Sources of Return from Investing in a Fixed-rate Bond

Sources of Return from Investing in a Fixed-rate Bond

Sources of Return

Investors in fixed-rate bonds achieve returns through the following:

  • Receipt of anticipated coupon and principal payments.
  • Reinvestment of coupon payments.
  • Capital gains or losses are realized when the bond is sold prior to its maturity.

Discount bonds feature a coupon rate below the current market rate, while premium bonds have a coupon rate above the market rate. Over time, the book value of a bond is amortized to match its face value upon reaching maturity. The carrying value represents the bond’s purchase price, adjusted for any amortized discount or premium. Rising interest rates decrease bond prices (and vice versa). This affects the total return, specifically if the bond is sold before maturity.

Yield to Maturity (YTM)

This metric is crucial for bond investors. If an investor holds a bond until maturity, avoids any bond defaults, and consistently reinvests coupons at the prevailing interest rate, the YTM accurately reflects the investor’s actual rate of return.

Investment Horizon and Interest Rate Risk

The investment horizon is critical in assessing interest rate risks and returns. The interest rate risk comprises two offsetting risks:

  • Coupon reinvestment risk.
  • Market price risk.

Reinvestment Risk

Reinvestment risk pertains to the possibility that an investor may not be able to reinvest the cash flows from an investment at a rate matching the investment’s existing rate of return (yield to maturity). Two factors affect the degree of reinvestment risk:

  • Maturity: The longer the bond’s maturity, the higher the reinvestment risk. This is because of the high possibility that interest rates will be lower than they were at the time the bond was purchased;
  • The coupon rate of the bond: The higher the coupon rate, the higher the payments that have to be reinvested and, consequently, the higher the reinvestment risk. In fact, a bond selling at a premium is more dependent on reinvestment income than another bond selling at par. The only fixed-income instruments that do not have reinvestment risk are zero-coupon bonds since they have no interim coupon payments.

Market Risk (Price Risk)

Bond market prices will decrease in value when the prevailing interest rates rise. In other words, if an investor wishes to sell the bond prior to maturity, the sale price will be lower if rates are higher.

As noted earlier, these two risks offset each other to an extent. The dominant risk depends partially on the investment horizon. The lower the investment horizon, the lower the reinvestment risk, but the higher the market risk.

Horizon Yield (Realized Rate of Return)

This metric delves deeper, offering insight into an investor’s internal rate of return (IRR). It considers the total return, which is composed of reinvested coupons and the sale/redemption amount divided by the purchase price of the bond.

\[r = \left( \frac{\text{FV} + \text{Sale}/\text{Redemption Amount}}{PV} \right)^{\frac{1}{T}} – 1\]


  • \(FV =\) Future value of reinvested coupons.
  • \(PV =\) Purchase price of the bond.
  • \(T =\) Holding period.

Example: Sources of Return

An investor initially buys a 5-year, \(8\%\) annual coupon payment bond at the price of 85.00 per 100 of par value.

Case 1: Holding the Bond Until Maturity

The yield to maturity of the bond is calculated as follows.

\[85 = \frac{8}{(1 + r)^{1}} + \frac{8}{(1 + r)^{2}} + \frac{8}{(1 + r)^{3}} + \frac{8}{(1 + r)^{4}} + \frac{108}{(1 + r)^{5}};\ r = 12.18\]

The bond’s yield-to-maturity is \(12.18\%\). The easiest way to determine the value of \(r\) is to use the financial calculator:

\[n = 5;PV = – 85;PMT = 8;FV = 100;CPT = > I/Y = 12.18\]

So the investor receives the series of 5 coupon payments of 8 (per 100 of par value), a total of 40, plus the redemption of principal (100) at maturity. Besides collecting the coupon interest and the principal, there is an opportunity to reinvest the cash flows. If the coupon payments are reinvested at \(12.18\%\) immediately after they are received, the coupon’s future value on maturity date will amount to 51 per 100 par value, calculated as per the following table.

$$\begin{array}{|c|c|c|c|c|} \hline \textbf{End of Year 1} & \textbf{End of Year 2} & \textbf{End of Year 3} & \textbf{End of Year 4} & \textbf{End of Year 5} \\ \hline \$ 8 \times (1.1218)^{4} & \$ 8 \times (1.1218)^{3} & \$ 8 \times (1.1218)^{2} & \$ 8 \times (1.1218)^{1} & \$ 8 \times (1.1218)^{0} \\ \hline \end{array}$$

The \(1^{\text{st~}}\) coupon payment of \(\$ 8\) is reinvested at \(12.18\%\) for 4 years until the end of the \(5^{\text{th~}}\) year, the \(2^{\text{nd~}}\) is invested for 3 years, and so forth. The amount in excess of the coupons, \(11\ ( = \ 51\ –\ (5 \times \ 8)),\) is called “interest-on-interest” gain from compounding.

