Fixed Income Mathematics - Day

This course explores and analyzes the mathematics of bond prices and yields as well as a variety of quantitative analytical methodologies. The course begins with an in-depth investigation of the industry conventions for calculating price and yield applied to plain vanilla bonds, including the exploration of implicit assumptions and interpretation of resulting numbers. The course then turns to a variety of tools used in the pricing, valuation and quantification of the risk of fixed income securities and portfolios. The tools are then applied to a variety of other fixed income instruments: bonds with embedded options, mortgage-backed securities and interest rate futures.

04-Aug-2008 -- 05-Aug-2008New YorkUSD$2375
NY Institute of Finance - Downtown9:00am - 4:30pm Instructional Method:
Group-Live
Instructor(s): [ Douglas Carroll; ] Mon Tue Level: Intermediate
CPE Credits: 14

14-Oct-2008 -- 15-Oct-2008New YorkUSD$2375
NY Institute of Finance - Downtown9:00am - 4:30pm Instructional Method:
Group-Live
Instructor(s): [ Douglas Carroll; ] Tue Wed Level: Intermediate
CPE Credits: 14

09-Dec-2008 -- 10-Dec-2008New YorkUSD$2375
NY Institute of Finance - Downtown9:00am - 4:30pm Instructional Method:
Group-Live
Instructor(s): [ Douglas Carroll; ] Tue Wed Level: Intermediate
CPE Credits: 14

Portfolio managers, institutional sales staff, research analysts, back office professionals, financial analysts, cash/money managers, auditors, and compliance staff.
No advance preparation required.
Students will be able to:
  • Calculate and interpret price, yield and accrued interest
  • Discuss yield to maturity as an expression of current value versus expected return
  • Identify by security appropriate interest compounding and day count conventions
  • Describe the various types of duration (Macualey's, modified, dollar, effective), as well as their application in quantifying and managine interest rate risk
Fixed Income Markets I or equivalent knowledge. Financial calculator required.
"Excellent instructor!"
  • Yield Curve Analysis
    • Day 1

    Interest Rates and Pricing Conventions

    • What is an interest rate: definitions
    • Interest conventions: simple and compound interest

    Financial mathematics

    • Time value of money
    • Bond math basics
    • Accrued interest

    Conventional yield measures

    • Nominal yield
    • Current yield
    • Yield to maturity
    • Yield to call
    • Conventions for yield quotes

    Expected risks versus expected returns

    • Sources of return
    • Risks of fixed income securities

    Yield to maturity reconsidered

    • As alternative expression of price
    • Why YTM is a poor proxy for future returns

    Estimating returns

    • Realized compound yield
    • Total return (horizon) analysis

    Types of yield curves

    • Security type
    • Construction

    Interest rate levels and shape of the yield curve

    • Nominal interest rates (yields to maturity)
    • Related Considerations
    • Yield curve theories

    Factors determining volatility

    • Non callable bonds
    • Callable bonds

    Macauley's Duration

    • Developed as a measure of a bond's life
    • Immunizing portfolios

    Quantifying price sensitivity to changes in market yields

    • Modified duration
    • Dollar duration
    • Impact of convexity

    Day 2

    Bond Price Volatility Part 2

    • Curvature of the price/yield function
    • Rate of change of duration
    • Second derivative of the price/yield function

    Callable bonds

    • Effective duration
    • Negative convexity

    Other uses of duration and convexity

    • Portfolio applications
    • Bond swap

    Nature of futures contracts

    • What is a futures contract?
    • Role of the clearinghouse in futures trading
    • Forward contracts versus futures

    Characteristics of futures contracts

    • Standardized contract specifications
    • Daily settlement
    • Margins

    Fixed income futures contracts

    • T-bond and T-note futures
    • Eurodollar and t-bill futures

    Financial futures/forward contracts pricing relationships

    • Cost of carry (carrying charges)
    • Cost of carry (arbitrage) pricing
    • Cash and carry trade example
    • Yield curve shape versus cash/futures relationship
    • Expectations in the pricing of futures/forwards

    Hedging with futures contracts

    • definition
    • hedging considerations
    • hedging example

    Introduction to mortgage backed securities

    • Mortgage loans
    • Participants

    Mortgage pass through securities

    • Types of mortgage pass through securities
    • Characteristics of pass throughs
    • Prepayment of principal (prepayment risk)
    • Mortgage pool characteristics
    • Mortgage pool prepayment considerations
    • Quantifying prepayment speed
    • Analysis of pass through securities

    Collateralized mortgage obligations (CMOs)

    • CMO basics
    • Z-Bond tranches
    • Planned amortiztions class (PAC) bond tranches
    • One sided PACs
    • Floating rate CMO structures
    • Stripped mortgage backed securities

    Analytic tools for MBS

    • Total return analysis
    • Option valuation of pass through securities
    • Estimating price volatility

    Clients who register for this course will receive a complimentary 6 month subscription to the Financial Times and FT.com. The Financial Times is the world's most respected financial newspaper providing a broad assessment on finance, business and the industrial sector. Subscriptions will start within 6-8 weeks of the application process, and are limited to one per client. For questions about your subscriptions call 800-628-8088 or email uscirculation@ft.com. US and Canada enrollees only.

    Lunch included for all students taking day classes.