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Centre Emile Bernheim Research Institute in Management Sciences Perspectives and a Quantitative Model for Structured Microfinance Gregor Dorfleitner and Christopher Priberny We study the perspectives and develop a quantitative model for structured microfinance instruments, which have suffered as a result of the financial crisis of 2008/2009. A survey addressed to relevant world-wide experts on microfinance shows that structured instruments are still regarded as an important means for refinancing microfinance institutions in the future. In a second step we introduce a quantitative credit risk model that takes into account the peculiarities of microfinance institutions and can be used for pricing purposes and analyzing the risk inherence in different tranches of a structured microfinance vehicle. In a realistic application we check the robustness and demonstrate the advantages of the model presented.
CEB Working Paper N° 10/015 February 2010
Université Libre de Bruxelles – Solvay Brussels School of Economics and Management
Centre Emile Bernheim ULB CP 145/01 50, avenue F.D. Roosevelt 1050 Brussels – BELGIUM e-mail: [email protected] Tel. : +32 (0)2/650.48.64 Fax : +32 (0)2/650.41.88
Perspectives and a Quantitative Model forStructured Microfinance
Gregor Dorfleitner∗
Department of Finance
University of Regensburg, Germany
Christopher Priberny†
Department of Finance
University of Regensburg, Germany
February 22, 2010
We study the perspectives and develop a quantitative model for structuredmicrofinance instruments, which have suffered as a result of the financial crisis of2008/2009. A survey addressed to relevant world-wide experts on microfinanceshows that structured instruments are still regarded as an important means forrefinancing microfinance institutions in the future. In a second step we intro-duce a quantitative credit risk model that takes into account the peculiaritiesof microfinance institutions and can be used for pricing purposes and analyzingthe risk inherence in different tranches of a structured microfinance vehicle. Ina realistic application we check the robustness and demonstrate the advantagesof the model presented.
∗e-mail: [email protected]†e-mail: [email protected]
1
1. Introduction
While a few years ago microcredit was mainly seen as a means to reduce poverty and boostthe economies of developing countries, it has now become an increasingly attractive invest-ment opportunity. The investment instruments at hand are stocks, bonds, microfinanceinvestment funds (MFIFs) and microfinance collateralized debt obligations (MiCDOs).1
Taxonomies of structured microfinance vary: According to Byström (2007) structured mi-crofinance is defined as direct and indirect securitization. Direct refers to the securitizationof a microcredit portfolio by the MFI itself. An example is the “BRAC Micro Credit Secu-ritization Series I Trust” by the Bangladeshian MFI BRAC2. As opposed to this, indirectsecuritization means the securitization of a portfolio of debt instruments issued by MFIs.The indirect transactions are more frequent than the direct ones. One example for the in-direct type is the “BlueOrchard Microfinance Securities I” which was the first MiCDO everissued. However, using the example of the European Fund for Southeast Europe (EFSE),Glaubitt et al. (2008) show how structured elements can also be applied to MFIFs. Thissupports the broader definition by Jobst (2007), who identifies three forms of structured mi-crofinance, namely MFIFs, direct securitization or local issuance, and indirect securitizationor external issuance, all of which we comprise by the term “structured microfinance vehicle”(SMFV). In any case the instrument has a CDO-type cash flow structure implying that theSMFV holds a pool of debt instruments on the asset side of the balance sheet and severaltranches on the liability side. The accruing cash flows of the pool are distributed to theinvestors, i.e. the holders of the tranches, according to an a-priori fixed scheme with regardto the different seniorities of the tranches, ranging from the highest ranked senior trancheto equity at the bottom. The first losses in the asset pool affect the equity tranche. Afterthis tranche is eliminated the other tranches are hit.Structured microfinance entails several advantages often cited in literature in the context ofMiCDOs, which we shortly want to summarize in the following.According to Glaubitt et al. (2008) structured microfinance can reduce regulatory capital,as MFIs securitize parts of their loan portfolio. However this holds true only for indirectsecuritizations.MFIs can profit from improved access to capital markets. Compared to commercial bondsthe volume of MFI bond issues is considerably smaller, which makes it more difficult forMFIs to refinance themselves by utilizing the international capital markets. Pooling thesmaller liabilities of MFIs is a means to reach a customary size. Another aspect is thatMFIs are often rated lower than institutions of equal credit risk in developed countries dueto higher country specific risks3, which makes MFI bonds less interesting for institutionalinvestors. By participating in a SMFV the MFI can separate its credit risk from the countryrisk and thereby also attain improved access to capital markets. This improvement allowsMFIs to diversify their founding resources.4 According to Watson (2009) MFIs were financedby middle- to long-term debt with an average share of 36,2% in 2009. If this part of the debtis refinanced only by some few lenders the MFIs can be affected by serious financial distressif one of these is not willing to endure their engagement.
1See Dorfleitner and Leidl (2009) for an overview.2Cf. Hüttenrauch and Schneider (2008).3Cf. Glaubitt et al. (2008).4Cf. Glaubitt et al. (2008).
2
Glaubitt et al. (2008) suggest that MFIs can acquire reputation on international capitalmarkets by joining MiCDOs issued by recognized financial institutions. Due to the tranchingprocess different risk-return profiles can be created from a relatively homogeneous assetpool. This helps to attract new investors, whose individual risk preferences can be metmore easily.5 According to Byström (2008) structured microfinance also helps to overcomethe asymmetric information problem introduced by Akerlof (1970) as “lemon phenomenon”,which is particularly evident in microfinance. Since publicly available information is verylimited for individual investors they in turn demand additional premia for compensation.This problem can be mitigated if the much better informed issuer invests in the equitytranche and hence signals that he is willing to take the most risky part himself.All of these advantages contributed to the development that has made structured products,in particular MiCDOs, the preferred investment vehicle in microfinance in recent years.6
However, due to the global financial crisis, the issuing of structured microfinance productsdid become impossible in 2009 (Littlefield and Kneiding (2009)) and it seemed unclearwhether there was any future to this kind of refinancing instrument. For these reasons wedecided to ask experts on microfinance capital markets on their views on the problems andchances of SMFV. The results of this survey are presented in Section 2. In Section 3 weintroduce a quantitative credit risk model for MFI debt instruments, which can be used forpricing and the risk analyzing of the tranches of a SMFV by performing MC simulation.We develop a modular concept in the sense of an easy-to-use toolbox for SMFV analysis.Section 4 provides an application of this model to a realistic SMFV consisting of a MFI bondportfolio. Section 5 concludes.
2. Survey on structured microfinance
From April 20th, 2009, to July 31st 2009 we conducted a web-based survey asking 132microcredit investment experts on how they judged the market atmosphere of structuredinstruments in microfinance, in particular MiCDOs, with regard to the financial crisis. Theaddressees of the survey were affiliated to larger MFIs, institutions investing in or managingSMFVs. Furthermore we asked a few recommended scientists. We used a standardized onlinequestionnaire to facilitate anonymity. Responses from more than one person per companywere allowed. We collected 35 responses, which is a relatively high response rate of 26,5%.The descriptive analysis is done via the standard measures mean, median, standard devia-tion, minimum and maximum. In some of the questions we ask for the level of agreementto presented theses. Thereby the different levels of agreement follow a numeric rating scale.The explicit coding is shown in Table 13 in the Appendix. Additionally to the purely de-scriptive view, we apply the Wilcoxon signed rank test7 to test for significance. Regardingthe 35 responding experts as a representative sample, the test allows us to make conclusionson the whole microfinance investment scene. Whereas most questions asked the participantsfor agreement or disagreement with the theses presented we test for both directions (agree-ment or disagreement) with a significance level of α = 5% and the comparative neutral valuecorresponding to the null hypothesis. The detailed results of these tests are shown in Tables
5Cf. Byström (2008).6Cf. Jobst (2008).7Cf. Crawley (2007).