The investor’s total return is 151, the sum of reinvested coupons (51), and the redemption of principal at maturity (100). Therefore, the realized rate of return is \(12.18\%\).

\[85 = \frac{151}{(1 + r)^{5}};\ r = 12.18\%\]

As case 1 demonstrates, the yield-to-maturity at the time of purchase equals the investor’s rate of return under the following three assumptions:

  • The investor holds the bond to maturity.
  • There is no default by the issuer.
  • The coupon interest payments are reinvested at that same rate of interest.

Case 2: Selling the Bond Before Maturity

If another investor buys the same bond but chooses to sell it after four years and reinvests all coupon payments at 12.18%, the future value of these reinvested coupons will be 38.3356% of the bond’s face value at the end of the fourth year. This is calculated as follows:

$$\begin{array}{|c|c|c|c|} \hline \textbf{End of Year 1} & \textbf{End of Year 2} & \textbf{End of Year 3} & \textbf{End of Year 4} \\ \hline \$ 8 \times (1.1218)^{4} & \$ 8 \times (1.1218)^{3} & \$ 8 \times (1.1218)^{2} & \$ 8 \times (1.1218)^{1} \\ \hline \end{array}$$

Total \(= \$ 38.3356\)

The interest-on-interest gain from compounding is \(6.3356( = 38.3356 – 32)\).

At the time the bond is sold, it has one year remaining until maturity. If the yield-to-maturity remains \(12.18\%\), the sale price of the bond (calculated as the PV of anticipated cash flows) is:

\[\text{Price}_{t = 4} = \frac{108}{1.1218} = 96.2738\]

Therefore, the total return is \(134.6094( = 38.3356 + 96.2738)\), and the realized rate of return is \(12.18\%\).

\[85 = \frac{134.6094}{(1 + r)^{4}};\ r = 12.18\%\]

Case 2 demonstrates that the realized horizon yield matches the original yield-to-maturity provided two conditions are met:

  • Coupon payments are reinvested at the same interest rate as the original yield-to-maturity.
  • The bond is sold at a price on the constant-yield price trajectory, i.e., the investor does not have any capital gains or losses when the bond is sold. The price trajectory is the time series of a bond’s prices from some date (usually the date on which the bond is purchased) until its maturity.


For a fixed-rate bond, what will most likely happen to its market price if interest rates rise?

  1. The market price will rise.
  2. The market price will remain unchanged.
  3. The market price will fall.


The correct answer is C.

Bond prices and interest rates have an inverse relationship. Thus, when interest rates increase, bond prices tend to fall.

A is incorrect: As mentioned, bond prices and interest rates have an inverse relationship. So, the market price won’t rise with rising interest rates.

B is incorrect: Bond prices are sensitive to changes in interest rates, so they will not remain unchanged.

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop Graduate Admission Exam Prep

    Sergio Torrico
    Sergio Torrico
    Excelente para el FRM 2 Escribo esta revisión en español para los hispanohablantes, soy de Bolivia, y utilicé AnalystPrep para dudas y consultas sobre mi preparación para el FRM nivel 2 (lo tomé una sola vez y aprobé muy bien), siempre tuve un soporte claro, directo y rápido, el material sale rápido cuando hay cambios en el temario de GARP, y los ejercicios y exámenes son muy útiles para practicar.
    So helpful. I have been using the videos to prepare for the CFA Level II exam. The videos signpost the reading contents, explain the concepts and provide additional context for specific concepts. The fun light-hearted analogies are also a welcome break to some very dry content. I usually watch the videos before going into more in-depth reading and they are a good way to avoid being overwhelmed by the sheer volume of content when you look at the readings.
    Kriti Dhawan
    Kriti Dhawan
    A great curriculum provider. James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them. Thank you ! Grateful I saw this at the right time for my CFA prep.
    nikhil kumar
    nikhil kumar
    Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures.
    Great support throughout the course by the team, did not feel neglected
    Benjamin anonymous
    Benjamin anonymous
    I loved using AnalystPrep for FRM. QBank is huge, videos are great. Would recommend to a friend
    Daniel Glyn
    Daniel Glyn
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.