Working with the FTS Factor Module
The objective of this write-up is to provide a fast start to working with the FTS factor module. This module complements the Portfolio Returns and Efficient Portfolios Module by extending the single index model to allow for multiple sources of systematic risk. Of interest is to see whether the multiple sources of systematic do explain additional sources of return variance. When this is the case the multi-index model will take this out as additional sources of covariance. That is, the minimum variance frontier will appear to be more variable because of the additional sources of covariance teased out from the additional factors. In this module you can plot how the minimum variance frontier shifts both over the entire period by plotting frontier or over a rolling sequence of sub periods by using the Animate button. This is illustrated below.
The module assumes complete data. The user is responsible for correcting all cells that have missing data in the spreadsheet before linking to the module. The spreadsheet link makes this simple because it lets you apply the convention of your choice directly in Excel (e.g., use the previous observation, interpolate between previous and next observations etc.,). .
To follow this example, first download the spreadsheet titled DJIAFac.xls by clicking on the hypertext and open this in an Excel spreadsheet.
You are now ready to work through the following five steps:
Step 1: In this step you will link to an Excel worksheet to bring in either historical price or return data. We illustrate this with return data. First click on the button labeled Find Excel Spreadsheet. You will see DJIAFac.xls if you have only one spreadsheet open, otherwise select it from the workbooks you have open. This contains DJIA stock prices (monthly) from January 1990 to August 2003.
Enter the following data by filling the data into the text boxes:
Names in Row 1
First Row with Data: 2
Last Row with Data: 165
First Column with Data: B
Last Column with Data: AE
That is, this tells the module to get the return data from rows 2-165 and columns B to AE. Security names are provided in row 1.
Important: From the drop down select Price Data (not return data).
Next click on the button Initialize and then double click above the security label AA to select all stocks.
Now click OK and you should see the data below. Now you have your data in successfully.
Step 2: The objective of this step is to get the factor data. Click on the button Factor Data and repeat the steps from Step 1. This time our four factors are in: Columns AF to AK and rows 2-165. These factors are:
S&P500 Index
Corporate (BAA) - Treasury Bond Spread
Consumer Price Index
Constant maturity 10-year risk free rate
plus two Fama and French Factors
SMB (Small Stock Returns minus Big Stock Returns measured in levels)
HML (High growth minus Low Growth Returns measured in levels)
Important Note: Below Convert factors to returns there is a note about the number of factor observations you need. You should not mix factors specified in returns with factors specified in a form that needs to be converted to returns. Otherwise the time periods will not align correctly. Returns are computed from times (t+1) - t so if factors are to be converted to returns they must be specified in rows 3-165 but in this current example they are already in the form that is to be converted to returns and therefore are contained in rows 2-165.
Next select Convert factors to returns (if you forget this you will generate an error). Then click on Initialize, double click above Factor 1 to select all, and then click on OK.
Now from steps 1 and 2 you should have both return and factor data in the Factor Module.
Next click on the button Portfolios.
Step 3: The objective of this step is illustrate some of features built into the Factor Module. First, click on Plot Securities. You will see a scatter plot in Risk/Return space. Securities 1-30.
Check that Allow Short Sales is checked and Risk Free Rate and Factor Model boxes are unchecked. Now click on Frontier to Plot Frontier to compute the minimum variance frontier over this time period for the securities (not including the factors).
An Important Note on Scaling: Initially ensure that the Use depicted scale box is unchecked and click on Plot Frontier. This will compute the scale for you automatically. You may want to refine this first pass scale number. For example, risk is scaled from 0 to 0.2285 automatically. Change this to 0 to 0.1 by deleting 0.2285 in the text box and typing in 0.1 followed by Enter. Finally, select Use Depicted Scale to freeze this new scale.
Now leave Factor Model unchecked and plot Frontier and then check Factor Model and plot frontier. You will observe that the minimum variance frontier with factors lies within the Minimum variance frontier without factors.
Why is this the case if factors are supposed to help?
The answer is that when this is the case the factors are explaining an additional source of Variance --- this is being isolated via the covariance terms in the factor model. As a result, covariance is increasing when the factors are added but not being traded.
Step 4: The objective of this step is illustrate some of features built into the Factor Module. First, click on Clear to clear the Display Screen. Then select 60 as the block size (i.e., estimate the minimum variance frontier from 60-months of data). Finally, scroll the Scroll bar below Frontier in Period ... to 60. Finally, click on the button Animate. This plots how the frontier shifts over time rolling forward 1-month at a time using a blocksize of 60-months.
You will observe that with factors this appears to be more variable than without. The region where it is more variable illustrates the return regions where the factors are having the most influence upon the risk.
From a trading perspective by trading proxies for these factors will provide greater potential control over the dynamics of the minimum variance frontier in these regions.