3
11 and 12 in the Appendix.The summary of the analysis is presented in Table 1. According to our survey the imageof MiCDOs in 2009 is not as bad as we had expected. We cannot find any significantevidence suggesting that MiCDOs were seriously damaged by the financial crisis. However,it should be noted that in all questions regarding this instrument the participants in oursurvey are sharply divided into two groups. The thesis of MiCDOs being the most promisingrefinancing instrument in microfinance can not be supported. Nevertheless, in the secondsection of the questionnaire we present eight reasons for the outstanding image of MiCDOs inthe past few years. The survey significantly confirms five of them, namely improved accessto capital markets by pooling smaller liabilities, reputation building, creation of differentrisk-profiles through the tranching process, diversification of funding resources and solutionfor the asymmetric information problem.Even if the image of MiCDOs is expected to recover fully within the next 3 years there isevidence that they will be replaced as preferred structured investment vehicle in microfi-nance. One possible alternative is (significantly) seen in structured investment funds, likethe European Fund for Southeast Europe (EFSE), which also uses elements like trancheswith different seniority. The following refinancing instruments were also confirmed as im-portant within the next two years: Deposits, donors, classical MFIFs, structured MFIFs andprivate equity.We also asked the experts on how critically they see different aspects of CDO modelingin the context of the financial crisis. With the exception of dependency modeling, everyaspect is significantly seen as critical, namely misspecified ratings of underlyings, the PDterm structure modeling, the significance of a tranche’s rating8, complex structure. This isa little surprising since dependency modeling is in general seen as a very critical aspect ofCDO rating and pricing, because it is often said to be one of the central aspects that led toa false estimation of the risk profiles of subprime credit CDOs.9 However, there is significantconfirmation of the dependency modeling issue on the 10% level.
8This relates to the fact that risk profiles of CDO tranches have often been compared to those of equallyrated bonds. By doing so one ignores that CDO tranches react much more sensitively to systematicmarket changes than bonds. See Hamerle et al. (2008).
9Cf. Choros et al. (2009).
4
Question
mean
med
ian
sdmin
max
NA
Nsign
.(α
=5%
)
1.0
How
impo
rtan
tis
therole
ofCDOsin
microfin
ance?
5.3714
61.89
561
80
352.0
Pleaserate
thefollo
wingad
vantag
esof
CDOsin
thecontextof
microfin
ance!
2.1
Regulatorycapitalrelief
3.0000
31.12
821
51
342.2
Solution
fora
symmetricinform
ationprob
lem
(e.g.originator
keepse
quity
tran
che)
3.3824
41.10
141
51
34agreem
ent
2.3
Improved
access
tocapitalm
arkets
bypo
olingsm
allerlia
bilities
4.02
944
0.9370
15
134
agreem
ent
2.4
Reputationbu
ildingforMFIs
withrecogn
ised
tran
sactionpa
rtners
3.5000
41.16
121
51
34agreem
ent
2.5
Improved
access
tocapitalm
arkets
bysepa
rating
cred
itrisk
from
inferior
risk
likecoun
tryrisk
3.1765
31.14
071
51
34
2.6
Creationof
diffe
rent
risk-profiles
throug
hthetran
chingprocess
4.2647
40.96
321
51
34agreem
ent
2.7
Diversific
ationof
fund
ingresources
4.20
594
0.9138
15
134
agreem
ent
2.8
Fees
3.1515
30.9722
15
233
3.0
How
critically
doyo
useethefollo
wingaspe
ctsof
CDO
valuationin
contextof
thesubp
rimecrisis?
3.1
Misspecified
rating
ofun
derlying
s4.0645
40.96
392
54
31critical
3.2
Dep
endenc
ystructuremod
eling
3.2903
30.97
271
54
313.3
Term
structuremod
eling
3.4194
40.76
481
44
31critical
3.4
Sign
ificanceof
atran
che’srating
3.7097
40.9016
15
431
critical
3.5
Com
plex
structure(e.g.CDO
2.triggers)
4.0323
41.07
961
54
31critical
4.0
Istheim
ageof
MiCDOsseriou
slyda
mag
edby
thecurrentfin
ancial
crisis?
3.0000
31.03
281
54
315.0
Wekn
owthat
projects
oflaun
chingnew
MiCDOsha
vebe
enstop
ped.
Are
MiCDOscurrentlydead
?2.7742
31.25
721
54
31
6.0
Doyo
uthinkMiCDOswill
recoveragain?
When?
Within...
2.2333
21.04
001
55
30within3years
7.0
Cou
ldinvestmentfun
dswithstructured
elem
ents
liketran
ching.
waterfall
structure...
beasustaina
blealternativeto
MiCDOs...?
4.0968
40.83
092
54
31agreem
ent
8.0
How
impo
rtan
twill
thefollo
winginstruments
becometo
prov
idecapitalfor
Microfin
ance
Institutions
(MFIs)withinthenext
twoyears?
8.1
MiCDOs
5.45
166
2.2337
18
431
8.2
bond
-placement
5.61
296
1.7640
39
431
8.3
depo
sits
7.4516
71.2066
59
431
impo
rtan
t8.4
dono
rs6.90
327
1.8139
39
431
impo
rtan
t8.5
classicalM
FIFs(M
icrofin
ance
InvestmentFu
nds)
7.3226
71.1941
59
431
impo
rtan
t8.6
structured
MFIFs
6.7097
71.75
492
94
31im
portan
t8.7
privateequity
6.38
716
1.7258
39
431
impo
rtan
t
Tab
le1:
Que
stiona
irean
dresultsof
thesurvey.The
last
columnindicatessign
ificanc
y
5
3. A quantitative model for structured microfinance
Default risk modeling of a microcredit portfolio in general should consider the peculiaritiesof microcredits, namely the small nominal amounts for each loan, the aim of stimulatingproductive activities and the often missing collateral. Further properties that can often beobserved empirically are high interest rates, low default rates, a greater number of loansassigned to women than men and lower default rates for female borrowers.However, since most of the SMFVs like MFIFs and MiCDOs are indirect investment in-struments, we restrict our quantitative model to a portfolio of debt instruments of MFIs.Therefore the above-mentioned properties are only of indirect importance and we ratherhave to capture peculiarities of MFIs as obligors, namely the low correlation with worldwidestock markets10, a large variety in profitability, and a possible geographical dependence ofMFIs active in the same region induced for example by climatic risks11. In our model wetry to capture these properties.The model that we develop in this section serves the purpose of being the basis for MonteCarlo simulations, i.e. applying the model for risk analysis or the valuation of tranches isdone by simulating cash flows of the structured instrument according to the model.First we will develop a basic version of the structured instruments’ cash flow model. In asecond subsection we will discuss variations and extensions of this model.
3.1. The basic model
We start with a set of n obligors (MFIs) whose debt instruments (loans or bonds), which werefer to as the asset pool, are held by the structured instrument. All cash flows originatedby the asset pool are distributed to the tranche owners via an a-priori fixed distributionscheme following the so-called waterfall principle. As the cash flows of the asset pool in turndepend only on the possible defaults of the obligors, the default times of the asset pool andtheir dependency structure are crucial for an exact description of cash flows received by thetranche owners.
Modeling dependent default times Our considerations build on the modern approachpresented by Bluhm and Overbeck (2007), which is based on copulae as frequently demandedby various authors12 and often used for valuation purposes13.The model can be summarized as follows. The PD term structure captures the probabilityof default over time and is obligor specific. We denote the PD term structure of obligor i byt 7→ Fi(t) := PD
(t)i with i = 1, . . . , n. This function captures the probability that obligor i
defaults within the given time interval [0, t]. The question of how to specify the PD termstructure is treated below. The stochastic default time τi of obligor i is now defined by
τi = F−1i [N(CWIi)] (1)
10Cf. Krauss and Walter (2008).11Cf. Churchill and Frankiewicz (2006).12Cf. Bluhm and Overbeck (2007), Choros et al. (2009), Lando (2004), Lucas et al. (2006), Schönbucher
(2003)13Cf. Mounfield (2008).
