basel ii and structured finance

8/2/2019 Basel II and Structured Finance

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Basel II capital requirements for structured

credit products and economic capital: a

comparative analysis

Luca Giaccherini, Giovanni Pepe

first draft August 2007, this version Febraury 2008

Abstract

The huge development experienced by structured credit products has oc-

curred under a banks capital adequacy regime inconsistent with the inherent

complexity of these securities. The new prudential framework (Basel II) con-

tains a specific section devoted to tranched products, which puts much store

on public ratings. In this paper we try to evaluate the reliability of Basel

II treatment for securitization exposures comparing the forthcoming charges

for structured products with an estimate of their risk, a topic that deserves

additional attention after the recent market turmoil. The results obtained cast

some doubts about the actual degree of conservatism of the choice to mapfrom ratings to prudential charges.

Keywords: Basel II, CDO, economic capital, regulatory capital, Value at Risk.

Contents

1 Introduction 3

2 Collateralized debt obligation (CDO) 4

2.1 Single-Tranche CDOs . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Regulatory treatment 7

3.1 The rational behind the RBA and SFA approaches . . . . . . . . . 8

4 A model for the conditional loss distribution 10

4.1 The pricing model . . . . . . . . . . . . . . . . . . . . . . . . . . 13

The view expressed in the study are those of the authors and do not involve the responsibility of

the institution to which they belong.Banca dItalia, Banking Supervision Department. E-mail: [email protected] dItalia, Banking Supervision Department. E-mail: [email protected]

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5 Risk measures and economic capital 14

6 Fitch model: VECTOR 16

7 Comparative analysis 18

8 Results 19

9 Conclusion 20

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1 Introduction

From a certain perspective, the great success obtained by tranched securities can

be depicted as a remarkable example of capital arbitrage strategies played by banks

under the previous version of the Basel Accord: a system of risk weights largely

based on notional amount of investments has proven to be a strong incentive for

banks to reduce the capital requirements without shedding a proportional deal of

risk.

To curb this incentive the new regulatory treatment of structured credit products

(from now on the terms structured credit productand tranched security are used as

synonyms) has been designed along the principles of:

Capital neutrality Economic capital centrality

Economic capital centrality implies prudential rules able to align closely regulatory

charges and risks, while capital neutrality is obtained if these rules do not induce

banks either to hold assets on balance sheet or to securitize them.

The new regulatory treatment does not allow a big role for internal risk esti-

mates, as in this case regulators choose to link capital charges to public ratings;

this holds true even for banks judged suitable to determine on their own the risk

components of traditional credit exposures, so-called Internal Rating Banks (IRB

banks, a category that virtually includes all major banking groups).

For these institutions two alternative approaches have been introduced, depend-

ing on the existence of a public rating for the structured product to which they are

exposed: should a rating exist, the capital charge comes from a coefficient to beapplied to the exposures notional amount (Rating Based Approach, RBA); for un-

rated products, instead, IRB banks must provide internal estimates of probability

of default (PD) and recovery rate (1-LGD) for the underlying assets, as an input of

a formula set by regulators (Supervisory Formula Approach, SFA).

An analysis of the two prudential regime performed by Fitch over a range of

structured credit products [4] appointed RBA as the most advantageous method,

suggesting a race to rating.

This issue gained additional relevance as the turmoil that recently affected the

market for structured credit products highlighted the drawbacks of credit ratings

when used beyond their intended meaning of opinions regarding the default risk

associated with either an issuer or an issue.This paper deals with the coherence between the economic capital absorbed by

structured products and their regulatory treatment, focusing on iTraxx tranches, a

stylized and actively traded version of corporate CDOs, that in our opinion offers

a useful boot camp for the forthcoming prudential regulation.

Tranches ratings have been assigned using the Fitchs methodology for CDOs

evaluation, Vector. The announcement of a proposal review of this approach

allowed us to gets a sense of the prudential side-effects of the initiatives that rating

agencies are now undertaking to improve the robustness of CDOs ratings.

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The paper is organized as follows: section 2 introduces synthetic CDOs, section

3 provides an overview of the new prudential rules for tranched products, sections4 and 5 describe the methodologies used to obtain an estimate of the tranches risk-

iness, section 6 contains a brief overview of the model used by Fitch for assessing

CDOs credit worthiness, section 7 and 8 illustrate the results of the comparison

between economic capital and prudential requirements; the final section reports our

conclusions.

2 Collateralized debt obligation (CDO)

Collateralised Debt Obligations could be defined as fixed income securities orig-

inated by engineering the risk of a portfolio of credit instruments. Mixing securi-

tisation and credit derivative techniques, these products are mainly used to trans-

fer the risks arising from a portfolio of corporate exposures (so-called corporate

CDOs), or a pool of securitized retail credits conveyed by a collection of Asset

Backed Securities (CDO of ABS, at center stage of the recent financial markets

crisis)1.

In all CDOs a priority scheme governs the loss absorbtion with each tranche

suffering a reduction of its notional amount when losses in the portfolio breach

the tranches attachment point(Lb), expressed as a percentage of the total pool no-tional. The investment will be wiped out should portfolio losses reach the tranches

detachment point (Hb). The thickness of each tranche is defined by the differencebetween Hb and Lb.

The first tranche to suffer losses is usually called the equity, as its risk-reward

profile resembles that of equity investments. Next comes the mezzanine and then

one or more senior tranches, where the one that sits at the top of the CDOs cap-

ital structure is usually termed as super-senior. The credit enhancement enjoyed

by a tranche does not depend only on its position in the capital structure, as the

contractual rules that govern the allocation of portfolios cash-flows (cash-flow

waterfall) could make some partial changes to the strict prioritization scheme

provided by the sequence of attachment and detachment points (i.e. Lb and Hbvalues).

Basically, the waterfall rules aim to offer additional protection for senior tranches

against the case of a prominent collateral pool deterioration; the first source for

this credit enhancement comes from the cash accumulated along the transaction

life due to the so-called excess spread, which is the difference between cash gen-

erated by the collateral pool and that needed to pay the interests promised to bond

holders. The diversion of cash-flows from the devised plan is usually triggered by

the eventual breach of a certain threshold of a test aimed to monitor the collateral

performance.

1Although corporate exposures and ABS can be viewed as the most popular form of CDOs

collateral, many other credit assets have been used as underlying of these transactions comprising

project financing loans, trust preferred securities, as well as other CDOs.

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The sequential allocation of portfolio losses along the CDO concentrates much

of the pool credit risk in the lower tranches. Offering a return many times higherthan that rewarded by a direct investment in the collateral pool, these notes are

often referenced as leveraged positions; at the opposite, senior tranches allow

investors to get a deleveraged exposure as they embody a much lower amount

of risk compared to that bore by an investment of corresponding notional in the

underlying pool.

