transprobgrouptotals
Aggregate credit ratings information into fewer rating categories
Description
aggregates the credit ratings information stored in the
totalsGrouped
= transprobgrouptotals(totals
,groupingEdges
)totals
input into fewer ratings categories, which are
defined by the groupingEdges
argument.
Examples
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 Data_TransProb.mat
.
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
Input Arguments
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 size1
-by-nRatings1
.totalsMat
— A sparse matrix of sizenRatings1
-by-nRatings2
withnRatings1
≤nRatings2
.algorithm
— A character vector with values'duration'
or'cohort'
.
For the 'duration'
algorithm,
totalsMat
(i,j)
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 (IG
),
Speculative Grade (SG
), and Default
(D
), and the following
information:
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'
For the 'cohort'
algorithm,
totalsMat
(i,j)
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
information:
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
transprob
:
sampleTotals
— A single structure summarizing the totals information for the whole dataset.idTotals
— A struct array with the totals information at the ID level.
Data Types: struct
| structure
groupingEdges
— Indicator for grouping credit ratings into categories
numeric array
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 1
to 4
are
IG
, ratings 5
to
7
are 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 groupingEdges
has
K elements edge1
<
edge2
< ...
<edge
K, ratings
1
to edge1
(inclusive) are
grouped in the first category, ratings
edge1
+1
to
edge2
in the second category, and so
forth.
Regarding the last element,
edge
K:
If n
Ratings1
equals nRatings2
, thenedge
K must equal nRatings1
. This leads to K groups, and nRatingsGrouped1
= nRatingsGrouped2
= K.If n
Ratings1
< nRatings2
, then either:edge
K equals nRatings1
, in which case ratingsedge
K+1
,...,nRatings2
are treated as categories of their own. This results in K+(nRatings2
-edgeK) groups, withnRatingsGrouped1
= K andnRatingsGrouped2
= K + (nRatings2
–edge
K); oredge
K equalsnRatings2
, in which case there must be a jth edge element,edge
j, such thatedge
j equalsnRatings1
. This leads to K groups, andnRatingsGrouped1
= j andnRatingsGrouped2
= K.
Data Types: double
Output Arguments
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 size1
-by-nRatingsGrouped1
.totalsMat
— A matrix of sizenRatingsGrouped1
-by-nRatingsGrouped2
.algorithm
— A character vector,'duration'
or'cohort'
.
nRatingsGrouped1
and
nRatingsGrouped2
are defined in the description
of groupingEdges
. Each structure contains
aggregated information by categories, based on the information provided
in the corresponding structure in totals
, according
to the grouping of ratings defined by groupingEdges
and consistent with the algorithm
choice.
Following the examples in the description of the
totals
input, suppose IG
and
SG
are grouped into a single
ND
(Not-Defaulted) category, using the
edges[2 3]
. For the 'cohort'
algorithm, the output
is:
totalsGrouped.totalsVec = [6380 1145] totalsGrouped.totalsMat = [6341 39 0 1145] totalsGrouped.algorithm = 'cohort'
'duration'
algorithm:totalsGrouped.totalsVec = [6362.45 1162.05] totalsGrouped.totalsMat = [0 39 0 0] totalsGrouped.algorithm = 'duration'
More About
Cohort Estimation
The 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
transprob
.
Duration Estimation
Unlike the 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
transprob
.
References
[1] Hanson, S., T. Schuermann. "Confidence Intervals for Probabilities of Default." Journal of Banking & Finance. Vol. 30(8), Elsevier, August 2006, pp. 2281–2301.
[2] Löffler, G., P. N. Posch. Credit Risk Modeling Using Excel and VBA. West Sussex, England: Wiley Finance, 2007.
[3] Schuermann, T. "Credit Migration Matrices." in E. Melnick, B. Everitt (eds.), Encyclopedia of Quantitative Risk Analysis and Assessment. Wiley, 2008.
Version History
Introduced in R2011b
See Also
Topics
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