IDB WORKING PAPER SERIES N IDB-WP-697

Multilateral Development Bank Ratings
and Preferred Creditor Status

William Perraudin
Andrew Powell
Peng Yang

Inter-American Development Bank
Department of Research and Chief Economist
July 2016
Multilateral Development Bank Ratings
and Preferred Creditor Status

 William Perraudin*
 Andrew Powell**
 Peng Yang*

  * Risk Control Limited
  ** Inter-American Development Bank

July 2016
Cataloging-in-Publication data provided by the
Inter-American Development Bank
Felipe Herrera Library

Perraudin, William.
    Multilateral development bank ratings and preferred creditor status / William

Perraudin, Andrew Powell, Yang Peng.
    p. cm. -- (IDB Working Paper Series ; 697)
    Includes bibliographic references.
    1. Development banks. 2. Credit ratings. 3. Debtor and creditor. I. Powell, Andrew.

II. Yang, Peng. III. Inter-American Development Bank. Department of Research and
Chief Economist. IV. Title. V. Series.
IDB-WP-697

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                                                    Abstract1
         This paper analyzes influences on the credit standing of Multilateral Development
         Banks (MDBs). We focus on the quality, diversification and single name
         concentration of their portfolios, and on the market practice known as Preferred
         Creditor Status (PCS). PCS refers to the fact that sovereigns which default on
         other debt rarely fail to meet their obligations to MDBs. The paper examines how
         rating agencies assess MDB ratings, looking, in particular, at how Standard &
         Poor's (S&P) evaluates capital adequacy. We benchmark the agency's approach
         against an industry-standard, ratings-based Credit Risk Model (CRM). We
         implement the approaches for a specific MDB: the Inter-American Development
         Bank (IDB).The paper shows that S&P's approach is highly conservative in its
         treatment of single name concentration risk and makes insufficient allowance for
         PCS. Calibrating the CRM with risk-neutral distributions, we examine the effect
         of PCS on MDB funding spreads.
         JEL classifications: G11, G12, G24
         Keywords: Multilateral development banks, Preferred creditor status, Credit
         ratings, Rating agencies

1 William Perraudin is Director of Risk Control and Adjunct Professor of Imperial College, London. Andrew Powell
is the Principal Advisor in the Research Department at the IDB. Peng Yang is a Senior Quantitative Analyst in Risk
Control. The authors thank the IDB for support and Elisa Cencig for research assistance. We would also like to
thank Federico Galizia, Jos Juan Ruiz Gmez and particularly Frank Sperling and Jonas de Oliveira Campino for
their comments and access to data. We also thank two anonymous reviewers. The views expressed are strictly those
of the authors and not necessarily those of their respective institutions. The authors' email addresses are
william.perraudin@riskcontrollimited.com, andrewp@iadb.org and peng.yang@riskcontrollimited.com.

                                                          1
Executive Summary

Multilateral Development Banks (MDBs) play an important role in international financial
markets, raising money by issuing bonds and lending to their borrowing member countries.

         In so doing, they benefit from a market practice known as Preferred Creditor Status
(PCS). PCS refers to the fact that sovereign borrowers typically continue to service their loans
from MDBs even in the unlikely event that they default on other claims. This confers on the
loans of MDBs a type of de facto seniority.

         The business model followed by MDBs requires that they maintain a high credit standing.
For this reason, their assessment by ratings agencies is an important consideration in MDB
decision making and agency ratings are widely perceived as a constraint on their lending.

         In evaluating MDB credit standing, one influential rating agency, Standard & Poor's
(S&P), relies on a transparent quantitative measure: the Risk-Adjusted Capital (RAC) ratio. The
RAC ratio equals forecast common equity divided by the MDB's Risk Weighted Assets
(RWAs). To be judged by S&P as having a strong capital position, an MDB must maintain a
RAC ratio greater than a given target value. If the level of common equity is given, this requires
that the MDB limit its RWAs.

         S&P's measure of RWAs equals a weighted sum of assets (with weights dependent on
rating and jurisdiction). This weighted sum is adjusted for three factors: diversification (across
countries and sectors), Single Name Concentration (SNC) and PCS. The assumptions adopted by
S&P in making these adjustments are important in determining whether S&P's credit risk
evaluation constrains an MDB's lending.

         In this paper, we analyze S&P's methodology. We look, in particular, at the approaches
the agency employs in adjusting for i) diversification, ii) SNC and iii) PCS. We focus on a
particular MDB, the Inter-American Development Bank (IDB), and investigate possible
alternatives to the adjustments employed by S&P. Our analysis suggests that S&P's treatments of
SNC and PCS are extremely conservative in the case of the IDB.

         To benchmark the S&P approach, we formulate an industry-standard, ratings-based
Credit Risk Model (CRM) and apply this to the IDB's portfolio. By design, the CRM rigorously
allows for diversification and SNC. To adjust for PCS we consider adjustments to CRM inputs,
specifically to the recovery rates on sovereign loans in the IDB's portfolio.

                                                          2
         In rating Collateralized Debt Obligations (CDOs), S&P employs target probabilities of
default (PDs) associated with different maturities. Using the CRM and the target PDs, we are
able to deduce the capital levels that the IDB needs to obtain a AAA rating. (The analysis
abstracts from additional, qualitative criteria applied in the rating process.)

         For the IDB to obtain a rating of AAA, the CRM suggests it should hold capital in excess
of $14-15bn. One may compare this to the figure of $33bn that is required for the IDB to achieve
the highest S&P category of capital adequacy. (Note that our calibration is based on December
2014 data and does not allow for the steps IDB has recently taken i) to consolidate different
balance sheets and ii) to exchange assets with other MDBs. These steps have reduced the degree
to which the RAC ratio constrains IDB lending.)

         The CRM may also be simulated using risk-adjusted distributions in order to assess the
"risk-adjusted probability" that the IDB will exhaust its capital. Assuming a recovery rate, and
working out the expected loss under such a risk adjusted distribution, permits the estimation of
the spreads that the market would charge the IDB to borrow. This calculation may be performed
with and without adjustment for PCS. The effect of PCS may then be inferred by comparing
these two estimates. We find that before the PCS adjustment, the IDB's market spread equals 19
to 37 basis points (bps), depending on maturity. After adjustment, the spread falls to 7 to 14 bps.

         To conclude, the paper indicates that S&P's approach is highly conservative in its
treatment of single name concentration risk and makes insufficient allowance for PCS.

                                                          3
1. Introduction

Multilateral Development Banks (MDBs) play an important role in international financial

markets. Owned by groups of countries that provide equity capital, MDBs raise money by

issuing bonds in global capital markets and lend to their borrowing member countries. Income

from lending is either reinvested in the business by boosting capital or used to pay for grant
financing, concessional lending, technical assistance, salaries and other expenses.2

         Over time, the role of MDBs has evolved. For example, the World Bank initially acted as

a facilitator of post-war reconstruction and has subsequently assumed a mandate of alleviating

worldwide poverty. Similarly, the European Bank for Reconstruction and Development (EBRD)

was created to foster a transition to a market economy but has since taken on a wider role of

furthering development; see Buiter and Fries (2002), Clemens and Kremer (2016) and Ravallion
(2016). Academics and others have discussed the value of the activities in which MDBs engage,3

including knowledge creation and diffusion, pure financing (including counter-cyclical and crisis
lending) and the provision of incentives through loans for countries to pursue reforms.4

         In this paper, we examine the creditworthiness of MDBs and analyze the levels of capital

they must hold to achieve high credit status. MDBs are capital constrained in that they cannot, of

themselves, issue new capital instruments without going through complex negotiations with

shareholders. Hence, the scale of their activities and the level of risk that they can assume are

limited by the market's view of their solvency as reflected in credit spreads and agency credit

ratings.

         In analyzing MDB creditworthiness, we focus on a particular institution, the Inter-

American Development Bank (IDB). We examine and apply the approach to calculating credit

2 MDBs do not typically pay dividends to their shareholders.
3 Gilbert, Powell and Vines (1999) argued that the World Bank i) needed to transition from a reliance on
conditionality to a knowledge bank with lending focused more on countries with sound economic policies and ii)
that its value-added came from the bundling of lending and knowledge services and attempts to unbundle these
activities were misplaced. Boz (2011) studies the nature of emerging market borrowing from international financial
institutions, including MDBs. The author finds that such borrowing tends to be counter-cyclical and smaller in
magnitude than borrowing from private sector sources and that lending for budget or balance of payments support
tends to come with strings attached in the form of conditionality arrangements.
4 For a general discussion, see Chapter 6 in Inter-American Development Bank (2006). Wezel (2004) presents
evidence that MDB lending gives borrowing countries an incentive to honor commitments and thereby reduces
agency costs, stimulating private sector financing flows in parallel to the MDB loans. Perraudin and Sibert (2000)
analyze bargaining on conditionality between an MBD and a sovereign borrower under asymmetric information.
Buiter and Fries (2002) emphasize the useful mechanisms that MDBs have for monitoring and enforcing loans and
applying subsidies, and argue that MDBs should not be agencies for allocating grants or effecting redistribution
internationally.

                                                          4
risk capital employed by the rating agency Standard & Poor's (S&P). S&P is prominent in
assessing MDBs, and the agency's methodology relies to a significant degree on a transparent
quantitative assessment of capital adequacy. Our analysis compares results obtained using S&P's
approach with those implied by an industry-standard, credit portfolio model. We also look at
bond market perceptions of MDB risk as revealed by relative MDB and sovereign bond spreads.

         We focus on particular factors influencing credit standing of MDBs, specifically
diversification and the market practice known as Preferred Creditor Status (PCS). PCS describes
the phenomenon that, when sovereigns default on claims to private institutions, they commonly
continue to service debt held by official creditors including MBDs. PCS means that loans made
by MDBs are effectively senior to private commercial debt and often to bilateral official debt.
One popular database lists22 recent bond exchanges, 13 of which involved a reduction in
principal with an average haircut of 48.3 percent; none of these include any reduction in the face
value of debt from MDBs.5

         Such favorable loss experience suggests that PCS should play a large role in credit
assessments of MDBs and, hence, has important implications for the capital MDBs must hold to
achieve high ratings. The ratings agencies adjust for PCS in rating MDBs, but whether they do so
to the extent justified by the actual loss experience of MDB institutions is controversial.

         Consider the example of the IDB: S&P reduces its estimate of the IDB's risk weighted
assets (and hence of the capital it must hold to achieve a given standalone credit standing) by 10
percent to reflect the beneficial effects of PCS. Such a small reduction might be questioned in the
light of the IDB's loss experience. According to IDB estimates of those occasions in its entire
history on which its borrowers have defaulted on commercial debt, the IDB itself has suffered
non-accrual events on only about 11 percent of those occasions. Moreover, even in the cases of
these non-accrual events, the IDB did not experience any write-offs or write-downs from its
ordinary capital.6

         Another important determinant of MDB credit quality is the degree to which MDB
portfolios are diversified or concentrated. Like conventional commercial banks, the degree of
diversification across geographical regions and sectors is an important influence on key credit

5 See Cruces and Trebesch (2013) and the 2014 update of the dataset available at:
https://sites.google.com/site/christophtrebesch/data
6 This abstracts from those low income countries that obtained debt relief through the internationally negotiated
Multilateral Debt Relief Initiative (MDRI).