The original scheme of CDOs has changed a lot from its appearance at the be-

ginning of 90s; along this path of evolution the use of credit derivatives to transfer

the risk of the underlying portfolio has been a structural break-trough, which gave

life to a class of product on its own, the so-called synthetic CDOs. The first

version of synthetic CDOs required a stand-alone company ( special-purpose en-

tity, SPE) selling protection on an underlying pool by synthetically referencinga portfolio of single-name credit default swaps (CDS). The SPE then offsets the

risk issuing a range oftranchednotes, each one with a different risk profile.

In case defaults hit the portfolio, the SPE will refund the swap counterparts for

losses incurred on defaulted assets using the money gathered from investors when

issuing the notes.

As the use of single name CDS allowed to enlarge the supply of CDOs beyond

the limit of existing loans or bonds, the appearance of CDS indexes (basically

portfolios of single-name CDS) entitled investment banks to go even further, by

providing them a standard collateral pool. It was then a small step to propose a

CDO referenced to the contracts comprised into the index, where the issuer was

able to sell just one tranche, hedging away the risks associated with unsold piecesby taking offsetting positions on the index: the Single-Tranche CDO.

2.1 Single-Tranche CDOs

The distinctive features of Single-Tranche CDOs is represented by the absence

of a SPE, as the contract is a derivative agreement between two counterparts which

mimics perfectly the payout of a CDO governed by a straightforward losses allo-

cation rule. The success quickly achieved by this product induced a rapid stan-

dardization of the terms on which it was offered by different dealers. Nowadays

many investment banks operate as licensed dealers of two standard contracts, quot-

ing four tranches of the Dow Jones indexes that equally weight the 125 most liquidCDS referred to top European investment grade companies, (iTraxx), and their

American counterparties, (CDX.NA.IG)2

In both cases most trades regard the index series that comprise CDS whose

maturity is of 3, 5 and 7 years, with very tight bid-ask spreads for the on the run

ones, which is the jargon name for the version of the indexes lastly revised.

2A complete description of the rules governing the composition and the rolling process of both

the iTraxx and CDX.NA.IG indexes can be found at www.indexco.com, while the templates of the

documentation used for trading both indexes and their tranches are available at www.markit.com.

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Figure 1: Single tranche CDOs.

While in traditional CDOs there is a clear distinction between the arranger and

the investor, in this case the difference is blurred, as it is possible to assume either

short or long positions. Investment banks act as market makers being prepared to

buy protection from protection sellers and sell it to protection buyers.

Who enters into the deal as a protection seller is entitled to receive the agreed

spread on a quarterly basis, while the protection buyer is to be paid should losses

in the pool breach the tranches Lb; in this case the contract doesnt terminate untilthe detachment point is reached, but the incurred losses are taken into account to

determine the notional value on which the cost of protection is to be paid.

If we look to the investor position, i.e. the seller of protection, we can isolate

three different sources of risk: one arising from changes of credit spreads on the

underlying portfolio (market risk); another linked to the eventual default of one

or more firms in the pool (default risk); the last one emerging from changes in

the level of expected default correlation between index constituents (correlation

risk). The same risks are faced by the buyer of protection, unless she has been

able to place the entire capital structure (i.e. all CDOs tranches).

Both the seller and the buyer of protection can immunize themselves, by dy-

namically managing a hedge portfolio, which anyway will leave them exposed to

model and liquidity risks.

The easiest risk to hedge away is the market risk, which requires buying pro-

tection (for the protection seller) in CDS referenced to each company in the pool,

or in the swap referenced to the index as a whole.

In both cases, the amount of protection to be traded is a multiple (the delta) of

the tranches notional value and is calculated using the CDOs pricing model. Delta

represents the sensitivity of the tranche value to a shift of the reference portfolio

credit spreads and therefore can be interpreted as a measure of the transactions

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leverage /deleverage3.

3 Regulatory treatment

By deviating from a general openness to the prudential use of internal risk mea-

sures, the Basel Committee preferred to link risk weights for securitization prod-

ucts to public ratings, appointing rating agencies as supervisors delegated moni-

tors.

The new prudential regulation [1] provide banks with different methods to de-

termine the regulatory capital charges of structured credit products, depending on

whether the bank will implement the Internal Rating Based approach or the stan-

dardized one for the underlying exposures4.

Under the standardized approach the capital charges are linked to the securitys

external credit rating by a set of weights to be applied to notional exposures (ta-

ble 2). For unrated positions banks must hold one unit of capital for each unit

of exposure (known as a dollar-by-dollar capital charge), being a strong capital

disincentive against this kind of exposures.

Capital charges for IRB banks depend on whether the position held has a credit

rating from a recognized credit rating agency.

Should ratings exist banks must use what is known as the Rating Based Ap-

proach (RBA). Primarily targeted to banks that invest in a securitization they did

not originate, RBA maps from the tranches external rating to its capital charge via

a specific look-up table (table 3). The weights for tranches of a given rating vary

according to the tranche seniority and the pool granularity 5. Further, if a tranche is

the most senior in its structure and enjoys an investment grade rating, it attracts a

lower risk weight than the base case, as long its underlying pool is perceived to be

sufficiently granular (N > 6). Moreover, the RBA allows unrated positions to beassimilated to the first subordinated tranche which enjoys a rating ( inferred rating),

provided that its maturity is equal or longer than the unrated position.

Where a rating couldnt be inferred IRB banks must use a bottom up approach,

in which a set of parameters related to the pool credit quality and to the contractual

terms governing the cash flow waterfall are plugged into the Supervisory Formula,

SFA. The formula, conceived for banks that act as originators of a securitization,

3These hedging positions are frequently reported to contribute materially to the booming growthexperienced by credit derivatives volume. It is worth to notice that the actual performance of hedging

strategies relies mainly on the stability of the parameters that govern the hedge ratio quantification.

For this reason the extreme movements experienced by default correlation during market turmoils

have been disruptive for these strategies.4Under the Internal Rating Based (IRB) approach, banks are allowed to calculate prudential

charges for traditional credit exposures by providing internal estimates of probabilities of default

(PD) and recovery rates (1-LGD)5A pool is said to be highly granular if it contains a large number of exposures, none of which

contributes a large part of the total risk. As a measure of granularity it is used the statistic N =(EADi)

2 \EADi where EAD denotes the exposure at default of the i-th exposure in the

pool.

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depends on five inputs of which only one reflects banks internal estimates (the

Kirb, which is the capital charge that the bank would face if the exposures hadbeen retained on balance sheet).

