Duration and the Rate Shock
A pension fund holds a £40m portfolio split 60% in a 10-year gilt (modified duration 8.2) and 40% in a 2-year gilt (modified duration 1.9). The fund's liabilities have a present value of £38m and a duration of 7.5 years. The investment committee expects the Bank of England to raise rates by 75 basis points over the next quarter. A junior analyst proposes shifting 30% of the portfolio from the 10-year into the 2-year gilt to 'reduce interest-rate risk'. The fund is also considering using a 10-year interest-rate swap (pay fixed, receive floating) to hedge.
1. Calculate the portfolio's current modified duration and the expected change in value if rates rise 75bp.
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Weighted modified duration:
- 10-year: 60% × 8.2 = 4.92
- 2-year: 40% × 1.9 = 0.76
- Portfolio MD = 5.68
Value impact of +75bp: ΔV ≈ −MD × Δy × V = −5.68 × 0.0075 × £40m = −£1,704,000 (≈ −4.26%).
So the portfolio would lose roughly £1.7m on a 75bp rise. Note this is a first-order (duration) estimate; convexity would slightly soften the loss for a parallel shift, but the direction and scale are clear.
2. Evaluate the analyst's proposal to shift 30% from the 10-year to the 2-year gilt. Does it achieve the stated aim, and is it appropriate given the liabilities?
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New allocation: 10-year = 60% − 30% = 30%; 2-year = 40% + 30% = 70%.
New MD: (30% × 8.2) + (70% × 1.9) = 2.46 + 1.33 = 3.79.
Does it reduce rate risk? Yes - MD falls from 5.68 to 3.79, so the loss on +75bp shrinks to ≈ −3.79 × 0.0075 × £40m = −£1.14m (vs −£1.70m). The analyst is arithmetically right that it lowers duration.
But is it appropriate? No - it creates a liability mismatch. Liabilities have duration 7.5; the portfolio MD is 5.68 (already below liabilities) and the proposal cuts it to 3.79, widening the duration gap from −1.82 to −3.71. The fund would become more exposed to falling rates (liabilities would rise faster than assets). This is the classic error of optimising assets in isolation. The correct aim is to match liability duration (~7.5), not to minimise asset duration. The proposal should be rejected; if anything, the fund needs higher asset duration.
3. Explain how a pay-fixed 10-year swap could be used to hedge, and assess whether it fits this fund's position.
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Mechanism: In a pay-fixed/receive-floating swap, the fund pays a fixed rate and receives floating (e.g. SONIA). If rates rise, the fixed leg becomes relatively cheap (the fund pays below-market fixed) and the floating receipts rise - the swap gains value. This offsets the loss on the fixed-income assets. A pay-fixed swap therefore adds duration to the portfolio (it behaves like a short position in a bond, i.e. it increases rate sensitivity in the direction that profits from rising rates).
Fit for this fund: The fund's assets (MD 5.68) are shorter than liabilities (7.5). It is exposed to falling rates (liabilities outrun assets). A pay-fixed swap would increase asset duration toward the liability duration - that is directionally correct for closing the gap.
Caveat: The committee expects rates to rise, which would help the swap but hurt the assets. The hedge should be sized to the duration gap, not the rate view. To lift portfolio MD from 5.68 toward 7.5, the notional of a 10-year pay-fixed swap (duration ~8–9) needed is roughly: gap (1.82) × £40m ÷ swap duration (~8.5) ≈ £8.6m notional. The swap is appropriate as a liability-matching tool, provided it is sized to the gap and the fund accepts the counterparty/collateral obligations.