Duration Gap and Liquidity in a Fixed Annuity Block
Coastal Annuity Company has a $5.0 billion general account supporting fixed deferred annuities with a current crediting rate of 4.25% and a minimum guaranteed rate of 2.00%. The liabilities have an estimated duration of 7.2 years. Invested assets are 55% investment-grade corporate bonds with duration 6.5, 25% U.S. Treasuries with duration 5.0, 12% agency MBS with duration 4.2 and negative convexity, 5% commercial mortgages with duration 7.0, and 3% equities. The portfolio's weighted duration is 5.8 years. Rates have risen 150 basis points over the past year, and policyholders are surrendering at a 9% annualized rate, up from 5%. The CFO is considering a duration-extension program using 30-year Treasury bonds and interest-rate swaps. The chief risk officer is concerned about liquidity and hedging cost.
1. Calculate the dollar duration gap and explain what it implies for the block's economic surplus if rates fall by 100 basis points.
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Asset dollar duration is $5.0B × 5.8 = $29.0 billion. Liability dollar duration is $5.0B × 7.2 = $36.0 billion. The dollar duration gap is $29.0B − $36.0B = −$7.0 billion, meaning the liabilities are more rate-sensitive than the assets.
If rates fall by 100 basis points, assets gain approximately $29.0B × 0.01 = $290 million, while liabilities increase by approximately $36.0B × 0.01 = $360 million. Economic surplus falls by about $70 million before convexity. The MBS allocation makes this worse: falling rates accelerate prepayments, shorten MBS duration, and reduce the asset price gain. Conversely, a 100 basis point rate rise would improve surplus by roughly $70 million, but that gain is not a reason to run the gap because the company is exposed to a low-rate stress.
2. Recommend a specific hedging or rebalancing action to close the duration gap, including the notional amount. Show your calculation.
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The company needs to add $7.0 billion of asset dollar duration. A simple purchase of 30-year Treasuries with duration 16 would require $7.0B / 16 = $437.5 million if funded from cash. But if the purchase is funded by selling 5-year Treasuries with duration 4.5, the sale removes dollar duration: each dollar purchased adds 16 and removes 4.5, for a net 11.5. The required purchase is therefore $7.0B / 11.5 = $609 million.
A swap alternative avoids changing the cash portfolio. A receive-fixed interest-rate swap has positive duration similar to a long bond. If the swap duration is 15, the notional required is $7.0B / 15 = $467 million. The CFO should compare the funding cost and balance-sheet impact of the Treasury purchase with the collateral and counterparty requirements of the swap. In either case, the hedge should be sized to the full gap, not a partial gap, unless the CRO deliberately retains some exposure.
3. Evaluate the CRO's liquidity concern in light of the 9% surrender rate. What additional information would you request, and what safeguard would you recommend?
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A 9% surrender rate on a $5.0 billion block implies roughly $450 million of annual withdrawals, or about $37.5 million per month. That is manageable only if a meaningful share of the portfolio is liquid without forcing sales of illiquid corporates or mortgages at a discount. The MBS position is not a reliable liquidity source because prepayment behavior is rate-dependent, and the commercial mortgage allocation is the least liquid asset class.
The CRO should request the surrender-charge schedule, a 12-month cash-flow projection, asset-level liquidity haircuts, and the size of any committed credit facility. A safeguard is to hold at least $500 million in short Treasuries or repo-eligible collateral, or to arrange a committed line equal to six months of stressed surrenders. The duration-extension program should not consume all liquid assets; if swaps are used, the company must plan for variation margin calls in a rate-rise scenario.