                                                          5
quality measures such as the probability of default. Unlike most commercial banks, some MDBs
have, in addition, significant single name concentration risk in that they have relatively high
proportionate exposures to particular sovereigns. We examine different approaches to assessing
diversification and single name concentration risk and illustrate the sensitivity of S&P's rating
assessment to the choice of approach in the case of the IDB.

         In our analysis of IDB portfolio risk using an industry standard credit portfolio model, we
allow explicitly for PCS and compare our findings with the allowance made for PCS by S&P.
Our model also allows for diversification and single name concentration risk in a rigorous and
consistent fashion, so we are again able to check the accuracy of the approximations and
methodological choices adopted by S&P.

         We do not attempt to adjust for the impact of MDBs' callable capital. Some allowance is
made for this by ratings agencies, but it is difficult to assess through calculation whether their
approach is conservative or not. By performing comparisons that make no allowance at all for
callable capital, we ensure that our conclusions are highly conservative in this regard.

         The spreads demanded of MDBs that borrow from the international bond market shed
light on the credit quality of these institutions as perceived by the bond market. To examine the
impact of PCS on bond market pricing, we implement a variant of our portfolio credit risk model
using risk adjusted (rather than historical) distributions. We show that implied spreads with no
allowance for PCS are higher than those observed in the market whereas, when PCS is
introduced, model-implied spreads more closely resemble market levels.

         The paper is organized as follows. Section 2 presents evidence of MDB credit standing
and discusses the nature of PCS and how one might expect it to influence MDB solvency risk.
Section 3 sets out the methodologies we employ in analyzing the portfolio risk of our example
MDB, the IDB. We present S&P's methodology for rating MDBs, providing interpretation and
comments on the quantitative modeling approach the agency employs. We also present the
ratings-based credit portfolio model that we apply to the IDB's portfolio.7 Section 4 describes the
IDB's portfolio and how we mapped it into appropriate inputs for the portfolio analysis. Section
5 presents the results of our analyses, and Section 6 concludes.

7 This latter model is i) multi-period, so one may employ it to analyze risk over multiple horizons, and ii) may be run
using either historical or risk-adjusted distributions extracted from spreads. So, one may both analyze appropriate
capital and infer market spreads at which the IDB could borrow under different assumptions about the nature of its
portfolio.

                                                          6
2. MDB Credit Status

Multilateral Development Banks (MDBs) provide finance to developing countries for projects in
virtually all sectors and general budget support normally linked to policy reforms. One may think
of MDBs as risk-poolers. Non-borrowing MDB member countries face a choice between lending
directly to a borrowing country (in which case they may select projects or countries that accord
with their specific development or political objectives) or may provide capital to an MDB. In the
latter case, the non-borrowing country gains scale in its lending (through the leverage of the
MDB) and may gain technical expertise and diversify its own risks.8

Table 1. Key Risk Indicators for MDBs

                    Share- Equity to

Share- S&P S&P Net Total holders' Assets Total                Adjusted

Bank Est. holders Rating SACP Loans Assets equity Ratio Liabilities RAC RAC

IDB 1959 48 AAA aa+ 74,215 106,299 23,697 0.23 82,602 31                     16

EIB 1958 28 AAA aa+ 524,078 656,650 73,327 0.11 583,323 17                   15

EBRD 1991 68 AAA aaa 23,593 63,546 17,130 0.27 46,416 22                     15

IBRD 1946 188 AAA aaa 154,861 351,634 37,078 0.11 314,556 25                 30

ADB 1966 67 AAA aaa 55,925 115,660 16,938 0.15 98,722 29                     17

IFC 1956 184 AAA aaa 22,536 91,246 24,035 0.26 67,211 16                     29

CEB 1956 41 AA+ aa  15,263 30,927 3,081 0.09 27,846 32                       18

AfDB 1964 78 AAA aa+ 17,618 32,335 8,980 0.28 23,354 24                      18

CAF 1968 19 AA- aa- 18,999 30,495 8,763 0.29 21,731 26                       14

CABEI 1960 13 A a   5,236 7,537 2,268 0.30 5,269 25                          12

Note: Data are taken from the 2015 S&P Ratings Direct reports. All figures are in millions of U.S. dollars. The
euro-dollar conversion rate used for EIB, EBRD and CEB data is the rate on 31 December 2014. For AfDB, we
used the SDR-USD conversion rate of December 30, 2013. EBRD shareholders include the EU and the EIB.
Most institutions shown in the table lend to both public and private sectors. Institutions such as the IFC focus
exclusively on lending to the private sector. The lack of PCS for private lending, diversification issues, and its
use of equity investments make the IFC somewhat different from MDBs such as the IDB or IBRD. Note that
these 2015 figures for the IDB do not include the positive impacts of the recent Argentina upgrade nor other
recent changes that improve capital ratios.

8 Bobba and Powell (2006) argue in favor of this trade-off and present empirical results to illustrate the inferred
preferences of non-borrowing countries given the pattern of their bilateral aid. Bobba and Powell (2007) show that
politics (proxied by the voting correlations at the United Nations) does play a role in the cross-country distribution
of bilateral aid and using this as an instrument show aid extended to countries with the closest alignments in voting
patterns tends to be less effective.

                                                          7
         The ability of MDBs to leverage through their borrowing in international capital markets
is significantly enhanced by their high credit standing.9 Table 1 shows the rating of the primary

MDBs as of June 2015. Only one MDB has a rating of less than AA-, while just three have

current ratings below AAA. Table 1 also documents the long, stable track record of lending of

many MDBs, most of which were established in the late 1950s or early 1960s.

         The financial data contained in Table 1 illustrate the sources of MDBs' high credit

standing, particularly their strong equity capitalization. Equity to assets ratios (shown in column

9 of Table 1) are higher than those observed in commercial banks, being mostly in the range 20-

30 percent. The exceptions are the IBRD (which has a diversified lending book and an
accounting treatment of swaps quite different from that employed by other MDBs10), and the two

European institutions, EIB and CEB (the assets of which mainly comprise relatively high-quality

loans to developed-country borrowers).

         Two other sources of financial strength from which MDBs benefit are i) shareholder

support through callable capital and ii) Preferred Creditor Status (PCS).

         On i), MDBs enjoy promises of additional capital injections from their shareholders

should the MDB in question experience financial difficulties. There is some variation across

member countries as to how automatic such additional contributions would be if the capital were

actually called or whether these contributions would have to be ratified by some political

process. Rating agencies tend to allow some proportion of this additional callable capital to count

as actual capital, but it is less than 100 percent. In particular, for MDBs aiming for an AAA

rating, S&P only makes allowance for callable capital promised by shareholders that have AAA
S&P ratings.11

         To appreciate the impact of i) on rating agency evaluations of callable capital, one may

examine the fifth column of Table 1, which shows S&P's Stand Alone Credit Profile (SACP) for

9 The degree to which ratings add information has been studied by numerous authors. Cavallo, Powell and Rigobn
(2008) find that sovereign ratings and outlooks, controlling for current spreads, improve predictive power and so add
information. Eijffinger (2012) shows that spreads led ratings and outlook changes in the 2010-2011 sovereign debt
crisis in Europe. Kiff, Nowak and Schumacher (2012) present evidence that rating agency assessments affect the
cost of funding of sovereign issuers and argue that this fact raises financial stability concerns. Baum, Karpava,
Schfer and Stephan (2013) show that, at least in periods of crisis, sovereign ratings affect exchange rates and the
borrowing terms that sovereigns face.
10 The IBRD includes swaps on a gross basis in its accounts, which boosts the size of its balance sheet substantially.
11 This notably excludes promises of callable capital from the US. Ignoring callable capital from non-AAA-rated
shareholders implies that changes in shareholder ratings may trigger somewhat questionable MDB downgrades or
upgrades. Promises of callable capital from lower rated shareholders are taken into account if the MDB aims for a
lower rating than AAA.

                                                          8
the different MDBs. This measure, expressed in a lower-case version of the agency's main issuer

rating scale, reflects S&P's view of the credit standing a given MDB would have in the absence

of additional capital support from its shareholders. One may observe that, in practice, the

allowance S&P makes for callable capital boosts its rating assessment by one notch for four of

the 10MDBs shown.12

         On ii), as explained in the introduction, PCS is a market practice whereby distressed

sovereigns service their obligations to some lenders even while defaulting on other debts. This

practice results in an effective increase in seniority of MDB claims compared to claims that

would otherwise have the same seniority.13 One should note that there is no legal basis for PCS.

It constitutes a market practice attributable to the incentives faced by distressed sovereign

borrowers. PCS may reflect the concern of defaulting sovereigns to remain on good terms with

multilateral institutions that maintain lending when private sector funding dries up. Unlike IMF

loans, however, MDB lending is not made in periods of private or bilateral debt renegotiations,

and some have questioned whether loans by MDBs are counter-cyclical; see Perry (2009).

         What explains the phenomenon of PCS? First, it is reasonable to expect that distressed

sovereign debtors will favor lenders that continue to lend even through very difficult economic

times. MDBs have traditionally played such a role, acting as counter-cyclical providers of

funding, and hence, one might expect them to enjoy PCS.14

         Second, the mutual nature of some MDB institutions is likely to encourage PCS. One

may note that the degree of mutuality varies across MDBs. At one extreme, the CAF (Latin

12 The boost could be up to three notches according to the methodology, but only if the Business Profile is
"Extremely Strong" in which case the institution is unlikely to need it.
13 The case of Argentina is instructive in several respects. Following its 2002 default on commercial debt and despite
a severe economic crisis, Argentina remained current on all payments to the IDB and fully repaid IMF loans in
advance of their final maturity. Furthermore, during the recent court case of Argentina vs. NML Capital Ltd. (NML)
(one of the hold-out investors that did not accept the terms of the 2005 or 2009 offers), while NML sought to disrupt
Argentina's international payments and eventually succeeded in preventing Argentina from paying bondholders that
agreed to the restructurings, MDBs' preferred creditor status was apparently not questioned.
14 PCS has been extensively discussed in the context of the International Monetary Fund (IMF). PCS was not
mentioned in the IMF's articles of agreement but, in 1988, the IMF's board of governors' interim committee "urged
all members within the limits of their laws to treat the Fund as a preferred creditor" (see Boughton, 2001). Martha
(1990) examines whether international law offers guidance in setting priorities in external debts settlements and in
particular what this implies for Preferred Creditor Status of the IMF. He concludes that the IMF PCS could be
placed on a more explicit legal basis through recognition in debt contracts. Raffer (2009) also makes the case for
more explicit legal recognition of PCS. Schadler (2014) argues that the IMF's PCS is threatened by the effective
relaxation in lending criteria that occurred when it lent to Greece in 2010. "The IMF's PCS is well-justified,
provided the IMF is charged with, and capable of, carrying out its role as a catalyst of market finance or, when
market access has been totally closed down, as a facilitator of early return to market access."

