M8: Yield and Yield Spread Measures for Floating-Rate Instruments

What is a floating-rate note (FRN)?

A debt instrument whose coupon periodically resets based on a market reference rate (MRR) plus a fixed quoted margin (QM).

What determines an FRN's coupon rate?

Coupon rate = MRR + Quoted Margin (QM).

What is the market reference rate (MRR)?

A short-term market interest rate used as the floating benchmark for an FRN's coupon.

When is the MRR typically observed and the coupon paid?

The MRR is observed at the start of the period, while interest is paid at the end of the period (in arrears).

What is the quoted margin (QM)?

The fixed spread over or under the MRR specified when the FRN is issued.

Does the quoted margin change over the life of an FRN?

No. QM is fixed at issuance and does not change.

What does the quoted margin compensate investors for?

Primarily the issuer's credit risk relative to the risk reflected in the MRR.

What is the discount margin (DM)?

The spread over MRR that investors currently require to hold the FRN at par on a reset date; also called the required margin.

What can cause the discount margin to change?

Changes in the issuer's credit risk, liquidity, tax status, and market conditions.

What is the easiest way to distinguish QM from DM?

QM = what the bond Gives; DM = what the market Demands.

What happens when QM = DM?

The FRN trades at par: Price = 100.

What happens when QM > DM?

The FRN trades at a premium: Price > 100 because it pays a larger spread than investors currently require.

What happens when QM < DM?

The FRN trades at a discount: Price < 100 because it pays a smaller spread than investors currently require.

If an FRN issuer's credit quality improves, what generally happens to DM and price?

DM falls; if DM falls below QM, the FRN trades above par.

If an FRN issuer's credit quality deteriorates, what generally happens to DM and price?

DM rises; if DM rises above QM, the FRN trades below par.

What is the fixed-rate bond analogy for QM versus DM?

Fixed bond: coupon rate vs required YTM. FRN: quoted margin vs required discount margin.

What determines the periodic coupon in the simplified FRN model?

Periodic coupon = [(MRR + QM) × FV] ÷ m.

What rate is used to discount FRN cash flows in the simplified model?

Periodic discount rate = (MRR + DM) ÷ m.

What does m represent in the FRN pricing formula?

The number of coupon/payment periods per year.

What does N represent in the FRN pricing formula?

The number of remaining payment periods until maturity.

What is the simplified FRN pricing formula conceptually?

Price = PV of coupons based on MRR + QM + PV of principal, discounted using MRR + DM.

Why is an FRN's price mainly sensitive to the difference between QM and DM?

MRR appears in both the coupon rate and required discount rate, so much of an MRR change offsets itself.

How do you solve for DM using a BA II Plus?

Calculate PMT = [(MRR + QM) × FV] ÷ m; enter N, PV, PMT, FV and CPT I/Y; then use DM = (I/Y × m) − MRR.

If BA II Plus gives I/Y when solving an FRN with quarterly payments, is I/Y directly the DM?

No. I/Y is the periodic rate = (MRR + DM) ÷ 4. Annualise it and subtract MRR to obtain DM.

What is the formula for recovering DM from the periodic rate r?

DM = (r × m) − MRR.

An FRN has QM = 250 bps and DM = 329 bps. Premium or discount?

Discount, because QM < DM. The market requires 79 bps more than the FRN pays.

Why do FRNs generally have lower interest-rate sensitivity than fixed-rate bonds?

Their coupons reset with market interest rates, automatically adjusting cash flows as rates change.

How does a longer reset period affect an FRN's interest-rate sensitivity?

A longer reset period increases interest-rate sensitivity because the coupon remains unchanged for longer before resetting.

What is a money market instrument?

A short-term debt instrument with an original maturity of one year or less.

What is the key difference between discount rate (DR) and add-on rate (AOR)?

DR measures interest relative to redemption/face value; AOR measures interest relative to the amount actually invested.

What is the discount rate (DR) formula?

DR = [(FV − PV) ÷ FV] × (Year ÷ Days).

What denominator does the discount rate use?

Future/redemption value (FV).

What is the intuition behind the discount rate?

It measures the discount from the amount that will be received at maturity.

Why does DR understate the investor's return relative to an equivalent add-on rate?

DR divides interest by the larger redemption value rather than the smaller amount actually invested.

What is the price formula when a discount rate is given?

PV = FV × [1 − (Days ÷ Year) × DR].

What is the add-on rate (AOR) formula?

AOR = [(FV − PV) ÷ PV] × (Year ÷ Days).

What denominator does the add-on rate use?

The purchase price/current value (PV), i.e. the amount actually invested.

Why is AOR more intuitive as an investment return than DR?

It measures profit relative to the amount the investor actually invested.

For the same positive-return instrument and same day-count basis, which is larger: DR or AOR?

AOR > DR because AOR divides by PV while DR divides by the larger FV.

What is holding-period yield (HPY)?

The actual simple return earned over the investment's holding period before annualisation.

What is the HPY formula for a pure-discount instrument?

HPY = (FV − PV) ÷ PV.

Is HPY an annualised return?

No. It measures return only over the actual holding period.

What is money market yield (MMY)?

HPY annualised using a 360-day year without compounding.

What is the MMY formula?

MMY = HPY × (360 ÷ Days).

What is bond equivalent yield (BEY) for money market instruments?

HPY annualised on a 365-day basis without compounding, allowing comparison on a common basis.

What is the BEY formula for a money market instrument?

BEY = HPY × (365 ÷ Days).

What is effective annual yield (EAY)?

The annual return after accounting for compounding over a 365-day year.

What is the EAY formula?

EAY = (1 + HPY)^(365 ÷ Days) − 1.

Why is EAY generally greater than BEY for a positive-return short-term instrument?

EAY incorporates compounding, while BEY uses simple annualisation.

What is the difference between MMY and BEY?

Both simply annualise HPY, but MMY uses 360 days while BEY uses 365 days.

What is Actual/360?

Actual days in the investment period are used, with 360 as the annual denominator.

What is Actual/365?

Actual days in the investment period are used, with 365 as the annual denominator.

What is Actual/Actual?

Actual days in the investment period divided by the actual number of days in the year: 365 or 366.

Why can Actual/365 and Actual/Actual differ?

In a leap year, Actual/Actual uses 366 while Actual/365 still uses 365.

How should two money market instruments quoted using different conventions be compared?

Convert both yields to the same convention/basis before comparing them.

What is the typical conversion path from a discount rate to BEY?

DR → calculate PV → calculate HPY → annualise HPY on a 365-day basis to obtain BEY.

What is the key memory rule for DR versus AOR?

DR = profit ÷ what I Receive (FV); AOR = profit ÷ what I Actually invested (PV).

What is the key memory rule for HPY, MMY, BEY, and EAY?

HPY = holding-period return; MMY = simple annualisation using 360; BEY = simple annualisation using 365; EAY = annualisation using 365 plus compounding.

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