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Interest Rate Risk and Return

2024 Curriculum CFA® Program Level I Fixed Income

Overview

Prior lessons on yield measures established that a fixed-income investor’s rate of return will equal a bond’s yield-to-maturity (YTM) under certain assumptions. In these lessons, we explore the sources of return for fixed-income investments and demonstrate investment returns in different scenarios, including the one embedded in the YTM calculations. Prior lessons also established interest rate risk. We show how investment horizon, in relation to a bond’s features, is a key determinant of interest rate risk for investors and how different investors in the same fixed-income investment can have different returns and views on risk. Finally, we introduce Macaulay duration, a weighted-average measure of the time to receipt for a bond’s cash flows, and demonstrate how holding a bond for its Macaulay duration balances reinvestment and price risks.

  • There are three sources of return for fixed-rate bond investors: (1) coupon and principal payments, (2) reinvestment of coupons, and (3) gain or loss on the sale of the bond if the bond is sold prior to maturity.
  • The rate of return on a fixed-rate bond investment is found by using the holding period, the future value of coupons received, the sale price, and the purchase price to calculate a compounded, annualized rate of return.
  • If all cash flows are received at scheduled dates, coupons are reinvested at the same rate as a bond’s YTM, and the bond is held to maturity, an investor’s annualized compounded rate of return will equal the bond’s YTM. If any of those assumptions do not hold, the investor’s rate of return will vary.
  • Reinvestment risk and price risk are types of interest rate risk and have an inverse relationship. Reinvestment risk is the risk of decreasing reinvestment returns on cash flows, which occurs when interest rates fall. Price risk refers to declining prices and occurs when interest rates rise.
  • The longer the investment horizon, the more important reinvestment risk is relative to price risk. If an investor’s investment horizon equals the Macaulay duration of a bond, the risks equally offset each other.
  • Macaulay duration is the weighted-average time to receipt of a bond’s cash flows, where the weights of each cash flow in the calculation are each cash flow’s share of the bond’s full price (i.e., present value).
  • When the investment horizon is greater than (less than, equal to) a bond’s Macaulay duration, coupon reinvestment risk is higher than (lower than, equal to) the bond’s price risk.

     

Learning outcomes

The candidate should be able to:

  • calculate and interpret the sources of return from investing in a f ixed-rate bond;
  • describe the relationships among a bond’s holding period return, its Macaulay duration, and the investment horizon;
  • define, calculate, and interpret Macaulay duration.

1 PL Credit

If you are a CFA Institute member don’t forget to record Professional Learning (PL) credit from reading this article.