In principle RBA and SFA risk weights have to be applied both to banking and

trading book exposures; an exception is granted for banks able to model the credit

risk of trading items not caught by standard VaR models, even if the prudential

guidelines on this topic have not been realesed yet.

However, when the rules will be issued banks should calibrate these additional

charges (so-called Incremental Default Risk charges) to the banking book ones.

In the meantime, the securitisation framework will also apply to structured credit

products held with trading intent unless the existence of a liquid market for these

exposures grants a clear opportunity to hedge away their default risk, like in the

case of iTraxx tranches.

3.1 The rational behind the RBA and SFA approaches

Decisions about the levels of structured credit product capital charges generated by

the RBA and SFA approaches have been strongly influenced by studies performed

by analysts at the Federal Reserve Board and the Bank of England.

Rating based approach

Peretyatkin and Perraudin [14] examined the robustness of RBA weights on a port-

folio of stylized tranched products, checking the impact of different maturities,

granularity and correlation between the pool and the wider bank portfolio risk fac-

tors.

For this purpose they developed a Monte Carlo model aimed to calculate the

marginal Value at Risk of different tranches of stylized CDOs held into a well

diversified portfolio; the model was used, along with two other simpler ones, to

evaluate both the consistency of rating based charges with model based risk mea-

surements, and the alignment of RBA weights with prudential capital that banks

would have to hold in case they maintained the loans on balance sheet.

They found the prudential requirements for investment quality tranches broadly

consistent with the model based capital estimates, provided that the correlation be-

tween risk factors driving the structured exposures pool and the banks wider port-

folio is set towards 60%. Moreover, they also detected non negligible effects played

by pools granularity, asset correlation of the underlying exposures and maturity.

Supervisory formula approach

The supervisory formula has been designed in order to allocate the capital require-

ment of a given portfolio (Kirb) along the capital structure of a structured creditproduct built upon this pool of assets. Given the difficult task to consider the myr-

iad possible deal-specific features of each product, the formula was developed on

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a limited set of information regarding the cash-flow waterfall.

Pykthin and Dev [11], [12] tried to summarize the waterfall for a particulartranche in terms of its thickness T and credit enhancement level 6. They assumedthe allocation of the pools economic losses to be governed deterministically along

tranches, according to a strict loss prioritization rule (SLP).

Let denote the tranches credit enhancement level and T its thickness (bothvalues easily observable for a market participant), under the SLP rule each tranche

absorbs losses only in excess of, up to a maximum ofT; that is, ifL denotes poollosses, then the loss for the tranche can be defined as min[L, + T] min[L, ].

Notwithstanding its simplicity, the SLP approach brings an unsatisfactory knife-

edge property when used to determine capital requirements: for an infinitely grained

pool, the capital requirement for a tranche is dollar by dollar if+T is less or equal

to Kirb and zero thereafter7.Gordy and Jones [8] generalized the SLP approach by adding a stochastic ele-

ment to the distribution of losses across tranches in order to address the uncertainty

about the true characteristics of the cash-flow waterfall. In doing this they assumed

that the credit enhancement i represents the ex-ante expected protection againstlosses in the pool, while the actual protection provided by the waterfall is randomly

determinated (they indicated with Z(i) - where Z is a random variable - the un-known level of credit enhancement) and known only at the horizon.

Based on this intuition they devised a model (Uncertainty in Loss Prioriti-

zation) Uncertainty in Loss Prioritisation (ULP) that smooths the step function

for capital charges that comes out when one employs a strict prioritization rule to

allocate the underlyings capital charge along the tranches of a structured creditproduct.

The supervisory formula is based on an approximation of the ULP along with

some supervisory overrides, like a dollar for dollar capital requirements for tranches

whose credit enhancement fall short of Kirb, and an imposed floor level for mostsenior positions8.

6The thickness Ti is defined as the ratio between the i-th tranche notional Ci and that of theunderlying portfolio, Ti = Ci/Ci; the credit enhancement is defined as the sum of the notionalvalues of all more-junior tranches.

7To have an idea about the flows of this digital capital allocation, one can consider that subor-

dinated tranches are entitled to get some payouts prior to more senior investors being paid out in full,

hence not deserving such a harsh treatment.8To compute the capital charge via SFA we need to solve a function on the following seven

parameters:

Kirb

n: number of names on the pool

LGD: exposure-weighted loss given default of the pool

: tranches credit enhancement

T: tranches thickness

: parameter that sets the level of uncertainty capital allocation between the tranches (fixedby regulators );

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4 A model for the conditional loss distribution

From the protection sellers perspective the value of a single tranche CDO is simply

the difference between the discounted value at time t0 of the spread payments sheexpects to receive (fee leg), and the present value at time t0 of the sum due whendefaults affect the tranche (contingent leg):

V alue(t0) = M tM(t0) = f ee(t0) contingent(t0) (1)

The key input to evaluate both the fee and the contingent leg is the expected loss of

the tranche to be computed of the probability distribution of losses in the pool.

The market standard approach to generate the portfolios loss distribution re-

lies on the so-called One Factor Gaussian Copula Model based upon Vasiceks

model [16]9. To derive the portfolio loss distribution the normal copula is typically

implemented using either Monte Carlo simulation or quasi-analytical methods, as

that described by Andersen, Sidenius and Basu [15], and Laurent and Gregory [7].

The appealing features of the copulas models is that they allow to decouple the

specification of the individual stand-alone distributions from the identification of

the correlation structure. While any valid correlation matrix could be used, it has

become common practice to restrict the correlation structure to that described by a

single common factor.

One-firm default probability

The main benefit of the single-factor restriction is connected to the reduction inthe number of parameters required by the model, which gave rise to effective tech-

niques to obtain contracts values in closed-form. Most of the techniques rely on the

observation that once the value of the common factor is fixed, then the individual

obligor defaults are conditionally independent.

Based on the Merton approach for pricing corporate debt [13] a company de-

faults when the value of its assets decreases below the level of the firms liabilities

(). In this framework the evolution of the firms assets (Ai) is supposed to bedriven by a systematic factor X, that can be interpreted as a proxy of the general

state of economy, and a idiosyncratic component i.

Ai = wiX+

1 w2i i (2)where X and i are supposed to be uncorrelated standard normal variables (X N(0, 1), i N(0, 1) and E[Xi] = 0).

The correlation between obligors i and j is wiwj , so the range of possiblecorrelation matrices is quite limited. In fact, the most common application is to

: parameter that governs the LGD distribution.