6
where F−1i is the inverse of Fi and CWIi is a time-independent latent random variable
called the credit worthiness index corresponding to obligor i. The symbol N denotes thecumulative distribution function of the standard normal distribution.To capture the default dependence between the obligors the variable CWIi is modeledlinearly dependent on a systematic and an idiosyncratic risk component. The systematicfactor is denoted by Ψc, which can be interpreted as a macroeconomic measure of the countryc. This means that
CWIi = αiΨc(i)︸ ︷︷ ︸system. risk
+ εi︸︷︷︸idiosync. risk
(2)
with c(i) denoting the country to which obligor i belongs and
Ψc(i) ∈ {Ψ1, . . . ,ΨC} .
The parameter αi is determined as the square root of the R-squared obtained by a linearregression of the obligor’s i asset returns against the returns corresponding to the same timeinterval of the macroeconomic variable.It is assumed that the residuals εi are independent and identically distributed and also inde-pendent of the systematic factor Ψc(i). For the calculation of the default time τi accordingto equation (1) the variable CWIi must be standard normally distributed. To this end wemake specific assumptions concerning the distributions of systematic factor and residuals,namely
Ψc(i) ∼ N(0, 1) and εi ∼ N(0, 1− α2i ) . (3)
Note that by the construction given the CWIi follows a standard normal distribution andN(CWIi) follows a uniform distribution on [0, 1].It is common practice in credit risk modeling to use a country specific stock index as macroe-conomic variable Ψc(i).14 However, this approach is not suitable for the context of microfi-nance for the following reason. According to Krauss and Walter (2008), who used MFI-datafrom 1998 to 2006, one can expect a very low dependence between the returns of MFIs andcountry specific or even global stock indices. Krauss and Walter (2008) also indicate thatstock indices of developing countries are often dominated by only a few larger companies andtherefore poorly reflect the country’s economical development and are often not publishedby financial data providers like e.g. Thomson Financial Datastream.Therefore, in our context using stock indices (if available) as systematic factors would resultin αi estimates close to zero, which in turn leads to an approximate independence between thedifferent obligors. This would have a distorting impact on the model, because diversificationeffects would be overestimated.As a solution to this problem we suggest a self-constructed MFI index for each country. Inparticular, a capital-weighted return-on-equity index ROEX(t) seems to be a good alterna-tive. The calculation is as follows:
ROEX(t) =
I∑i=1
E(t)i∑I
j=1E(t)j
ROE(t)i (4)
14Cf. Bluhm and Overbeck (2007).
7
with E(t)i representing the book value15 of obligor’s i equity and analogously ROE
(t)i as
the rate of return on equity. The alpha factors of the MFIs with respect to each country’sROEX can be derived via linear regression, where αi equals the square root of the regression’sR-squared16.Furthermore we take into account the dependency structure of the systematic factors byassuming a multivariate normal distribution NC with covariance matrix ΓC .
Cash flow distribution As already mentioned, the owner’s cash flows are determined by thedependent default times τi of the asset pool’s debt instruments and the SMFV’s distributionscheme. Every debt instrument in the portfolio has a particular cash profile depending onwhether and when it defaults. A typical bond’s profile may for instance be the following.
• If no default occurs during time to maturity then the coupon payment takes place inevery period t (including T ) as well as the repayment of the nominal at maturity T .
• If a default occurs during time to maturity then the coupon payments in the periodsbefore default time τi take place but no more payments17 afterwards.
The distribution scheme works as follows. The pool’s incoming cash flows are distributedtop-down according to every tranche’s seniority. This means that after deducting a non-obligatory management fee the remaining cash flows are used to pay each tranche an a-priori committed payment following the cascade-principle. The cash remaining is retainedby the equity tranche. Consequently, the equity tranche suffers the first losses caused bydefaulting obligors before the more senior tranches are affected. Due to the focus on cash-based instruments in microfinance18, realizing losses is equivalent to a reduction of a tranche’snominal value.The remaining nominal of tranche TR at time t is defined as N (t)
TR and can be described withregard to the upper attachment points UAPTR and lower LAPTR attachment point and the(cumulated) portfolio loss L(t)
P at time t:
N(t)TR = N
(0)TR − L
(t)TR (5)
with N(0)TR = (UAPTR − LAPTR) ·N (0)
P
and L(t)TR = min[(UAPTR − LAPTR) ·N (0)
P ,max(L(t)P − LAPTR ·N (0)
P , 0)]
The variable N (0)P is the nominal value of the portfolio at time of initiation and L
(t)TR the
realized tranche loss at time t.According to the seniority and therefore to the inherent risk a fixed rate is arranged initiallybetween the SPV and the tranche owners. Then the pool’s cash flow is distributed eachperiod t, here quarters, in the following way.
15As the market value of MFI equity is often not observable due to the lack of public trading, we use thebook value as a proxy.
16Cf. Bluhm and Overbeck (2007, p. 125).17We do without a recovery payment in order to keep things simple. But for more precise results we
recommend implementing a microfinance specific recovery rate.18Because the raising of funds and not regulatory benefits is in the center of interest.
8
First of all management fees are conducted, then the senior tranche ST receives a paymentwhich equals the fixed tranche rate rST times the remaining nominal N (t)
ST . Then the re-maining cash is used to pay the following tranches analogously according to the waterfallprinciple. The equity tranche instead receives the complete cash that remains after thedistribution. Additionally, at maturity every tranche’s remaining nominal is repaid.One advantage of the model is the modular concept. Thus one can easily implement differentspecifications for the PD term structure and the dependence modeling. In the next subsectionwe present some model extensions.
3.2. Further model elements and extensions
Copulae as an alternative for modeling dependency structures In credit risk, particularlyin CDO-modeling, copula based approaches have become popular in recent years.19 Onereason for this development is that according to the Sklar (1959) any multivariate distributioncan be described by its marginals and a suitable copula function which allows modelers touse distributions closer to the real one as standard approaches.Here we present two important copula functions and show how these can be integrated inthe model.20
Gaussian copulaThe Gaussian copula is equivalent to the multivariate normal distribution Nm used in thecore-model with correlation matrix Γ in which the inverses of the univariate normal distri-bution N−1 are inserted.
Cn,Γ(u1, . . . , un) = Nn[N−1(u1), . . . , N−1(un); Γ] (6)
Gaussian copulas are often used21 as they are easy to implement, because the correlationmatrix Γ is the only parameter to be estimated. Because of the lack of tail dependencethe use of Gaussian copulas could lead to errors in cash flow mapping, as the probability ofextreme events is underestimated.Student-t copulaAs the Student-t copula equals the multivariate t-distribution ΘΓ,d with correlation matrixΓ and d degrees of freedom in which the inverses of the univariate t-distribution Θ−1
d havebeen inserted, it entails fatter tails. This copula is defined as:
Cn,Γ,d(u1, . . . , un) = Θn,Γ,d[Θ−1d (u1), . . . ,Θ−1
d (un)] . (7)
With increasing d the Student-t copula converges to the multivariate normal distribution.The integration into our model is done using the link function22
CWIt−copulai =
√d · (αiΨi + εi)︸ ︷︷ ︸
CWIi
/√X with X ∼ χ2(d) . (8)
19Cf. Bluhm and Overbeck (2007), Choros et al. (2009), Lando (2004), Mounfield (2008), Lucas et al. (2006),Schönbucher (2003).
