Yield and Yield Spread Measures for Floating-Rate Instruments

Fixed Income

Yield and Yield Spread Measures for Floating-Rate Notes

Learning Outcome Statement:

calculate and interpret yield spread measures for floating-rate instruments

Summary:

This LOS focuses on understanding the yield and yield spread measures for floating-rate instruments, including floating-rate notes (FRNs) and loans. These instruments adjust their interest payments based on a reference rate, offering less price risk during periods of interest rate volatility. The yield spread measures, such as the quoted margin and discount margin, help in assessing the credit risk and pricing of these instruments.

Key Concepts:

Quoted Margin

The quoted margin is the additional interest rate over the reference rate that compensates the investor for the issuer's credit risk. It remains fixed unless renegotiated.

Discount Margin

The discount margin is the required yield spread over the reference rate that makes the FRN's price equal to its par value at the reset date. It reflects changes in the issuer's credit risk and market conditions.

Price Volatility

FRNs exhibit less price volatility compared to fixed-rate bonds because their interest payments adjust with market rates. However, their price can still fluctuate based on changes in the discount margin and the time until the next reset date.

Pricing Model

The pricing of FRNs can be modeled using a simplified formula that accounts for the present value of future cash flows, adjusted by the market reference rate and the margins. This model helps in determining the fair value or market price of an FRN.

Formulas:

FRN Pricing Model

PV = \sum_{t=1}^{N} \frac{(MRR + QM) \times FV}{m} \times \frac{1}{(1 + \frac{MRR + DM}{m})^t} + \frac{FV}{(1 + \frac{MRR + DM}{m})^N}

This formula calculates the present value of an FRN by discounting its future cash flows, which are determined by the sum of the market reference rate and the quoted margin, adjusted by the discount margin for each period until maturity.

Variables:

$PV$ :: Present value or price of the floating-rate note
$MRR$ :: Market reference rate, annual percentage rate
$QM$ :: Quoted margin, annual percentage rate
$FV$ :: Future value or par value of the bond
$m$ :: Number of payment periods per year
$DM$ :: Discount margin, required margin as an annual percentage rate
$N$ :: Number of evenly spaced periods to maturity

Units: Percentage or monetary units

Yield Measures for Money Market Instruments

Learning Outcome Statement:

calculate and interpret yield measures for money market instruments

Summary:

Money market instruments are short-term debt securities with original maturities of one year or less, including repos, CDs, commercial paper, Treasury bills, and others. Yield measures for these instruments differ from bonds in that they are annualized but not compounded and can be quoted on either a discount rate or add-on rate basis. The pricing and yield calculations for these instruments require specific formulas depending on whether they are quoted on a discount rate or add-on rate basis.

Key Concepts:

Discount Rate Basis

Instruments quoted on a discount rate basis calculate the present value by adjusting the face value by a factor that accounts for the discount rate over the period until maturity. This method understates the rate of return to the investor as it uses the face value in the denominator.

Add-On Rate Basis

Instruments quoted on an add-on rate basis calculate the future value by adding the interest (calculated over the period until maturity based on the add-on rate) to the principal amount. This method shows the total amount to be received at maturity, including interest.

Bond Equivalent Yield

The bond equivalent yield is used to convert a discount rate or add-on rate to an annualized rate based on a 365-day year, allowing for comparison with other investment yields such as bonds.

Formulas:

Discount Rate Pricing Formula

PV = FV \times (1 - \frac{Days}{Year} \times DR)

Calculates the present value of a money market instrument quoted on a discount rate basis.

Variables:

$PV$ :: Present Value
$FV$ :: Future Value
$Days$ :: Number of days from settlement to maturity
$Year$ :: Number of days in the year
$DR$ :: Discount Rate (annual percentage rate)

Units: currency units

Add-On Rate Pricing Formula

PV = \frac{FV}{(1 + \frac{Days}{Year} \times AOR)}

Calculates the present value of a money market instrument quoted on an add-on rate basis.

Variables:

$PV$ :: Present Value
$FV$ :: Future Value
$Days$ :: Number of days from settlement to maturity
$Year$ :: Number of days in the year
$AOR$ :: Add-On Rate (annual percentage rate)

Units: currency units

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