[R-SIG-Finance] Risk Model Mapping

[Gerlanc, Daniel]

Hello,

My problem involves mapping between different proprietary risk models,
specifically the Barra USE3L model and the Barra GEM model.  Allow me to
provide some background.

We subscribe to proprietary risk models developed by Barra.  These risk
models provide are grouped largely by region so we have a US model
(USE3L) and a global model (GEMM).  These models provide the covariance
of equities with different factors such as size, value, growth, momentum
and also map each security to one or more industries.

Each model contains different sets of factors.  For example, the USE3L
has 13 risk factors and GEM has 4 risk factors.  Some of these factors
refer to similar concepts. The US model has a factor called success and
the global model has a factor called momentum, and the relationship
between them is fairly linear.  The US model also maps each security to
up to 5 different industries with each industry having its own weight.
The global model maps each security to a single industry in a binary
manner.  A security either belongs to that industry or it does not.

The USE3L model covers some Canadian securities, but not all the
Canadian securities I would like it to.  Fortunately, these securities
are included in the GEMM model.  What I would like to do is continue
using the USE3L model, but find a way to shoehorn the GEM Canadian
stocks into the USE3L model.

Here are the approaches I've considered for doing this:

1. Estimate a linear model between style factors such as success and
momentum using the US and global data, and use the estimated regression
equation to map the GEM risk values to USE3L values.

2. Estimate the correlations between different industries in GEM and
USE3L.  Map GEM industries to the USE3L industries with the largest,
positive significant correlation.  Alternatively, keep the top 3
positively, significantly correlated industries; however, this will
likely assign related industries that a company may not actually
participate in.

3. Look up the data for each company and calculate its exposure to each
industry by the average amount of revenue it has generated in the last 3
years by industry.

In addition, I need some type of metric for determining how well the
mapping has worked.  Ultimately, what I want to produce is a correlation
matrix between stocks.  I would hope that the correlations produced by
the modified USE3L model would be similar to the correlations produced
by the GEM model.  To test this, I planned to subtract the GEM
correlation matrix from the USE3L correlation matrix after subsetting
out only the Canadian stocks.  Taking the absolute value of the matrix
and summing the values would give me an idea of the cumulative absolute
difference between the new and old model.

Any ideas on better ways to map between the models or a better metric
for testing how successful the mapping is?

Thanks!


Daniel Gerlanc
Associate Analyst
Geode Capital Management
1 Post Office Sq, Floor 28
Boston, MA 02109
Daniel.Gerlanc at geodecapital.com