Let’s look at what would have happened for pricing a 15 years index-linked (RPI) annuity for years starting between end-1985 and end-2008 (there are 24 periods). The price is based upon the initial ILG yield, with no allowance made for expenses. The returns are those on the long ILGs TRI because the income is actually even less important than when they were first issued. Allowing for returns and indexed payments of £1,000 pa, the fund at the end should be zero.

Over the 24 periods, the mean experienced RPI increase was 3.10% pa, with  standard deviation of 0.41% pa, a minimum of 2.71% pa and a maximum of 3.97% pa. The end-year ILG yields varied between 0.82% pa and 4.49% pa (see blue line)

Using figures spanning end-1985 until end-2000, the initial yield was 3.87% pa, giving an initial price of £11,217. After 15 years, the residual fund is £1,097 which is not what we wanted. To obtain the right outcome, the yield needs to be increased by 0.38% pa to 4.25% pa, giving an amended price of £10,923.

The price reduction of 2.61% for 1985-2000 is somewhat modest, averaging 13.72% over the 24 periods and being as (absolutely) high as 27.61% for 2006-2021. The figures for all periods are tabled and the yields and prices are charted