9The two articles by Li [9][10]are cited as the first application of the model to pricing CDOs

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set the weight parameters wi equal for all obligors so to consider just one pairwise

correlation value for the entire portfolio, equal to the square of the factor loading10:

ij = E[AiAj ] = w2 (3)

Going backward to Mertons approach, starting from a default probability for

the i-th obligor we get the default threshold

Ai = wX +

1 w2i < (P Di(t)) (4)and so the conditional default probability

qi(t|X = x) = 1(P Di(t)) x

1

(5)A relevant choice regards the initial probability measure to use in (4): risk

neutral or objective probabilities of default. If one is interested in pricing, model-

ing under the risk neutral measure is the natural choice; when estimating the capi-

tal absorbed by an investment, one could instead adopt an actuarial-like approach

choosing historical probabilities.

Loss distribution

From (5) we see that once the value of the common factor is fixed, starting with

observed PD, we can obtain individual default probability conditionally indepen-

dent. Then, the portfolio loss will be equal to the sum of the independent obligorlosses and the conditional portfolio loss distribution will be the convolution of the

individual obligor loss distributions.

The simplest implementation of the single factor copula model, known asLarge

Homogeneous Pool (LHP), assumes the portfolio composed by infinitely many

small positions (perfect granularity) all sharing the same of probability of default

(P Di = P D), recovery rate (Ri = R) and notional amount (Ai = A).A more realistic approach, known as Homogeneous pool is broadly used by

market participants to get quick estimates of tranches prices (see [3] for a survey of

the various implementation of the one factor copula model). The Homogenous pool

diverges from the LHP with respect to the number of counterparties, assumed equal

to the true number of companies in the portfolio, while shares the assumptionsabout the common value of default probability (equal to the one obtained by the

quoted index spread), recovery rate and individual notional amount.

Respect to the LHP the homogeneous approach allows to account for the fact

that portfolio losses can only occur in discrete increments which introduces some

idiosyncratic risk into the pricing framework. A structural difference between the

two variants is that the exact model11 still allows some idiosyncratic risk: once

10To get this result we must further assume uncorrelation between the idiosyncratic components

E[ij = 0])11In this contest we use exact model as a synonym for the homogeneous one

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we condition on the single factor there is still some variability in the portfolio

which depends, among other things, on the number of obligors in the portfolio.In contrast, in the large pool model, the realization of the single factor uniquely

determines the realization of portfolio loss.

As a further step away from the large homogeneous paradigma we can remove

the hypothesis of creditworthiness equality among obligors P Ds. Its commonunder the homogenous framework set the unique PD equal to the one derived from

the average spread or from the index spread if there exists. Clearly this approxima-

tion could undermine the pricing accuracy in that it fails to consider the dispersion

between the portfolio components. Further this approximation prevent us to distin-

guish between the different underlying names for hedging purposes: the simplified

model can only produce a portfolio hedge consisting of equal weights on all

the underlying names. On the other hand the unique PD is quite attractive in that itsignificantly reduces the amount of information necessary to describe the structure.

Having in mind the above considerations for our analysis we adopted a sort

of Heterogenous Pool approach. We considered exactly 125 names each with its

own P D (P Di) derived from market data. We slightly deviate from the real het-erogenous approach described in [2] in that we assume a constant recovery rate

R (conventionally fixed at 40%12) as well as the same invested amount for eachcompany, A. The latter assumption doesnt represent a simplification in that theiTraxx index is made up by equally weighted exposures13.

The constancy of both recovery rates and exposures weights makes the com-

putation of the loss distribution easier. Under this assumptions each credit either

will take no loss or a loss of A(1 R), so that the distribution of losses on thereference portfolio will take on N+ 1 discrete values corresponding to no defaults,one default, two defaults, and so on up to N defaults. Under this assumption, thedistribution of losses and the distribution of the number of defaults become inter-

changeable: simply multiply the number of defaults by A(1 R) to get losses.An easy way to compute the entire default distribution p(l, t) is to implement

the iterative algorithm proposed by Andersen, Basu and Sidenius [15].

Let pk(l, t|X) to denote the conditional probability to observe exactly l de-faults at time t in a portfolio containing k credit exposures. If we know the entiredistribution pk(l, t|X) (for l = 0, . . . , k), using the following iteration we get thedefault distribution for a k + 1 portfolio:

pk+1(0, t|X) = pk(0, t|X)(1 qk+1(t|X))pk+1(l, t|X) = pk(l, t|X)(1 qk+1(t|X)) +pk(l 1, t|X)qk+1(t|X)

pk+1(k + 1, t|X) = pk(l, t|X)qk+1(t|X) (6)12The 40% recovery rate is thought to be coherent with the historical rate observed on the US

unsecured bond market.13For lack of simplicity in the following we assume an invested total amount of 1 unit. ThereforeN

i=1Ai = 1 andAi indicates at the same time the amount invested on name i as well as the weight

on name i.

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where qk+1(t|X) is the default probability of the k+1 exposure added to thek-portfolio.

Starting from the degenerate default distribution for k = 0, p0(0, t|X) = 1, wecan then use the recursion (6) to solve for the default distribution of the reference

portfolio ofN credits:pN(l, t|X)l = 0,...,N (7)

Once we have the conditional default distribution, the unconditional default

distribution p(l, T) can be solved as14:

p(l, t) =

pN(l, t|X)g(X)dX (8)

where g is the probability density of X. The integral is solved numerically. It is

worth noting that the shape of the portfolio loss distribution depends largely on the

strong assumption about defaults interdependence. In our framework the uniform

pairwise correlation impacts on the individual conditional default probability (5)

and, by (6), affects the entire distribution, influencing the allocation of the risk

along the capital structure (see section 7).

As the risk of different tranches varies with asset correlation so does their fair

values: asset correlation is indeed the most important parameter for Single-Tranche

pricing, as highlighted by the market practice to quote the tranches implied corre-

lation rather than its fair spread15.

4.1 The pricing modelLet fL(c, t) be the density of the cumulative portfolio loss16 at time t. Given fL(.)we can compute the expected loss for a given tranche in a risk neutral world as:

EQt [CL(t)] =

HbLb

(c Lb)fL(c, t)dc (9)

Provided that the index components share the same notional amount and hold for

true the assumption of constant recovery rate across the pool, it is easy to see

that the loss distribution will assume discrete values: let N denote the exposurescomprised in the reference portfolio, the loss distribution will assume N+ 1 values(from 0 to N defaults).

The (9) will then reduce to17:

Et[L] =Nl=0

p(l, t){min(lA(1 R), Hb) min(lA(1 R), Lb)} (10)

14To simplify the notation there on we omitted the suffix N15In the market jargon the implied correlation is the number that makes the fair or theoretical value

of a tranche equal to its market quote under the One Factor Gaussian Copula Model16With c we refer to the cumulative loss of the portfolio.17We omitted the Q since this quantity will be computed under both the risk neutral and real world

measures

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where p(l, t) is the probability to get l defaults by time t computed by (8) and N is

the number of single name CDS composing the underlying portfolio.The settlement convention to pay the contingent at the payment dates following

the default further simplifies the pricing, as it allows us to determine the expected

loss only on a quarterly basis.