                                                          9
America's Development Bank) has a board that only includes borrowing countries.15 At the other
extreme, at the World Bank (specifically the IBRD), non-borrowing countries hold the majority
of equity. The IDB is intermediate between these two cases in that, of its 48 member countries,
the United States holds the largest equity share but its 26 borrowing member countries16 own a
majority of the institution's equity.17

         While the ratings agencies take PCS into account in evaluating MDB credit standing, one
may question whether they do so to an appropriate extent. Moody's and Fitch rate MDBs using
methodologies that are comparatively qualitative and are not fully disclosed to the market.
However, S&P uses a relatively transparent and largely quantitative approach to rate MDBs. The
S&P approach includes a specific adjustment for PCS. Below, we examine the magnitude of the
S&P PCS adjustment in the case of the MDB on which we focus our analysis, the IDB.

Table 2. Example MDB Spreads

               IBRD spreads in bps

           1 year 3 year 5 year     10 year
                                          31
2015       27  20  16                     47
2014                                      46
2013       28  13  7                      75
2012                                      48
All years  33  34  24
                                    10 year
2015       21  31  51                     26
2014                                      43
2013       27  26  26                     58
2012                                      60
All years      IDB spreads in bps         47

           1 year 3 year 5 year

           28  21  19

           17  14  14

           28  16  18

           41  23  21

           30  19  18

Note: Entries in the table are average daily spreads
(annualized and in basis points) over US Treasury
benchmarks. "All years" refers to the average across
the years.
Source: Reuters.

15 Ocampo and Titelman (2009) and Seatzu (2014) describe the relatively successful development of multilateral
financial institutions within Latin America.
16 The most recent members include Korea and China. Haiti is a borrowing member country, although it currently
receives only grant financing from the IDB and no loans. See http://www.iadb.org/en/about-us/how-the-inter-
american-development-bank-is-organized,5998.html
17 Humphrey and Michaelowa (2013) discuss the relationship between MDB shareholder structures and how they
are used as a source of funding by borrower countries while Humphrey (2014) analyzes how MDB shareholder
arrangements affect the ways in which MDBs price their loans.

                                                         10
         Bond market spreads are also important indicators of credit standing. Table 2 shows
estimates of spreads on MDB bond issues for two example institutions, IBRD and the IDB. Short
and medium maturity spreads have varied over time as concerns about emerging market
borrowers have evolved but for both institutions, typical spreads have been in the range 20 to 30
basis points. Below, we show what an analysis of the IDB portfolio implies for spreads on the
bank's debt and obtain estimates broadly consistent with the figures shown in Table 2.

3. Methodologies

3.1 Two Methodologies
In this section, we describe two methodologies for assessing MDB credit quality and the impact
of PCS. We apply these methodologies to data from a particular example MDB, namely the
Inter-American Development Bank (IDB). The first approach is that employed by the rating
agency, Standard & Poor's (S&P). The S&P methodology for rating MDBs relies heavily on the
Risk Adjusted Capital (RAC) ratio that the agency developed for assessing commercial banks. In
broad terms, for a given bank, the RAC is the ratio of its forecast equity (based on specific S&P
definitions) to its risk weighted assets (where the weights are defined by S&P).18

         The second approach described in this section, consists of a ratings-based, credit risk
model. Models of this type are widely used by large banks in calculating their own economic
capital and also for Pillar II concentration risk analysis. The technique consists of simulating the
correlated ratings of the bank's exposures up to a given horizon and then valuing the exposures
conditional on their ratings. The approach yields Monte Carlo estimates of the distribution of the
bank's portfolio value at future points in time (typically one year hence) from which risk
measures such as Value at Risk (VaR) or default probabilities may be readily calculated.

3.2 The S&P Approach
Here, we provide a concise description of S&P's methodology for rating MDBs. The agency's
approach is set out in Standard & Poor's (2012a). It builds on the methodology the agency
employs in rating commercial banks, as detailed in Standard & Poor's (2010).19

18 S&P states that the RAC ratio has a weighting of just 25 percent in the rating assessment of an MDB. However, if
multiple indicators are combined and one has greater variability than others, then it is possible for that indicator to
dominate the determination of the ranking even if it only has a relatively small weight.
19 See also Standard & Poor's (2012b).

                                                         11
         A schematic description of S&P's approach to rating MDBs appears in Figure 1. The
methodology combines judgmental assessments of the MDB's business profile with an
evaluation of its financial profile. The financial profile combines analysis of i) the capital and
earnings position of the bank and ii) its funding and liquidity position.

         The starting point for S&P's methodology is the agency's Risk Adjusted Capital (RAC)
ratio (see Standard & Poor's, 2010). This ratio consists of the bank's forecast future capital
resources (current capital adjusted for projected earnings) divided by its Risk Weighted Assets
(RWAs). RWAs comprise the bank's exposure multiplied by exposure-class-specific Risk
Weights (RWs) devised by S&P. We describe how S&P calculates RWAs in detail below.

         Having calculated the RAC ratio of a given MDB, S&P uses the ranges in Table 3 to
determine a capital adequacy category. For the highest category of Extremely Strong, an MDB
must attain an RAC ratio in excess of 23 percent. Combining the capital adequacy category with
an assessment of the bank's funding and liquidity position, based on the mappings in Table 4, the
agency determines the MDB's financial profile (which takes one of seven possible values).

                       Figure 1. Standard& Poor's Approach to Rating MBDs

          Note: The figure shows the decision process followed by S&P in assigning ratings to MDBs. The
          process determines the Standalone Credit Profile combining a Business Profile score and a
          Financial Profile score, the latter evaluation depending heavily on the Risk Adjusted Capital ratio
          (adjusted for additional factors).

                                                         12
                  Table 3. RAC Ratio Thresholds for Different Capital Adequacy Categories

                  Assessment                             The RAC Ratio is:*
                  Extremely Strong                       Above 23%
                  Very Strong                            Above 15% and up to 23%
                  Strong                                 Above 10% and up to 15%
                  Adequate                               Above 7% and up to 10%
                  Moderate                               Above 5% and up to 7%
                  Weak                                   Above 3% and up to 5%
                  Very Weak                              Lower than 3%

                  Note: This table shows how S&P categorizes the capital and earnings profile of an MDB based
                  on its RAC ratio. If the RAC ratio is within 10 percent of a particular threshold, S&P
                  incorporates qualitative forecast in assigning the MDB to a financial profile category.
                  Source: Standard & Poor's (2012a).

Table 4. Combining Capital and Funding and Liquidity Scores to Obtain Financial Profile

                                                                   Capital Adequacy

                          Extremely Strong Very Strong Strong                Adequate Moderate Weak                  Very Weak

Funding and       Very Strong Extremely strong Extremely strong Very strong  Strong     Adequate          Moderate   Weak
    Liquidity                                                                Adequate   Moderate          Weak       Very weak
                  Strong  Extremely strong Very strong Strong                Moderate   Weak              Very weak  Very weak
                                                                             Weak       Very weak         Very weak  Very weak
                  Adequate Very strong Strong            Adequate            Very weak  Very weak         Very weak  Very weak
                                                                             Very weak  Very weak         Very weak  Very weak
                  Moderate Strong              Adequate  Moderate

                  Weak    Moderate             Moderate  Weak

                  Very Weak Weak               Weak      Very weak

Note: This table shows how S&P combines capital adequacy and funding and liquidity scores to obtain the
financial profile of a multilateral development bank.
Source: Standard & Poor's (2012a).

         Lastly, the agency combines the financial profile with a judgmental assessment of the
MDB's business profile using the mappings in Table 5 to obtain a (lower case) letter rating.

                                    Table 5. Combining the Financial and Business Profile

                                                                             Financial Profile

                                    Extremely  Very Strong Strong            Adequate           Moderate  Weak       Very Weak
                                    Strong
Business Profile  Extremely Strong  aaa        aaa/aa+   aa+/aa              aa/aa-             a+/a      a-/bbb+    bbb/bbb-
                  Very Strong       aaa/aa+    aa+/aa    aa/aa-              a+/a               a/a-
                  Strong            aa+/aa     aa/aa-    a+/a                a/a-               bbb+/bbb  bbb+/bbb bb+/bb
                  Adequate          aa/aa-     a+/a      a/a-                bbb+/bbb           bbb/bbb-
                  Moderate          a+/a       a/a-      bbb+/bbb            bbb/bbb-           bb+/bb    bbb/bbb- bb/bb-
                  Weak              a-/bbb+    bbb+/bbb  bbb/bbb-            bb+/bb             bb/bb-
                  Very Weak         bbb+/bbb   bbb/bbb-  bb+/bb              bb/bb-             b+/b/b-   bb+/bb     b+/b

                                                                                                          bb-/b+     b/b-

                                                                                                          b+/b/b-    ccc+/ccc/ccc-

                                                                                                          ccc+/ccc/ccc- cc

Note: This table shows how S&P combines the business and financial profiles of a multilateral development
bank in order to form its Stand-Alone Credit Profile (SACP).
Source: Standard & Poor's (2012a).

                                                               13
3.3 Methodologies Applied by Other Ratings Agencies
The S&P methodology in rating MDBs may be compared with those employed by other ratings
agencies. Of these, the DBRS approach resembles that of S&P most closely, with ratings being
based on a combination of scores for intrinsic assessment and support assessment. The intrinsic
assessment relies in part on a capital to Risk Weighted Assets ratio, but in the DBRS approach
the RWAs are a slightly modified version of the Basel RWAs.

         Fitch issues intrinsic and support ratings for each MDB. The approach mixes qualitative
and quantitative indicators via a scoring system. Fitch does not employ a notion of Risk
Weighted Assets. It measures capital adequacy using three ratios: i) Shareholders' equity/total
assets and guarantees (15.0 percent of the total rating evaluation), ii) Paid-in capital/subscribed
capital (3.5 percent) and iii) Outstanding debt/shareholders' equity (12.5 percent).

         Like Fitch, Moody's (2013) employs a scorecard approach. Capital adequacy and
liquidity factors are used to infer Intrinsic Financial Strength. This is then combined with a
scoring of Member Support to obtain a final rating range. Capital adequacy is assessed using the
following indicators: i) Position (weighted 50 percent) comprising two indicators: Asset
Coverage Ratio and Leverage as measured by Debt as percentage of Usable Equity; ii) Asset
Quality (weighted 40 percent) comprising two indicators: Borrower Quality (based on Weighted
Average Borrower Rating) and Non-Performing Assets (expressed as NPLs as a percentage of
Total Loans); and iii) Profitability (weighted 10 percent) comprising two indicators: Return on
Assets (in percent), Net Interest and Dividend Margin-to-Earning Assets (in percent). These are
then subject to the following Adjustment Factors ranging from -3.5 to +1 notches based on three
factors: Portfolio Concentration, Operating Environment and History. No use is made of Risk
Weighted Assets.

