amounts fallendue.

Finally, the loan methodology and accounting treatmentin some village banking programs may not mesh wellwith a PAR measure. For instance, a disbursement to a30-woman village bank will usually be booked as a singleloan. An MFI will often accept partial payment from agroup, especially if only 1 or 2 members out of 30 misstheir installment. How is delinquency measured in thiscase? A standard PAR measure would treat the entireoutstanding balance for all 30 women as being at higherrisk, which seems overstated. The MFI would probablybe better off using one or more collection rate indica-tors. One analyst proposes an interesting alternative forsuch situations: using an arrears rate, but provisioning afull 100 percent of all arrears.12

F. D i s a g g r e g a t i n g D e l i n q u e n c y

M e a s u r e m e n t

MFIs offering multiple loan products often do well incollecting one kind of loan but poorly in collecting an-other. Any delinquency measurement that lumps all loanstogether will obscure this important information. Tothe maximum extent possible, MFIs ought to be able todisaggregate delinquency information, not only by loan

product, but also by region and branch, by loan officer,and in some cases by client characteristics or even by thetime period during which the loan was first granted. Thisinformation can be extremely useful in tracking and man-aging a portfolio.

G . I n a N u t s h e l l

By now the reader may feel like the seven-year old stu-dent whose book review said, “This book told me moreabout whales than I wanted to know.” On the first pageof this paper the author observed that delinquency mea-surement can get complicated; perhaps he has illustratedthis point too thoroughly. But amidst all the complex-ity, the important messages are really quite simple:

• Any mention of a delinquency ratio should includea precise description of the ratio’s numerator anddenominator—otherwise the ratio cannot be inter-preted meaningfully, and may well suggest an un-duly optimistic impression of portfolio quality.

• No single delinquency indicator works well for allMFIs.

• Most MFIs should track multiple delinquency indi-cators, because no indicator answers all the relevantquestions.

• An MFI’s outstanding portfolio tends to be roughlyone half of the original disbursed amount of its loans.

• Collection rates, which divide amounts paid byamounts falling due during some period, are usefulindicators but are subject to drastic misinterpreta-tion: an MFI can have a 97 percent collection rateand still be losing a third of its portfolio every year.

• To estimate annual loan loss, a current or cumula-tive collection rate must be doubled and then multi-plied by the average number of loan cycles per year.

• The most useful collection rate for day-to-day port-folio management is often an on-time collection ratethat tracks success in collecting payments when theyfirst fall due, supplemented by a clean-up report thattracks collection of late payments.

EIG

HTE

EN

11 This same dynamic occurs with arrears rates as well. If loans onwhich no payment has yet fallen due constitute a large percentageof the loan portfolio, any delinquency ratio that uses total portfo-lio (without excluding these loans) as its denominator will under-state risk.

12 William R. Tucker, “Measuring Village Bank Delinquency,” un-published manuscript, 1997.

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O c c a s i o n a l P a p e r N o . 3

• MFIs should avoid using the Asian collection rate,which includes past-due amounts from prior peri-ods in the denominator of the ratio.

• Prepayments and late payments can create fluctua-tions that limit the usefulness of collection rates otherthan the on-time collection rate for measuring per-formance over a short period.

• Frequent renegotiation—rescheduling or refinanc-ing—of problem loans makes it hard for an MFI totrack and measure its repayment risk.

• Renegotiated loans should always be flagged and seg-regated from normal loans in a delinquency report.

• MFIs should usually not use arrears rates, whichdivide the amount of late payments by some mea-sure of total portfolio or loan volume, because suchmeasures tend to understate risk.

• Almost all MFIs should follow international bank-ing standards by tracking and reporting portfolio atrisk (PAR): this measure analyzes outstanding bal-ances of late loans as a percentage of total outstand-ing portfolio.

• MFIs with weak information systems may wish touse a simplified PAR based on the number of loanaccounts rather than the amount of account balances.

• When tracking PAR it is useful to age the portfolio:loans are broken down by degree of lateness, usingtime intervals that correspond to the MFI’s paymentperiod and loan management process. Any PAR re-port should specify the time interval(s) being used.

• PAR information, supplemented by analysis of his-torical portfolio performance, can generate a so-phisticated estimate of probable loan losses.

• In judging an MFI’s portfolio quality, PAR infor-mation needs to be interpreted in light of the MFI’swrite-off policy and experience.

• PAR and arrears rates understate risk when a portfoliois growing very rapidly, or when there are long grace pe-riods, unless loans on which no payment has yet fallendue are excluded from the denominator of the ratio.

• To the extent possible MFIs should disaggregatetheir delinquency measurement and reporting byloan product, region, branch, loan officer, and per-haps client characteristics.

Finally, for readers who like really concise summaries, here is the entire long-winded paper boiled down intoa single table:

T a b l e 6 : R e p o r t c a r d f o r c o m m o n d e l i n q u e n c y i n d i c a t o r s

NIN

ETEEN

TEST:* INDICATOR Red Flag Fire Bell Bottom Line Smoke and Mirrors Cash-Flow

On-time collection ratew ith clean-up reportAsian collection rateCurrent collection ratew ith loan loss rate calculationCumulative collection ratew ith loan loss rate calculationArrears rateAged portfolio at riskw ith historical reserve scheduleSimplified portfolio at risk

*Red flag: highlights day-to-day operational issues Fire bell: draws attention to major emergencies Bottom line: permits estimate of actual loan losses likely to result Smoke and mirrors: doesn’t encourage inappropriate loan renegotiation or write-off policy Cash-flow: helps management estimate cash receipts from portfolio in future periods

+ +

--

-

++

+

+

-+

- / +

-+

+

-

-+ +

+

-+

-

-

-+

+

-- / +

- / +

- / +

-+

- / +

--

-

CGAP THE CO NSULTATIVE GROUP T O ASS IST THE P O OREST [A M I CROF I NAN CE PRO GRAM ]

The main text indicated that either a current collec-tion rate or a cumulative collection rate can be usedto estimate an annual loan loss rate, and provided asimplified formula for doing so. This annex pro-vides a more precise treatment of that process.