20The notation used is based on Bluhm and Overbeck (2007).21Cf. Choros et al. (2009), Finger (2000), Bluhm and Overbeck (2007).22Cf. Bluhm and Overbeck (2007, p. 127).
9
and CWIi defined as the original latent variable of the basic model (2) are mixed with ad-ditional χ2(d)-distributed random variables.23 As CWIt−copula
i is now Student-t distributedequation (1) is modified to
τi = F−1i [Θd(CWIt−copula
i )] . (9)
Specification of the PD term structure As mentioned above the PD term structure t 7→PD
(t)i describes the distribution of the default times of obligor i. Markov chains are often
used in this context because they allow us to model the future dependent solely on the lastobserved state.24 We present two different approaches using Markov chains.The first and most straight-forward approach is the exponential distribution in the formof
PD(t)i = 1− e−t·PDi (10)
where PDi is an default intensity parameter capturing the continuous propensity to default.The idea behind this formula is that the probability of default of obligor i for a given timehorizon is constant no matter how long the preceding history without a default is.A second approach is the time-homogeneous, continuous Markov chain approach HCTMCapproach presented by Bluhm and Overbeck (2007). It is a generalization of the exponentialdistribution term structure where we only have two states (default, non-default). HCTMCcaptures changes in the obligor’s creditworthiness represented by rating changes. This featureis an important advantage because rating changes can be observed very often as opposedto real defaults. We start considering a rating migration matrix as published every year byall major rating agencies25. As an example Table 2 displays the rating migration matrix ofFitch Rating.
AAA AA A BBB BB B CCCtoC DefaultAAA 94.90 5.10 0.00 0.00 0.00 0.00 0.00 0.00
AA 0.08 91.65 7.84 0.35 0.02 0.02 0.00 0.04A 0.02 2.34 92.48 4.73 0.21 0.07 0.06 0.09
BBB 0.00 0.24 4.29 90.70 3.71 0.53 0.24 0.28BB 0.03 0.06 0.16 8.53 80.63 7.20 1.83 1.55
B 0.00 0.00 0.26 0.72 10.62 82.07 4.34 1.99CCCtoC 0.00 0.00 0.00 0.27 1.08 19.46 54.59 24.59
Table 2: Fitch’s global rating migration matrix for the period 1990-2008 (data in %) accord-ing to FitchRating (2009)
Every line displays relative frequencies of one-year rating migrations based on corporate bonddata from 1990 to 2008. We use these historical rating migrations as a proxy for the real
23The calculation of CWIi is the same as in the basic model. So the ROE factors are still multivariatenormally distributed and the assumptions on the parameter distributions (Equation 3) are valid as well.
24Cf. Kreinin and Sidelnikova (2001), Bluhm and Overbeck (2007).25These are Fitch Rating, Standard & Poor’s, Moody’s Investor Service.
10
transition probabilities from the rating in the first column to the other rating classes. We arestill interested in the continuous PD term structure by taking into account the probabilitiesof different stages between the default.Since we consider a continuous time setting we need to calculate a Markov generator Q thatsatisfies the following equation26:
MM (1) != exp(Q ∗ 1) . (11)
The PD term structure PD(t)i is then derived by27:
PD(t)i = [exp(tQ)]l,m (12)
where l is the row of the initial rating of obligor i and m is the last column, which repre-sents the default stage. Figure 1 shows the PD term structures derived from Fitch’s ratingmigration matrix for all of the initial rating classes.
Risk-neutral tranche pricing The basic model does not yet make any statements on thevaluation or on determining the spreads of the different tranches. In this subsection wedevelop a possible extension for calculating credit spreads for senior and mezzanine tranchesof a SMFV on the assumption that they are supposed to be priced to par.It is well-known that investors demand risk premia for accepting credit risk. There are severalways to take these risk premia into account. The standard approach in derivative pricing isto use a risk neutral probability measure and then to take expectations. This methodologythat is based on arbitrage-free pricing is also standard in CDO valuation in the form of riskneutral probabilities of default. According to Duffie and Singleton (2003, p. 101) the riskneutral probabilities of default are chosen in a way such that the market price equals thepresent value of the expected cash flows discounted with the risk free interest rate. It shouldbe indicated that the PD term structures introduced in the previous subsection describe thephysical, actually observable values, which are remarkably lower than the risk neutral onesbecause the demanded risk compensation has to be covered. When doing MC simulationand pricing a tranche we can discount the cash flow profile of each path derived by using arisk neutral PD term structure simply with the risk free interest rate. In a second step, anaveraging over all paths approximates taking the expectation and thus yields the price of aspecific tranche.Bluhm and Overbeck (2007, p. 268) show a way of deriving the risk neutral PD(t)
i,rn from
any physical PD term structure PD(t)i with regard to a proxy for the obligor’s i one year
risk neutral PD(1)i,rn by
PD(t)i,rn = N
[N−1(PD
(t)i ) + [N−1(PD
(1)i,rn)−N−1(PD
(1)i )]√t]. (13)
The proxy PD(1)i,rn can be derived from suitable spreads of one-year credit default swaps.
This suggestion is a comfortable way to get a hold of risk neutral PD term structures inline with the HCTMC-approach, but it causes some hurdles that are difficult to overcome in
26For an overview of how to calculate Markov generators see Kreinin and Sidelnikova (2001).27Cf. Bluhm and Overbeck (2007).
11
0 10 20 30 40 50
0.0
0.2
0.4
0.6
0.8
1.0
Time in years
PD
term
stru
ctur
e
CCC to C
B
BB
BBB
A
AA
AAA
Figure 1: PD term structures based on the HCTMC approach using Fitch’s rating migrationmatrix(Tabelle 2)
an empirical application, especially in microfinance, due to the lack of corresponding CDSdata. As there are no CDS for MFIs, further assumptions are necessary.Using the PD(t)
i,rn a tranche is priced, if the present value of the expected loss equals theexpected cash flows caused by the spread.
T∑t=1
δ(t)E(L(t)TR − L
(t−1)TR ) =
T∑t=1
δ(t)STRηE(N(t)TR) (14)
where STR is the spread of tranche TR, η is the payment period28 and δ(t) is the discountfactor. The expected values E(.) are calculated as mean of the simulation data.Solving equation (14) for STR leads to:
STR =
∑Tt=1 δ
(t)E(L(t)TR − L
(t−1)TR )∑T
t=1 δ(t)ηE(N
(t)TR)
(15)
28In the following we set the payment period to 0.25, which equals 4 interest payments per year.
12
Risk analysis Given a specific SMFV with fixed spreads of the tranches and given aninterest rate term structure one can still price tranches of the instrument by using the aboverisk-neutral pricing approach. However, we rather suggest using the real-world PD termstructure and considering the risk explicitly for several reasons: CDS spreads for derivingrisk neutral PDs are not available for MFIs. One can use a proxy for the same rating classbut then the MFI is forced into resembling companies from a completely different industry.The risk neutral approach assumes no-arbitrage pricing which is not possible with the illiquiddebt titles of MFIs. Furthermore microfinance investors need not necessarily behave in aneoclassical way. They might want to have a look at the complete risk profile of a trancheand then set their price and the risk premium individually. They also might include a socialreturn in their considerations29.For that purpose we use a MC based risk analysis in the spirit of Hertz (1964), were we usedifferent risk measures such as the Value-at-Risk (VaR) and the shortfall probability withregard to the internal rate of return (IRR). Furthermore we can take into consideration thewhole IRR distribution. In addition to pricing purposes this analysis is a well-suited toolfor making inherent risks apparent and therefore it can be used in risk management.
