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# Fixed Income Mathematics

Duration: 2 days
• Introduction to Fixed Income Mathematics
• Review of Basic Financial Mathematics
• Bond Analytics – Yield and Risk
• Total Return Analysis
• Yield Curve Analysis
• Bond Refinancing with REPOs
• Term Structure of Volatility
The objective of this highly practical seminar is to give you a good understanding of the mathematical methods used in fixed income analysis and bond trading. We start with general introduction to financial mathematics and its uses in the bond markets. We then give a thorough review of the basic building blocks in fixed income mathematics, including all-important concepts such as time value of money, compounded interest, annuities, and discount factors. We present the formulas for these analytics and give examples of their calculation under various conventions. We then explain the uses of the basic formulas in the risk-return analysis of bonds and other fixed income structures.

Next, we describe how different yield measures are calculated and interpreted, illustrated by a number of practical examples. We take a closer look at the risk analytics such as duration, modified duration, dollar duration and convexity. We also show how to calculate portfolio key ratios for interest rate sensitivity. Further, using Total Return Analysis, we demonstrate how you can project returns on fixed income investments under various assumptions and how you can use scenario analysis to obtain estimates of return distributions for assessing the trade-off between return and risk on single-instrument and portfolio investments.

We then give a thorough introduction to the “yield curve” as an analysis tool. We explain how the spot curve is derived from market data and we demonstrate how this curve can used for pricing and risk analysis of fixed income instruments. We also explain how forward rates can be derived from the curve and used for the projection of reinvestment rates and for break-even investment analysis.

Further, we demonstrate how bond positions and portfolios can be refinanced using repos, and we thoroughly explain the mechanics and key concepts related to theses important financing tool. Finally, we explain the “term structure of volatility” and discuss the importance of “mean reversion” and other volatility features in fixed income analysis.

## Day One

### 09.15 - 12.00 Introduction to Fixed Income Mathematics

• Why Understanding Fixed Income Mathematics Has Become More Important
• Building Blocks of Fixed Income Analysis
• Uses of FI Mathematics in Bond Markets

### Review of Basic Financial Mathematics

• The Anatomy of Fixed Income Instruments
• Establishing Cash Flows of FI Instruments
• Time Value of Money
• Calculating Present Value
• Calculating Future Value
• Different Compounding Conventions
• Discount Factors
• Annuities
• Present Value of Annuities
• Future Value of Annuities
• Exercises

### 13.00 - 16.30 Bond Analytics - Yield and Risk

• Price and Yield Analysis
• The Price/Yield Relationship
• Calculating Yield Using Different Conventions (Euro, US, Japan,..)
• Decomposing and Interpreting Yield
• Exercises
• Risk Analysis
• Risks of Bond Investing
• Macaulay Duration
• Modified Duration, BPV and Dollar Duration
• Convexity and Dollar Convexity
• Using Duration and Convexity in a Taylor Series to Estimate Price Changes
• Portfolio Key Ratios
• “Value-at-Risk” for a Bond Portfolio
• Exercises

## Day Two

### 09.15 - 12.00 Total Return Analysis

• Calculating Expected Horizon Value
• Calculating Expected Returns
• Sensitivity Analysis
• Using “Babcocks Formula” in Total Return Analysis
• Exercises

### Yield Curve Analysis

• Introduction to Yield Curve Analysis
• Types of Yield Curve
• Estimating the Zero Coupon Curve
• Bootstrapping
• Cubic Splines of Discount Factors
• Applications of the Yield Curve
• Pricing Bonds
• Calculating Forward Rates
• Exercises

### 13.00 - 16.00 Bond Financing with REPOs

• Introduction to REPOS as a Refinancing Tool
• Types of REPOs
• REPO Pricing
• Cost-of-Carry Model
• Calculating the Repo Rate
• Calculating the Repurchase Price
• Examples of Bond Financing Transactions with REPOS
• Managing Counterparty Risk in REPO Transactions

### The Term Structure of Volatility

• Introduction to the Term Structure of Volatility
• How the Term Structure of Volatility is Estimated
• “Mean Reversion” Explained
• Examples of How the TS of Volatility is Used in Fixed Income Pricing

### Summary, Evaluation and Termination of the Seminar  