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LM07 Yield and Yield Spread Measures for Fixed-Rate Bonds 2025 Level I Notes © IFT. All rights reserved 1 LM07 Yield and Yield Spread Measures for Fixed-Rate Bonds 1. Introduction ........................................................................................................................................................... 2 2. Periodicity and Annualized Yields ................................................................................................................ 2 3. Other Yield Measures, Conventions, and Accounting for Embedded Options ............................. 3 4. Yield Spread Measures for Fixed-Rate Bonds and Matrix Pricing .................................................... 6 Summary ...................................................................................................................................................................10 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
LM07 Yield and Yield Spread Measures for Fixed-Rate Bonds 2025 Level I Notes © IFT. All rights reserved 2 1. Introduction This learning module covers:  How to calculate the annual yield on a bond for varying compounding periods in a year  Yield and yield spread measures for fixed-rate bonds 2. Periodicity and Annualized Yields Periodicity is the number of compounding periods in a year, or number of coupon payments made in a year. The stated annual rate for a bond will depend on the periodicity we are assuming. The stated annual rate is also called the annual percentage rate or APR. Instructor’s Note A quarterly coupon paying bond has a periodicity of four, while a semi-annual bond has a periodicity of two, and a monthly-pay bond with a given annual yield would have a periodicity of twelve. “Compounding more frequently within the year results in a lower (more negative) yield-to- maturity.” Consider a 5-year, zero-coupon bond priced at 80 per 100 par value. What is the stated annual rate for periodicity = 4, periodicity = 2, and periodicity = 1? When periodicity = 4: compounding happens four times a year. N = 20; (5 years x 4 = 20). PMT = 0 as it is a zero-coupon bond. PV = -80; FV = 100; CPT I/Y = 1.12. This is the rate for each quarter. The stated annual rate is 1.12 x 4 = 4.487%. When periodicity = 2: N = 10; PV = -80; PMT = 0; FV= 100; CPT I/Y = 2.2565. The stated annual rate is 2.25 x 2 = 4.51%. When periodicity = 1: N = 5; PV = -80; PMT = 0; FV= 100; CPT I/Y = 4.56%. With a periodicity of 1, the stated annual rate is the same as the effective annual rate. The formula for conversion based on periodicity is (1 + APRm m ) m = (1 + APRn n ) n Example A 4-year, 3.75% semi-annual coupon payment government bond is priced at 97.5. Calculate the annual yield to maturity stated on a semi-annual bond basis and convert the annual yield to: 1. An annual rate comparable to bonds that make quarterly coupon payments. 2. An annual rate comparable to bonds that make annual coupon payments.
LM07 Yield and Yield Spread Measures for Fixed-Rate Bonds 2025 Level I Notes © IFT. All rights reserved 3 Solution to 1: The stated annual yield to maturity on a semiannual bond basis can be calculated using a financial calculator: N = 8; PMT = 1.875; FV = 100; PV = -97.5; CPT I/Y. I/Y = 2.2195%. Hence, the stated annual yield to maturity = 2.2195% x 2 = 4.439%. (1 + 0.04439 2 ) 2 = (1 + APR4 4 ) 4 APR4 = 4.415% The annual rate of 4.439% for compounding semiannually compares with 4.415% for compounding quarterly. Solution to 2: (1 + 0.04439 2 ) 2 = (1 + APR1 ) APR1 = 4.488% The annual percentage rate of 4.439% for compounding semiannually compares with an effective annual rate of 4.488%. The effective annual rate (EAR) is the yield on an investment in one year taking into account the effects of compounding. This rate has a periodicity of one as there is only one compounding period per year. EAR is used to compare the rate of return on investments with different frequency of compounding (periodicities). Semiannual bond equivalent yield: Yield per semi-annual period times two. If the yield per semi-annual period is 2%, then the semi-annual bond equivalent yield is 4%. 3. Other Yield Measures, Conventions, and Accounting for Embedded Options Other Yield Measures and Conventions  Street convention: It is the yield to maturity using a 30/360-day convention assuming payments are made on scheduled dates, even if the payment date fell on a weekend or a holiday.  True yield: Yield to maturity calculated using an actual calendar of weekends and holidays. For instance, assume the coupon date falls on 15 March 2015, which is a Sunday. Street convention assumes the payment is made on that date, whereas true yield assumes the payment is made on 16 March if it is a business day. The coupon payment is discounted back from 16 March instead of 15 March.  Government equivalent yield: Yield to maturity calculated using the actual day/count convention used for U.S. Treasuries.  Current yield (Simple yield): Sum of the coupon payments received over the year divided by the flat price. It is also called the income or interest yield. Example: A 5-year, 8%
LM07 Yield and Yield Spread Measures for Fixed-Rate Bonds 2025 Level I Notes © IFT. All rights reserved 4 semiannual coupon payment bond is priced at $960. Its current yield is 80/960 = 0.0833 = 8.33%. Current yield is not an accurate measure of the rate of return as it ignores the frequency of coupon payments, reinvestment income, and capital gain/loss on a bond. Current yield = Annual cash coupon payment Bond price Bonds with Embedded Options For bonds with embedded options the following yield measures are used.  Yield-to-call: Calculates the rate of return on a callable bond if it is bought at market price and held until the call date. The difference between YTM and the yield-to-call is that YTM assumes the bond is held to maturity. Calculation of yield-to-call is the same as YTM where N = number of periods to call date and FV= call price.  Yield-to-first call (YTFC): It is the internal rate of return if the bond was bought at market price and held until the first call date.  Yield-to-second call: Similarly, the yield on a callable bond if it was bought at market price and held to the second call date is called yield-to-second call.  Yield-to-worst: Yield is calculated for every scenario. The lowest yield is called the yield- to-worst.  Option adjusted yield: The option-adjusted yield is the required market discount rate whereby the price is adjusted for the value of the embedded option. For example, investors pay a lower price for the callable bond than if it were option-free. If the bond were non-callable, its price would be higher. The option-adjusted price is used to calculate the option-adjusted yield. Example An analyst observes the following statistics for two bonds: Bond A Bond B Annual Coupon Rate 6.00% 10.00% Coupon Payment Frequency Semi-annually Quarterly Years to Maturity 4 years 4 years Price (per 100 par value) 95 110 Current Yield ? ? Yield to Maturity ? ? 1. Calculate both yield measures for the two bonds. 2. How much additional compensation, in terms of yield to maturity, does a buyer of Bond A receive for bearing additional risk compared with Bond B Solution to 1: The current yield for Bond A is 6/95 = 6.316% and the yield to maturity for Bond A is