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
allimportant 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 riskreturn 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 tradeoff between return and risk on
singleinstrument 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
breakeven 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
09.00  09.15 Welcome and Introduction
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
12.00  13.00 Lunch
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
 “ValueatRisk” for a Bond Portfolio
 Exercises
Day Two
09.00  09.15 Brief recap
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
12.00  13.00 Lunch
13.00  16.00 Bond Financing with REPOs
 Introduction to REPOS as a Refinancing Tool
 Types of REPOs

REPO Pricing
 CostofCarry 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
