DB计划资金：一些实证结果和考虑

DB Scheme Funding:Some Empirical Results And Considerations May2023 Authors Professor Iain Clacher & Dr Con Keating Cover image:Annie Sprattwww.anniespratt.com Introduction We have been collecting the reported funding ratios of DB schemessinceDecember 2022.Through this analysis we are finding some fairly large discrepancies between reported fundingratios and the widely broadcast narrative of highly significant improvements of those ratiosacross the sector. Onebasicfigure from our analysis is that range of funding ratios spans 50%to 161%. In this note, we touch upon some of the notable points of our collected sample of 350schemes. Of course, at slightly less than 7% of the universe of private sector funded DBschemes, this sample is not large enough, norsufficiently assured of being representative, toprove or disprove anything, but it is sufficiently large to raise questions and concerns. First, there is no scheme in this sample which reported a positive return on assetsin 2022.The best three reportedresults are losses of 3.8%, 4.6%,and 5.1%; the worstperformancesshow losses in excess of40%.This means that any improvements in funding ratios musthavebeenderivedsolelyfrom declines in the present value ofschemeliabilities. Second, 32% of oursample saw their funding ratios deteriorate over the year. The mediandeterioration was 4.1%. There is a pronounced difference in thesymmetry of thedistributionof improvements/deterioration. The median improvement was 11.6%.The median fundinglevel ofouroverallsample was 95.4% in December 2021, and this improves to just 102.1%bythe end of December 2022. It is also evident from the sample that schemes which were in deficit in 2021 were far moreprone toexperiencedeteriorations in the 2022 funding ratios than schemesthatwere insurplus, which exhibited a tendency to improve further. Expectations Before illustrating whyschemes which were in deficitwere far more prone to experiencedeteriorations(seeTable1 below), it is worth considering how much the returns of fundsmight be expected to have been.With the gaindue to the decline in the present value ofliabilities for schemes overall estimatedbythe PPF to be 38.8%, hedging 50% ofinterestrateexposure would suggest a gain from this of 19.4%. With, say,50% of the fund invested in othergrowth assets which lost, say, 10%, we would have expectedour sampleto return 14.4%(19.4%–0.5*10%)1.Our results are consistent in terms of both the overall results (6.7% gain),and the gain (11.6%) and loss (4.1%) partitions, when the allocation ofthoseschemes togrowth assets was44% and schemes were overall 72% hedged. This can also serve as a sensecheck for the claims of 15% or more overall improvement inscheme funding. This would have required LDI hedging of only 49%, far below its level by mostaccounts and in our sample. We would also notethat with the presence of the present value of liabilities in thedenominator of the funding ratio, the ratio may improve even though the amount of surplusfunds has fallen.A constant cash surplus of say £10 and a funding ratio of 110% in 2021withliabilities at £100, wouldbereportedasan improvement to 16.34% in 2022,if the liabilities havedeclined to £61.2% (this isassuminga 38.8% decline as reported by PPF for the market overall). The best three improvementsin the samplewere from 58% to 90%, from 68% to 104% andfrom88% to 137%.These improvements,to schemes thatwere in deficit,are all of schemeswhich were not employing LDI or doing soonlyto a very limited extentand without leverage.The worst deteriorations were from 97% to 74%, from 88% to 69% and from 83% to 65%. Thelargest gain in funding ratio was 55.2% and the greatest loss, 23.2%. 41.5% of our sample were in deficit ontheirsection 179 value at December 2021, whichagrees closely with the PPF’s overall estimate of 41.3% at that date. However, the PPF’sestimate that, atDecember 2022, just 13.4%of schemeswere in deficit disagrees significantlyfrom oursampleestimateof 22%. Box 1Illustration of the LDI problem for schemes in deficit The table below shows a notional scheme in deficit which has assets of £80 andliabilities of £100; itwas at end 2021,80% funded.If we assume the schemeadoptedan LDI strategy which perfectly(andwithout any costs)hedges the interest rate sensitivity of the liabilities. In 2022, thisLDI strategyresultsin a loss on the hedgeof £34, the amount by which liabilities have declined (from £100 to £66) Table1.A Scheme In Deficit Box I Continued The result is that assets decline by £34 from £80 to £46. The liabilities have declined by 34% but theassets have declined by 42.5%.The funding ratio of thisnotionalscheme declines from 80% to 69.7%.This provides a direct challenge to the wisdom of fully hedging the interest rate sensitivity of liabilitieswhen schemes are in deficit. To quote one of our correspondents: “For most of these (schemes with low or inadequate asset coverage of liabilities) TPR has encouragedan overtly defensive attitud