Ravi: a BBB corporate bond, duration and a £100,000 liability in two years
Ravi, 58, holds £250,000 nominal of a five-year BBB-rated UK corporate bond paying a 6% annual coupon. It was bought at par two years ago, so three years remain to maturity, and the bond is currently priced to yield 7% to maturity. Ravi is divorced, has £60,000 in cash and £180,000 in a diversified portfolio, and plans to stop work at 60. He has agreed to lend his daughter £100,000 in two years to help her buy a flat and intends to fund that from the bond. He tells his adviser he is 'not worried about the price because I'll get my £250,000 back at maturity' and asks whether he should buy more of the same bond because the 7% yield looks attractive compared with his savings account. The bond trades in £1,000 nominal lots and its spread has widened from 15 basis points to 60 basis points over the past quarter.
1. Calculate the bond's price per £100 nominal at a 7% yield to maturity and explain why it trades below par.
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The price is the present value of the coupon and redemption flows discounted at 7%:
- Coupons: £6 a year for three years, discounted at 7%: 6/1.07 + 6/1.07² + 6/1.07³ = 5.607 + 5.241 + 4.898 = £15.75
- Redemption: £100/1.07³ = £81.63
- Price: 15.75 + 81.63 = £97.38 per £100 nominal
(A three-year annuity factor at 7% is 2.6243, so 6 × 2.6243 = 15.75; the discount factor is 0.8163.)
It trades below par because the coupon of 6% is lower than the 7% yield investors require. The buyer receives only £6 a year, so the price must fall until the total return, including the £2.62 capital gain to redemption, equals 7%. If the yield fell below 6% the bond would trade at a premium.
Ravi's £250,000 nominal is therefore worth about £243,450, not £250,000. His statement that he will 'get £250,000 back' is true only at maturity and only if the issuer does not default; in the meantime the holding is exposed to price movements.
2. Estimate the modified duration and the price effect of a 100 basis point rise in yield, and explain the reinvestment assumption behind the yield to maturity.
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Macaulay duration. Weight each present value by its time:
- Year 1: 5.607 × 1 = 5.607
- Year 2: 5.241 × 2 = 10.482
- Year 3: (4.898 + 81.63) × 3 = 259.58
- Total weighted PV = 275.67; divided by price 97.38 = 2.83 years
Modified duration. 2.83/1.07 = 2.65.
Price change. For a 100bp parallel rise, approximate price change = −2.65 × 1% = −2.65%, so the price falls to about £94.80, a loss of roughly £2.65 per £100 or about £6,600 on £250,000 nominal. For a 100bp fall, the gain is slightly larger because of convexity.
Reinvestment assumption. The 7% yield to maturity is only realised if every coupon is reinvested at 7% until maturity. If yields fall, coupons are reinvested at lower rates and the realised return is below 7%; this is reinvestment risk. If yields rise, coupons reinvest at higher rates. For a bond held in isolation, price risk and reinvestment risk offset each other only when the holding period equals the duration, which is the basis of immunisation. Ravi's two-year horizon is shorter than the 2.83-year duration, so price risk dominates if he sells early.
3. Advise Ravi on funding the £100,000 loan from his bond holding, addressing credit, liquidity and suitability issues.
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Mismatch. Ravi needs £100,000 in two years. Selling £100,000 nominal at £97.38 raises only about £97,380, leaving a shortfall even before dealing costs and the wider spread. The bond's duration of 2.83 years is longer than his two-year horizon, so a rise in yields would worsen the shortfall.
Credit. The bond is BBB-rated, the lowest investment-grade band. The spread has widened from 15bp to 60bp, which may signal deteriorating credit conditions or simply reduced liquidity. If spreads widen further, the price falls regardless of his holding intention, and default would mean losing coupons and possibly principal. A single-issuer holding of this size is a concentration risk.
Liquidity. The wider spread means dealing costs have risen; selling £100,000 nominal may move the price against him. £1,000 lots are not a guarantee of a deep market.
Suitability. He should not buy more. The £100,000 liability should be matched with assets that mature when the cash is needed, such as short-dated gilts or a fixed-term deposit, held inside his cash and ISA allowances where possible. The remaining bond exposure should be reviewed against his risk capacity, diversification needs and two-year retirement horizon. If he keeps the bond, he should understand he is taking credit and duration risk for a yield that is not guaranteed in the short run.