Module 8 · Fixed Income

Yield and Yield Spread Measures for Floating-Rate Instruments

EN: Coupon resets, quoted & discount margins, money-market yields.
VN: Coupon reset, margin, money-market yields.

1. FRN Coupon Core

\[ \text{Coupon}_t = (\text{Reference rate}_{t-1} + \text{Quoted margin}) \cdot \frac{\text{Days in period}}{\text{Day count}} \]

Components

Ref rate SOFR, EURIBOR, etc. — set at start, paid at end of period.
Quoted margin (QM) Spread above reference rate, fixed for life of bond.
Discount margin (DM) Spread that, when added to reference rate, makes PV of CF = price. DM = QM if credit unchanged.

Practice problem

Reference rate at last reset = 4%, quoted margin = 1.5%, day count 90/360. Compute current period coupon as % of face.

Show solution

Coupon = (4% + 1.5%) × 90/360

= 1.375% per period

2. Money-Market Yields Core

\[ \text{Discount basis: } r_{BD} = \frac{F - P_0}{F} \cdot \frac{360}{T} \] \[ \text{Add-on rate (AOR): } r_{AOR} = \frac{F - P_0}{P_0} \cdot \frac{360}{T} \] \[ \text{Bond Equivalent Yield: BEY} = \frac{F - P_0}{P_0} \cdot \frac{365}{T} \]

T = days to maturity; F = face; P₀ = purchase price.

Practice problem

60-day T-bill bought at $995, face $1,000. Compute discount, AOR, BEY.

Show solution

Discount: (5/1000)(360/60) = 3.00%

AOR: (5/995)(360/60) ≈ 3.015%

BEY: (5/995)(365/60) ≈ 3.057%

Discount 3.00%; AOR 3.015%; BEY 3.057%

Practice problem Practice

Practice problem

A 90-day T-bill has face $1,000 and is bought at $990. Compute the discount-basis rate and bond-equivalent yield.

Show solution

Discount: r_BD = (1000 − 990)/1000 × 360/90 = 0.01 × 4 = 4.00%

BEY: (10/990) × 365/90 ≈ 0.01010 × 4.0556

Discount = 4.00%; BEY ≈ 4.10%