Check for robustness It is clear that the estimation of the input parameters, in particular ofthe correlation matrix Γ, may suffer due to relatively short time series for MFIs. Additionally,it can also be less reliable because it is taken from balance sheet data that may be biased.For this reason we suggest checking the robustness of the model against an erroneous Γ byadding a random error to the ROEX indices. This can be achieved in our simulation basedapproach by interfering one randomly chosen value in the dataset in the following way:
˜ROEX(t)c = ROEX(t)
c · eΘ (16)
where Θ is a normal distributed random variable. With this extension we are in line withWilmott (2009) who requires financial models to be made more robust as one lesson learnedfrom the financial crisis of 2008/2009. Furthermore one can use the difference in the resultingIRR distributions to derive a risk premium for the model risk inherence. We regard this as aresponsible way of dealing with the still evident problem of data availability in microfinance.
A multi-factor extension incorporating climatic risk In credit risk modeling it is alsocommon to extend equation (2) with industry factors. Since MFIs belong to only oneindustry the more important question would be whether MFIs lend their money mostly toone type of entrepreneurial activity. The most important type could be agricultural activity,where we have a strong influence of the weather. Therefore it is natural to assume the creditrisk of MFIs as dependent on the credit exposure in the agricultural sector, which in turn isdependent on the weather. In this sense we suggest a multi-factor extension also comprisinga local weather index variable, namely
CWIi = αi
wi ·Ψc(i) + vi · Ξc(i)√w2i + v2
i + 2wiviCORR[Ψc(i),Ξc(i)]+ εi (17)
29Cf. Dorfleitner et al. (2009).
13
with Ψc(i) ∼ N(0, 1), Ξc(i) ∼ N(0, 1), εi ∼ N(0, 1 − α2i ) and Ξc(i) representing the weather
index for country c(i). The weights wi and vi represent the strength of the influence of bothfactors. We let wi equal the incremental contribution of factor one to the R-squared of aregression of the ROEX on both factors divided by the corresponding incremental contribu-tion of factor two and vi equal to 1. This is a generalization of the approach by Bluhm andOverbeck (2007), who set both weights equal to 1. As above, αi is the root of the R-squaredof the regression comprising both factors.
The model does not necessarily need to be restricted to a special weather index. However,according to World-Bank (2005) growing degree days are a common index in the agriculturalsector and a biologically accurate measure for growing activity of grains and fruits. Thereforewe use a growing-degree-day index regarding the following structure:
GDD =T∑t=1
max(Tempt − L; 0) (18)
with Tempt denoting the daily average temperature, L the critical threshold temperatureunder which no growing activity is observable, and T the number of days in the year underconsideration.
4. Empirical Application
In this section we show how the model developed in the previous section can be used in arealistic application. For that purpose we arrange a SMFV like a plain vanilla CDO or astructured MFIF. In this example we first derive the risk neutral tranche spreads for theupper tranches. As we see, this part cannot be carried out without extensive assumptions.Nevertheless we use those in the next steps, where we show the risk inherence in each trancheby analyzing the simulated internal rate of returns (IRR) on the basis of the one and twofactor case and check for the robustness of the model.To keep the example simple, the SMFV considered consists only of senior, mezzanine andequity tranche. The exact structure and the attachment points are shown in table 3.
Tranche lower attachement point upper attachement pointsenior 0.350 1.000mezz. 0.125 0.350equity 0.000 0.125
Table 3: Structure of the SMFV
For the underlying asset pool we assume that it consists entirely of bullet bonds with identicaltime to maturity to the SMFV, namely five years with quarterly interest payments. Theobligors are existing Latin American MFIs having been assigned a commercial rating of FitchRatings which is necessary for applying the HTCMC-approach.30
30For unrated MFIs we would recommend using the exponential PD term structure with estimated one yearPDs.
14
MFI Country Fitch Rating Exposure LGD R-squared PDrn (1 Year) CouponAgroCapital BO BBB 2,000 1 0.68094 0.00638 0.05912BancoSol BO A 3,400 1 0.82168 0.00374 0.05612CRECER BO BBB 1,100 1 0.84264 0.00638 0.05901FIE BO A 4,500 1 0.52401 0.00374 0.05613Fundación MI-CROS
GT B 7,500 1 0.14992 0.03151 0.10961
CompartamosBanco MX AA 10,000 1 0.09191 0.00223 0.05132BANEX (Ex FIND-ESA)
NI BBB 4,600 1 0.01467 0.00638 0.05907
FAMA NI BBB 4,900 1 0.52147 0.00638 0.05895EDPYME CrearArequipa
PE B 7,000 1 0.62926 0.03151 0.10949
SUM 45,000
Table 4: Portfolio structure of the SMFV (Exposure in 1000 USD)
The portfolio of MFI bonds is displayed in Table 4. The information on the MFIs stems fromMixMarket, a web-based platform providing lots of data on MFIs. Each debt instrument’sshare of the pool is chosen with respect to the obligor’s rating and the aim of balancingthe overall investment per country. We take a USD investor’s perspective and realisticallyassume that the bonds are issued in USD. Since MFIs are not expected to have lots ofaccessible collateral we assume recovery payment of zero, which equals a loss given default(LGD) of 1. This assumption can of course easily be relaxed. The R-squared is derived bylinear regression with the MFIs ROE as dependent and the ROEX index (see table 5) asan independent variable. The risk neutral 1-year PDs are estimated from Itraxx-Data ofequivalent rated CDS provided by Giaccherini and Pepe (2008)31. As the Itraxx contains noB rated CDS the corresponding risk neutral PD is estimated by regression with log PDs andextrapolation. Finally we assume the single bonds to be priced at par and therefore derivethe coupons on the basis of simulation.The pool’s cash flows after deducting a realistic management fee of 1,3119% p.a.32 aredistributed following the cascade principle according to seniority: The upper tranches receivethe risk free interest rate (2,79% p.a.)33 plus spread on the remaining nominal and theequity tranche acquires the residuals. At maturity each tranche receives up to the remainingnominal.The ROEX indices are calculated based on all MFIs for which information about equityand ROE has been available from MixMarket for at least two years. Our results for Bolivia(BO), Guatemala (GT), Mexico (MX), Nicaragua (NI) und Peru (PE) are shown in table 5and the corresponding correlation matrix ΓC in table 6 which is required as a parameter ofthe multivariate normal distribution.As we wish to model the PD term structure according to the HCTMC-approach we need toderive a Markov generator Q with regard to Fitch’s rating migration matrix (see table 2).31In particular we used the mean of risk neutral PDs of equal rated CDSs. This step is quite critical as we
“mix” the Risk neutral PDs of different industries, which shows once again the problems inherent in thismethod.
32This equals the EFSE’s management fees in 2007 with regard to European Fund for Southeast Europe(2007).
33This is equivalent to the 5 year Treasury bond yield curve for 11.06.2009 (Source: Thomson Datastream).
15
ROEX(BO) ROEX(GT) ROEX(MX) ROEX(NI) ROEX(PE)2007 0.159644 0.095693 0.302575 0.190256 0.2590062006 0.130380 0.061891 0.309043 0.217373 0.2712052005 0.131750 0.021587 0.289835 0.226171 0.3163582004 0.145820 0.065640 0.365253 0.172658 0.2660862003 0.130886 0.063580 0.527800 0.117495 0.2745902002 0.056725 0.095500 0.495148 0.099309 0.3399202001 0.007760 0.042900 0.363944 0.113040 0.2142622000 0.007808 0.049900 0.444282 0.139155 0.1444591999 0.051953 0.229200 0.163467 0.140115 0.077709
Table 5: Country specific ROEX
ROEX(BO) ROEX(GT) ROEX(MX) ROEX(NI) ROEX(PE)ROEX(BO) 1.0000 -0.1449 -0.1121 0.6502 0.5359ROEX(GT) -0.1449 1.0000 -0.5219 -0.2423 -0.6102ROEX(MX) -0.1121 -0.5219 1.0000 -0.5357 0.4663ROEX(NI) 0.6502 -0.2423 -0.5357 1.0000 0.2159ROEX(PE) 0.5359 -0.6102 0.4663 0.2159 1.0000
Table 6: Correlation matrix ΓC of the ROEX
We do this by following Kreinin and Sidelnikova (2001)34.Now that the structure of the SMFV and its input parameters have been clarified, we analyzethe generation of different cash flow scenarios with Monte Carlo simulation. We start withderiving the tranche spreads based on risk neutral pricing. For this purpose, the followingsteps have to be taken:
1. Derive the risk neutral PD term structure of each MFI i from the physical PD termstructure calculated by the HCTMC approach and the risk neutral one-year PD byfollowing (13).