3.4 S&P's Risk Adjusted Capital Ratio
To calculate its RAC ratio, S&P employs a set of Risk Weights (RWs) for the various asset
classes that banks hold.20 These weights depend on the ratings of the claims as well as on the
asset class in question. Detail on the various RWs may be found in Standard & Poor's (2012a).

20 The risk weights (RWs) employed by S&P are represented by the agency as comparable to, but currently,
somewhat different from Basel regulatory RWAs. S&P suggests that the two may move closer over time as Basel III
rules are progressively implemented. In fact, as we explain below, the S&P RWs are quite different in conception
from the Basel RWs, and it would be highly surprising if the two sets of risk weights converged.

                                                         14
For MDBs that primarily lend to sovereigns, the most important weights are those shown in
Table 6. The weights depend on the rating of the sovereign and on the fraction of multilateral
debt in total external debt.

Table 6. Central Government Risk Weights

               Share of multilateral debt in the
               total external debt

               <25%  25%-  50%-  >75%
                      50%   75%

AA- and above  3     3     3     3

A+             3     3     3     5

A              3     3     5     9

A-             3     5     9 15

BBB+           5     9 15 23

BBB            9 15 23 34

BBB-           15 23 34 47

BB+            23 34 47 62

BB             34 47 62 79

BB-            47 62 79 99

B+             62 79 99 122

B              79 99 122 146

B- and below   99 122 146 173

Note: This table shows how S&P calculates risk
weights to account for PCS, depending on the
sovereign long-term foreign currency credit rating.
Entries are in percent. The right hand column contains
risk weights applied to debt par values when
multilateral debt is so large that the agency expected
PCS to play no role. For given ratings, weights in other
columns are lower to reflect the effect of PCS.
Source: Standard & Poor's (2012a).

         The latter dependence is intended to reflect how one might expect PCS to influence loss
experience.21 When all debt is multilateral (i.e., borrowings from MDBs and comparable
institutions like the IMF), a sovereign that wishes to lighten its debt burden by defaulting will be
unable to treat MDB loans as senior. On the other hand, a sovereign that has borrowed only a

21 Heavy reliance on PCS debt may distort outcomes in some cases. Steinkamp and Westermann (2014) examine the
implications of the increase in the fraction of some countries' debt that is owed to lenders enjoying PCS. Increasing
public lending may have the effect of increasing interest rates on private financing which becomes highly
subordinated. PCS may be seen as an element within the broader arrangements and conventions for restructuring
sovereign debt. These are discussed by Brooks et al. (2015), who propose various reforms.

                                                         15
fraction of its debt from multilateral institutions will be able to treat this debt preferentially if it
so chooses and still achieve a reduction in its debt burden.

         When S&P wishes to calculate RWs for sovereign exposures not allowing for PCS, it
employs the weights in the far-right column in Table 6. The adjustment for PCS that S&P then
suggests is to calculate total portfolio RWAs using this far-right column for sovereign exposures
minus portfolio RWAs when the weights contained in all the columns of the table are
employed.22

         The RAC ratio as described above using the far-right column of Table 6 is termed
"unadjusted" by S&P. By this, the agency means that the simple RAC is not adjusted for
concentration or diversification or for PCS. To arrive at an "adjusted RAC," S&P adjusts for
PCS as just described as well as adjusting for four types of dependence: i) country/region
concentration/diversification, ii) sector concentration/diversification, iii) business line
concentration/diversification, and iv) individual obligor concentration.

         RWA dependence adjustments for a, b and c are calculated using the same approach. The
adjustment is calculated by applying assumptions of correlations among different geographies,
sectors and business lines. Consider one of these three dimensions of dependence, s, where s is
one of a, b, or c. The adjustment for dimension s is calculated as follows:

      1()  1()   1      1(,)  1()  1()
                     
                                          -  ()  (1)

      ()  ()     (,)1   1     ()  ()

         Here, () is the unadjusted-RAC RWA for category j under dependence dimension s,
i.e. the weighted sum of exposure amounts in a particular category j where the weights are those
specified by S&P in Standard & Poor's (2012a). For example, if s were a, i.e., the adjustment in
question was for geographical regions, () would be the RWAs for a particular country.

         The weight () that appears in equation (1) is referred to by S&P as the concentration
factor for category j under dependence dimension s, while the constant (,) is the correlation of

22 The recognition of PCS in the ratings of MDBs (and related institutions like the IMF) is perhaps the most explicit
way in which PCS affects agency ratings. Early discussion of PCS by the ratings agencies focused on how PCS
might mitigate sovereign ratings ceilings. See Standard & Poor's (1998) and (2000) for example.

                                                         16
risk categories i and j under dependence dimension s. S&P uses separate correlation matrices for
geographic regions, industries and business lines. For geographic regions and industries
correlations, S&P estimates these correlations using MSCI equity indexes. Business line
correlations are derived judgmentally by the agency.

         In formula (1), () is the RWA after the adjustment for diversification under
dependence dimension s. The difference between the RWA after adjustment and the RWA
before adjustment is the adjustment for diversification. The adjusted RWA for all three
dimensions, denoted (,,) is then defined as:

                  (,,)  () + {,,}() - ()                                                            (2)

       Note that the geographic diversification adjustment is applied to both sovereigns and non-

sovereigns. The sector diversification adjustment, in contrast, is applied to non-sovereign

exposures only. In our analysis below, we make no adjustments for business line diversification.

       The last adjustment, in this case for individual exposure concentrations, is implemented

using very different and somewhat less consistent assumptions. (The reasoning above is

consistent in that RWAs are all based on volatilities and correlations.) For the top 20 exposures,

an adjustment to RWAs is made by adding a quadratic, scaled version of an upper bound for

concentration risk suggested by Gordy and Ltkebohmert (2007). The adjustment for corporate

exposures, following the Gordy and Ltkebohmert notation, is as follows:

   = 11.7  2 + 0.19                                                                               (3)

Here,

                        1  = 1  2          + (         -  1)(     - )  +  (      - )                (4)
                       2

where

         =          ,  is  the  share  of  the  total  portfolio  corresponding  to  exposure  .
             

        = max(,  = 1, ... , ), is the largest  among the top  exposures.

        =   ( + ) - , is used for notional convenience and = 4.83.

         = 2+ 25% (1-),                  can  be     viewed  as  a  stressed  LGD  using     its  normalized

                              

       variance.

                                                       17
 =    -11(- ) + 1- -1() -      , is

the Basel II unexpected loss for exposure .
 =   , is the expected loss for exposure .
 = = 1 , is the cumulative unexpected loss for the  largest exposures.
is the RAC charge for the entire corporate portfolio.
 = = 1 , is the cumulative expected loss for the m largest exposures.
is the S&P normalized loss for the entire corporate portfolio.

For sovereign exposures, the adjustment is simplified to:

   =                                                          1  =1  2     (5)
                                                             2

As noted above, the single name concentration risk adjustment is based on a different

modelling paradigm than the diversification adjustments employed by S&P. We will show in the

results section below that the agency's approach produces results that are much more

conservative than those obtained using a simple alternative approach, which is more in the spirit

of S&P's diversification adjustment.

To adjust for PCS, as explained in the context of Table 6, S&P calculates the unadjusted

RAC with lower central government risk weights than those included in the standard RAC

methodology. (The lower risk weights, which appear in Table 6 in columns other than the

rightmost, depend both on the sovereign's rating and on the share of multilateral debt in the

sovereign's total external debt.) The decrease in the RWA induced by this change in the risk

weights is then subtracted from the fully adjusted RWAs to obtain a final PCS-adjusted RWA.23

3.5 Theoretical Justification for the S&P Methodology

To understand the theoretical underpinnings of the S&P approach, suppose that an institution
defaults when its capital at a future date 1 (denoted 1) falls below a level . The probability of
default at date 0 may be written as:

 = (1 < )                                                                  (6)

23 This builds on Martin and Wilde (2003) and Gordy (2004).

                                                         18
Suppose that future capital has a distribution such that:

                               =  -0-                                       (7)

where 0 is initial capital and  equals the forecast increase in capital over the period in question

and  is the standard deviation of risky assets and  is a monotonically increasing function.

Distributions consistent with these assumptions include the family of elliptical distributions with

finite second moments such as Gaussian and Student's t distributions.

         If  = 0, inverting the above gives a relationship between the ratio of forecast capital,
0 +  to total asset volatility, , and the default probability.

                                  =  - -1()                                 (8)

                                

If one associates different ratings grades with different maximum default probabilities, given a

distribution, , one may determine ratings using minimum forecast-capital to total-asset-

volatility ratios.

To make such an approach operational, one must have ways of calculating the numerator

and denominator in the ratio on the left side of equation (8). Current capital plus forecast retained

earnings and net capital issues imply the numerator. Estimating the denominator in a simple

fashion is more challenging.

To understand the approach taken by S&P, suppose a bank invests in N asset classes, and

its holding of asset class i is Ai. Then,  may, in general, be written as:

                               = =1 =1 ,, ,,                                (9)

Here, the parameters ,, and , are asset correlations and volatilities, respectively. Note that
asset value volatility here is a quadratic expression and cannot be expressed as a weighted sum of
asset exposure values, i.e., as RWAs.

         If all the asset class returns are perfectly correlated, however, (i.e., ,, = 1), then:

                     = =1 =1  ,, = = 1  , =1 , = =1 ,                       (10)

Alternatively, suppose the portfolio is made up of many assets that are not perfectly

correlated but which have shares of risk () on a single risk factor and on idiosyncratic shocks

                              19
(1 - ) that wash out in a large portfolio. In this case, the total portfolio volatility would equal
 =1 ,. Hence, when returns are perfectly correlated (or alternatively, when the only
non-diversified risk in a large portfolio is exposure to a single risk factor), total portfolio
volatility equals a form of risk weighted assets or RWAs.

         The diversification adjustments employed by S&P are fully consistent with the above
formulation. In equation (1), the ()equals the risk weighted assets corresponding to a single
asset class (leaving aside diversification across multiple risk factors). Such single-asset-class
RWAs are combined using a correlation matrix for the multiple risk factors. This is consistent
with the RWAs being proportional to total asset volatility.

3.6 Comments on the S&P Methodology
Several aspects of the S&P methodology deserve comment. First, the sequential adjustment for
different dimensions of diversification a, b and c as described above is only approximate. To
calculate diversification effects rigorously across different dimensions (such as geographical
regions, sectors and business lines), one must expand the correlation matrices employed by S&P.
To be specific, for each region a full set of matrix rows corresponding to sectors and business
lines should be present in this expanded matrix. Using the notation of equation (1) and for
simplicity, abstracting from business lines, one would then perform a diversification adjustment
using a correlation matrix with J (a)  J (b) rows and columns.

         Given two matrices say for sector and region, banks use several different approaches to
infer a larger dimensional matrix. A common approach is to suppose that each obligor has an
exposure to one common factor which is a weighted sum of two factors, specifically the sector
and region factors corresponding to the sector and the region of the single exposure. While the
relative weight of the sector and region factors for each individual exposure is sometimes
estimated, at least some banks simplify by supposing that the composite factor for each
individual exposure is an equal weighted sum of a global sector and a region/country factor. A
second approach that is used by some banks to generate the larger dimensional correlation matrix
is to assume that it equals the Kronecker or tensor product of the two smaller matrices. Below, in
order to study the conservatism or otherwise of the S&P approximation, we apply these two
approaches to expanding the matrices.

