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# Bond Analysis - Advanced I

Duration: 3 days
• Review of Basic Financial Mathematics
• Bond Analytics - Yield and Risk
• Total Return Analysis
• Yield Curve Analysis
• Pricing Floaters
• Analysis of High-Yield Bonds
• Analysis of Callable Bonds
• Principal Components Analysis
The objective of this course is to give you a good understanding of and “hands-on” experience with advanced, state-of-the-art toolkits for analyzing bonds and other fixed income instruments.

We start with a brief review of “basic” financial mathematics and bond analytics. We explain how these analytics are measured at the single-position as well as at the portfolio level.

Using a “Horizon Analysis” approach, we explain how expected return and risk can be quantified, based upon explicit assumptions about reinvestment rates and horizon yields, including scenarios for non-parallel shifts in the yield curve. The very powerful “Babcock formula” will be presented to assess the uncertainties associated with the expected return.

We shall then explain in depth how zero coupon curves can be derived from observable market prices and how such yield curves can be used to price different bond structures, including Floating Rate Notes.

We show how an in-depth analysis of floaters can be conducted, decomposing the floater into a pure x-ibor part and a spread part. The difference between effective and nominal spread will be discussed and we shall calculate the sensitivities of different floaters where the effective spread has diverged from the nominal spread.

Next, we will discuss how “High Yield” bonds (i.e. low-rated corporate and emerging markets bonds) can be analyzed with explicit consideration of default probabilities, recovery rates, covenants and collaterals.

We will then look at how callable bonds and bonds with pre-payment options (e.g. Mortgage Backed Securities) can be valued using term structure models, pre-payment models and Monte Carlo Simulation. We will also show how to calculate option-adjusted key-ratios such as Option-Adjusted Yield, Option-Adjusted Spread, Option-Adjusted Duration, Static Spreads etc.

Finally, we will show how you can use Principal Components Analysis on historical yield curve data to identify statistically significant and independent return factors. We will also explain how you can use these factors and their associated “factor loadings” for trading and risk management purposes.

## Day One

### 09.15 - 12.00 Review of Basic Financial Mathematics

• Time Value of Money
• Future and Present Value
• Simple and Compound Return
• Return and Yield Volatility
• Return Distributions

### Bond Analytics – Yield and Risk

• Price and Yield Analysis
• Effective Maturity
• Dollar Duration and PVBP
• Modified Duration
• Convexity
• How Convexity adds value to the Bond in a volatile Environment
• Risk Measures for Portfolios
• Portfolio Cash-flow Approach
• Approximation Approach

### 13.00 - 16.30 Total Return Analysis (Horizon Analysis)

• Purpose of Total Return Analysis
• “Total Return” Defined
• Assessing Reinvestment Risk
• Assessing Principal Risk
• Calculating Expected Return
• Sensitivity Analysis
• Approximating the realized Return using the Babcock Formula
• Approximating the Uncertainty on the realized Return using the Babcock Formula

## Day Two

### 09.15 - 12.00 Yield Curve Analysis

• Bootstrapping the Zero Coupon Curve from Par Swap Rates
• The Coupon Yield Curve and the Spot Curve
• Interpretations of the Yield curve
• Pricing Bonds Using the Yield Curve
• Calculating Forward Rates and Break Even Rates

### Pricing Floaters

• General Features of Floaters
• Discounted Margin Model
• Price Sensitivity of Floaters
• Possible negative Duration
• Making a Cash-flow Projection for a Floater using the Zero Curve
• Accessing the Uncertainty of the Cash-flow (Cash-flow at Risk)

### 13.00 - 16.30 Analysis of High-Yield Bonds

• The High Yield Market
• High Yield Security Valuation
• Modelling the Yield of Non-Investment Grade Bonds
• High Yield Security Risk Analysis
• Historical Default and Recovery Rates
• Rating Migration and Credit Quality Correlation
• Modelling Bond Rating Changes for Credit Risk Estimation

## Day Three

### 09.15 - 12.00 Analysis of Callable Bonds

• Price Yield Relationship of Callable Bonds
• Price-yield diagram
• Why duration can be negative
• Why convexity can be negative
• A Generalised Model for Valuing Bonds with Embedded Options
• Pre-Payment Models
• Binomial Interest Rate Trees
• The BDT Model
• Option Adjusted Yield and Duration
• Yield to First Call
• Effective Duration

### 13.00 - 16.30 Principal Component Analysis

• Common Factors Affecting Bond Returns
• Overview of Multi-Factor Interest Rate Risk Models
• The Factor Model
• Eigenvalues, Eigenvectors and the Yield Curve  