2. MC-simulate the pool’s cash flows in the following way:
a) Generate the random variables εi and Ψ1, ...,ΨC with regard to the multivariatenormal distribution of systematic factors NC with covariance matrix ΓC .
b) Calculate the CWIi.
c) Calculate the dependent default times τi by inserting the CWIi into the inverseof the risk neutral PD term structure.
d) Derive the pool’s cash flows determined by the default times τi.
3. Calculate each tranche’s expected remaining nominal value N (t)TR following equation
(5) and occurring losses for each t. Repeat 2. and 3. many times.
34In particular we used the “weighted adjustment” for its superior adaptability compared to “diagonal ad-justment”.
16
Histogram of IRR: Senior tranche
IRR
Fre
quen
cy
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0e+
002e
+05
4e+
056e
+05
8e+
051e
+06
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
−10
−5
05
Log−Histogram of IRR: Senior tranche
IRR
Log−
dens
ity
Histogram of IRR: Mezz. tranche
IRR
Fre
quen
cy
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0e+
002e
+05
4e+
056e
+05
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
−8
−6
−4
−2
02
Log−Histogram of IRR: Mezz. tranche
IRR
Log−
dens
ity
Histogram of IRR: Equity tranche
IRR
Fre
quen
cy
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0e+
002e
+05
4e+
056e
+05
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
−10
−5
0
Log−Histogram of IRR: Equity tranche
IRR
Log−
dens
ity
Figure 2: Histograms and Log-Histograms of the IRRTR (Basic Model)
17
4. Calculate the risk-neutral spreads for the senior and mezzanine tranche according toequation (15).
To achieve an appropriate approximation to the real distribution we used 106 simulationruns. As result of our simulation we receive these calculated spreads: 15.1 bp for senior and397.2 bp for the mezzanine tranche. In the following we assume these spreads to be existentand analyze the risk inherence in the different tranches of the SMFV. It should be mentionedonce again that we use the real-world PD term structure for this purpose as opposed to therisk-neutral pricing approach.In order to simulate the tranches’ cash flows with regard to (pseudo-)random multivariatedefault times the following steps have to be conducted:
1. Generate the random variables εi and Ψ1, ...,ΨC with regard to the multivariate normaldistribution of systematic factors NC with covariance matrix ΓC .
2. Calculate the CWIi following equation (2).
3. Calculate the dependent default times τi by inserting CWIi into the inverse of thereal-world PD term structure.
4. Derive the pool’s cash flows determined by the default times τi.
5. Calculate each tranche’s cash flows depending on the distribution scheme and the IRRof each tranche. Repeat 1. to 5. many times.
Tranches “VaR (90%)” “VaR (99%)” SFP (< 0) Min. 1st Qu. Median Mean 3rd Qu. Max.senior 0.02980 0.02980 0.00042 -0.16490 0.02980 0.02980 0.02975 0.02980 0.02980mezz. 0.02922 -0.14229 0.02273 -1.00000 0.06942 0.06942 0.05600 0.06942 0.06942equity -0.13925 -0.24698 0.23540 -0.93780 0.04819 0.22150 0.13700 0.22150 0.22150
Table 7: Simulation results basic model: Risk measures and descriptive analysis of the IRRsof the tranches
In Table 7 we present the “VaR” of the IRRs at the 99% and the 90% level and also theprobability of receiving an IRR smaller than 0% (also shortfall probability or SFP) as resultsof our simulations. In addition it shows the standard descriptive measures of the IRRdistribution for a better overview. Figure 2 shows histograms of the entirely IRR distributionfor each tranche and—as losses occur rather rarely—also in logarithmic form. The reasonfor the mininmal IRR of mezzanine tranche being smaller than that of the equity trancheis caused by the distribution scheme in addition to the small and very heterogeneous assetpool. Thus the equity tranche can, in contrast to the mezzanine tranche, in very rare cases,still receive cash flow payments even if it has already completely defaulted upon. The reasonis that in these cases only higher rated obligors have defaulted and lower rated bonds arestill paying high interest rates.In the next step the model presented is checked for robustness against Γ errors. Thereforewe interfere each set of 500 MC simulation runs with a random entry of the REOX indicesaccording to (16) with re-estimating Γ in each run. For this reason, we set mean and standarddeviation of Θ equal to 0 and 0.1. For performance reasons we reduce the number of MC
18
runs for each of the 500 cases to 105.The resulting barplots representing the different realizations of risk and descriptive measuresare shown in Figures 4 and 5 in the Appendix. For a better overview we present the spanbetween minimum and maximum realization of each measure in Table 8. Note that only therealizations of the minimum differ by more than 1% for all tranches. Furthermore, remarkablespans are only observable for the equity tranche’s first quartile and the mezzanine’s tranche“VAR (99%)”. This indicates that our model reacts robustly to measurement errors in ROEXvalues.
senior mezz. equityVAR (99%) 0.00000 0.08875 0.00000VAR (90%) 0.00000 0.00068 0.00625SFP 0.00043 0.00409 0.00955Min. 0.17172 0.04020 0.573101st Qu. 0.00000 0.00000 0.02654Median 0.00000 0.00000 0.00000Mean 0.00003 0.00124 0.003203rd Qu. 0.00000 0.00000 0.00000Max 0.00000 0.00000 0.00000
Table 8: Simulation results robustness check: Span of realization of different risk and de-scriptive measures (values ≥ 1% in bold print)
In the following we demonstrate the implementation of a second factor. We use the GDDindex for each obligor’s country calculated according to (18) with L equaling 10◦ Celsiusbased on the average daily temperature of weather stations in the following cities: SantaCruz (BO), Guatemala (GT), Mexico-City (MX), Managua (NI), Lima (PE).35 The resultingGDD indices are shown in Table 14 and the correlation matrix Γtwofactors in Table 15 in theAppendix.Table 9 now presents the R-squared values as results of linear regressions of each obligor’sROE on ROEX, on GDD and on both factors. Note that adding GDD as second factorleads to higher R-squared values for many obligors, which in turn implies an increase in thesystematic risk component of the CWI.With all parameters at hand we MC simulate 106 runs according to the following scheme:
1. Generate the random variables εi and Ψ1, ...,ΨC ,Ξ1, ...,ΞC with regard to the multi-variate normal distribution of systematic factorsN2C with correlation matrix Γtwofactors
2. Calculate the CWIi following (17).
3. to 5. are identical to the above procedure.
35The data was drawn from www.wunderground.org. We solve the problem of lacking data between February22th 2000 and May 02th 2000 by interpolation of the accumulated GDD for that period.
