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__FTS Historical Interest Rate
Risk Analysis

Welcome to the Historical Interest Rate Risk Analysis Module. This module is designed to let you easily process the large amount of historical interest rate data that is continually updated on the Web. Retrieval is automated so that you can perform statistical and graphical analysis of this data at any time from the convenience of your own PC.

First, the module is designed to let you observe the behavior of interest rates over time.

For example, the module lets you compute volatilities, and correlations among different maturities for daily, weekly and monthly data. You can plot yield curves over time to observe how the shape changes. This lets you assess to what degree important statistical phenomena such as mean reversion influences the dynamics of the yield curve and thus the volatility of the short versus long end rates.

You can also perform a principal components analysis on the historical yield curve data. This lets users answer the question how many factors are required to describe the dynamics of the historical yield curves --- 1, 2 or more? The answer to this type of question is important for interest rate risk management and for predicting the value of interest rate derivatives.

**How Do I Get Started?**

**Step 1:** Select
Monthly, Weekly or Daily for the interest rate data you want to examine.

**Step 2:** Click on
the button titled "Get CMT Data." This will retrieve the data
automatically from the web for you. Otherwise, you can enter your
own data see the note below on Retrieving your own data from Excel.

**Step 3:** Click on
the button "Clean Data." This is useful to routinely use but
is most important if you are using daily data.

**Step 4:** Click on
the button "Process Data." This will process the historical
interest rate data.

**Note: Retrieving your own data from Excel**

You can either automatically retrieve the data from US Federal Reserve Bank or you can use your own data. To do the latter requires you set up a spreadsheet with titles in row 1, dates in column 1 (starting with row 2, row 3, etc.,), and yields to maturity by time to maturity across the remaining columns you want to use. Next fill in the text boxes to tell the module where the titles are (usually row 1 but do not have to be), and where the yields to maturity by maturity are. Finally, click on the button Find Excel Spreadsheet, identify the sheet with the data and click on Get Data from Excel to bring into the module.

Next click on the button **Curve
Analysis. **This will let you plot the history of how the yield curve
has evolved since 1994 to current. You are also encouraged to click on
the **Plot History **and** Animate** button to see how the yield curve has shifted since
1994. You can select to do this analysis using observed yield to
maturities (which mixes T-bills and T-Notes and Bonds), estimated yield to
maturities from the bootstrapped zero coupon bond curve, and finally the rates
from the implied forward rate curve.

You can then estimate the volatilities and correlations of the historical interest rate data. Finally, the button PCA performs a principal component (i.e., Factor Analysis) on the yield curve. This will allow you to observe how many factors (or dimensions) are required to describe how the yield curve shifts over time. Usually, you will observe that three factors account for the majority of the yield curve (either spot curve or more naturally the forward curve) variance.

The first factor captures a "levels effect" that is an approximate parallel shift and the second and third are interpreted as slope and curvature factors. This captures the fact that the yield curve tends to twist and changes shape over time. An readable discussion of the interpretation and application of yield curve factors is provided by a study of the South African yield curve which you can read by clicking on Maitland. You can also relate back the interpretation of yield curve factors to the Nelson-Siegel approach to interpolation the yield curve from a subset of observable market prices (see the FTS Treasury Calculator Module).

Understanding how the yield curve changes shape over time is critical knowledge for any fixed income position manager. As a result, the final two topics in the Interest Rate Risk module are designed to let you conduct back testing experiments using this module.

Duration Backtest: This lets you overlay a position on top of an existing liability (with a duration equal to 1-year, 3-year or 5-years) to eliminate the yield curve risk. The module solves for the position (revealed by clicking on the View Position button) from the set of fixed income instruments you estimate the yield curve from. It lets you test how well this overlay performs in terms of profits and realized errors. You can also repeat this analysis by focussing on Convexity as opposed to Duration.

PCA Backtest: This performs the same analysis but this time by exploiting either the first or first two factors that best describe the yield curve. When two factors are used a solution may not always exist (in the sense of exactly matching the target durations 1, 3 or 5 years).

These two topics provide a real world introduction into managing interest rate risk by either using Duration/Convexity or using the first two empirically fitted dimensions that best describe the dynamics of the observed yield curve.

OS Financial Trading System, PO Box 11356, Pittsburgh, PA 15238 USA, Phone 1-800-967-9897, Fax 1-412-967-5958, Email fts@ftsweb.com,

(C) Copyright 2000, OS Financial Trading System