From (10) the expected value of the payments due in case of defaults will be

equal to

contingent =nt=1

Dt(Et[L] Et1[L]) (11)

while the fee leg could be expressed as

F ee = s

nt=1

Dtt{(Hb Lb) Et[L]} (12)

where t = t (t 1), s is the yearly spread due by the protection buyer and Dtis the risk-free discount factor for payment date t.

In (12) the amount (Hb Lb) Et[L] indicates the notional reduction causedby defaults and reflects the right of the investor (protection seller) to get payments

only on the residual amount of the tranche.

Like interest rate swaps, at inception synthetic CDO tranches will have their

spreads set to constrain the mark-to-market value to zero; setting M tM = 0 in (1)and using (11) and (12) to solve for s, the par spread can be obtained as

spar = contingentnt=1 Dtt{(Hb Lb) Et[L]}

(13)

5 Risk measures and economic capital

The risk of a tranched product can be evaluated by different metrics. From now on

we describe those we believe could be eligible as proxies of the economic capital

absorbed by a corporate CDO, adopting the one-year time horizon chosen by Basel

II for all credit exposures.

We are aware that this time horizon is far too extended for index tranches that,

mostly held in the trading book, need a shorter period to be closed or hedged. In

this regard, the adoption of the 1-year regulatory constrained embodies the ideaof using these contracts as a proxy of corporate CDOs, whose scarce liquidity can

well justify the regulators choice, as showed by the recent upheavals in the market

for these products.

In line with the Value at Risk baseline methodologies on which Basel II relies

to assign capital charges on both credit and market exposures, we computed a first

measure of the economic capital absorbed by tranches using a VaR measure derived

from the Gaussian Copula model, taking the expected loss at the one year time

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horizon conditioned at the 99.9 th percentile of the systematic factor18.In our framework that is equivalent to solve (10) considering the probabilitydistribution conditioned to X = x99.9 (7):

Et1 [L|X = x99.9] =

Nl=0

p(l, t|X = x99.9){min(lA(1R), Hb)min(lA(1R), Lb)} (14)

Et1 [.] can be considered as a measure for the Unexpected Loss computed over thedisposed one-year time horizon.

This method, while based on a widely used methodology for computing Credit

VaR measures, fails to consider the additional risk encapsulated on the maturity of

these instruments being longer than the VaR time horizon. To be clear just consider

two different tenor but otherwise identical tranches, one with one-year maturity (t1)

and the other with five-years maturity (t5): if we compute (14) at t1 we end up withthe same unexpected loss for both tranches.

This additional risk, which encompasses the losses that could hurt the tranches

until the maturity (downgrade risk) has been take into account also by regulators

which impose to adjust the capital charge for all the credit exposures by the so-

called maturity adjustment.

Further, independently from regulatory prescriptions, the liquidity squeeze stemmed

from the recent turmoil on the mortgage related assets, strongly suggests to con-

sider a longer time horizon - may be the final maturity - when assessing the risk

embedded on structured credit products.

All things considered, we defined a more comprehensive risk measure based

on the loss suffered at t1 by an hypothetical investor which bought the tranches int0.

Such an investment is vulnerable to the losses occurring from t0 to t1 as wellas to the potential loss faced in case she decided to close the position at time t1.Accordingly, an effective risk measure should account for both losses.

Being a seller of protection, the investor is mainly concerned about an increase

on credit spreads which could make the quarterly premium fixed at time t0 inade-quate to cover the risk he brings. This of course will cause a drop on the value of

the cash flow she expects to receive during the holding period (t0 t1).However, the loss suffered during the holding period dont allow for the poten-

tial loss the investor could face as the effect of tranches evaluation at time t1. The

tranches value at time t1 clearly depends on the default observed from t0 to t1 onthe time to maturity as well as on the future evolution of credit spreads.

In order to consider both the sources of risks we computed the following mea-

sure of risk, that we called Modified Unexpected Loss:

U Lmod = E[CashFlow(t0, t1)|X = x99.9] + |M tM(t1, t5)| (15)18Gordy[6] shows that when dependence across exposures is driven by a single systematic risk

factor, and no exposure accounts for more than an arbitrarily small share of total portfolio (perfect

granularity), the loss distribution is completely described by the systematic factor distribution: this

allows to compute the VaR without generating the entire loss distribution.

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The first term largely resembles the unexpected loss as defined in (14) but it pro-

vides a more precise estimate for the loss suffered during the holding period in thatit considers the spreads cashed in by the investor. Moreover it is equivalent to the

mark to market of a contract with maturity of 1 year, having observed a negative

state of the economy during this time horizon (X = x99.9).The second one mainly accounts for the mismatch between the time horizon

of the VaR measure and the product maturity. Since its evaluation is equivalent to

that of a 4-year CDO written on the original pool of names starting at t1 and withmaturity at t5, it resembles the pricing of a forward starting CDO, an issue recentlystudied by Hull & White [18].

Forward starting CDOs represent contracts that compel two counterparties to

enter into a CDO transaction at a specified future time on a given portfolio at an

agreed spread; the contract is canceled out if during the period between the dealdate and the start date the portfolio experiences an amount of losses exceeding the

tranche detachment point. In line with standard CDOs, we define the forward CDO

spread as the specific spread value that determines a zero Mark to Market at the

deal date.

Market participants distinguish the case where the underlying portfolio cur-

rently exists (specific forward start CDOs), and may have suffered defaults before

the start date occurs, from the de novo portfolio which will come into existence at

the start date (general forward start CDOs).

Hull & White have showed that specific forward CDOs can be priced in a

consistent way by the One Factor Gaussian Copula Model, as it produces coherent

results with those obtained by a more general dynamic model [17]. Accordingly,to compute the M tM(t1) in (15) we used the One Factor Gaussian Copula Model,considering the reduction of the notional portfolio caused by losses incurred from

t0 to t1.In this respect we need to calculate the number of defaults (l) associated to the

losses incurred during the 1 year time horizon. To get l we compute the portfoliounexpected loss at time t1 by (14); hence, considering the equivalence

E1[L|X = x99.9] = lA(1 R)we obtain

l =E1

A(1

R)(16)

Once we known l from (16) we can easily compute M tM(t1, t5) just evalu-ating (14) starting from l = l.

