25556 Chap.11 Bond Investment Returns and Long-Term Yields
Bond Investment Returns and Long-Term Yields
The second half of Topic 5 asks what an investor actually earns from a bond. The answer has three parts: the coupons, the interest earned by reinvesting them, and either the sale price or the face value at maturity.
One annual rate, the holding period yield, combines them, and it can differ from the yield promised at purchase because of reinvestment risk and, for a bond sold early, price risk.
This chapter applies the holding period formula to a practical choice between holding a short bond to maturity and selling a longer one early, splits an ending value into its three sources, and explains why the two risks pull in opposite directions when yields move.
It closes with the forces behind long-term yields: expected inflation through the Fisher relation, and the flight to quality that pushed Treasury yields down during the GFC.
What this chapter covers
- 01
Three sources of a bond investment's return
- 02
Future value of reinvested coupons
- 03
Holding period yield on a bond
- 04
Reinvestment risk and price risk
- 05
Expected inflation and the Fisher relation
- 06
Flight to quality and credit spreads
Worked example · free
Find the reinvestment rate that would rescue the ending value of a 10-year bond sold early
- 1Target ending value: 99.206 × (1 + 0.0418/2) to the power 6 = 112.314 per $100.
- 1Coupons with interest needed: 112.314 − 97.654 = 14.660, against 13.500 + 0.658 = 14.158 at 3.80%.
- 1Solve 2.25 × [(1 + r/2) to the power 6 − 1] divided by (r/2) = 14.660 by trial: r = 6.58% gives 14.660, so the rate needed is about 6.58%.
- 1Verdict: 6.58% is far above the 3.80% on offer, so reinvestment cannot make up for the lower sale price.
Key terms
- Reinvestment risk
- The danger that coupons can only be reinvested at a rate below the purchase yield, lowering the realised return.
- Interest on coupons
- The extra amount earned by reinvesting each coupon from the date it is paid until the end of the holding period.
- Fisher relation
- An approximation stating that a long-term market yield equals the real interest rate plus expected inflation.
- Flight to quality
- A rush by investors out of riskier securities into government bonds during periods of stress.
- Real interest rate
- The return on a loan after allowing for expected inflation, which the Fisher relation treats as fairly stable.
Bond Investment Returns and Long-Term Yields FAQ
What are the three sources of return on a bond investment?
An investor receives the coupons, earns interest by reinvesting each coupon until the end of the holding period, and finally receives either the face value at maturity or the sale price if the bond is sold early. A single annual rate, the holding period yield, combines all three, and it is the figure to compare with the purchase yield.
Why can a bond held to maturity earn less than its purchase yield?
The purchase yield assumes every coupon is reinvested at that same yield. If coupons can only be reinvested at a lower rate, the accumulated value falls short and the realised return drops below the purchase yield. That is reinvestment risk.
How does selling a bond early change its risk?
A bond sold before maturity is exposed to price risk as well as reinvestment risk. If market yields have risen since purchase, the sale price is lower and a capital loss reduces the return; if they have fallen, a capital gain raises it.
What does the Fisher relation say about bond yields?
It says the market yield is roughly the real interest rate plus expected inflation. With a stable real rate, an increase in expected inflation lifts long-term yields by about the same amount, which lowers the prices of existing fixed-coupon bonds.
What happened to bond yields during the GFC flight to quality?
Investors sold riskier securities and bought Treasury bonds. Strong demand pushed Treasury prices up and their yields down, while yields on riskier bonds rose, so the gap between them, the credit spread, widened sharply. Investors already owning Treasury bonds made capital gains as a result.
Exam move
Treat every bond return question as three numbers to find before any yield: the coupons, the accumulated value of those coupons at the reinvestment rate, and the closing price or face value. Write each with its period count, then apply the holding period formula with n half-years. Practise one held-to-maturity case and one early-sale case side by side so you can say which risk is at work in each.
For the long-term yield material, rehearse a three-step answer: name the driver, state the direction of yields, then state the effect on bond prices, using expected inflation and the GFC flight to quality as your two examples.
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