Fixed Income Mathematics - Evening

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.

17-Jun-2008 -- 12-Aug-2008New YorkUSD$1975
NY Institute of Finance - Downtown5:45pm - 8:15pm Instructional Method:
Group-Live
Instructor(s): [ Douglas Carroll; ] Tue Level: Intermediate
CPE Credits: 20.0

27-Oct-2008 -- 15-Dec-2008New YorkUSD$1975
NY Institute of Finance - Midtown5:45pm - 8:15pm Instructional Method:
Group-Live
Instructor(s): [ Douglas Carroll; ] Mon Level: Intermediate
CPE Credits: 20.0

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 managing interest rate risk
Fixed Income Markets I or equivalent knowledge. Financial calculator required.
"Very good course content and very good instructor."
"Beyond the numbers and analysis, adequate real world context was provided"
"The instructor presented the course with clarity and knowledge. This is one of the best fixed income classes attended so far."
Schedule Note
There will be no class on Tuesday, July 1, 2008.
Session 1 - Interest Rates and Pricing Conventions

Interest Rates

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

Financial mathematics

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

Session 2 - Yields and Total Returns

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

Session 3 - Yield Curve 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

Yield curve movements and the real economy

  • Recent history
  • Historical relationships

Spot rates and the spot rate curve

  • Definitions
  • Construction/determination
  • Analytic applications
  • Treasury strip market

Implied forward rates

  • Riding the yield curve
  • Forward rates
  • Forward rate curves

Section 4 - Bond Price Volatility Part 1

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

Session 5 - Bond Price Volatility Part 2

Convexity

  • 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

Session 6 - Fixed Income Futures Part 1

Nature of futures contracts

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

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

Session 7 - Fixed Income Futures Part 2

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

Session 8 - Mortgage Backed Securities

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.