                                                         20
         Second, it is notable that the S&P diversification adjustments are made without
themselves being PCS-adjusted. PCS reduces the risk of defaults affecting not just the base case
unadjusted RWA, but also the deviations from this base case attributable to diversification. One
might consider it more appropriate, instead of following the S&P order of calculation, to
calculate the so-called unadjusted RAC ratio inclusive of PCS adjustments and then to introduce
diversification adjustments. Again, below, we evaluate the conservatism or otherwise of the S&P
approach.

         Third, one may enquire whether the adjustment in risk weights for PCS made by S&P is
appropriate in magnitude. The above discussion suggests that one may assess this issue by
looking at the relative volatility of debt that enjoys PCS status from that which does not.
Volatility for debt enjoying PCS status is not directly measurable as it is not publicly traded.
However, one may calibrate the differences in default probability and infer an adjustment in the
volatility of value. We shall perform such a calibration below, simulating the IDB portfolio with
and without PCS adjustments and then comparing the relative portfolio volatilities.

         Fourth, one may consider alternative approaches to allowing for single name
concentration risk. The approach taken by S&P appears quite inconsistent with the other
adjustments that the agency includes for correlation. While its diversification adjustments are
based on asset volatility adjustments, S&P employs for single name concentration the adjustment
described in equations (3)-(5) above, which is taken from Gordy and Ltkebohmert (2007).
These authors develop a granularity (or single name concentration) adjustment based on an
asymptotic expansion of the CreditRisk+ model (devised by CSFP, 1997). Their analysis builds
on Wilde (2002) which derives such adjustments for CRMs more generally.

         CreditRisk+ is a default mode model and in any case the asymptotic expansion is only
valid locally. The examples that Gordy and Ltkebohmert provide involve adjustments in capital
of between 2 percent and 15 percent. When applied to the IDB portfolio, the adjustment to
capital amounts to well over 100 percent. One may doubt whether a local approximation is
appropriate in this case.24 Below, we examine an alternative approach to adjusting for single
name concentration which is more in the spirit of the other adjustments S&P adopts for
diversification effects.

24 One may also question whether using an adjustment based on a default mode model is appropriate. Basel RWAs
as Gordy and Ltkebohmert (2007) note are derived from an economic-loss mode model.

                                                         21
         To summarize, several aspects of the S&P methodology merit further investigation and,
in the results section below, we return to these issues and evaluate the implications for MDB
ratings using the credit standing of the IDB as an example.

3.7 Portfolio Credit Risk Modeling

The second methodology that we apply to examine the credit standing of our primary example
MDB, the IDB, follows industry-standard credit risk modeling approaches. This approach,
widely used by banks and ratings agencies, consists of simulating the evolution of ratings using
techniques based on the Ordered Probit model employed in statistical analysis of discrete choice
data. Correlated random factors are simulated using Monte Carlo methods and these are mapped
into changes in the ratings of individual obligors based on a set of cut-off points. The cut-off
points are inferred from estimates of ratings transitions matrices.

         To understand more precisely how the model works, first consider the random behavior
of a set of ratings for individual loans. Suppose there is a set of credit exposures denoted by
 = 1,2,  , . Assume that at date , exposure  has a rating, Rit, taking one of  values,
1,2,  , . Here, indicates the default state, while state 1 indicates the highest credit quality
category.

         Since we need to analyze the actual ratings dynamics and perform pricing calculations,
we must distinguish between actual and risk-adjusted distributions of ratings changes. Assume
that under both actual and risk-adjusted probability measures, Rit evolves as a time
homogeneous Markov chain. The actual and risk-adjusted K  K transition matrices are denoted:
M and M respectively. The (i, j)-elements of M and M are mi,j and mi,j respectively. Let mi,j,
and mi,j, denote the (i, j)-elements of the -fold products of the matrices M and M, i.e. M and
(M).25

25 The actual transition matrix, M, may be estimated from historical data on bond ratings transitions. The risk-
adjusted transition matrix M may be deduced from bond market prices, in particular, from spread data on notional
pure discount bonds with given ratings. To see how one may achieve this, note that if credit risk and interest rate risk
are independent and spreads only reflect credit risk (i.e., there are no tax or liquidity effects), the -maturity spread
on a pure discount bond with initial rating i, denoted Si , satisfies:
exp-S(i) = mi,K,t, K, tmi,K,t)
Here,  is the expected recovery rate in the event of default.
Let   1, 2,  td denote a set of integer-year maturities. To infer the risk-adjusted matrix, we may choose mi,j,o
for i, j = 1,2, a set and tan to minimise:
minmi,j,m  iK==11(S(i) - (mi,K,m, K, mmi,K,m)))2

                                                         22
         We have just described a theoretically consistent set of the actual and risk-adjusted
marginal distributions of ratings for our set of I exposures. Now consider how one may simulate
changes in ratings incorporating dependence between ratings changes for different obligors.

         We employ the Ordered Probit approach widely used in ratings-based portfolio credit risk
models. For any row of M (say the jth row), one may deduce a set of cut-off points Zj,k for
k = 1,2,  , K - 1 by recursively solving the equations:

mj,1 = (Zj,1)

mj,2 = (Zj,2 - Zj,1)                                                                                 (11)

 

mj,K = 1 - (Zj,K-1)

Here,() is the standard normal cumulative distribution function. Doing this, we obtain a set of

ordered cut off points: Zj,1  Zj,2    Zj,K-1.

Given an initial rating, j, to simulate a change in the rating from t to t + 1 for exposure i,

we draw a random variable Xi,t+1. If Zj,k-1 < Xi,t+1  Zj,k (where by convention Zj,1 = - and

Zj,K = ), exposure i's rating at t + 1 is k.

         The latent variables Xi,t that determine changes in ratings are assumed to be standard
normal random variables. To include dependency between the ratings changes of different

exposures, assume that the Xi,t's, for exposuresi = 1,2,  , I, satisfy a factor structure, in that:

Xi,t = 1 - 2 Jj=1 ai,jfj,t + ii,t                                                                    (12)

Here, the fj,t are factors common to the latent variables associated with the different credit

exposures and the i,t are idiosyncratic shocks. The fj,t and the i,t are standard normal and the
weights ai,j are chosen so that the total factor component for exposure i denoted:(), 
Jj=1 ai,jfj,t, is also standard normal.

         If one knows the risk-adjusted probabilities of default for individual exposures and

assumes that defaults, recovery rates and shocks to interest rates are independent, the valuation

Here, note that the mi,K,, are implicitly functions of the mi,k. (Note, we attach penalties to the objective function if
entries in the transition matrix become negative in the course of minimization. This ensures the resulting risk
adjusted matrix is well-behaved.)

      In performing this calculation, we assume that the recovery rate  is 50 percent and that the maturities in  are
1, 2, . . . , 8 years. The spread data we employ are time averages of pure discount bond spreads calculated by
Bloomberg based on price quotes for bonds of different ratings and maturities issued by industrial borrowers.

                                                         23
of individual exposures at some future date conditional on ratings is straightforward. For
example, under these assumptions, the price Vt,R of a defaultable fixed rate bond with initial
rating R, coupons c, and principal Q is:

Vt,R = Ni=1 c exp-rt,t+ii (1 - mR ,K,i + mR ,K,i) + Q exp-rt,t+NN (1 - mR ,K,N + mR ,K,N)  (13)

         Here, rt,t+i is the i-period interest rate at date t. It is simple to derive pricing expressions
for floating rate loans and many other credit sensitive exposures under these assumptions as well.

Drawing together the various elements described above, one may simulate dependent

ratings for all  exposures. The steps involved are the following:

1. Draw the, and , and calculate the latent variables for each exposure and
    each period using equation (12).

2. Deduce the time path followed by the ratings by comparing the latent variable
    realizations with the cut-off point intervals ,-1 < ,+1  ,.

3. Conditional on the rating at the chosen future date, price and  exposures.
4. Repeat the exercise many times to build up a data set of value and rating

    realizations.

         The above list of steps explains how one may simulate the value of a portfolio of credit
risk instruments in order to calculate risk statistics such as Value at Risk or Expected Shortfall.
To simulate the portfolio value to estimating price, one may perform a comparable simulation by
using the risk adjusted transition matrix, M, instead of the actual transition matrix, M, as the
basis for the probabilities of transitions from one rating category to another. The price of any
security is then the expected payoff on that security calculated using these risk adjusted
distributions.

4. Data and Calibration

This section describes the IDB portfolio that we evaluate using both the S&P RAC ratio and
ratings-based CRM methodologies and the calibration we employ in the latter analysis. Table 7
summarizes the credit risk portfolio data as it is broken down for use in the S&P RAC ratio
calculation. One may observe the dominant role of Government and Central Bank credit

24
exposures, contributing 88 percent of credit exposures by par value.26 Financial institutions
contribute another 8 percent.

Table 7. Credit Risk Portfolio Data

Credit risk category    Exposure amount
Gov. and Central Banks                 106,951
Institutions                            10,269
Corporate                                 3,721
Securitization                              482
Other Assets                                482
Total                                  121,905

Note: Exposure amounts are in millions of USD and are
based on June 2015 information.
Source: IDB.

         In its own internal portfolio classification, the IDB breaks its credit risk exposures into
three broad categories: Sovereign (SG) loans, Non-sovereign (NSG) loans and Investments. SG
loans contribute 67 percent of the total credit portfolio, NSG loans account for 5 percent and
Investments represent 28 percent. For the credit exposures described in Table 7, 74 percent of
Government and Central Bank exposures fall into SG loans, while 24 percent fall into
Investments. Some 27.4 percent of Institution exposures belong to NSG loans, while 72.6
percent belong to Investments. Almost all corporate exposures (97 percent) consist of NSG
loans, the rest being Investments. All securitizations belong to Investments. We leave aside
consideration of Other Assets, which represent only a very small fraction of total assets.

         Table 8 shows the distribution of IDB's exposures to central government as a fraction of
its portfolio broken down by the share of indebtedness to multilateral lenders in its total external
debt. The figures in Table 8 should be compared with S&P's central government risk weights (by
rating and exposure to multilateral lenders) shown in Table 6. A significant share of the IDB's
portfolio consists of central government loans with ratings in the vicinity of BBB. For such
ratings, the risk weights without allowance for PCS (as shown in the far-right column of Table 6)
are around two to three times higher than when allowance is made.

26 Some MDBs lend extensively to the private sector on a non-sovereign-guaranteed basis. Romero and Van de Poel
(2014) describe such activities. In contrast, the IDB's portfolio consists mostly of sovereign loans.