19
MFI Country R-squared ROEX R-squared GDD R-squared two factorsAgroCapital BO 0.37071 0.38717 0.67453BancoSol BO 0.68007 0.14838 0.69210CRECER BO 0.35469 0.22276 0.48498FIE BO 0.13932 0.04595 0.16805Fundación MICROS GT 0.02679 0.00793 0.03894CompartamosBanco MX 0.00746 0.01001 0.01522BANEX (ex FINDESA) NI 0.04377 0.53169 0.56308FAMA NI 0.12278 0.15929 0.18924EDPYME Crear Arequipa PE 0.45761 0.51307 0.64789
Table 9: R-squareds of linear regressions of MFI ROE with of the ROEX, GDD and bothfactors
Tranches “VaR (90%)” “VaR (99%)” SFP (< 0) Min. 1st Qu. Median Mean 3rd Qu. Max.senior 0.02980 0.02980 0.00196 -0.30110 0.02980 0.02980 0.02960 0.02980 0.02980mezz. 0.02574 -0.30737 0.04904 -1.00000 0.06942 0.06942 0.04697 0.06942 0.06942equity -0.15577 -0.27084 0.24736 -1.00000 0.00932 0.22150 0.12990 0.22150 0.22150
Table 10: Simulation results two factor extension: Risk measures and descriptive analysis ofthe IRRs of the tranches
Table 10 presents the “VaR” of the IRRs to the 99% and the 90% level as well as theshortfall probability. In addition it also shows the standard descriptive measures of the IRRdistribution for a better overview. Figure 3 shows histograms of the whole IRR distributionfor each tranche and also in logarithmic form.
20
Histogram of IRR: Senior tranche
IRR
Fre
quen
cy
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0e+
002e
+05
4e+
056e
+05
8e+
051e
+06
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
−10
−5
05
Log−Histogram of IRR: Senior tranche
IRR
Log−
dens
ity
Histogram of IRR: Mezz. tranche
IRR
Fre
quen
cy
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0e+
002e
+05
4e+
056e
+05
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
−6
−4
−2
02
Log−Histogram of IRR: Mezz. tranche
IRR
Log−
dens
ity
Histogram of IRR: Equity tranche
IRR
Fre
quen
cy
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0e+
002e
+05
4e+
056e
+05
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
−10
−5
0
Log−Histogram of IRR: Equity tranche
IRR
Log−
dens
ity
Figure 3: Histograms and Log-Histograms of the IRRTR (Two-Factor Extension)
21
5. Conclusion
In this paper we study perspectives and a quantitative model for structured microfinanceinstruments, which have – like all structured instruments – suffered from the financial crisisof 2008/2009.
In a survey that addressed the relevant world-wide experts on investing in microfinanceit turned out that structured microfinance is still regarded as a very important means forrefinancing microcredit lending. The experts disagreed among each other on how badlyMiCDOs are affected by the financial crisis. However, they agree that MiCDOs are expectedto recover within a few years, perhaps under another name or in another form especially asMFIFs (like the EFSE).
As one lesson learnt from the financial crisis being that it is desirable to make investmentissues as transparent as possible, we restrict ourselves to considering structured microfinanceas a real cash flow instrument without any opaque peculiarities, a case that is very realistic inthe microfinance context. The microfinance vehicle we analyze has an asset pool consistingof debt instruments of several MFIs.
We model the joint default risk of several MFIs with a state-of-the-art factor approachand several extensions with a special focus on peculiarities of MFIs. Dependent on themultivariate vector of default times, that is basically the random variable we model and MCsimulate, we can construct the cash flows of the structured instruments tranches. Even ifwe suggest a sophisticated model, we make things as transparent as possible and introducean MFI return on equity index for each country under consideration instead of the usualstock market index. Additionally, we suggest risk analysis utilizing the IRR distributionrather than a blind trust in risk-neutral pricing approaches. Furthermore we highlight therobustness of the model with respect to the possibility of incorrect MFI balance sheet data.As a next step one should refrain from using risk neutral pricing and find alternatives toit because it imposes severe assumptions on the input data. We suggest that a possiblesolution can be built on the results of the risk analysis methodology presented in this paper.
In summary this paper is a supporting contribution to the future refinance of microcreditsin general and the development of structured microfinance in particular. We feel that thisis still a promising topic for investors as well as for the entrepreneurs among the poor whostill do not have enough access to microcredit markets.
22
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Lando, D. (2004). Credit risk modeling: Theory and applications. Princeton series in finance.Princeton, NJ [u.a.]: Princeton Univ. Press.
Littlefield, E. and C. Kneiding (2009). The global financial crisis and its impact on microfi-nance. Focus Note 52, Washington: CGAP .
Lucas, D. J., L. S. Goodman, and F. J. Fabozzi (2006). Collateralized debt obligations:Structures and analysis (2nd ed. ed.). Chichester: Wiley and John Wiley.
Mounfield, C. C. (2008). Synthetic CDOs: Modelling, valuation and risk management.Cambridge: Cambridge Univ. Press.
Schönbucher, P. J. (2003). Credit derivatives pricing models: Models pricing and implemen-tation. Wiley finance series. Chichester: Wiley.
Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications del’Institute Statistque del’Université de Paris 8, 229–231.
Watson, Y. (2009). From Crisis to Catharsis: How Microfinance Can Make it Through theGlobal Recession. Microfinance Insights 11 (2).
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24
A. Appendix
Question test-value p-value coparative value alternative hypothesis significancyQuestion1.0 229.5 0.162790 5 greater FALSEQuestion2.1 147.5 0.536045 3 greater FALSEQuestion2.2 260.5 0.035007 3 greater TRUEQuestion2.3 479 0.000015 3 greater TRUEQuestion2.4 314.5 0.014142 3 greater TRUEQuestion2.5 207 0.201970 3 greater FALSEQuestion2.6 551 0.000004 3 greater TRUEQuestion2.7 494 0.000005 3 greater TRUEQuestion2.8 116.5 0.184456 3 greater FALSEQuestion3.1 354 0.000023 3 greater TRUEQuestion3.2 98 0.055857 3 greater FALSEQuestion3.3 170 0.003574 3 greater TRUEQuestion3.4 281 0.000351 3 greater TRUEQuestion3.5 318.5 0.000095 3 greater TRUEQuestion4.0 138.5 0.500000 3 greater FALSEQuestion5.0 127.5 0.840531 3 greater FALSEQuestion6.0 36 0.001265 3 less TRUEQuestion7.0 387 0.000007 3 greater TRUEQuestion8.1 212 0.176731 5 greater FALSEQuestion8.2 269.5 0.063024 5 greater FALSEQuestion8.3 406 0.000002 5 greater TRUEQuestion8.4 379 0.000028 5 greater TRUEQuestion8.5 435 0.000001 5 greater TRUEQuestion8.6 281.5 0.000079 5 greater TRUEQuestion8.7 286 0.000397 5 greater TRUE
Table 11: Survey: Results of Wilcoxon signed rank test (test direction: agreement)
25
Question test-value p-value coparative value alternative hypothesis significancyQuestion1.0 229.5 0.84318493 5 less FALSEQuestion2.1 147.5 0.47595199 3 less FALSEQuestion2.2 260.5 0.96692026 3 less FALSEQuestion2.3 479 0.99998631 3 less FALSEQuestion2.4 314.5 0.98665604 3 less FALSEQuestion2.5 207 0.80552638 3 less FALSEQuestion2.6 551 0.99999623 3 less FALSEQuestion2.7 494 0.99999562 3 less FALSEQuestion2.8 116.5 0.82672382 3 less FALSEQuestion3.1 354 0.99997964 3 less FALSEQuestion3.2 98 0.94995834 3 less FALSEQuestion3.3 170 0.99684803 3 less FALSEQuestion3.4 281 0.99968398 3 less FALSEQuestion3.5 318.5 0.99991458 3 less FALSEQuestion4.0 138.5 0.51319163 3 less FALSEQuestion5.0 127.5 0.16637986 3 less FALSEQuestion6.0 36 0.99886842 3 greater FALSEQuestion7.0 387 0.99999364 3 less FALSEQuestion8.1 212 0.82987425 5 less FALSEQuestion8.2 269.5 0.93979509 5 less FALSEQuestion8.3 406 0.99999863 5 less FALSEQuestion8.4 379 0.99997456 5 less FALSEQuestion8.5 435 0.99999899 5 less FALSEQuestion8.6 281.5 0.99992982 5 less FALSEQuestion8.7 286 0.99964049 5 less FALSE
Table 12: Survey: Results of Wilcoxon signed rank test (test direction: non agreement)
26
Que
stion
Recod
ing
1.0
How
impo
rtan
tis
therole
ofCDOsin
microfin
ance?