6 Fitch model: VECTOR

While a detailed analysis of the process performed by rating agencies when evalu-

ating structured credit products is well beyond the goal of this paper, in this para-

graph we provide a general outline of the Fitch methodology we used to obtain the

tranches rating used under RBA (par. 3).

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Fitch assesses CDOs creditworthiness performing a two-stage process. In the

first stage, an analytical model is used to assess the pool credit risk, while thesecond stage is devoted to conduct a structural analysis of the transaction, which

crucially depends on deal specifics as laid out in the CDOs documentation19.

Due to the interactions between the two stages, ratings cannot be simply viewed

as the model outputs since they are the results of a formal committee process. In

the case of iTraxx tranches, their straightforward nature allows us to focus only

on model outputs and dismiss the effect of the evaluation regarding the qualita-

tive aspects of the transaction. Fitch itself used to provide model based credit

assessments for iTraxx tranches, even if they dont assure that an actual credit

rating will be the same as the assessment, or that the assessment will not materially

change over time.

The proprietary model used by Fitch to perform the first stage of CDOs rating(Vector) is a multi-period one, based on a structural form approach according to

which a company defaults when the value of its assets falls below the value of its

liabilities (default threshold). The full loss distribution is obtaneid using Monte

Carlo simulations: for each year correlated asset values are generated and com-

pared with the related default thresholds. When a default occurs, the recovery

amount is registered and the obligor is removed from the portfolio. The multi-step

feature of the simulation allows the incorporation of time-vary parameters such as

default probabilities.

The default threshold assigned to each obligor is derived from the Fitch CDO

Cumulative Default Matrix which contains for each rating the cumulative default

rates for different horizons.Vector requires the pools asset correlation as an input. For pools that com-

prises corporate exposures Fitch has developed a factor model that derives equity

return correlations between different countries and industries as a proxy of asset

correlation.

Vector is used to perform a credit risk analysis based on the following strat-

egy: first, the model estimates a default rate distribution of the collateral portfolio.

Next, asset specific recovery rates are used to obtain a loss distribution out of the

default distribution; the portfolio loss distribution is then employed to establish

representative stress scenarios, assigning to each scenario a realization probability.

Finally, the severest stress scenarios sustained by a tranche without monetary

losses determines the rating of that tranche.For instance, a tranche will enjoy a AAA rating only if the probability of real-

ization of the scenario that produces losses in the reference portfolio exceeding the

tranches attachment point has been estimated to be lower or equal to the histori-

cal frequency of default of a AAA credit exposure on a time horizon fixed to the

tranches maturity.

After the recent financial market turbulence a widespread criticism have been

19This step usually comprises a detailed cash-flow modeling as well as legal assessments and

evaluations of any third parties involved in the agreement, such as servicers and asset managers.

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addressed to the main rating agencies, regarding the crucial role they have been

playing in the structured finance space.An effect of this debate has been the deci-sion of the three major agencies to perform a thorough review of both their rating

models and processes.

A the beginning of 2008 Fitch posted to the financial industry a proposal for

a major review of its model for CDOs evaluation. While the overall models ar-

chitecture has been confirmed, material changes have been introduced for default

probabilities and recovery rates, in order to strengthen consistency with empirical

long-term observations. Default rate time series have been also updated to con-

sider the now prevailingly tighten credit market conditions and calibrating also the

model on historical peaks. The agency claims that these changes will have a rel-

evant impact on Fitchs corporate CDO ratings currently outstanding. The rating

on synthetic CDOs referencing investment-grade corporate exposures are expectedto be the most severely impacted, with model-implied downgrades on average of

around five notches; for some senior tranches the downgrades can be as severe as

from AAA to BB.

When performing our comparative analysis we used rating obtained using both

the Old and New methodologies so to compare the impact of these changes on

prudential charges.

7 Comparative analysis

We performed our analysis with respect to the standard tranches quoted on the fifth

series of the iTraxx index, using the market data as of September 15, 2006 for the

five year maturity.

For each tranche the economic capital absorbed has been computed under the

two proposed measures, using both risk neutral and real world PDs; the results

have been compared with the capital charges calculated under both the regulatory

approaches: RBA and SFA.

As first we checked the soundness of the pricing methodology by calibrating

the model (5-13) to tranches correlation values quoted by dealers (see table 4) to

obtain exactly the market spread of each tranche.

Risk neutral PDs have been derived from CDS spreads. We assumed a Poisson

process for default, implying P Di = 1

exp(

t). The annual default intensity has been obtained from the 5-year CDS spread quoted at September 1520; to keep

the computation simple we assumed a flat term structure for the default intensity

and a constant recovery rate of 40%.

Actual PDs have been computed using the assigned by Fitch to the 125 com-

panies listed in the fifth series of the iTraxx index. As a proxy for the PD we

considered the 5-year cumulative default rate (CRD) computed over a portfolio

encompassing all the corporate finance long-term debt issuer ratings assigned by

20 has been computed using the pricing formula of credit default swap, going backward from thequoted CDS spreads to the default intensity, .

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Fitch from 1990 to 2006 [5]. From these figures we derived the constant intensity

of default as = log(1 CRD)/5.It is widely known that actual PDs are, on average, lower that those resulting

from from CDS spreads, mainly due to scarcity of defaults occurred in the best

rating classes (see table (1) ). In our case moving from the risk neutral world to the

real world reduces the average default probability of Itraxx constituents on the five

year time horizon by half a percentage point (from 2.45% to 1.91%).

In order to evaluate the sensitivity of the two proposed risk measures to the

value of asset correlation in the collateral pool we considered values of rangingfrom 5% to 30%. We chose to use the same correlation measure for all tranches(we refer to the implied or compound correlation), as the same idea of multiple

correlation for the same pool lacks logical background and should be viewed as a

signal of the limited adequacy of the standard pricing model to explain the quotedtranche prices.

RBA charges are based on model implied ratings obtained using the Fitch pro-

prietary model (Vector 3.2): Old Ratings; we also used assessments produced

by the latest release of the same model recently proposed by the agency: New

Ratings.

In implementing the Supervisory Formula we obtained the Kirb parameter us-ing default probabilities derived by ratings assigned by Fitch to each firm in the

pool and assuming a common LGD value of 60%. The one year PD has been cal-

culated on the basis of the historical default rate observed in one year time for each

rating class along the seventeen years spanning from 1990 to 2006.

8 Results

For the most senior tranches we found RBA and SFA charges being closely aligned;

likewise, at the lowest end of credit spectrum the equity tranche faces comparably

stringent charges under both approaches (figure 2).

Rather than the result of a sensible calibration of regulatory approaches, this

is mainly due to the cap and floor that Basel II applies to the ULP model, which

bounds the resulting capital charges.