                                                         25
        Table 8. Portfolio Distribution

        Shares in total multilateral debt

Rating  <25% 25% - 50% - >75%
                    50% 75%

AA- and above 0.6% 0.0% 0.0% 0.0%

A+      0.0% 0.0% 0.0% 0.0%

A       0.0% 0.0% 0.0% 1.1%

A-      0.0% 0.0% 0.0% 0.0%

BBB+    17.5% 3.2% 0.0% 0.0%

BBB     2.5% 12.0% 0.0% 0.4%

BBB-    20.7% 0.0% 0.0% 0.0%

BB+     0.0% 0.0% 0.0% 0.0%

BB      0.0% 1.5% 5.6% 0.0%

BB-     0.0% 3.3% 0.0% 0.5%

B+      0.0% 0.0% 7.6% 0.0%

B       0.0% 2.0% 0.6% 1.4%

B- and below 3.4% 16.1% 0.0% 0.0%

Note: The table shows the shares of IDB's portfolio of
credit exposures to central governments broken down by i)
rating and ii) groups of countries for which multilateral
debt comprises percentages of total external debt falling
into particular ranges. The data pertain to June 2015.
Entries before rounding sum to 100 percent.

         To enter the SG loans, NSG loans and Investments into exposure types within our CRM,
we adopt the assumptions described below.

         All SG loans are modelled as Sovereign Floating Rate Notes (SFRN) with fixed spreads
over LIBOR. We assume that the coefficient on the idiosyncratic factor in equation (12), denoted
, equals zero. The mean and volatility of the recovery rate for SG exposures are assumed to
equal 0.5 and 0.25 respectively.27 The assumed duration of SG loans was calculated using IDB's
country-specific SG loan amortization schedules. The CRM requires that we specify the cash
flow characteristics of exposures. We assume a 115 bps spread and 50 bps commitment fee
except one outstanding Ecuador DSL which is another type of Contingent Loan. For this DSL,
the spread is 165 bps and commitment fee is 75 bps.28

27 These values are consistent with standard credit risk modelling assumptions for senior unsecured corporate bonds
and are conservative when applied to sovereign exposures.
28 Note that the IDB portfolio consists of relatively simple financial instruments. Credit exposures are almost all
conventional loans, bonds or deposits. Some authors have argued that MDBs should take on somewhat less standard

                                                         26
         NSG loans are modeled as defaultable Floating Rate Notes (FRNs). We employ a
detailed database of all NSG loans outstanding at June 2015 consistent with RAC ratio
calculation data.29 We assume the same commitment fees as the SG loans.

         For NSG loans, the credit quality is driven by a single country factor, a single industry
factor and idiosyncratic risk. The industry-country ratio is assumed to be 0.5 and the
idiosyncratic risk weight is 0.5. The mean recovery rate is assumed to depend on the loan's
seniority. Senior debt is assumed to have 0.5 mean recovery rate and sub-debt is assumed to have
0.3 recovery rate. Both seniorities have a recovery volatility of 0.25.30

         Investments comprise exposures to Government and Central Banks, Institutions,
Corporates and Securitizations (ABS-MBS). All investments are modeled as Fixed Rate
Bond/Loan exposures except Cash, which is modeled as a default-free bond with a 1 percent
interest rate. We assume a 5 percent coupon rate for all other Fixed Rate Bond/Loan exposures
and a 4 year maturity.

         Exposures to Government and Central Banks are modeled as Fixed Rate Sovereign Bond.
ABS-MBS, Institutions (excluding cash) and Corporates investments are treated as diversified
pool exposures.31These exposures are assumed to be driven by a single country factor and
idiosyncratic risk. The idiosyncratic risk weight is assumed to be 0.5.

         As there is no country/region information available for ABS-MBS, we assume ABS-
MBS is equally distributed in the regions Europe and North America. The diversified pool
exposures are assumed to be driven by a single country factor and idiosyncratic risk. The
idiosyncratic risk weight is assumed to be 0.5 for all diversified pool exposures.

5. Results

5.1 S&P Analysis of IDB

We begin by examining S&P's analysis of the IDB RAC ratio in Table 9. Column 2 of the table
sets out the agency's calculation. Column 3 shows our replication of this calculation based on the

exposures. MDBs typically operate with relatively conservative loans and commitments. For example, Humphrey
and Prizzon (2014) suggest that MDBs could extend their operations to include a wider use of guarantees. See also
Fitch Ratings (2006).
29 In one or two cases, where data is missing we interpolate using other data on similar loan-country combinations.
30 The recovery rate means and volatilities are consistent with those implied by Moody's historical recoveries data.
31 The diversified pool exposures we employ consist of infinitely granular loans pools modelled using a multi-period
generalization of the Vasicek loss distribution. Individual loans are assumed to default or not in each period and
parameters include period-by-period actual and risk adjusted default probabilities (the latter being used in pricing
calculations).

                                                         27
parameters given in Standard & Poor's (2012) and an estimate of the correlation matrices used
by S&P to perform the diversification adjustment. These matrices are not made public by S&P,
so we have estimated suitable correlation matrices based on MSCI equity indices. The
diversification adjustment we obtain is reasonably close but not identical to that of S&P.32

         The results shown in Columns 2 and 3 of Table 9 are notable in several regards. Firstly,
IDB's dominant exposure category is Government and Central Banks. This category contributes
$64 billion to IDB's total of $72 billion unadjusted credit risk RWAs. Secondly, the PCS
adjustment appears very small considering the bank's own loss experience. Considering cases
where sovereigns have defaulted on other debt since 1960, in only 11 percent of those cases was
there a non-accrual event for the IDB.33 Thirdly, the Industry and Geographical Region
diversification appears relatively small, reflecting the fact that the portfolio has significant
concentration to South American sovereigns. Fourthly, the single name concentration adjustment
is extremely large, leading almost to a tripling of credit risk RWAs after adjustment for
diversification and PCS.

         We wish to examine the issues with the S&P methodology raised in Section 3. These
issues include: i) sequential adjustment for diversification adjustments, ii) the fact that
diversification and Single Name Concentration (SNC) adjustments are performed before
adjustment for PCS, iii) the magnitude of PCS adjustments, and iv) the approach S&P takes in
adjusting for SNC. We analyze these issues in the next four subsections. The results of
sensitivity analyses of these issues are reported in Table 9.

32 There remain some aspects of the S&P calculation that are opaque. For example, it is unclear how exposures to
government bodies are treated in the sector diversification adjustment. We have made the assumption that they are
dropped, but this may not correspond to what S&P is actually doing in its calculation.
33 See "Annex  IDB's PCT Adjustment Methodology" to "Regulations Governing the Implementation of the
Capital Adequacy Policy" (unpublished document prepared by IDB Finance Department). Most non-accrual events
imply delayed payments of interest. So the only "losses" to the IDB in these cases is interest on those interest
payments (which is not charged) or penalty interest rates that might typically be included in a commercial loan
contract.

                                                         28
                        Table 9. Replication of S&P RAC Ratio Calculations

                                                     Sequential Diversification The

                                                     adjustment for and SNC after magnitude

                                   RWA (S&P RWA (RCL diversification PCS          of PCS          SNC

                                   calculation) calculation) dimensions adjustment adjustments concentration

Credit Risk

Gov. and Central Banks             64,116   64,116

Institutions                       2,550    2,550

Corporate                          4,859    4,859

Securitization                     302      302

Other Assets                       542      542

Total Credit Risk                  72,368   72,368   72,368               72,368          72,368       72,368

Total Operational Risk             4,295    4,295    4,295                4,295           4,295        4,295

RWA before adjustments             76,663   76,663   76,663               76,663          76,663       76,663

MLI Adjustments

Industry and Geo Diversifications  -8,310   -8,066   -8,112               -4,816          -8,066       -8,066

PCS                                -15,909  -15,909  -15,909              -15,909 -42,478              -15,909

SNC                                92,138   91,025   91,025               78,098          91,025       19,168

High Risk Exposure Cap             -8       -8       -8                   -8              -8           -8

Total MLI Adjustments              67,911   67,042   66,995               57,365          40,473       -4,815

RWA after adjustments              144,573  143,704  143,658              134,028 117,136              71,848

Adjusted common equity (ACE)       24,719   24,719   24,719               24,719          24,719       24,719

RAC Before Adjustments             32.24%   32.24%   32.24%               32.24%     32.24%            32.24%

RAC After Adjustments              17.10%   17.20%   17.21%               18.44%     21.10%            34.40%

AAA Callable                       12,095   12,095   12,095               12,095          12,096       12,095

RAC After Adjustments and AAA      25.46%   25.62%   25.63%               27.47%     31.43%            51.24%
callable

Notes: Figures are in millions of US dollars unless otherwise specified. In the first block, when comparing the
unadjusted RWA, we use the same data set as used in the IDB RAC ratio calculation. Our unadjusted RWA
calculation for each credit risk category is identical to what IDB has obtained. In the second block, when
calculating the industry diversification and single name concentration for NSG, we use a slightly different data
set, as we need to know the single sector information for individual obligor which is not provided in the IDB
RAC ratio calculation Excel work book. This is why we obtained slightly different numbers for Industry
Diversification and SNC adjustments. Figures do not include the impact of the recent Argentina upgrade.

5.2 Sequential Adjustment for Diversification Dimensions
Firstly, we examine the effects of the approximation involved in the sequential adjustment for
different dimensions of diversification. As noted in Section 3, the S&P approach involves an
approximation in that adjustment for diversification in multiple dimensions and is made
sequentially as a series of separate adjustments rather than making a single global adjustment. To
examine the impact of this approximation for region and sector diversification (we ignore
business line diversification), we estimate large dimensional correlation matrices and perform a
single diversification adjustment across region and sector simultaneously.

                                            29
         We generate large dimensional matrices using two approaches common in the industry: i)
a Kronecker or tensor product approach and ii) a Weighted-Sum-of-Indices technique. Approach
i) consists of estimating separate correlation matrices for region factors and for sector factors and
then constructing a large dimensional matrix as the Kronecker product of the two separate
matrices. Approach ii) consists of estimating a correlation matrix of region and global sector
factors and then generating a larger dimensional matrix consisting of the correlation matrix of all
possible pairs of a single region factor and a single sector factor.

         We compare the results of these two approaches with the S&P sequential adjustment
approach. The portfolio standard deviation is in each of the three approaches calculated as
follows:

1. The Kronecker product approach
    The correlation is estimated as:

          = (R)(S)                                                                  (14)

Here, (R) is the region correlation matrix and (S) is the sector correlation

matrix.

The standard deviation of a portfolio is then estimated as:

          =                                                                         (15)

2. The Weighted-Sum-of-Indicators Approach

The (Ns(i - 1) + j, Ns(k - 1) + l)th entry of the correlation is estimated as:

         (Ns(i-1)+j,Ns(k-1)+l)  =     Cov  ()+( )     ,   ()+()  =  1  ((Ri,k))  +  ((Ri,l,)S)  +
                                                                    4
                                                   2          2

                                                             ((Rk,,jS)) + ((Sj,l))  (16)

    Here, (R,S) is the region sector correlation matrix.
             The standard deviation is estimated in the same way as in equation (15).