1=un
impo
rtan
t,...5=de
term
ined,.
..9=
impo
rtan
t2.0
Pleaserate
thefollo
wingad
vantag
esof
CDOsin
thecontextof
microfin
ance!
1=Ido
n’tag
ree,
...3=de
term
ined
,...5=
Icompletelyag
ree
3.0
How
critically
doyouseethefollo
wingaspe
ctsof
CDO
valuationin
contextof
thesubp
rimecrisis?
1=no
tcritical,.
..3=
determ
ined
,...5=
very
critical
4.0
Istheim
ageof
MiCDOsseriou
slyda
mag
edby
thecu
rrentfin
ancial
crisis?
1=Ido
n’tag
ree,
...3=de
term
ined
,...5=
Icompletelyag
ree
5.0
Wekn
owthat
projects
oflaun
chingne
wMiC
DOsha
vebe
enstop
ped.
Are
MiC
DOscu
rrentlyde
ad?
1=Ido
n’tag
ree,
...3=de
term
ined,.
..5=
Icompletelyag
ree
6.0
Doyo
uthinkMiCDOswill
recoverag
ain?
Whe
n?W
ithin...
(not
necessary)
7.0
Cou
ldinvestmentfund
swithstructured
elem
ents
liketran
ching,
waterfallstruc-
ture
...be
asustaina
blealternativeto
MiC
DOs...?
1=Ido
n’tag
ree,
...3=de
term
ined,.
..5=
Icompletelyag
ree
8.0
How
impo
rtan
twill
thefollo
winginstruments
becometo
providecapitalfor
Microfin
ance
Institutions
(MFIs)withinthene
xttw
oyears?
1=un
impo
rtan
t,...5=de
term
ined
,...9=
impo
rtan
t
Tab
le13
:Survey:
Variable’srecoding
27
GDD(BO) GDD(GT) GDD(MX) GDD(NI) GDD(PE)2007 4838 3525 2281 6222 30112006 4954 3465 2275 6297 34262005 4825 3523 2483 6075 32062004 4330 3209 2133 5538 29042003 4785 3531 2393 6167 30832002 4965 3491 2400 6097 31682001 4700 3354 2068 6093 29252000 3438 2919 1900 5553 28871999 4807 3250 2055 5860 3329
Table 14: Country specific GDD indices
ROEX(BO) ROEX(GT) ROEX(MX) ROEX(NI) ROEX(PE) GDD(BO) GDD(GT) GDD(MX) GDD(NI) GDD(PE)ROEX(BO) 1.0000 -0.1449 -0.1121 0.6502 0.5359 0.4276 0.5792 0.6306 0.3197 0.2220ROEX(GT) -0.1449 1.0000 -0.5219 -0.2423 -0.6102 0.2253 -0.1040 -0.2521 -0.0868 0.4045ROEX(MX) -0.1121 -0.5219 1.0000 -0.5357 0.4663 -0.2447 0.0198 0.1881 -0.0158 -0.4424ROEX(NI) 0.6502 -0.2423 -0.5357 1.0000 0.2159 0.1396 0.2143 0.2810 0.1679 0.3546ROEX(PE) 0.5359 -0.6102 0.4663 0.2159 1.0000 0.4464 0.6863 0.8254 0.4631 0.0417GDD(BO) 0.4276 0.2253 -0.2447 0.1396 0.4464 1.0000 0.9045 0.7183 0.8059 0.6294GDD(GT) 0.5792 -0.1040 0.0198 0.2143 0.6863 0.9045 1.0000 0.8943 0.8771 0.4468GDD(MX) 0.6306 -0.2521 0.1881 0.2810 0.8254 0.7183 0.8943 1.0000 0.6695 0.4153GDD(NI) 0.3197 -0.0868 -0.0158 0.1679 0.4631 0.8059 0.8771 0.6695 1.0000 0.5277GDD(PE) 0.2220 0.4045 -0.4424 0.3546 0.0417 0.6294 0.4468 0.4153 0.5277 1.0000
Table 15: Correlation matrix Γtwofactors of the ROEX and GDD
28
Realizations of VAR 99% : Senior tranche
VAR 99%
rela
tive
freq
uenc
y
0.0298
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of VAR 99% : Mezz. tranche
VAR 99%
rela
tive
freq
uenc
y
−0.14229
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
Realizations of VAR 99% : Equity tranche
VAR 99%
rela
tive
freq
uenc
y
−0.24698
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of VAR 90% : Senior tranche
VAR 90%
rela
tive
freq
uenc
y
0.0298
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of VAR 90% : Mezz. tranche
VAR 90%
rela
tive
freq
uenc
y
0.02922
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Realizations of VAR 90% : Equity tranche
VAR 90%
rela
tive
freq
uenc
y
−0.13925
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
Realizations of SFP : Senior tranche
SFP
rela
tive
freq
uenc
y
0.00042
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
Realizations of SFP : Mezz. tranche
SFP
rela
tive
freq
uenc
y
0.02273
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
Realizations of SFP : Equity tranche
SFP
rela
tive
freq
uenc
y
0.2354
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
Realizations of Min. : Senior tranche
Min.
rela
tive
freq
uenc
y
−0.1649
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
Realizations of Min. : Mezz. tranche
Min.
rela
tive
freq
uenc
y
−1
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
Realizations of Min. : Equity tranche
Min.
rela
tive
freq
uenc
y
−0.9378
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
Realizations of 1st Qu. : Senior tranche
1st Qu.
rela
tive
freq
uenc
y
0.0298
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of 1st Qu. : Mezz. tranche
1st Qu.
rela
tive
freq
uenc
y
0.06942
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of 1st Qu. : Equity tranche
1st Qu.
rela
tive
freq
uenc
y
0.04819
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
Figure 4: Simulation results robustness check: Barplots of measure realizations (result ofIRR analysis in color)
29
Realizations of Median : Senior tranche
Median
rela
tive
freq
uenc
y
0.0298
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of Median : Mezz. tranche
Median
rela
tive
freq
uenc
y
0.06942
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of Median : Equity tranche
Median
rela
tive
freq
uenc
y
0.2215
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of Mean : Senior tranche
Mean
rela
tive
freq
uenc
y
0.02975
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Realizations of Mean : Mezz. tranche
Mean
rela
tive
freq
uenc
y
0.056
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
Realizations of Mean : Equity tranche
Mean
rela
tive
freq
uenc
y
0.137
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
Realizations of 3rd Qu. : Senior tranche
3rd Qu.
rela
tive
freq
uenc
y
0.0298
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of 3rd Qu. : Mezz. tranche
3rd Qu.
rela
tive
freq
uenc
y
0.06942
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of 3rd Qu. : Equity tranche
3rd Qu.
rela
tive
freq
uenc
y
0.2215
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of Max : Senior tranche
Max
rela
tive
freq
uenc
y
0.0298
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of Max : Mezz. tranche
Max
rela
tive
freq
uenc
y
0.06942
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Realizations of Max : Equity tranche
Max
rela
tive
freq
uenc
y
0.2215
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Figure 5: Simulation results robustness check: Barplots of measure realizations (result ofIRR analysis in color)
30