The formula given in the main text was

1 - CR T

where ALR is the annual loss rate (yearly loan lossesdivided by average outstanding loan portfolio); CRis the collection rate in decimal form; and T is theloan term, expressed in years.

Formula (1) owes its simplicity to an assumptionthat the outstanding balance of a given portfolio isequal to one half of the amount originally disbursedon the loans in that portfolio. How accurate thatassumption is depends on the number of instalmentsin the loans’ repayment schedules. Formula (2) ad-justs for this factor: N is the number of paymentsper loan.

1 - CR N T N + 1

The example presented in section C supposed a col-lection rate (CR) of 92.3 percent. The number ofpayments in a loan cycle (N) was 13, and the loanterm (T) was three months, or 0.25 years. Applica-tion of Formula (2) gives us the same result weworked out above, an annual loss rate (ALR) of 57percent of average outstanding portfolio:

1 - 0.923 13 0.25 13 + 1

Formulas (1) and (2) may overestimate the loss ratesomewhat when the repayment schedule includes along grace period, because in such a case averageoutstanding balance will be well above 50 percentof original principal amount. A similar distortioncan occur if an MFI’s portfolio is growing so fastthat the distribution of loans is heavily skewed to-ward younger loans. In these cases Formula (3) canbe used, where PD is the amount of principal thatwas disbursed under the loans presently in the port-folio, and OB is that portfolio’s outstanding (un-paid) balance.

1 - CR PD T OB

All three of the above formulas depend on the loanterm, expressed in years. In order to use any ofthem, an MFI that offers a variety of loan terms—for instance, some combination of three-month, six-month, and one-year loans—will need to estimate aweighted average loan term. Three methods can beused, depending on the information available.

Most MFIs can determine the average outstandingbalance of their loan portfolio over the course of a

year, by adding the start-of-year balance and theending balances for all the months, and then divid-ing the total by thirteen. Likewise, it is usually easyto determine the total amount disbursed over thecourse of the year. Formula (4) indicates that theweighted average loan term (T) can be estimatedby dividing the average outstanding balance (AOB)by total yearly disbursements (YD) and doublingthe result.

AOB YD

Formula (5) refines this estimate by adjusting it toreflect the average number of payments per loan(N).13

AOB N YD N + 1

Suppose that an MFI’s average outstanding loan bal-ance (AOB) for the year is 250,000 while its loandisbursements for the year (YD) total 900,000. Theaverage number of payments per loan (N) is 12.Formula (5) estimates that the weighted averageloan term (T) is roughly 0.5 years, or six months.

250,000 12 900,000 12 + 1

Finally, average loan term can also be estimated bya simple weighting scheme based on annual dis-bursed amounts for various types of loans. MFIsthat don’t have outstanding balance informationavailable for their loan portfolio would have to usethis method (they needn’t feel bad, because it’s themost accurate one). Suppose that over the courseof a year an MFI disburses about 500,000 in one-year loans and 1,200,000 in three-month loans.

(A) (B) (C)Loan term Annual amount in years disbursed (A) times (B) 1.00 500,000 500,000 0.25 1,200,000 300,000 Total: 1,700,000 800,000

Dividing the total of column (C) by the total of col-umn (B) produces a weighted average loan term of0.47 years, or about six months.

13 The MFI with a variety of loan products will need toestimate an average number of installments per loan(N) in order to use formulas (2) or (5). The authorhas fought off the temptation to burden this annexwith a method for calculating this variable. His ad-vice is simply to look at the portfolio and guess. Miss-ing the mark on the number of installments won’talter the final loan loss estimate very much, since thevalue of N/(N+1) will be close to one unless the num-ber of installments is very small. For instance, in theillustration following formula (2), the actual N is 13,and the resulting loss rate is 57.2 percent. If wegrossly misjudge N and use 20 instead of the truevalue 13, the result of the calculation becomes 58.7percent, hardly a material difference.

TWEN

TY

(1) ALR = x 2

(2) ALR =

x 2 x

(4) T = x 2

(5) T = x 2 x

0.51 = x 2 x

.572 =

(3) ALR = x

R i c h a r d R o s e n b e r g

wrote this paper. Robert

Christen suggested major

improvements. Other helpful

comments came from

Jacob Yaron, Brigit Helms,

Joyita Mukherjee, Gregory

Chen, J.D. Von Pischke, and

especially Mark Schreiner.

Production: Valerie Chisholm;

EarthWise Printing, Gaithersburg,

MD (301) 340-0690.

O c c a s i o n a l P a p e rN o . 3

TWEN

TY

A N N E X : C o n v e r t i n g C o l l e c t i o n R a t e s i n t o A n n u a l L o a n L o s s R a t e s

x 2 x