3. The S&P sequential adjustment approach
    The S&P approach is as follows:

 = 1 + ()()() - 1 + ()()() - 1                                                      (17)

                                           30
         In each of the above approaches, the correlation matrices (R),(S) and (R,S)are
estimated from MSCI equity indices.

         Table 10 presents a comparison of portfolio standard deviations obtained under the three
methods. The portfolio weights employed are those from the IDB's NSG portfolio. As one may
observe (and this remains true for other portfolios that we examined), the S&P approach yields
lower portfolio standard deviations than the more rigorous approaches of working with a larger
dimensional correlation matrix and adjusting for diversification across multiple dimensions in a
single step. In the case of the IDB NSG portfolio, the S&P approach yields results that are only
slightly less conservative. With other portfolios, one may find cases in which the S&P approach
is markedly less conservative than the more rigorous approaches.

Table 10. Estimated Standard Deviation Using Actual Weights34

                               sd from

                               Kronecker sd from

                               product of average of S&P

                               correlations correlations adjusted sd

Actual weights (IDB NSG only)           0.81      0.84    0.80

Note: The table shows the standard deviation of the IDB portfolio adjusted in three
different ways for diversification. The undiversified portfolio standard deviation is
normalized to unity. The three approaches consist of i) creating a large correlation
matrix from a region and a global sector matrix (both being estimated using MSCI
equity indices) by taking the Kronecker product of the two; ii) creating a large
correlation matrix by supposing that each factor corresponding to a region-sector
pair comprises the equally weighted sum of a region and a global sector index; and
iii) adjusting sequentially for region and sector correlations using the S&P
approach. The portfolio weights employed are those of the IDB NSG portfolio.

         To evaluate the impact of the S&P sequential diversification adjustment on the IDB's
RAC ratio calculations, we scale up the industry and geographic diversification adjustment for
the NSG portfolio only by the ratio: . (The change only affects the

                                                                              &

NSG portfolio because only this is broken down both by region and sector.) The result is a small

34 We also estimate the standard deviation using randomly simulated weights. We generate a random, uniformly
distributed weight w to each combination of country and sector; the portfolio weights are then normalized. The
estimated standard deviations for the three different approaches are 0.68, 0.8 and 0.65.

                                                         31
increase in the diversification adjustment. The corresponding adjustments and RAC ratios are
given in the fourth column of Table 9.

5.3 The Order of Calculation of the PCS Adjustment
The second issue we examine is the order of calculation of the PCS adjustment. One may
question whether it is appropriate to calculate the unadjusted RAC ratio without allowing for
PCS. This is material because the diversification and single name concentration adjustments are
calculated as deviations from a base (unadjusted) RWA figure. It would seem more reasonable to
calculate adjustments as deviations from an RWA figure that is inclusive of the PCA adjustment.

         Column 5 of Table 9 shows the results of using the PCS-adjusted RWA as the base case
for the diversification and single name concentration adjustments. The lower base means that
the magnitudes of adjustments as deviations from the base tend to be lower. The reduction in
RWA reflecting diversification falls from $8.1bn to $4.8bn when the PCS-adjusted base is used
instead of the unadjusted base. In this respect, the order of calculation implicit in the S&P
adjustment for diversification is not conservative.

         On the other hand, the adjustment for single name concentration falls by $12bn from
$90.5bn to $78.1bn. The RAC ratio after using the post-PCS-adjustment base case is 27.5 instead
of 25.7.

5.4 The Magnitude of PCS Adjustments
Thirdly, one may question the magnitude of PCS adjustments. We performed a Monte Carlo
(MC) simulation in our CRM to examine the impact on portfolio volatility of adjusting for PCS.
The portfolio we used in MC simulation is IDB SG portfolio only. With PCS adjustments, we
assume the default probabilities of sovereign loans are reduced by 80 percent. Given that the
IDB's loss experience is that it incurs losses on only 11 percent of occasions on which its
borrowers default, an 80 percent reduction seems reasonable. In this case, the SG portfolio
volatility drops by a factor of 3.04 from 1,458 to 480. This may be compared to the proportional
reduction in SG RWA assumed by S&P of 1.34.

         The RWA from the S&P calculation and the portfolio volatility from MC simulation are
given in Table 11.The corresponding RAC ratio estimates are presented in column 6 of Table 9.
If one applies the CRM scaling factor of 3.04 to the S&P SG RWAs, one obtains a reduction in

                                                         32
RWA attributable to PCS of $42.5bn instead of $15.9bn. This leads to the RAC ratio after all
adjustments of 31.6 instead of 25.7.

                 Table 11. S&P RWA and RCL Volatility

                             S&P RWA RCL volatility

                 Before PCS  63,326    1,458
                 After PCS
                 Ratio       47,417    480

                                 1.34  3.04

                 Note: The table shows S&P's RWAs and the
                 volatility of the IDB's portfolio value calculated
                 using the CRM described in Section 3. The results
                 "Before PCS" adjustment are estimated using the
                 baseline calibration. The "After PCS" results are
                 calculated after reducing the default probability of
                 sovereign credit exposures by 80 percent. The ratio
                 of pre- to post-PCS-adjustment results is 1.34 for
                 the S&P RWAs but 3.04 for the CRM volatilities.
                 Figures do not include the impact of the recent
                 Argentina upgrade.

5.5 Single Name Concentration Risk
Lastly, one may question the adjustment for single name concentration employed by S&P. This
approach is not consistent with the rest of the methodology which involves adjustments for the
impact of different factors on total portfolio volatility. Instead, S&P apply the analysis of Gordy
and Ltkebohmert (2007). This is developed on the basis of an approximation to a default mode
CreditRisk+ model, which is very different from the basic S&P methodology which derives
capital inclusive of diversification effects assuming that losses are elliptically distributed.

         As an alternative to the S&P, CreditRisk+ approximation, one may develop a simple
volatility adjustment for single name concentration. We describe this adjustment below and then
apply it in the case of the IDB portfolio. Suppose that RWA are proportional to total portfolio
volatility. Assume that each exposure has a random return  defined as follows:

                  =  + 1 -                                             (18)

Here,  is the volatility of the individual position,  and are factor and idiosyncratic risk
components respectively, and their relative contribution to total asset return risk is reflected in

the parameter .

                             33
         Consider a large, granular portfolio in which idiosyncratic risk is diversified away. This
corresponds to the case with no single name concentration. In this case,

(=1 ) = =1  = (=1 )2                                                                    (19)

One may consider this as proportional to the base or unadjusted RWA for the portfolio.

If idiosyncratic risk is not diversified away,

                                                    

   =    +   1 - 

=1                                     =1           =1
                                       = =1 2 + (1 - ) = 1 22
                                                                                        (20)

Using equations (19) and (20), one may deduce a scaling adjustment for base case RWA

to reflect single name concentration.

    =    +(1-)                                                                         (21)

         The adjustment depends on the factor share parameter, , and  which is the Herfindahl
index of shares of RWAs in individual asset classes:

     = = = 1 22                            = 1( )2                                      (22)
                                           = 1  2
           = 1 2

We estimate  using the RWAs calculated from IDB top 20 SG and the top 20 NAG single

names. The unadjusted RWAs are shown in Table 12.

One may calculate the scaling factor:

                                       +(1-)                                            (23)

for different values of the factor risk share parameter  ranging from 0.05 to 0.5 using the above
estimated  parameter. The resulting scaling factor estimates are shown in Table 13.

         Considering Table 13, one should note that the scaling factor increases as the  parameter
decreases. What is a plausible value for this parameter? The Basel single risk factor model
assumes that corporate asset values have coefficients on common risk factors ranging from 12

percent to 24 percent. Assuming  equals 20 percent, one obtains a scaling of RWA of 1.3.
Scaling up the base RWA by 1.3 to reflect single name concentration, one obtains the RAC ratios
shown in column 7 of Table 9, i.e., 51.2 instead of 25.7.

                                           34
         Table 12. Top 20 SG RWA and Top 20 NSG Single Names RWA

Country      RWA NSG single name                                                           RWA

Argentina    22,391 Panama Canal Expansion Program                                         435

Brazil       7,892 Costa Rica Reventazon Hydroelectric Power Plant                         317

Ecuador      5,021 Peru LNG Project                                                        284

Venezuela    4,828 Argentina IMPSA Wind Energy Investment Program                          262

Mexico       3,276 Mexico Etileno XXI                                                      261

Dominican Republic 2,621 Costa Rica ICE Debt Refinancing                                   231

Colombia     2,568 Argentina AUSA Road Safety and Urban Mobility Program                   203

El Salvador  2,472 Regional Isolux Corporate Loan                                          184

Jamaica      2,191 Uruguay Montes del Plata                                                164

Guatemala    1,846 Brazil Pcem Thermoelectric Power Plant Project                         136

Honduras     1,192 Peru Chaglla Hydroelectric Power Project                                136

Costa Rica   991 Regional Hidrovias Transport                                              132

Paraguay     946 Paraguay Promoting Soybean Industrialization in Paraguay                  120

Bolivia      833 Regional IIG Regional Trade Finance Facility                              105

Nicaragua    759 Ecuador Quito International Airport                                       99

Uruguay      738 Regional Central American Mezzanine Infrastructure Fund                   95

Panama       689 Brazil Embraport Project                                                  93

Peru         601 Jamaica Transjamaican Highway Project                                     91

Barbados     434 Brazil Delba Vessel                                                       87

Suriname     425 Dominican Republic Boulevard Turstico del Atlntico Toll Roa 80

Note: The table shows the IDB's largest exposures in USD millions to single names.
Specifically, the data consist of the largest 20 exposures to central governments and the largest
20 exposures to corporates. Figures do not incorporate the effect of the recent Argentina
upgrade.

                  Table 13. Scaling Factors

             rho        scaling factor

                  0.05                                       2.0

                  0.1                                        1.5

                  0.2                                        1.3

                  0.3                                        1.2

                  0.4                                        1.1

                  0.5                                        1.1

         Note: The table shows the scaling factor defined in equation (23). The parameter

          (estimated using IDBs base-case S&P RWAs) equals 0.15. The results are
         shown for different values of the factor share parameter, .

5.6 Credit Portfolio Model Analysis
The previous sections have examined approximations and adjustments in the S&P RAC ratio
methodology. In some cases, we have employed the CRM described in Section 3 to calibrate
particular aspects of the RAC ratio calculations.

                                     35
         The CRM may alternatively be used directly to calculate capital appropriate for the IDB
portfolio that we use as the example for our analysis of MDB credit quality. Through its flexible
Monte Carlo approach, the CRM rigorously deals with diversification, single name concentration
and PCS adjustments. When calibrated using risk adjusted rather than historical distributions, the
CRM may also be used to link the analysis of credit risk to bond market spreads.

         We produced results for the following two cases: i) using a non-PCS adjusted calibration
for SG, and ii) using a PCS-adjusted calibration for SG. As noted above, PCS effectively boosts
de facto seniority in that when defaults occur, sovereigns generally continue to service their
debts to MDB. We, therefore, adjust for PCS by assuming a reduced expected Loss Given
Default rate.

