9.a Interest Rates
Transition to Fixed Income
Moving from derivatives to fixed income, covered in Chapters 9, 10, and 18.
Notes that material overlaps between these chapters.
Focus will be on interest rates in this session.
Bond Pricing Formula
Price of any asset = Expected cash flow discounted by the level of risk.
For fixed income assets or bonds:
Price = (Coupon Payment / (1 + Interest Rate)) + (Coupon Payment Next Period / (1 + Interest Rate)^2) + ... + (Coupon Payment Last Period + Face Value) / (1 + Interest Rate)^N
This represents a net present value calculation (more like present value since nothing is subtracted out).
Financial Calculator Inputs
Review of five time value of money inputs (solving for one):
Present Value (PVA) = Price
Future Value (F.B.) = Face Value (commonly $1,000 for corporate bonds).
Number of periods (for semiannual bonds) = adjusts payments and periods accordingly.
Coupon Rate:
Example: 8% coupon = $80 annually or $40 semiannually.
Impact of Interest Rates on Bond Prices
The relationship: Higher interest rates lead to lower prices and vice versa.
The interest rate is the driver of bond prices.
Types of Yield
Coupon
Stated rate, remains fixed (e.g. 8% coupon = $80 annual payment, paid semiannually).
Current Yield
Calculated as Annual Coupon / Bond's Current Price.
Changes based on bond price fluctuations.
Yield to Maturity (YTM)
Total expected return from a bond (cash flow + capital gains).
Dependent on required return and risk factors; higher risk = higher required return.
Factors Influencing Yield
Required return for stocks: Risk-free rate + market risk premium × beta.
For bonds: Required return = Risk-free rate + risk premium.
Risk Premium Factors
1. Default Risk Premium (DRP)
Based on bond ratings (investment-grade vs. junk-grade).
Lower ratings = higher required returns due to increased risk of default.
2. Maturity Risk Premium (MRP)
Longer-term bonds usually have higher yields due to increased risk over time.
3. Liquidity Premium (LP)
Bonds that are not actively traded require higher returns due to the difficulty of selling them.
Market-level Risk Factors
Market risk premium as seen with stock returns applies here as well.
Interest rate history demonstrates economic circumstances affecting rates (e.g., recession vs. expansion).
Inflation Premium
Key market driver affecting interest rates.
Taxability Premium
Some fixed-income instruments may have different tax implications affecting required returns (e.g., municipal bonds).
Summary of Risk Factors
Remember: Increases in risk premiums lead to increases in interest rates resulting in lower bond prices.
Understanding interest rate changes is crucial for bond trading.