The alignment relaxes moving to the center of capital structure, as SFA charges

become significantly higher than the RBA ones, at least as long as Old Ratings

are used (3.5 times in the case of the tranche 3-6).

The opposite happens when we deal with the RBA charges stemming from

New Ratings, providing clear evidence of the additional degree of prudence

adopted by Fitch when developing the latest Vector release.

Our most relevant finding, however, is that RBA charges, expected to be the

preferred criteria for measuring the regulatory capital for CDOs held into the bank-

ing book, do not fully cover the economic risk of tranches.

Using risk neutral PDs and a correlation value of 15% or greater, our estimates

of economic capital absorption (U Lmod) exceed the RBA charges for all tranches

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but the equity 21(table 6).

The gap is sizable for the mezzanine investments, with the regulatory capitalbeing 15 times lower than the EC (for the 3 6% tranche, see figure 3).

Regulatory and economic capital are more aligned using New Ratings. In

this case the ratio between EC and RBA CC plummets from 15 to about 1 for the

junior mezzanine tranche with a correlation of 15%, but widens again as we let

the correlation to increase. This pattern emphasizes the key role played by default

correlation in explaining the differences between CC and EC. From a regulators

perspective this finding is quite relevant: asset correlation tend to increase during

economic downturns, which is precisely the situation regulatory capital has to cope

with.

Part of the gap depends on the use of risk neutral probabilities of default when

computing risk metrics. In this regard we argue that it seems inadvisable computingeconomic capital measures without considering market information; the attention

paid by rating agencies to CDS spread as leading indicators for implied ratings

seems to confirm our point.

Finally, our results are influenced by the Basel II time horizon for banking ex-

posures. In this respect we are aware that one year is clearly too extended for iTraxx

tranches, that need a shorter time period to be closed or hedged. This regulatory

horizon become acceptable as we think to index tranches as a proxy of plain corpo-

rate CDOs held in the banking book; the scarce liquidity of these products, that the

recent upheavals in the market has just confirmed, can well justify the regulators

choice implemented in our excercise.

9 Conclusion

Like polo shirts, that come only in small, medium and large sizes, ratings are dis-

crete in nature and address just one dimension of structured products risk, the prob-

ability of default.

For this reason they are not the right tool for capital allocation, that should be

based on tailor made metrics linked to extreme values of the loss distribution.

We think that it would be useful to explore the robustness of rating based pru-

dential charges with respect to less stylized corporate CDOs or other structured

credit products, like CDOs of ABS.

In the event the same findings emerge it should be questioned whether the Basel

II mapping from ratings to capital is the right choice or it is encouraging new forms

of arbitrage.

21Being unrated, the equity tranche is entitled of a dollar by dollar (100%) capital charge.

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References

[1] The capital requirements directive 2006/48/ec. European Parlament.

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RiskMetrics Group, 2004.

[4] FitchRatings. Basel 2: Bottom-line impact on securitization markets. Special

report, FitchRatings, 2005.

[5] FitchRatings. Fitch ratings global corporate finance 2006 transition and de-

fault study. Special report, FitchRatings, 2007.

[6] M. Gordy. A risk-factor model foundation for rating-based bank capital rules.

Journal of financial intermediation, 12:199232, 2003.

[7] J.P. Laurent J. Gregory. Basket default swaps, cdos and factor copulas. Work-

ing paper, BNP Paribas, 2003.

[8] M. Gordy D. Jones. Random tranches. Risk, march:7883, 2003.

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[11] A. Dev M. Pykhtin. Credit risk in asset securitizations: an analytical model.

Risk, may:s16s20, 2002.

[12] A. Dev M. Pykhtin. Coarse-grained cdos. Risk, january:113116, 2003.

[13] R.C. Merton. On the pricing of corporate debt: the risk structure of interest

rates. Journal of finance, 29:449470, 1974.

[14] V. Peretyatkin W. Perraudin. Capital for structured products. Mimeo 4-2,

RiskContrl, 2004.

[15] L. Andersen L. S. Basu J. Sidenius. All your hedge in one basket. Risk,

November, 2003.

[16] O. Vasicek. Probability of loss on loan portfolio. White papers, KMV, 1987.

[17] J. Hull A. White. Dynamic models of portfolio credit risk: A simplified

approach. Working paper, University of Toronto, 2006.

[18] J. Hull A. White. Forwards and european options on cdo tranches. Working

paper, University of Toronto, 2007.

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Figure 2: SFA vs RBA CC)

Figure 3: EC vs RBA (Old rating)

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Figure 4: EC vs RBA (New rating)

Figure 5:

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Names Rating (Fitch) Real PD (%) Risk Neutral PD (%)

Abn Amro AA- 0.03 0.93Accor BBB 3.74 3.15

Adecco S.A. BBB- 4.76 3.58

Aegon N.V. AA 0.15 1.21

Akzo A- 1.42 2.00

Allianz A+ 0.37 0.91

Altadis BBB+ 2.24 2.56

Arcelor BBB 3.74 3.31

Auchan A 0.5 1.15

Aviva A+ 0.37 1.19

AXA AA- 0.03 1.24

BAA A- 1.42 4.09BAE system BBB 3.74 2.36

Banca BPI BBB 3.74 2.32

Banca Intesa AA- 0.03 1.09

Banca MPS A+ 0.37 1.32

Banco Bilbao AA- 0.03 1.07

Banco Comercial Portugues A+ 0.37 1.14

Banco Espirito Santo A+ 0.37 1.24

Banco Santander AA 0.15 1.28

Barclays AA+ 0.03 0.79

Bayer Aktiengesellschaft BBB+ 2.24 2.56

Bayerische Motoren Werke A+ 0.37 1.11Bertelsmann BBB+ 2.24 2.76

Boots BBB 3.74 2.64

British American Tobacco A- 1.42 2.16

British Telecommunications BBB+ 2.24 3.39

Cadbury Schweppes BBB 3.74 2.84

Capitalia A- 1.42 1.40

Carrefour A 0.5 1.13

Centrica A 0.5 1.96

Ciba Specialty Chemicals BBB 3.74 3.89

Commerzbank A 0.5 1.72

Compagnie de Saint-Gobain A- 1.42 2.24Compagnie Financiere Michelin BBB+ 2.24 3.04

Compass BBB+ 2.24 3.08

Continental BBB+ 2.24 2.92

DaimlerChrysler BBB+ 2.24 4.39

Degussa BBB- 4.76 7.26

Deutsche Lufthansa BBB- 4.76 3.93

Deutsche Telekom A- 1.42 3.47

Deutshe bank AA- 0.03 1.11

Diageo A+ 0.37 1.24

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Names Rating (Fitch) Real PD (%) Risk Neutral PD (%)