         To illustrate, if the recovery rate for market borrowings unaffected by PCS is 50 percent
and defaulting sovereigns maintain their servicing of MDB debt half the time, the adjusted LGD
would be 25 percent, corresponding to an adjusted recovery rate of 75 percent. For the PCS-
adjusted and non-adjusted cases, we perform our calculation using actual transition matrices and
risk adjusted transition matrices (RATM).

5.6.1 Results with a Non-PCS Adjusted Transition Matrix for SG
Figure 2 and Figure 3 are the portfolio value distribution histograms using a non-PCS adjusted
transition matrix for SG. We focus on 2.3, 11.9 and 98.8 basis point VaR quantiles. These
confidence levels correspond to the 1-year, 3-year and 10-year default probabilities that are
thresholds for AAA status according to a table of idealized default probabilities provided by
S&P. The mean values of the total portfolio and the VaRs at 1-year, 3-year and 10-year horizons
are shown in Table 14. These VaRs may be interpreted as the capital levels that the bank would
have to exceed in order to keep its default probability below the idealized default probabilities
associated with AAA status.

                                                         36
Figure 2. Portfolio Value Distributions without PCS Adjustment

1-year horizon, actual TM without PCS adjustment  10-year horizon, actual TM without PCS adjustment

1-year horizon,RATM without PCS adjustment        10-year horizon, RATM without PCS adjustment

Note: The figure displays the distributions of total portfolio value at 1 and 10 year horizons (left and right-hand panels, respectively). The data employed are
from the IDB's portfolio as of June 2015. The upper and lower pairs of panels show the distributions using actual and risk-adjusted transition matrices
respectively.

                                                                                37
Figure 3. Portfolio Value Distributions with PCS Adjustment (reduce LGD by 50 percent)

1-year horizon, PCS-adjusted actual TM  10-year horizon, PCS-adjusted actual TM

1-year horizon, PCS-adjusted RATM       10-year horizon, PCS-adjusted RATM

Note: The figure displays the distributions of total portfolio value at 1 and 10-year horizons (left and right-hand panels, respectively) inclusive of adjustments for
Preferred Creditor Status (default probabilities are reduced by 80 percent). The data employed is that of the IDB's portfolio as of June 2015. The upper and lower
pairs of panels show the distributions using actual and risk-adjusted transition matrices, respectively.

                                                                              38
Table 14. Portfolio VaR

                  Actual transition matrix

                  1-year 3-year 10-year

                  horizon horizon horizon

Mean value        113,228 117,093 128,196

VaR 98.8bp                        18,387

VaR 11.9bp                18,038

VaR 2.3bp         17,163

Note: This table shows risk statistics including expected
portfolio value and Value at Risk (VaR) for the IDB's
portfolio over 1, 3 and 10 year horizons and using actual
and risk-adjusted transition matrices. The results are
expressed in USD millions. The confidence levels of the
VaRs employed (2.3, 11.9 and 98.8 basis points)
correspond to those used by S&P as thresholds for
achieving AAA rating status for 1, 3 and 10 year
maturity bonds respectively. These thresholds come
from a table of idealized rating-specific default
probabilities distributed to S&P to structures in the CDO
market.

         The actual IDB capital (adjusted common equity) in June 2015 was $24.7bn. One may
compare this capital level to the required VaR capital numbers of $17.2bn, $18bn and $18.4bn
that the Table 10 results suggest would be required to obtain a rating of AAA over the three
horizons of 1, 3 and 10 years. (Note again that these capital estimates are made so far with no
adjustment for PCS.) Again, one may compare this with the capital of $33.3bn that S&P would
require (see Tables 4 and 9) to designate IDB as having an "Extremely Strong" RAC ratio.

         Table 15 shows the default probabilities implied by the simulations. These represent the
share of occasions on which, at the VaR horizon, the simulated portfolio value falls below the
mean value of the portfolio minus the bank's capital. The respective default probabilities are
0.01, 1.1 and 24.8 basis points for the three horizons of 1, 3 and 10 years. One may simulate the
model using risk adjusted distributions and calculate the risk adjusted default probabilities. Using
the formula shown in equation (24), one may calculate the spread on the bank's debt.

            =  -  (+(1-))                                 (24)
                         

Here,  is the recovery rate for IDB debt which is assumed to be 0.5. The spreads implied by

these calculations are 37.2, 35.34 and 18.79basis points for the maturities of 1, 3 and 10 years,

                  39
respectively. These spreads appear high compared to the actual spreads that MDBs face. The
calculations so far make no allowance for PCS, which may explain why the spreads are high.

Table 15. Distribution Implied PD, Rating and Spread

                 Actual transition matrix  Risk adjusted transition matrix

                 Mean -      Implied       Mean -          Implied

                 capital PD  rating        capital PD      spread(bps)

1-year horizon   88,508 0.0001% AAA        87,078 0.7425%  37.20
3-year horizon
10-year horizon  92,374 0.0113% AAA        87,420 2.1090%  35.34

                 103,477 0.2480% AAA       87,967 3.7223%  18.79

Note: The table shows default probabilities (PDs) for IDB based on Monte Carlo exercises
employing the CRM. The PDs are generated by calculating the share of iterations for which the
portfolio value at the simulation horizon is less than the initial mean portfolio value minus the
IDB's capital. The implied rating is then inferred by comparing the PD (based on actual
transition matrices) with the threshold PDs in the idealized default probability table circulated by
S&P to CDO structurers. To achieve an AAA rating, 1, 3 or 10 year obligations must have PDs
less than 2.3, 11.9 and 98.8 basis points, respectively. The implied spreads are calculated using
equation (24), assuming a recovery rate of 50 percent, and the PDs based on risk adjusted
transition matrices.

5.6.2 Results with a PCS Adjusted Transition Matrix for SG
To adjust for PCS, we suppose the LGD of sovereign loans are reduced by 50 percent. As noted
above, the IDB has experienced losses on only 11 percent of the occasions on which its
borrowers have defaulted. As an adjustment for PCS, therefore, one may view an 50percent
reduction in LGD as quite conservative.

                 Table 16. Portfolio VaR (PCSadjusted)

                             Reduce LGD by 50%

                             1-year 3-year 10-year

                             horizon horizon horizon

                 Mean value  126,530 128,874 134,793

                 VaR 98.8bp                        13,675

                 VaR 11.9bp                15,059

                 VaR 2.3bp   14,928

Note: See notes to Table 14. The table shows results comparable to Table 14 except that
the transition matrices employed in the CRM Monte Carlo exercises to generate the risk
statistics are adjusted for Preferred Creditor Status (PCS) in that default probabilities
for central government credit exposures are reduced by 80 percent and 50 percent.

                             40
         Table 16 shows the capital required to achieve AAA status if, in adjusting for PCS, we
reduce the LGD by 50 percent. Specifically, for the three horizons, 1, 3 and 10 years, the capital
necessary to achieve AAA according to the S&P look-up table of idealized default probabilities
is $14.9bn, $15.1bn and $13.7bn, respectively.

         Table 17 shows the probabilities (for 1, 3 and 10 year horizons) that the portfolio value
will fall below the mean value minus the bank's capital inclusive of PCS adjustments. With a
PCS adjustment to the LGD, calculating with risk adjusted distributions and assuming a recovery
rate of 75 percent, one obtains spreads of 7 to 14 basis points. Note that our analysis uses paid up
equity capital not adjusted for callable capital. Including this latter would reduce the implied
spreads further.

Table 17. Distribution Implied PD, Rating and Spread (PCS adjusted)

               Actual transition matrix  Risk adjusted transition matrix

               Mean -      Implied Mean -            Implied
               capital PD  rating capital PD         spread(bps)
                           Reduce LGD by 50%

1-year horizon 101,810 0.0000% AAA 100,778 0.2810%   14.06

3-year horizon 104,155 0.0019% AAA 100,854 0.8099%   13.53

10-year horizon 110,074 0.0308% AAA 100,861 1.3245%  6.64

Note: See notes to Table 15. The table shows results comparable to Table 15 except that
the transition matrices employed in the CRM Monte Carlo exercises to generate the risk
statistics are adjusted for Preferred Creditor Status (PCS) in that default probabilities for
central government credit exposures are reduced by 80 percent and 50 percent.

6. Conclusion

The ability of MDBs to realize their international development objectives is limited in practice
by the need to maintain access to low cost financing in international debt markets. Even though
many MDBs currently enjoy highly favorable borrowing terms, they regard their agency ratings
as placing constraints on the volume and riskiness of the loans they can offer. The importance for
public policy of the limits placed by rating agency views on MDB activity is emphasized by
Group of Twenty (2015)35and Humphrey (2015).36

35 Griffith-Jones, Griffith-Jones and Hertova (2008) also argue for the importance of MDBs in achieving policy
objectives and advocate the creation of new regional development banks.
36 It is interesting to compare the debate on capital limits faced by MDBs by ratings agencies with the parallel debate
on the appropriate level of capital for commercial banking determined by regulators. For example, Baker and

                                                         41
         This paper examines in greater detail the methodology applied by the most influential
ratings agency for MDBs, Standard & Poor's (S&P), taking as an example the evaluation of the
Inter-American Development Bank (IDB). To benchmark S&P's approach (which contains
several approximations and proprietary calibrations), an industry-standard, ratings-based Credit
Portfolio Model (CRM) is applied to the IDB portfolio.

         The paper identifies two areas in which S&P's practice appears extremely conservative.
First, Preferred Creditor Status (PCS) is an important factor reducing the risk of MDB portfolios.
The magnitude of the S&P adjustment for PCS appears much smaller than that justified by the
loss experience of the IDB and other MDBs. Moreover, employing the cost of IDB borrowing
and backing out the market perceived value of PCS (motivated by the fact that PCS is a market
practice) also indicates that a much larger adjustment would be warranted. Second, the Single
Name Concentration (SNC) risk adjustment employed by S&P more than doubles the IDB's
Risk Weighted Assets (RWA) according to S&P's approach. The adjustment deployed by S&P is
based on a particular methodology which is not directly consistent with other aspects of the
agency's approach. An alternative, more consistent approach leads to a smaller adjustment.

         Using an industry-standard portfolio CRM conservatively calibrated, we calculate the
capital necessary to maintain the IDB's default probability lower than threshold idealized default
probabilities. This model avoids many of the approximations implicit in the S&P methodology.

         We perform these calculations with and without adjustments for PCS. We find that
without adjustment for PCS, the IDB would need around $17bn in capital to achieve a rating of
AAA. This compares with the bank's actual capital of $24bn.37Including PCS adjustments, the
capital required to achieve AAA drops to $14-15bn. This may be compared to the capital of
$33bn that S&P would require in order to designate the IDB as having an "Extremely Strong"
RAC ratio. Clearly, the bank faces risks in addition to the credit risk that we analyze but these
calculations also make no allowance for callable capital.

Wurgler (2013) discuss whether capital requirements have any economic impact on bank behavior or whether
Modigliani-Miller-style capital neutrality holds.
37 These figures do not include the impact of the recent Argentina upgrade or other changes that have improved the
IDB's capital ratios.

                                                         42
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