Title LM10 Interest Rate Risk and Return IFT Notes.pdf ✅

LM10 Interest Rate Risk and Return 2025 Level I Notes © IFT. All rights reserved 1 LM10 Interest Rate Risk and Return IFT Notes 1. Introduction ........................................................................................................................................................... 2 2. Sources of Return from Investing in a Fixed-Rate Bond ...................................................................... 2 3. Investment Horizon and Interest Rate Risk .............................................................................................. 9 4. Macaulay Duration ...........................................................................................................................................11 Summary ...................................................................................................................................................................12 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
LM10 Interest Rate Risk and Return 2025 Level I Notes © IFT. All rights reserved 2 1. Introduction This learning module covers:  Sources of return from investing in a fixed rate bond  How investors are exposed to different interest rate risk if the same bond is held for different time periods.  Macaulay duration 2. Sources of Return from Investing in a Fixed-Rate Bond The total return is the future value of reinvested coupon interest payments and the sale price (or redemption of principal if the bond is held to maturity). The horizon yield (or holding period rate of return) is the internal rate of return between the total return and the purchase price of the bond. Total return on a bond = reinvested coupon interest payments + sale/redemption of principal at maturity A bond investor has three sources of return:  Receiving the full coupon and principal payments on the scheduled dates.  Reinvesting the interest payments. This is also known as interest-on-interest.  Potential capital gain or loss on sale of the bond, if the bond is sold before maturity date. Now, we will look at a series of examples that demonstrate the effect on two investors’ realized rate of returns when one of these variable changes: time horizon, interest rate at which the coupons are reinvested, and market discount rates at the time of purchase and at the time of sale. In Examples 1 and 2, we look at the realized rate of return for two investors with different time horizons for the same bond. Example 1: Calculating the total return on a bond that is held until maturity Investor 1: A “buy-and-hold” investor purchases a 5-year, 10% annual coupon payment bond at 92.79 per 100 of par value and holds it until maturity. Calculate the total return on the bond. Solution:
LM10 Interest Rate Risk and Return 2025 Level I Notes © IFT. All rights reserved 3 92.79 = 10 (1 + r) 1 + 10 (1 + r) 2 + 10 (1 + r) 3 + 10 (1 + r) 4 + 110 (1 + r) 5 Use the following keystrokes to calculate the bond’s yield to maturity: N = 5; PV = -92.79; PMT = 10; FV = 100; CPT I/Y; Hence, r = 12%. This is the yield to maturity at the time of purchase. However, this holds good only if all of the following three conditions are true:  The bond is held to maturity.  The coupon and final principal payments are made on time (no default or delay).  The coupon payments are reinvested at the same rate of interest. To calculate the total return on the bond, we first need to calculate the interest earned when coupon payments are reinvested. Coupon reinvestment:  The investor receives 5 coupon payments of 10 (per 100 of par value) for a total of 50, plus the redemption of principal (100) at maturity. The investor has the opportunity to reinvest the cash flows. If the coupon payments are reinvested at 12% (i.e., yield to maturity), the future value of the coupons on the bond’s maturity date is 63.53 per 100 of par value. [10 x (1.12) 4 ] + [10 x (1.12) 3 ] + [10 x (1.12) 2 ] + [10 x (1.12) 1 ] + 10 = 63.53  The first coupon payment of 10 is reinvested at 12% for 4 years until maturity, the second is reinvested for 3 years, and so on. The future value of the annuity is obtained easily using a financial calculator: N = 5; PV = 0; PMT = 10; I/Y = 12; CPT FV. FV = -63.53  The amount in excess of the coupons, 13.53 (= 63.53 – 50), is the ‘interest-on-interest’ gain from compounding.  The investor’s total return is 163.53, the sum of the reinvested coupons (63.53) and the redemption of principal at maturity (100). The realized rate of return is 12%. 92.79 = 163.53 (1+r)5 , r = 12% Example 2: Calculating the total return on a bond that is sold before maturity Now let us consider investor 2 who buys the same 5-year, 10% annual coupon payment bond but sells the bond after three years. Assuming that the coupon payments are reinvested at 12% for three years, calculate the total return on the bond. Solution: The future value of the reinvested coupons is 33.74 per 100 of par value. [10 ∗ (1.12) 2 ] + [10 ∗ (1.12) 1 ] + 10 = 33.74 The interest-on-interest gain from compounding is 3.74 (= 33.74 – 30). After three years,
LM10 Interest Rate Risk and Return 2025 Level I Notes © IFT. All rights reserved 4 when the bond is sold, it has two years remaining until maturity. If the yield to maturity remains 12%, then the sale price of the bond is 96.62. 10 (1.12) 1 + 110 (1.12) 2 = 96.62 The total return is 130.36 (= 33.74 + 96.62) and the realized rate of return is 12%. 92.79 = 130.36 (1 + r) 3 , r = 12% This ‘r’ is called the horizon yield, the internal rate of return between the total return and the purchase price of the bond. Horizon yield is equal to the original yield to maturity if:  Coupon payments are reinvested at the same yield to maturity calculated at the time of purchase of the bond. In our case, it is 12% as calculated in Example 1.  There are no capital gains or losses when the bond is sold. It is sold at a price on the constant-yield price trajectory. We arrive at the price 96.62 by taking 12% as the constant yield for the remaining two years. If the yield is more than 12%, then losses occur. Similarly, if the yield is less than 12%, then capital gains occur. This concept is elaborated below: Constant-yield price trajectory for a 5-year, 10% annual payment bond The price of the bond at different time periods for a yield of 12% is plotted in the graph below: The calculations for determining the price are shown below: Year Price Calculation 0 92.79 N = 5 ; I/Y = 12 ; PMT = 10 ; FV = 100 ; CPT PV 1 93.93 N = 4 ; I/Y = 12 ; PMT = 10 ; FV = 100 ; CPT PV 2 95.19 N = 3 ; I/Y = 12 ; PMT = 10 ; FV = 100 ; CPT PV 3 96.62 N = 2 ; I/Y = 12 ; PMT = 10 ; FV = 100 ; CPT PV 4 98.21 N = 1 ; I/Y = 12 ; PMT = 10 ; FV = 100 ; CPT PV 5 100