Annuity  The term is 15 years and the instalments are £1,000 pa, paid annually in arrears. Payments are fixed and certain, with no demographic assumptions required. The RPI-linked case based upon index-linked gilts is shown here.

Assets  In theory, one should be able to match the annuity payments by buying a series of redeemable conventional gilts, maturing over the term, using income and capital redemptions during the 15 years. A minor problem is that the income is spread across the year so that one would need to make assumptions about reinvesting the income until it needs to be distributed; the reinvestment assumption seems unlikely to be significant but I’ve not tested it. Far worse, there are gaps in redemption dates in the CG market. It seems that the Financial Times no longer lists all CGs. Both of those can be tackled by notionally investing in, and selling down, a CG TRI; I have chosen the “over 15 years”. No allowances are made for expenses, at least not yet.

Timeframe Periods of 15 years starting at the end of 1953 through the end of 2009 are considered separately. Of the 57 periods, 36 led to a surplus and 21 to a deficit.

Methodology  It is first assumed that the annuity can be priced using the initial redemption yield, which should be a pretty good estimator of the return. Then the cashflows are compared to see if sales of the notional investment match the payments. The required pricing yield is then assessed to make the closing fund zero.

Yields  Ranging between 3.71% (2008) and 16.27% (1974), the redemption yields had a mean of 7.90%, with a standard deviation of 3.42%. Ranging between (0.16%) and 19.84%, the required yields had a mean of 8.14%, with a standard deviation of 4.60%.

Adjustments  Ranging between (3.96%) and 3.57%, the yield addition had a mean of 0.22%, with a standard deviation of 1.94%. While the mean is near to zero, the deviations are enormous.

Start Funds  The actual start funds ranged between 5,506 and 11,347 with a mean of 8,881 and a standard deviation of 1,690. The required start funds ranged between 4,707 and 15,188 with a mean of 8,991 and a standard deviation of 2,435. The start fund adjustments ranged between (1,990) and 3,912 with a mean of 143 and a standard deviation of 1,325.

Matching fixed annual payments with CGs is by no means as safe a proposition as might have been supposed. The same is correspondingly true for index-linked gilts.