Duration, Carry and the 'Paper Loss' Argument
A 63-year-old client holds €400,000 in a euro investment-grade corporate bond fund. Modified duration is 7.2 years, yield to maturity 3.40%, average credit spread 110 basis points. The ECB is widely expected to raise policy rates by 1.00% over the next twelve months. Your economist expects 0.80% of that to show up at the ten-year point on the swap curve, with the rest concentrated in two- and five-year yields. The client plans to retire in two years and will then draw €25,000 a year from the portfolio. Eurozone inflation is 3.1% and consensus is 2.4% a year over five years. He argues there is nothing to do: "the fund yields 3.40%, and anyway a fall in price is only on paper."
1. Quantify the price impact of the expected rate move and calculate how long the fund's yield takes to recover it. Add a plausible spread-widening scenario.
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Rate impact (first-order, modified duration):
- Ten-year point +0.80% → price change ≈ −7.2 × 0.80% = −5.76%, i.e. about −€23,000 on €400,000.
- If the move were fully parallel at +1.00% → −7.2 × 1.00% = −7.2%, about −€28,800.
- Short and intermediate yields rising faster than the ten-year steepens or flattens the curve depending on direction; with duration concentrated in the 5–10 year area, assume the 0.80% figure as the working estimate and treat 1.00% as the stress case.
Spread scenario: a recession-driven widening of 50bp adds −7.2 × 0.50% = −3.6%. Combined with the 0.80% rate move: approximately −9.3%, or −€37,000. Note this is the double hit corporate bond funds take - rates and spreads can move together in a growth scare.
Breakeven / recovery period:
- Rate-only case: 5.76% price loss ÷ 3.40% annual carry ≈ 1.7 years of total yield to get back to par value of capital.
- Combined case: 9.3% ÷ 3.40% ≈ 2.7 years.
The critical point: that recovery arithmetic assumes the yield stays at 3.40% and that he reinvests every coupon. It also ignores that his €25,000 annual drawdown (6.25% of the portfolio) is nearly twice the fund's yield, so he will be selling capital into the drawdown rather than waiting it out.
2. Evaluate the 'only on paper' argument. What is wrong with it in this client's specific circumstances?
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The argument is true only for an investor who (a) holds to maturity or to a duration-matched horizon and (b) reinvests coupons at the new, higher yield. Neither holds here.
1. He has no maturity. A perpetual fund has no redemption date, so there is no date at which price loss is guaranteed to be recovered by pull-to-par. The fund recovers through higher reinvestment yields, which takes roughly the duration of the fund - about 7 years for full recovery, not the 1.7 years of carry quoted above.
2. He is a forced seller. Drawing €25,000 a year from €400,000 is a 6.25% withdrawal rate against a 3.40% yield. He must sell units every year. Selling units after a 6–9% fall crystallises the "paper" loss permanently and reduces the base on which the recovery has to work. Sequence risk is real: a fall in the first two years is far more damaging than the same fall in year eight.
3. The carry is not real compensation. Real yield = 1.0340 / 1.031 − 1 ≈ +0.29%. He is being paid almost nothing in purchasing-power terms to take 7.2 years of duration risk. Against consensus inflation of 2.4% the real yield is 1.0340/1.024 − 1 ≈ +0.98% - better, but still thin for a 7.2 duration.
4. The inflation linkage is one-sided. If inflation surprises upward, the nominal coupons erode while the central bank hikes - both hits land at once. There is no offset.
Conclusion: the phrase describes a bond investor's balance sheet, not this client's cash flow. He is running a 2-year horizon liability against a 7.2-year asset.
3. What would you actually recommend, and what is the trade-off you are asking him to accept?
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Match the asset to the drawdown, not to the yield.
Structural recommendation:
- Years 1–3 of drawdowns (roughly €75,000): cash, short-dated deposits, or a money-market/short-duration fund. This is what removes the forced-seller problem. It earns less; that is the price of not selling into a drawdown.
- Core bond exposure: cut duration from 7.2 toward 2–3 years (short-dated corporate, floating-rate notes, or a 1–5 year ladder). This reduces the rate sensitivity from −7.2 per 1% to roughly −2.5 per 1% and lets him roll maturing bonds into higher yields.
- The remainder: keep some intermediate duration for the inflation-hedge and recession-insurance role, plus inflation-linked exposure if he wants his real return protected.
- A genuine conversation about the 6.25% withdrawal rate. €25,000 from €400,000 plus a State pension is plausible but leaves no margin for a bad decade.
The trade-off to state plainly: shortening duration gives up roughly (7.2 − 2.5) × the expected yield-curve steepness - perhaps 40–80bp of yield - in exchange for removing most of the interest-rate risk. He is not being offered a free lunch; he is being asked whether ~50bp is a fair price for not being forced to sell at the bottom.
Do not simply say "stay the course". Staying the course is a valid answer for a 35-year-old with no withdrawals and an accumulating portfolio. He is neither.