**Fixed Income II**

**Reading 46. Understanding Fixed-Income Risk and Return**

**Learning Outcome Statements**

a. calculate and interpret the sources of return from investing in a fixed-rate bond;

*CFA Curriculum, 2020, Volume 5*

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### Subject 1. Sources of Return

There are three sources of return on a fixed-rate bond:

less initial purchase price = $941.12

less coupon interest payments = 15.00% * $1000 * 18.50 = $2,775.00

less capital gain (add capital loss) = $1000 - $941.12 = $58.88

= $12,455.27

- Receipts of the promised coupon and principal payments on the scheduled dates.
- Reinvestment income - interest income generated by reinvesting coupon interest payments. Interest income, which is the sum of coupon payments and reinvestment income, is the return associated with the passage of time.
- Any capital gains or losses if the bond is sold prior to maturity. These are caused by a change in the yield-to-maturity.

*Example*Harshal Shahe purchases a bond, but isn't sure how much of his total return will come from reinvested interest compared to coupon interest and capital gain. What is the total reinvested interest (i.e., interest on interest) that Herschel earns, assuming a price of $941.12, coupon of 15.00%, 18.5 year maturity and a market interest rate of 16.00%?

First calculate total future cash flows: PV x (1+r)

^{N}= Price of bond of $941.12 x (1 + Market Interest rate 16.00% divided by 2)^{37}= $16,230.27less initial purchase price = $941.12

less coupon interest payments = 15.00% * $1000 * 18.50 = $2,775.00

less capital gain (add capital loss) = $1000 - $941.12 = $58.88

= $12,455.27

The yield-to-maturity measures an investor's return from the bond correctly only if these assumptions are true:

- The bond is held to maturity.
- The coupon reinvestment rate is the same as the YTM.
- The issuer does not default.

The total return is the sum of:

- the future value of reinvested coupon payments.
- the sale price, or redemption of principal if the bond is held to maturity.

There are two types of interest rate related risks:

**Reinvestment risk**. Future interest rates may be less than the YTM. Two factors can affect the degree of reinvestment risk:**Maturity**. The longer the maturity, the higher the reinvestment risk. This implies that the yield to maturity measure for long-term coupon bonds tells little about the potential return that an investor may realize if the bond is held to maturity. For long-term bonds, in high-interest rate environments the reinvestment income component may be as high as 70% of the bond's potential total dollar return.**Coupon rate**. The higher the coupon rate, the higher the reinvestment risk. This implies that a bond selling at a premium will be more dependent on reinvestment income than a bond selling at par. Zero-coupon bonds have no reinvestment risk if held to maturity because there is no periodic cash flow to be reinvested.

**Market price risk**. If the bond has to be sold prior to maturity, its sale price will be lower if rates are higher.

These risks offset each other to a certain extent. Which one dominates depends on the bondholder's investment horizon. The shorter the investment horizon, the smaller the coupon reinvestment risk, but the bigger the market price risk.

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**User Contributed Comments**
5

You need to log in first to add your comment. ###### Haag

Shorter horizon = smaller reinvestment risk but bogger market price risk

###### tomalot

I prefer the term culchie

###### AggelosAnd

Why 15% * 1000 * 18.5 instead of 15% * 1000 * 37? The coupon is annual?

###### nmech1984

ok then. (15%/2) * 1000 * (18.5*2)

###### nmech1984

Aggele to epiases?! :)