Aggregate credit ratings information into fewer rating categories
Aggregate the Credit Ratings Information Stored in the totals Input
Use historical credit rating input data from
Data_TransProb.mat. Load input data from file
load Data_TransProb % Call TRANSPROB with two output arguments [transMat, sampleTotals] = transprob(data); transMat
transMat = 8×8 93.1170 5.8428 0.8232 0.1763 0.0376 0.0012 0.0001 0.0017 1.6166 93.1518 4.3632 0.6602 0.1626 0.0055 0.0004 0.0396 0.1237 2.9003 92.2197 4.0756 0.5365 0.0661 0.0028 0.0753 0.0236 0.2312 5.0059 90.1846 3.7979 0.4733 0.0642 0.2193 0.0216 0.1134 0.6357 5.7960 88.9866 3.4497 0.2919 0.7050 0.0010 0.0062 0.1081 0.8697 7.3366 86.7215 2.5169 2.4399 0.0002 0.0011 0.0120 0.2582 1.4294 4.2898 81.2927 12.7167 0 0 0 0 0 0 0 100.0000
Group into investment grade (ratings 1-4) and speculative grade (ratings 5-7); note, the default is the last rating (number 8).
edges = [4 7 8]; sampleTotalsGrp = transprobgrouptotals(sampleTotals,edges); % Transition matrix at investment grade / speculative grade level transMatIGSG = transprobbytotals(sampleTotalsGrp)
transMatIGSG = 3×3 98.5336 1.3608 0.1056 3.9155 92.9692 3.1153 0 0 100.0000
Obtain the 1-year, 2-year, 3-year, 4-year, and 5-year default probabilities at investment grade and speculative grade level.
DefProb = zeros(2,5); for t = 1:5 transMatTemp = transprobbytotals(sampleTotalsGrp,'transInterval',t); DefProb(:,t) = transMatTemp(1:2,3); end DefProb
DefProb = 2×5 0.1056 0.2521 0.4359 0.6537 0.9027 3.1153 6.0157 8.7179 11.2373 13.5881
totals — Total transitions observed
structure | struct array
Total transitions observed, specified as a structure, or a struct array of length nTotals, with fields:
totalsVec— A sparse vector of size
totalsMat— A sparse matrix of size
algorithm— A character vector with values
contains the total transitions observed out of rating
i into rating j (all the
diagonal elements are 0). The total time spent on rating
i is stored in
totalsVec(i). For example, you
have three rating categories, Investment Grade (
Speculative Grade (
SG), and Default
D), and the following
Total time spent IG SG D in rating: 4859.09 1503.36 1162.05 Transitions IG SG D out of (row) IG 0 89 7 into (column): SG 202 0 32 D 0 0 0
totals.totalsVec = [4859.09 1503.36 1162.05] totals.totalsMat = [ 0 89 7 202 0 32 0 0 0] totals.algorithm = 'duration'
contains the total transitions observed from rating i
to rating j, and
totalsVec(i) is the initial
count in rating i. For example, given the following
Initial count IG SG D in rating: 4808 1572 1145 Transitions IG SG D from (row) IG 4721 80 7 to (column): SG 193 1347 32 D 0 0 1145
totals.totalsVec = [4808 1572 1145] totals.totalsMat = [4721 80 7 193 1347 32 0 0 1145 totals.algorithm = 'cohort'
Common totals structures are the optional output arguments from
sampleTotals— A single structure summarizing the totals information for the whole dataset.
idTotals— A struct array with the totals information at the ID level.
groupingEdges — Indicator for grouping credit ratings into categories
Indicator for grouping credit ratings into categories, specified as a numeric array.
This table illustrates how to group a list of whole ratings into
investment grade (
IG) and speculative grade
SG) categories. Eight ratings are in the
original list. Ratings
SG, and rating
8 is a category of its own. In this example, the
array of grouping edges is
[4 7 8].
Original ratings: 'AAA' 'AA' 'A' 'BBB' | 'BB' 'B' 'CCC' | 'D' | | Relative ordering: (1) (2) (3) (4) | (5) (6) (7) | (8) | | Grouped ratings: 'IG' | 'SG' | 'D' | | Grouping edges: (4) | (7) | (8)
In general, if
edge1 (inclusive) are
grouped in the first category, ratings
edge2 in the second category, and so
Regarding the last element,
edgeK must equal n
Ratings1. This leads to K groups, and n
Ratings2, then either:
edgeK equals n
Ratings1, in which case ratings
nRatings2are treated as categories of their own. This results in K+(
nRatings2-edgeK) groups, with
nRatingsGrouped1= K and
nRatingsGrouped2= K + (
nRatings2, in which case there must be a jth edge element,
edgej, such that
nRatings1. This leads to K groups, and
nRatingsGrouped1= j and
totalsGrouped — Aggregated information by categories
structure | struct array
Aggregated information by categories, returned as a structure, or a
struct array of length
nTotals, with fields:
totalsVec— A vector of size
totalsMat— A matrix of size
algorithm— A character vector,
nRatingsGrouped2 are defined in the description
groupingEdges. Each structure contains
aggregated information by categories, based on the information provided
in the corresponding structure in
to the grouping of ratings defined by
and consistent with the
Following the examples in the description of the
totals input, suppose
SG are grouped into a single
ND (Not-Defaulted) category, using the
[2 3]. For the
algorithm, the output
totalsGrouped.totalsVec = [6380 1145] totalsGrouped.totalsMat = [6341 39 0 1145] totalsGrouped.algorithm = 'cohort'
totalsGrouped.totalsVec = [6362.45 1162.05] totalsGrouped.totalsMat = [0 39 0 0] totalsGrouped.algorithm = 'duration'
cohort algorithm estimates the
transition probabilities based on a sequence of snapshots of credit ratings at
regularly spaced points in time.
If the credit rating of a company changes twice between two snapshot dates,
the intermediate rating is overlooked and only the initial and final ratings
influence the estimates. For more information, see the Algorithms section of
cohort algorithm, the
duration algorithm estimates the transition probabilities
based on the full credit ratings history, looking at the exact dates on which
the credit rating migrations occur.
There is no concept of snapshots in this method, and all credit rating
migrations influence the estimates, even when a company's rating changes twice
within a short time. For more information, see the Algorithms section of
 Hanson, S., T. Schuermann. "Confidence Intervals for Probabilities of Default." Journal of Banking & Finance. Vol. 30(8), Elsevier, August 2006, pp. 2281–2301.
 Löffler, G., P. N. Posch. Credit Risk Modeling Using Excel and VBA. West Sussex, England: Wiley Finance, 2007.
 Schuermann, T. "Credit Migration Matrices." in E. Melnick, B. Everitt (eds.), Encyclopedia of Quantitative Risk Analysis and Assessment. Wiley, 2008.