Title LM12 Yield-Based Bond Convexity and Portfolio Properties IFT Notes.pdf ✅

LM12 Yield-Based Bond Convexity and Portfolio Properties 2025 Level I Notes © IFT. All rights reserved 1 LM12 Yield-Based Bond Convexity and Portfolio Properties 1. Introduction ........................................................................................................................................................... 2 2. Bond Convexity and Convexity Adjustment .............................................................................................. 2 3. Bond Risk and Return Using Duration and Convexity .......................................................................... 4 4. Portfolio Duration and Convexity ................................................................................................................. 6 Summary ...................................................................................................................................................................... 8 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
LM12 Yield-Based Bond Convexity and Portfolio Properties 2025 Level I Notes © IFT. All rights reserved 2 1. Introduction This learning module covers:  Bond convexity and convexity adjustment  Calculating the percentage price change of a bond given its duration and convexity  Calculating the portfolio duration and convexity for a portfolio of bonds 2. Bond Convexity and Convexity Adjustment The graph below shows the relationship between bond price and YTM. It shows the convexity for a traditional fixed-rate bond. Interpretation of the diagram:  Duration assumes there is a linear relationship between the change in a bond’s price and change in YTM. For instance, assume the YTM of a bond is 10% and it is priced at par (100). According to the duration measure, if the YTM increases to 11% the price moves down to a point on the straight line.  Similarly, the price moves up to a point on the straight line if the YTM decreases.  The curved line in the above exhibit plots the actual bond prices against YTM. So, in reality, the bond prices do not move along a straight line but exhibit a convex relationship.  For small changes in YTM, the linear approximation is a good representation for change in bond price. That is, the difference between the straight and curved line is not significant.  In other words, modified duration is a good measure of the price volatility.  However, for large changes in YTM or when the rate volatility is high, a linear approximation is not accurate and a convexity adjustment is needed.

LM12 Yield-Based Bond Convexity and Portfolio Properties 2025 Level I Notes © IFT. All rights reserved 4 The relationship between various bond parameters with convexity is the same as with duration. For a fixed-rate bond,  The lower the coupon rate, the greater the convexity.  The lower the yield to maturity, the greater the convexity.  The longer the time to maturity, the greater the convexity.  The greater the dispersion of cash flow or cash payments spread over time, the greater the convexity. 3. Bond Risk and Return Using Duration and Convexity In this section we will see how to estimate the percentage price change of a bond for a specified yield change, given the bond’s duration and convexity. Example: Calculating the full price and convexity-adjusted percentage price change of a bond A German bank holds a large position in a 6.50% annual coupon payment corporate bond that matures on 4 April 2029. The bond's yield to maturity is 6.74% for settlement on 27 June 2014, stated as an effective annual rate. That settlement date is 83 days into the 360- day year using the 30/360 method of counting days. 1. Calculate the full price of the bond per 100 of par value. 2. Calculate the approximate modified duration and approximate convexity using a 1 bp increase and decrease in the yield to maturity. 3. Calculate the estimated convexity-adjusted percentage price change resulting from a 100 bp increase in the yield to maturity. 4. Compare the estimated percentage price change with the actual change, assuming the yield to maturity jumps to 7.74% on that settlement date. Solution: There are 15 years from the beginning of the current period on 4 April 2014 to maturity on 4 April 2029. 1. The full price of the bond is 99.2592 per 100 of par value. FV = 100, I/Y = 6.74, PMT = 6.50, N = 15, CPT PV; PV = -97.777. Full Price = 97.777 × 1.0674 83 360 = 99.2592. 1. PV+ = 99.1689 . FV = 100, PMT = 6.5, I/Y = 6.75, N = 15, CPT PV; PV = -97.687. PV+ = 97.687 × 1.0675 83 360 = 99.1689. PV_ = 99.3497.