Chapter 8

Yield and Yield Spread Measures for Floating-Rate Instruments

Understanding the unique yield measures and risk characteristics of floating-rate bonds and their valuation methodologies

1

Introduction to Floating-Rate Instruments

Floating-rate bonds, also known as floaters or variable-rate notes, are debt securities where the coupon rate is reset periodically based on a reference rate (benchmark rate) plus a quoted margin. These instruments provide protection against interest rate risk by adjusting their coupon payments in response to changes in market interest rates.
Key Characteristics of Floating-Rate Bonds
  • Reference Rate: A benchmark rate such as LIBOR, SOFR, or Treasury rates
  • Quoted Margin: A fixed spread added to the reference rate
  • Reset Frequency: How often the coupon rate is adjusted (quarterly, semi-annually, etc.)
  • Reset Date: The date on which the new coupon rate becomes effective
  • Rate Cap and Floor: Maximum and minimum coupon rates that may apply
Floating-Rate Coupon Formula

Coupon Rate = Reference Rate + Quoted Margin

Where:
Reference Rate = Benchmark rate (e.g., LIBOR, SOFR)
Quoted Margin = Fixed spread over reference rate
2

Discount Margin (DM)

The discount margin is the yield measure most commonly used for floating-rate bonds. It represents the margin over the reference rate that makes the present value of the bond's cash flows equal to its market price.
Discount Margin Calculation
The discount margin is found by trial and error, similar to calculating yield to maturity for fixed-rate bonds. The present value equation for a floating-rate bond is:
Discount Margin Present Value Formula

PV = Σ[(Reference Rate + Quoted Margin) × Principal / n]
÷ (1 + (Reference Rate + DM) / n)^t
+ Principal / (1 + (Reference Rate + DM) / n)^N

Where:
PV = Present Value (market price)
DM = Discount Margin
n = Number of coupon payments per year
N = Total number of periods
t = Period number
Important Note
The discount margin assumes that the reference rate remains constant over the life of the bond, which is an important limitation of this measure.
Example: Calculating Discount Margin
A floating-rate bond has:
  • Face value: $1,000
  • Current reference rate: 3.5%
  • Quoted margin: 150 basis points
  • Semi-annual reset
  • 2 years to maturity
  • Current market price: $995
The discount margin would be calculated by finding the DM that makes the present value equal to $995.
3

Yield Spread Measures

Types of Yield Spreads for Floaters
Several spread measures are used to evaluate floating-rate bonds relative to benchmark securities:
Spread Measure Definition Use Case
Discount Margin Margin over reference rate that equates PV to market price Primary yield measure for floaters
Quoted Margin Fixed spread specified in the bond indenture Contractual spread determination
Required Margin Market-determined spread for similar credit risk Relative value analysis
Relationship Between Margins
  • If Discount Margin > Quoted Margin: Bond trades at a discount to par
  • If Discount Margin = Quoted Margin: Bond trades at par
  • If Discount Margin < Quoted Margin: Bond trades at a premium to par
4

Interest Rate Risk of Floating-Rate Bonds

While floating-rate bonds provide protection against interest rate risk, they are not completely immune to price volatility due to several factors:
Sources of Interest Rate Risk
Reset Period Risk
Between reset dates, the bond behaves like a fixed-rate bond for the remainder of the current coupon period. The longer the reset period, the greater the interest rate risk.
Credit Risk Changes
Changes in the issuer's creditworthiness can cause the required margin to differ from the quoted margin, leading to price changes.
Caps and Floors Impact
Rate caps and floors can significantly affect the behavior of floating-rate bonds:
  • Rate Cap: Limits the maximum coupon rate, providing downside protection to the issuer but limiting upside for investors
  • Rate Floor: Sets a minimum coupon rate, providing downside protection to investors
  • Collar: Combination of cap and floor that limits both maximum and minimum rates
5

Valuation Considerations

Modified Duration of Floaters
The modified duration of a floating-rate bond is approximately equal to the time until the next reset date. This makes floaters much less sensitive to interest rate changes compared to fixed-rate bonds.
Floating-Rate Bond Duration Approximation

Modified Duration ≈ Time to Next Reset Date

Note: Floating-rate bonds have very low duration
because coupons adjust with market rates
Valuation at Reset Dates
On reset dates, a floating-rate bond without caps or floors will trade very close to par value, assuming:
  • The quoted margin reflects the current required margin
  • No changes in credit quality have occurred
  • The reference rate is available and reliable
Example: Duration Calculation
A floating-rate bond resets quarterly. If today is 45 days after the last reset:

Time to next reset = (90 - 45) / 365 = 0.123 years
Modified Duration ≈ 0.123 years

This low duration explains why floaters are relatively insensitive to interest rate changes.
6

Inverse Floaters and Structured Notes

Inverse floaters are structured securities where the coupon rate moves inversely to the reference rate. These instruments have unique risk and return characteristics.
Inverse Floater Mechanics
Inverse Floater Coupon Formula

Inverse Floater Coupon = C − L × (Reference Rate)

Where:
C = Maximum coupon rate
L = Leverage factor
Reference Rate = Benchmark interest rate
High Interest Rate Sensitivity
Inverse floaters have very high modified duration, often several times that of a comparable fixed-rate bond. They are extremely sensitive to interest rate changes and are considered high-risk investments.
Creation Through Structured Finance
Inverse floaters are often created by splitting the cash flows of fixed-rate bonds:
  • Floater Class: Receives variable-rate coupons
  • Inverse Floater Class: Receives the residual cash flows
  • Total Cash Flow: Must equal the original fixed-rate bond