Tiêu đề LM11 Yield-Based Bond Duration Measures and Properties IFT Notes.pdf ✅

LM11 Yield-Based Bond Duration Measures and Properties 2025 Level I Notes © IFT. All rights reserved 1 LM11 Yield-Based Bond Duration Measures and Properties 1. Introduction ........................................................................................................................................................... 2 2. Modified Duration ............................................................................................................................................... 2 3. Money Duration and Price Value of a Basis Point ................................................................................... 5 4. Properties of Duration ....................................................................................................................................... 7 Summary ...................................................................................................................................................................11 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
LM11 Yield-Based Bond Duration Measures and Properties 2025 Level I Notes © IFT. All rights reserved 2 1. Introduction This learning module covers:  Measures of interest rate risk: Modified duration, money duration, and the price value of a basis point (PVBP)  How a bond’ maturity, coupon, and yield levels affect its interest rate risk 2. Modified Duration The duration of a bond measures the sensitivity of the bond’s full price (including accrued interest) to changes in interest rates. In other words, duration indicates the percentage change in the price of a bond for a 1% change in interest rates. The higher the duration, the more sensitive the bond is to change in interest rates. There are two categories of duration: yield duration and curve duration.  Yield duration measures a bond’s price sensitivity to changes in its own yield-to- maturity and assumes underlying cash flows are certain.  Curve duration measures a bond’s price sensitivity to changes in a benchmark yield curve and accounts for the possibility that a bond may default. As indicated in the diagram above, the main yield duration measures are: Macaulay duration, modified duration, money duration, and the price value of the basis point (PVBP). Curve duration measures are covered in later learning modules. Macaulay duration is a weighted average of the time to receipt of the bond’s promised payments, where the weights are the shares of the full price that correspond to each of the bond’s promised future payments.
LM11 Yield-Based Bond Duration Measures and Properties 2025 Level I Notes © IFT. All rights reserved 3 Modified duration provides an estimate of the percentage price change for a bond given a change in its yield to maturity. It represents a simple adjustment to Macaulay duration as shown in the equation below: Modified duration = Macaulay duration 1 + r where: r is the yield per period. Therefore, percentage price change for a bond given a change in its YTM can be calculated as: %ΔPVFULL ≈ −AnnModDur x ΔYield The AnnModDur term is the annual modified duration, and the ΔYield term is the change in the annual yield to maturity. The ≈ sign indicates that this calculation is estimation. The minus sign indicates that bond prices and yields to maturity move inversely. Example: Calculating the modified duration of a bond A 2-year, annual payment, $100 bond has a Macaulay duration of 1.87 years. The YTM is 5%. Calculate the modified duration of the bond. Solution: Modified duration = 1.87/(1 + 0.05) = 1.78 The percentage change in the price of the bond for a 1% increase in YTM will be: -1.78 * 0.01 * 100 = -1.78%. Approximate Modified Duration Modified duration is calculated if the Macaulay duration is known. But there is another way of calculating an approximate value of modified duration: estimate the slope of the line tangent to the price-yield curve. This can be done by using the equation below: Approximate Modified Duration = (PV−) − (PV+) 2 ∗ ∆yield ∗ PV0 where: PV_ = price of the bond when yield is decreased; PV0 = initial price of the bond PV+ = price of the bond when yield is increased
LM11 Yield-Based Bond Duration Measures and Properties 2025 Level I Notes © IFT. All rights reserved 4 Source: CFA Program Curriculum, Understanding Fixed-Income Risk and Return Interpretation of the diagram:  PV0 denotes the original price of the bond.  PV+ denotes the price of the bond when YTM is increased and PV_ denotes the bond price when YTM is decreased.  Change in yield (up and down) is denoted by Δ yield.  For slope calculation: vertical distance = PV− − PV+ and horizontal distance = 2 x Δ yield. How to calculate approximate modified duration (or estimate the slope of the price-yield curve):  The yield to maturity is changed (increased/decreased) by the same amount.  Calculate the bond price for a decrease in yield (PV-).  Calculate the bond price for an increase in yield (PV+).  Use these values to calculate the approximate modified duration. Once the approximate modified duration is known, the approximate Macaulay duration can be calculated using the formula below: Approximate Macaulay Duration = Approximate Modified Duration x (1 + r) Example: Calculating the approximate modified duration and approximate Macaulay duration Assume that the 6% U.S. Treasury bond matures on 15 August 2017 is priced to yield 10% for settlement on 15 November 2014. Coupons are paid semiannually on 15 February and 15 August. The yield to maturity is stated on a street-convention semiannual bond basis. This settlement date is 92 days into a 184-day coupon period, using the actual/actual day-count convention. Compute the approximate modified duration and the approximate Macaulay