The 85% Funded Scheme and the Equity Temptation
A defined-benefit scheme has assets of KES 8.2bn against a liability present value of KES 9.6bn, discounted at 9.0%. The actuary reports a liability duration of 11.5 years. The asset portfolio is 60% equities and 40% short-dated bonds, with a duration of 5.2 years. Last year the fund returned 11.2% while liabilities accrued at 10.1%. The sponsor has offered KES 250m a year for five years, first payment in one year, and rules out further contributions. The investment committee proposes lifting equity to 70% to close the gap, arguing equities have returned 13% against 11% on bonds. Trustees want a written opinion before the next meeting.
1. Quantify the funding position and test whether the sponsor's offer closes the shortfall.
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Funding ratio: 8.2 / 9.6 = 85.4%; shortfall KES 1.4bn (on a discounted basis).
Value of contributions at the 9.0% discount rate:
Annuity factor, 5 years at 9% = [1 - 1.09^-5]/0.09 = 3.8897 PV = 250 x 3.8897 = KES 972m
Residual shortfall = 1,400 - 972 = KES 428m in present-value terms, before any adverse experience.
So the offer is helpful but not sufficient: on unchanged assumptions the scheme remains about 4.5% underfunded. Two further points the trustees must hear:
- The contributions fix the level of the gap but not the sensitivity. Duration is untouched, so a 100bp fall in the discount rate still widens the deficit by roughly (11.5% x 9.6bn) less (5.2% x 8.2bn) = 1,104 - 426 = KES 678m, wiping out two-thirds of the contribution programme in a day.
- Last year's 11.2% return against 10.1% liability accrual is a 110bp surplus gain, roughly KES 90m - progress, but not 428m of progress.
2. Compute what it would take to close the duration gap using physical bonds versus a swap overlay, and advise.
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Physical route. Let x be the weight in bonds of duration 13.0:
5.2(1 - x) + 13.0x = 11.5 5.2 + 7.8x = 11.5 x = 6.3 / 7.8 = 80.8%, i.e. KES 6.63bn
That would leave under 20% in return-seeking assets - the scheme would have no realistic route to its return target and would still be a forced seller if it needed cash. Also unrealistic in Kenyan long-bond depth.
Overlay route. Receive-fixed interest rate swap notional N to add the required duration:
N = (11.5 - 5.2) x 8.2 / 13.0 = 6.3 x 8.2 / 13.0 = KES 3.97bn notional
This adds duration without disturbing the 60/40 growth portfolio, and is the standard answer. Conditions: a collateral waterfall and liquidity buffer (a 100bp move on 3.97bn at duration 13 is roughly KES 500m of variation margin), ISDA documentation, and a trustee-approved hedge ratio with a rebalancing band of, say, +/-1.0 year of duration.
Advice: adopt the overlay at 50%-70% of the calculated notional first (roughly KES 2.0-2.8bn) to keep collateral calls survivable, and pair it with the contribution schedule.
3. Evaluate the 70% equity proposal using expected returns and risk, and give the trustees a bottom line.
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Expected return: 0.70 x 13.0% + 0.30 x 11.0% = 12.4% against liability accrual of 10.1% - a 230bp expected surplus gain, roughly KES 190m a year on 8.2bn, in the expected case.
Risk: equity volatility of about 20% on 5.74bn gives a one-year 95% VaR of 1.645 x 0.20 x 5.74 = KES 1.89bn - larger than the entire KES 1.4bn deficit. The committee is proposing to gamble the gap on a favourable draw from a distribution whose bad tail is the size of the problem.
Worse, the proposal ignores the real driver. The deficit is a duration problem. A 100bp rate fall costs 678m in surplus under the current mix, and raising equity to 70% makes it worse, not better, because it lowers asset duration toward 4 and increases the mismatch.
Bottom line for trustees: reject the 70% equity proposal. Accept the contributions, implement a partial swap overlay to move asset duration from 5.2 toward 9-10 years, retain the growth portfolio, and review the discount rate assumption with the actuary - 9.0% on a 11.5-year liability is doing a lot of quiet work in this valuation.