Explain how a bond's price converges to par as maturity nears
The idea
A bond priced away from par converges toward par as maturity approaches, because the redemption amount is fixed and the number of remaining coupons that create the premium or discount falls. A premium bond therefore declines in price toward par even with yields unchanged, and a discount bond rises. This is the constant-yield price trajectory, and it means a premium bond's total return is below its coupon rate and a discount bond's above it. An investor comparing coupon income across bonds without accounting for this is comparing figures that do not mean the same thing.
A practice question
What happens to the price of a premium bond as maturity approaches, with yields unchanged?
- It rises further above parWhy not: The premium exists because above-market coupons are still to come. Each one paid leaves fewer, so the premium shrinks.
- It declines toward par — correct
- It remains constant until maturityWhy not: It would then have to drop to par in one step on the final day. The amortisation is gradual and mechanical.
Redemption is at par, so the premium must be amortised away over the remaining life. The decline is not a loss caused by the market but a mechanical certainty.
A harder one
Why is a premium bond's total return lower than its coupon rate?
- Because premium bonds carry more credit riskWhy not: The premium reflects a high coupon, not a weak issuer. A government bond issued years ago at a high rate trades at a premium with no credit question at all.
- Because coupons on premium bonds are taxed more heavilyWhy not: The coupon is taxed like any other, at whatever rate applies to the holder. The reason is arithmetic rather than fiscal.
- Because the price decline toward par offsets part of the coupon income — correct
The high coupon is paid for up front in the purchase price. The yield to maturity already nets the two effects, which is why it, not the coupon, describes the return.
The hardest tier
Two bonds have the same yield to maturity, one at a large premium and one at a deep discount. What differs for a taxable investor?
- The timing and character of the return — correct
- Nothing, since the yields are identicalWhy not: Identical *pre-tax*. Where coupon income and capital gains are taxed differently, the same yield produces different after-tax returns.
- The credit risk, which is higher for the discount bondWhy not: A discount reflects a coupon below the current market rate, which is usually a matter of when the bond was issued rather than of the issuer's health.
The premium bond delivers more of it as taxable coupon income and the discount bond more as capital gain. Equal pre-tax yields can produce very different after-tax returns where income and gains are taxed at different rates or in different periods, and asset location decisions turn on exactly this.
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