Duration gap in a large immediate annuity portfolio
A life insurer has written ₹8,000 crore of immediate annuities over five years. The liability duration is 12.4 years, while the backing fixed-income assets have a duration of 8.1 years. Of the assets, 60% are 10-year government securities, 25% are AA-rated corporate bonds with an average maturity of 7 years, and the remainder is equity held in a participating fund that is not legally available to support annuity liabilities. New business is being written at an implicit yield of 6.2%, while the marginal reinvestment yield on 20-year paper has fallen to 6.5% from 7.6% two years ago. The regulator requires the annuity fund to be segregated and broadly matched. A 100 bp fall in yields would raise the liability by about 11% but the assets by only 8%. Derivatives are permitted for hedging only, counterparty exposure to any single bank is capped at ₹250 crore, and the internal model allocates ₹180 crore of capital to interest-rate risk.
1. Quantify the mismatch and explain its economic, not accounting, consequences.
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Size of the gap. Duration gap = 12.4 − 8.1 = 4.3 years. For a 100 bp fall, liabilities rise by about 11% of ₹8,000 crore, or ₹880 crore. Fixed-income assets of roughly ₹7,600 crore rise by about 8%, or ₹608 crore. The net economic loss is therefore around ₹250–280 crore, and it is larger for bigger falls because the liability has higher convexity than the assets. The ₹180 crore of allocated interest-rate risk capital is insufficient to absorb a 100 bp move, let alone a 150 bp move.
Why it matters economically. The insurer has promised fixed nominal payments for 25–35 years and has bought assets that mature too early. When the early assets mature, they must be reinvested at 6.5% instead of the 7.6% assumed two years ago. The spread earned over the annuity rate therefore compresses precisely in the scenario where the guarantee is most expensive. This is a real transfer of value from shareholders to policyholders, not a timing difference: it will show up eventually in lower surplus and in the solvency ratio.
Second-order effects. The equity in the participating fund provides no support and adds volatility to the group balance sheet while contributing nothing to the annuity matching. The concentration in 10-year government securities and 7-year AA paper suggests the portfolio was built for yield rather than for cash-flow matching. The 6.2% new-business yield also looks inconsistent with the 6.5% reinvestment yield once expenses and the cost of hedging are added.
2. Recommend a matching programme within the derivative and counterparty constraints.
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Target. Reduce the duration gap to no more than 1.5–2.0 years and cash-flow-match the first 10–12 years of annuity payments, because short-dated cash flows can be matched without derivatives.
Tools.
- Physical bonds: buy the longest available government securities and state development loans, laddered to the annuity payment dates. Supply is limited, so expect to cover perhaps 3–4 years of duration.
- Receive-fixed swaps: layer 10-, 15- and 20-year swaps to extend duration. With a ₹250 crore cap per bank, split notional across at least four counterparties and use central clearing where available to reduce bilateral exposure.
- Forward-starting swaps: hedge the reinvestment risk on maturing 10-year paper, which is the main source of the gap.
- Cash-flow matching: dedicate a portfolio to years 1–10 of payments; immunise the remainder by duration and convexity.
Impact. Hedging from 8.1 to about 10.5 years would cut the 100 bp loss from roughly ₹270 crore to ₹150 crore; full matching is not achievable because of supply and counterparty limits, so some residual gap must be capitalised. The capital allocation should rise to at least ₹300 crore, or the residual should be covered by a reinsurance or longevity/interest-rate hedge where available.
Governance. Set duration triggers (for example, review if the gap exceeds 3 years), report the gap monthly to the asset-liability committee, and measure the cost of hedging against the yield given up. Do not use derivatives to take a view on rates.
3. Should the insurer keep writing new annuities at a 6.2% implicit yield?
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The arithmetic. If the marginal 20-year yield is 6.5% and hedging the duration gap costs roughly 0.3–0.4%, the effective reinvestment cost is about 6.8–6.9% before expenses and capital. Writing at 6.2% therefore locks in a negative spread of about 0.6–0.7% plus capital strain. Every additional ₹1,000 crore of annuity business widens the gap and consumes capital that is already insufficient for a 100 bp move.
Recommendation. Suspend or reprice new business towards 6.8–7.0% until the long end steepens or hedging costs fall. If competitive pressure makes suspension unacceptable, then:
- write only shorter-duration or deferred products whose cash flows can be matched with existing paper;
- introduce reviewable or participating annuity rates so that some reinvestment risk is shared;
- cap new-business volume at the amount that can be hedged with available long paper and swap capacity;
- price in an explicit hedging cost and a capital charge in the profit test rather than using the gross yield.
Check the accounting. The apparent profitability may be flattered by holding assets at amortised cost or by a valuation rate above the current market yield. Re-run the embedded value using market-consistent yields and a 14% risk discount rate; if new business has negative embedded value, it should not be written merely to grow the balance sheet. Report the decision and the supporting analysis to the board and, where required, to the regulator.