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LM08 Yield and Yield Spread Measures for Floating-Rate Instruments 2025 Level I Notes © IFT. All rights reserved 1 LM08 Yield and Yield Spread Measures for Floating-Rate Instruments 1. Introduction ........................................................................................................................................................... 2 2. Yield and Yield Spread Measures for Floating-Rate Notes .................................................................. 2 3. Yield Measures for Money Market Instruments ...................................................................................... 4 Summary ...................................................................................................................................................................... 9 Required disclaimer: IFT is a CFA Institute Prep Provider. Only CFA Institute Prep Providers are permitted to make use of CFA Institute copyrighted materials which are the building blocks of the exam. We are also required to create / use updated materials every year and this is validated by CFA Institute. Our products and services substantially cover the relevant curriculum and exam and this is validated by CFA Institute. In our advertising, any statement about the numbers of questions in our products and services relates to unique, original, proprietary questions. CFA Institute Prep Providers are forbidden from including CFA Institute official mock exam questions or any questions other than the end of reading questions within their products and services. CFA Institute does not endorse, promote, review or warrant the accuracy or quality of the product and services offered by IFT. CFA Institute®, CFA® and “Chartered Financial Analyst®” are trademarks owned by CFA Institute. © Copyright CFA Institute Version 1.0
LM08 Yield and Yield Spread Measures for Floating-Rate Instruments 2025 Level I Notes © IFT. All rights reserved 2 1. Introduction This learning module covers:  Yield spread measures for floating rate instruments – instruments with variable rather than fixed coupons  Yield measures for money market instruments – instruments with original maturities of one year or less 2. Yield and Yield Spread Measures for Floating-Rate Notes Floating-rate notes (FRN) are instruments where coupon/interest payments change from period to period based on a reference interest rate. Some important points to note about floating-rate notes:  The objective is to protect the investor from volatile interest rates.  The reference rate, usually a money market instrument such as a T-bill or a market reference rate (MRR), is used to calculate the interest payments. This rate is determined at the beginning of each period, but the interest is actually paid at the end of the period. This payment structure is called ‘in arrears.’  Often, the coupon rate of an FRN is not just the reference rate, but a certain number of basis points, called the spread, is added to the reference rate.  The specified yield spread over the reference rate is called the quoted margin.  The spread remains constant throughout the life of the bond. The amount of spread depends on the credit quality of the issuer. Example of a Floating Rate Note Moody’s assigned a long-term credit rating of A2 to Nationwide, U.K.’s largest building society. Nationwide issued a perpetual floating-rate bond with a coupon rate of 6-month MRR+ 240 basis points. The 2.4% quoted margin is a reflection of its credit quality. On the other hand, AAA-rated Apple sold a three-year bond at 0.05% over 3-month MRR in 2013 as its credit risk was very low. Coupon rate of a FRN = reference rate + quoted margin The required margin is the spread demanded by the market. We saw that the quoted margin, or the spread over the reference rate, is fixed at the time of issuance. But what happens if the floater’s credit risk changes and investors demand an additional spread for bearing this risk? The required margin is the additional spread over the reference rate such that the FRN is priced at par on a rate reset date. If the required margin increases (decreases) because of a credit downgrade (upgrade), the FRN price will decrease (increase). For example, assume a floater has a coupon rate of 3-month MRR plus 50 basis points. Six months after issuance, the issuer’s credit rating is downgraded and the market demands a required spread of 75 basis points. The coupon paid by the floater is lower than what the
LM08 Yield and Yield Spread Measures for Floating-Rate Instruments 2025 Level I Notes © IFT. All rights reserved 3 market demands. As a result, the floater would be priced at a discount to par as the cash flow is now discounted at a higher rate. The amount of the discount will be the present value of differential cash flows, i.e., the difference between the required and quoted margins. Conversely, if the credit rating of the issuer improves, the required margin would be below the quoted margin, and the market will demand a lower spread. How required margin affects a floater’s price at reset date Relationship between quoted and required margin Floater’s price at reset date Required margin = quoted margin Par Required margin > quoted margin Discount (below par) Required margin < quoted margin Premium (above par) The required margin is also called the discount margin. FRNs can be valued using the model shown below. PV = (MRR + QM) ∗ FV m (1 + MRR+DM m ) 1 + (MRR + QM) ∗ FV m (1 + MRR+DM m ) 2 + ⋯ + (MRR + QM) ∗ FV m + FV (1 + MRR+DM m ) N where: PV = present value of the FRN MRR = the market reference rate, stated as an annual percentage rate QM = quoted margin, stated as an annual percentage rate FV = future value paid at maturity, or the par value of the bond m = periodicity of the floating-rate note, or the number of payment periods per year DM = discount margin; the required margin stated as an annual percentage rate N = number of evenly spaced periods to maturity Equation 1 for reference: PV of bond = PMT (1+r)1 + PMT (1+r)2 + ⋯ + PMT+FV (1+r)N How to interpret the floating-rate note equation:  Think of it as an extension of Equation 1, we will draw similarities between the two equations.  (MRR + QM) ∗ FV m is the first interest payment similar to PMT of Equation 1, which is the coupon payment per period.  (MRR + QM) is the annual rate.  Since it is divided by periodicity we get the interest payment for that period.  In Equation 1, cash flows are discounted at 1 + r. For FRN, the cash flow for the first period is discounted at 1+ MRR+DM m , for the second period at (1 + MRR+DM m ) 2 , and so on. This is considered a simple model because of the following assumptions:
LM08 Yield and Yield Spread Measures for Floating-Rate Instruments 2025 Level I Notes © IFT. All rights reserved 4  The value is calculated only on reset dates. There is no accrued interest, so the flat price is the full price.  The model uses a 30/360 day-count convention, which means periodicity is always an integer.  The same reference rate is used in the numerator and denominator for all payment periods. Example A 3-year Italian floating-rate note pays 3-month MRR plus 0.75%. Assuming that the floater is priced at 99, calculate the discount margin for the floater if the 3-month MRR is constant at 1% (assume 30/360 day-count convention). Solution: The interest payment for each period is (1.00% + 0.75%) / 4 = 0.4375%. The keystrokes to calculate the market discount rate are: PV = -99, PMT = 0.4375, FV = 100, N = 12, CPT I/Y = 0.5237 * 4, I/Y = 2.09% The discount margin for the floater is 2.09% - 1% = 1.09% or 109 bps. 3. Yield Measures for Money Market Instruments Money market instruments are short-term debt securities. They have maturities of one year or less, ranging from overnight repos to one-year certificates of deposit. Differences in Bond Market and Money Market Yields Bond Market Yields Money Market Yields YTM is annualized and compounded. Rate of return is annualized but not compounded; stated on a simple interest basis. YTM calculated using the standard time value of money approach using a financial calculator. Non-standard calculation using discount rates and add-on rates. YTM stated for a common periodicity for all times to maturity. Instruments with different times to maturity have different periodicities for the annual rate. The calculation of interest of a money market instrument is different from calculating accrued interest on a bond. Money market instruments can be classified into two categories based on how the rates are quoted:  Discount rates: T-bills, commercial paper (CP), and banker’s acceptances are discount instruments. It means they are issued at a discounted price, and pay par value at maturity. They do not make any payments before maturity. The difference between the purchase price and par value at redemption is the interest earned. Note: Do not confuse