The Bond That Doesn't Add Up
A private client holds £250,000 nominal of a 4.5% UK gilt with exactly 6 years to maturity, currently priced at £98.50 per £100 nominal (clean). The client's adviser quotes a gross redemption yield of 4.9% and tells the client the bond is 'cheap versus the 4.75% coupon gilt maturing in 2031, which trades at £101.' The client asks you to sanity-check the yield, because she believes the yield should be closer to the running yield she has seen quoted elsewhere (4.57%). She also notes the settlement date is in 47 days' time and that she is a 45% taxpayer on coupon income but pays no CGT on gilts.
1. Distinguish running yield from gross redemption yield and explain why the adviser's 4.9% figure is plausible or not, given the clean price is below par.
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Running yield = coupon ÷ clean price = 4.5 ÷ 98.50 = 4.57%. This ignores capital gain and time value, so it understates return on a bond bought below par.
Gross redemption yield (GRY) accounts for the pull-to-par capital gain and the timing of cash flows. Buying at 98.50 and redeeming at 100 gives a gain of 1.50 per 100 nominal over 6 years, roughly 0.25% p.a. added to the running yield, plus the reinvestment/timing effect. A GRY of ~4.9% is arithmetically plausible - it sits above the running yield precisely because the bond is at a discount. The client's instinct that 'yield should equal running yield' is the error; running yield is only a rough income measure.
Key teaching point: for a discount bond, GRY > running yield; for a premium bond, GRY < running yield. The adviser's figure is directionally correct.
2. Evaluate the adviser's claim that the 4.5% 2031-maturity bond at £101 is directly comparable and that the 6-year bond is 'cheap'.
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The comparison is flawed on two counts:
Different maturities. A 2031-maturity bond has a different duration and interest-rate sensitivity. 'Cheap' vs 'rich' must be assessed on a yield-curve basis, not raw price. A premium bond (£101) will mechanically show a lower GRY than a discount bond with the same coupon, so comparing prices alone says nothing about relative value.
Coupon and price interaction. The 2031 bond at £101 is at a premium, so its GRY is below its running yield. To call the 6-year bond cheap you must compare yields to maturity on a like-for-like maturity-adjusted basis (e.g. spread over the curve at the relevant tenor), not clean prices.
A correct relative-value judgement: compute both GRYs, adjust for the yield curve (the 6-year point vs the 2031 tenor), and only then decide if the spread is anomalous. Price alone is not evidence of cheapness.
3. The client is a 45% taxpayer and settlement is in 47 days. Explain the accrued interest and after-tax income implications she should weigh.
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Accrued interest: With 47 days since the last coupon, the buyer pays accrued interest on top of the clean price. Accrued = 4.5 × (47/365) ≈ 0.58 per £100 nominal, i.e. ~£1,450 on £250,000 nominal. The dirty price = 98.50 + 0.58 ≈ 99.08. The client effectively pre-pays coupon she will receive, so the cash-flow timing (not total return) is affected - she should not mistake the higher dirty price for a worse deal.
Tax: Coupon income is taxed at 45%, so net coupon ≈ 4.5 × 0.55 = 2.475% on nominal. Capital gains on gilts are CGT-exempt for UK residents, so the pull-to-par gain is tax-free. This makes discount gilts relatively attractive for a high-rate taxpayer versus a premium bond where part of the return is taxable coupon. The after-tax GRY therefore differs materially between the two bonds - a factor the adviser's simple pre-tax comparison ignored.