Dsg International BBB+ 2.24 2.96

E.ON AA- 0.03 0.99

EADS A 0.5 1.76

Edison BBB 3.74 1.44

EDP - Energias de Portugal A 0.5 1.09

Electrcite de France AA- 0.03 0.66

Electrolux BBB+ 2.24 3.08

EnBW Energie Baden-Wuerttemberg A- 1.42 0.99

Endesa A- 1.42 1.17

Enel A+ 0.37 0.99

Finmeccanica BBB 3.74 1.72

Fortum A+ 0.37 1.07

France Telecom A- 1.42 2.88

Gallaher Group BBB 3.74 2.52

Gas Natural A+ 0.37 1.44

Generali AA- 0.03 0.95

GKN Holdings BBB- 4.76 4.59

Glencore International BBB- 4.76 7.15

GUS BBB+ 2.24 3.06

Hannover Rueckversicherung A+ 0.37 2.08

Hellenic Telecommunications BBB 3.74 3.35

Henkel A- 1.42 1.36

HVP A 0.5 1.07

Iberdrola A+ 0.37 1.42

Imperial Chemical Industries BBB 3.74 3.11

Imperial Tobacco BBB 3.74 3.15

ITV BBB- 4.76 2.41

Kingfisher BBB 3.74 3.78

Koninklijke A- 1.42 10.17

Koninklijke Philips Electronics BBB+ 2.24 1.64

Lafarge BBB 3.74 2.92

Linde Aktiengesellschaft BBB- 4.76 3.94

Louis Vuitton BBB 3.74 1.88

Marks and Spencer BBB+ 2.24 2.60

Metro BBB 3.74 2.52

mmO2 BBB+ 2.24 2.08

Muenchener Ruck AA- 0.03 1.58

National Grid BBB+ 2.24 2.12

Nestle AAA 0.03 0.33

Nokia A+ 0.37 0.91

Pearson BBB+ 2.24 3.11

Peugeot A- 1.42 2.30

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Names Rating (Fitch) Real PD (%) Risk Neutral PD (%)Portugal Telecom Internat. Finance BBB 3.74 3.94

PPR BBB- 4.76 3.78

Reed Elsevier A- 1.42 1.80

Renault BBB+ 2.24 3.00

Rentokil Initial 1972 BBB 3.74 1.88

Repsol BBB+ 2.24 2.32

Reuters A- 1.42 1.80

RWE A+ 0.37 1.01

Safeway BBB 3.74 3.55

Sanofi Aventis AA- 0.03 1.60

Sanpaolo Imi AA- 0.03 1.09Siemens AA- 0.03 0.91

Sodexho Alliance BBB 3.74 2.12

Stora Enso BBB 3.74 3.19

Suez A 0.5 0.99

Svenska Cellulosa Aktiebolaget BBB+ 2.24 2.12

Swiss Reinsurance Company AA- 0.03 1.64

Tate & Lyle BBB 3.74 2.44

Technip BBB 3.74 2.00

Telecom Italia BBB+ 2.24 5.64

Telefonica BBB+ 2.24 3.47

TeliaSonera A- 1.42 3.55Tesco A+ 0.37 1.07

The Royal Bank o Scotland AA+ 0.03 0.75

Thomsom BBB 3.74 5.23

Unicredir A+ 0.37 1.30

Unilever A+ 0.37 1.24

Union Fenosa BBB+ 2.24 2.28

United Utilities BBB+ 2.24 1.56

UPM-Kymmene BBB 3.74 3.11

Valleo BBB 3.74 7.80

Vattenfall Aktiebolag A+ 0.37 1.07

Veolia Environnement A- 1.42 2.12Vivendi Universal BBB 3.74 3.51

Vodafone Group A- 1.42 2.56

Volkswagen A- 1.42 1.96

Volvo A- 1.42 2.82

Wolters Kluwer BBB 3.74 3.78

WPP 2005 BBB+ 2.24 2.44

Zurich Insurance Company A 0.5 1.68

Table 1: Risk neutral vs Real world5-years probabilities for the 125 names.

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Rating classes

Counterpart AAA A+ BBB+ BB+ B+

to AA- to A- to BBB- to BB- to B- below B- unrated

Sovereign 0% 20 % 50% 100% 100% 150% 100%

Banks (options 1) 20% 50 % 100% 100% 100% 150% 100%

Banks (options 2) 20% 50 % 50% 100% 100% 150% 100%

Corporates 20% 50 % 100% 100% 150% 150% 100%

Securitisation 20% 50 % 100% 350% Capital Capital Capital

products deduction deduction deduction

Table 2: Standard approach. Risk weights.

Tranche type

Long Term Rating Senior Base case Backed by non granular pools

Aaa/AAA 7% 12% 20%

Aa/AA 8% 15% 25%

A1/A+ 10% 18%

A2/A 12% 20% 35%

A3/A 20% 35%

Baa1/BBB+ 35% 50%

Baa2/BBB 60% 50%Baa3/BBB- 100%

Ba1/BB+ 250%

Ba2/BB 425%

Ba3/BB- 650%

Ba3/BB-Unrated Deduction

Table 3: RBA risk weights.

5Y Index spread 27Tranches Mid Spread Base Corr Comp Corr Delta

0 3 500+15.65% 12.7% 12.7% 26x3 6 49.5 22.5% 6.4% 5x6 9 14.5 29.7% 13.4% 1.5x

9 12 6.5 35.4% 17.5% 0.75x12 22 3 51.3% 25% 0.3x

Table 4: iTraxx trading screen

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Tranche Ratings RBA Ratings RBA FSA

(Old) (Old) (New) (New)

0 3 NA 100.00 NA 100 92.003 6 A- 2.80 BB 36.00 10.006 9 AAA 0.56 AA- 1.44 0.56

9 12 AAA 0.56 AAA 0.56 0.5612 22 AAA 0.56 AAA 0.56 0.56

22 100 NA 0.56 NA 0.56 0.56

Table 5: RBA and SFA Capital Charges

Tranche 5% 15% 25% 30%

0 3 48.7 100 100 1003 6 6 43.5 78.4 1006 9 0 4.4 29 55

9

12 0 0.6 4 912 22 0 0 0.5 1.2

22 100 0 0 0 0Table 6: U Lmod - Risk neutral PDs

Tranche 5% 15% 25% 30%

0 3 31 76.6 100 1003 6 6 20 60 786 9 0 0.8 8.4 20.4

9 12 0 0 1.3 2.612 22 0 0 0 0.3

22 100 0 0 0 0Table 7: U Lmod - Real World PDs

28

basel ii and structured finance

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