Factor Structure

A Factor Structure is a World Variable which is used to generate scenarios from the World State to which it is assigned. Such scenarios are necessary for calculating Advanced Measures on Portfolios.

The following is a display of a Factor Structure:

fctrstr1.gif

There are various steps involved in using a Factor Structure.

Specification of World State Data to be Varied:

The first step is to identify all the data that needs to be simulated during the scenario generation. This is done by reviewing all the World Variables that are in the World State which will be used, and then identifying those World Variable Data that are to be simulated.

This data is represented in the Factor Structure as Factor Structure Variables. Each such variable must be created in the Factor Structure and an appropriate volatility for its value must be specified.

The following display shows a Factor Structure Variable:

fctrstr2.gif

This shows that the Factor Structure Variable DEM_R360 assigned to the Factor Structure named RM_FS has a current volatility of 8.68093 % and it obtains this value from an External Data Variable called DEM_R360_VOLD.

The next step is the specification of all the correlations that must be considered during the set up of scenario generation.

The following display shows a correlation between two Factor Structure Variables:

fctrstr3.gif

This shows that the correlation between Factor Structure Variables CAD_R030 and DEM_R360 has a current value of -0.028091 and it obtains this value from an External Data Variable called CAD_R030_DEM_R360_CORD.

If no correlation is specified between two Factor Structure Variables, then this correlation is assumed to be zero.

In order to see all the correlations that are to be considered, click on the "Matrix" button to display the full correlation matrix:

fctrstr4.gif

To return to the main display, click on the "Restore" button.

Setting Up the Scenario Generation Parameters:

Once all the input data has been set up, it is necessary to decide how detailed the scenario generation will be. To help in this decision the correlation matrix is decomposed using principal components into its factors. These factors are ordered from the most to the least important in their ability to explain the variability found in the correlation matrix. [See Jamshidian.]

The factors are calculated by clicking on the "Compute Factor Decomposition" button and the results are displayed in a list as follows:

fctrstr5.gif

This list shows that the most important factor explains 45.071 % of the total variation in the correlation matrix. And the second most important factor explains 14.922 % of the total variation. Together, the first and the second factor explain 59.993 % of the total variation as show in the "Cumulative" column.

The next step is to decide on how many factors are to be used in the simulation. From the factor decomposition results select the number of factors required to simulate the desired percentage of the total variation. For example, to use six factors enter '6' in the Simulation Formula Details section as shown here:

fctrstr6.gif

In order to carry out the scenario generation, additional variables are necessary. These variables are created by clicking on the "Compute" button in the display shown above. The additional variables are created as External Data Variables and Computed Data Variables.

To simulate scenarios using six factors it is necessary to be able to specify a six-dimensional Factor Space. The External Data Variables created by the "Compute" operation are used to specify the values of the six independent factors. To view these variables click on the "View EDVs" button to display:

fctrstr7.gif

Each Factor Space EDV is created as a Constant with the value set to zero. During a simulation this value is changed over the range of values computed for this factor dimension during the "Compute Factor Space" operation discussed below.

For each point in the factor space a corresponding scenario needs to be generated. The scenarios are generated by using a multiplier for each of the Factor Structure Variables identified above. These multipliers are created as Computed Data Variables by the "Compute" operation. To view these variables click on the "View CDVs" button to display:

fctrstr8.gif

This display shows the multiplier corresponding to the Factor Structure Variable CAD_R030:

EXP((

-0.2076 * EDV(RM_FS_FCTR_01)

+0.308727 * EDV(RM_FS_FCTR_02)

-0.670706 * EDV(RM_FS_FCTR_03)

+0.0119778 * EDV(RM_FS_FCTR_04)

-0.508546 * EDV(RM_FS_FCTR_05)

+0.220783 * EDV(RM_FS_FCTR_06)

) * SQRT(DT_YRS) * (

EDV(CAD_R030_VOLD)

))

The formula shows the importance of each of the factor dimensions (also known as factor loadings) for this Factor Structure Variable. It also shows the relationship of changes in this variable to changes in time and the variable's volatility. Since the default settings for all the factors is zero, the default value of the multiplier will be one.

To generate the range of values that will be used for each of the factor dimensions, it is necessary to click on "Compute Factor Space" in the Simulation Factor Space Details:

fctrstr9.gif

This operation uses the information specified by the "Minimum Number of Pts." field to distribute that number of points across the factor dimensions weighted by the explanatory power of each factor dimension. The result is that each factor dimension will be allowed to vary over a certain number of points and the product of these points (the Actual Number of Points) will be as close as possible to the desired number of points. The scenario simulation will be conducted over this Actual Number of Points.

The factor space results can also be influenced by toggling the "Nearest Actual No./Rounded Up Actual No." Check Box. If "Nearest Actual No." is selected, then the number of points calculated per factor dimension is always rounded to the nearest integer number. Otherwise, if "Rounded Up Actual No." is selected, then the number of points calculated for each factor dimension is always rounded to the next highest integer number.

Using the Factor Structure in a World State:

Once all the input data has been set up and the Scenario Simulation variables and parameters have been specified, it is necessary to connect the generated multiplier variables to the appropriate World Variable Data variables that are to be simulated.

To connect a multiplier to its World Variable Data, insert the multiplier into the formula for that World Variable Data.

For example, in order to add the multiplier for the Factor Structure Variable CAD_XS in the Factor Structure names RM_FS it is necessary to find the appropriate World Variable Data. After we find this data in the Exchange Rate Structure called FX_RM, we can insert the multiplier called RM_FS_CAD_XS_MULTIPLIER as shown below:

fctrstr0.gif

It is important that the multiplier be identified as a Computed Data Variable by enclosing it in CDV(…).

Important Considerations:

Scenarios can only be generated for World States that have a Factor Structure assigned to them. Furthermore, the Factor Structure multipliers should only be used in World Variables that are assigned to this same World State.

Although, the factor loadings may not change appreciably on a daily basis, it is highly recommended that the correlations between Factor Structure Variables be defined using External Data Variables. In this way, as these correlations change over time, they can be uploaded into the Factor Structure and a new Factor Decomposition can be computed. This new decomposition will alter the multiplier formulas as necessary to reflect the latest correlation data.

The source of volatility and correlation data must be considered carefully before deciding to set up a Factor Structure for regular use in a trading and risk management operation. A commonly referenced source is J.P. Morgans's RiskMetrics® data which is available through Reuters.

If only time series data is available for the variables of interest, then it will be necessary to calculate the volatility and correlation data from this time series data. There are various vendors that provide such software and services.

Naming Convention:

The names for correlations between Factor Structure Variables are automatically created by alphabetically adding the Factor Structure Variable names to the end of the name chosen for the Factor Structure.

The names for the EDVs that are used as the factors are generated by adding FCTR_nn at the end of the name chosen for the Factor Stucture, where 'nn' is the number of that factor. For Example, the second factor in a Factor Structure called RM_FS will be called RM_FS_FCTR_02.

The names for the CDVs that are used as the multipliers for the Factor Variables, are generated by adding the Factor Variable name and the word MULTIPLIER to the end of that name chosen for the Factor Structure.