FRTB Partial RiskFactor

Partial RiskFactor:-
       
           In FRTB, partial RiskFactor approach is specified under Revised Standardised Approach as a preferred way of arriving at risk weights. In this approach instruments with similar characters are grouped together in buckets and regulatory prescribed risk weights will be applied to their notional positions.
       
         We have implemented Partial RiskFactor using Clustering procedure of SAS!!! Happy Reading.

Partial RiskFactor Implementation:-
           In SAS CLUSTER can be used, CLUSTER hierarchically clusters the observations in a SAS dataset by using one of 11 methods. PROC CLUSTER computes possibly squared Eucledian distance as part of Clustering.  The methods differ by how distance between two clusters is computed(refer Appendix).

          We have used Wald's method for clustering as it is robust and reliable among the available options.  Please see the portfolio data:-

Input Data:-
 data Portfolio;
      input IReturn IRisk Sector Instrument$20.;
      datalines;
   14.7  5.7  5  Instr1    
   24.7  6.7  4  Instr5
   20.7  5.7  5  Instr9
   24.7  5.7  4  Instr13
   11.5 11.9  3  Instr2
   12.5 12.9  3  Instr10
   :
   ;

Clustering Process:-

To obtain approximate estimate of  pooled within-cluster covariance matrix using aceclus. 
     proc aceclus data=Portfolio out=Ace p=.03  noprint;
         var IReturn IRisk Sector;
     run;

To perform clustering of Instruments use below steps:-
     proc cluster data=Ace method=ward ccc pseudo print=7 outtree=Tree;
        var IReturn IRisk Sector;
         id Instrument;
     run;
     proc tree data=Tree ncl=6 out=clus3;
        copy IReturn IRisk Sector;
     run;

After clustering we can see the hierarchical grouping of instruments and their groups as in below.

Obtaining cluster Membership:-

To obtain cluster & their constituent instruments use the below procedures.

proc sort data=clus3; by cluster;

proc print data=clus3; by cluster;
var IReturn IRisk Sector;
run;

Cluster Analysis of Portofolio                                                                  

CLUSTER=1

Obs	IReturn	IRisk	Sector
1	13.4	11.7	2
2	13.4	11.7	2
3	13.4	11.7	2
4	13.4	11.7	2
5	12.0	12.4	1
6	12.0	12.3	1
7	11.5	11.9	3
8	12.3	11.9	3
9	11.0	12.4	1
10	12.5	12.9	3

CLUSTER=2

Obs	IReturn	IRisk	Sector
11	24.7	6.7	4
12	24.7	5.7	4

CLUSTER=3

Obs	IReturn	IRisk	Sector
13	20.7	5.7	5

CLUSTER=4

Obs	IReturn	IRisk	Sector
14	14.7	5.7	5

CLUSTER=5

Obs	IReturn	IRisk	Sector
15	12.5	1.2	3

CLUSTER=6

Obs	IReturn	IRisk	Sector
16	3	12.4	1

Using the above procedure we can decide which instruments will go into which cluster.

How to assign RiskWeight:-
     Based on Risk&Return attributed of the cluster supervisor will decide that :) .
     Here cluster2,cluster3 will have less riskweights, cluster6 will have more risk weights.

As per your problem choose the required clustering methods( listed in appendix),number of clusters, instrument attributes.

Thanks & Regards
Srinivasan

Appendix
The following are the types of clustering methods:-

     

	Description	Disadvantage
Average Linkage	Distance between two clusters is the average distance between pairs of observations, one in each cluster. Tends to join clusters with small variances.	Slightly biased toward producing clusters with the same variance.
Centroid Method	Distance between two clusters is defined as the (squared) Euclidean distance between their centroids or means. The centroid method is more robust to outliers than most other hierarchical methods.	Might not perform as well as Ward’s method or average linkage.
Complete Linkage	Distance between two clusters is the maximum distance between an observation in one cluster and an observation in the other cluster.	It can be Severely distorted by moderate outliers. Strongly biased toward producing clusters with roughly equal diameters.
Density Linkage	Class of clustering methods that use nonparametric probability density estimates. Density linkage consists of two steps: 1) A new dissimilarity measure, , based on density estimates and adjacencies is computed. 2) A single linkage cluster analysis is performed using dissimilarity analysis is performed. Types are:- kth-Nearest-Neighbor Method Uniform-Kernel Method Wong’s Hybrid Method
Maximum Likelihood	Similar to Ward’s minimum-variance method but removes the bias toward equal-sized clusters.	EML is somewhat biased toward unequal-sized clusters.
Single Linkage	Distance between two clusters is the minimum distance between an observation in one cluster and an observation in the other cluster. Single linkage has many desirable theoretical properties.	Sacrifices performance in the recovery of compact clusters in return for the ability to Detect elongated and irregular clusters. Tends to chop off the tails of distributions before separating the main clusters.
Ward’s Minimum-Variance Method	Distance between two clusters is ANOVA sum of squares between the two clusters added up over all the variables. At each generation, the within-cluster sum of squares is minimized over all partitions obtainable by merging two clusters from the previous generation.	Strongly biased toward producing clusters with roughly same number of observations. Also very sensitive to outliers