Estimating the value of an inflation-capped pension from market data

November 1, 2021

The University Superannuation Scheme (USS) is planning to introduce a cap of 2.5% for inflation adjustments to its members’ accrued pensions. The effect of this cap is to increase new accrued pension benefits in line with official consumer prices (CPI) but only up to 2.5% per year. If inflation runs hotter than 2.5%, that year’s pension increase will be limited to 2.5%.

To evaluate such a proposal, it would be useful to know the effect such an inflation cap would have on expected pensions. One way to obtain such an estimate is to simulate future paths of inflation using historical data as shown in an earlier post. Another option is to use market data from UK government inflation-linked bonds. Why these bonds? Pensions accrued by USS members (or any other defined-benefit pension scheme) can be interpreted as assets that promise a real payoff at the pension date (i.e., a lump sum) or a stream of real payoffs from the pension date (i.e., a pension). The real value of this payoff is known, and the nominal value depends only on UK inflation rates.

A link to UK inflation rates can also be found in inflation-linked bonds. UK index-linked gilts have payoffs linked to the retail price index (RPI), a feature that makes them almost ideal for comparisons against CPI-linked pensions. So-called breakeven inflation rates can be estimated from the market prices of these instruments. The breakeven rate is defined as the future inflation rate that would make the value of a conventional bond equal to that of an inflation-linked one. It is is the difference between the nominal yield on a fixed-rate bond and the real yield on an inflation-linked bond of similar maturity and credit quality. For a comparison against an inflation cap, we need inflation rates by year in the future and then adjust them for the expected difference between RPI and CPI. The Bank of England (BoE) publishes implied forward inflation rates, which approximate an RPI breakeven rate. Historically, RPI has been about 0.75% higher than CPI. Once this long-run difference is subtracted from estimated breakeven rates, the cap of 2.5% can be subtracted to obtain a loss estimate per year. These losses relative to a pension that has been increased according to CPI can then be summed up or multiplied (depending on whether we work with instantaneous or discrete rates) for the entire planning horizon.

The forward curve of implied CPI inflation rates on 29 October 2021 is shown in Figure 1. It is obtained, essentially, from yield differences between UK index-linked gilts and conventional gilts, adjusted for the long-run difference between CPI and RPI. For example, the CPI inflation expected for next year (year 1) is 4.7%. The annual inflaton expected in five years’ time is about 3.1%. Inflation is expected to be above the 2.5% cap for the next 20 years. To be precise, actual future inflation is expected to be lower than the corresponding breakeven inflation rate, because the estimated breakeven rate consists of the expected inflation plus a premium for inflation risk, which compensates for variations in future inflation rates. However, for owners of an inflation-linked asset such as a defined-benefit pension, this risk premium is a yield component of this asset and cannot be ignored.

Technical note on Figure 1: Inflation forward rates provided by the BoE do not include the first two years, which must be estimated separately. This can be done by first estimating spot rates for index-linked gilts and conventional gilts separately, calculating forward rates based on these spot rates, and then calculating breakeven inflation rates as the difference between forward rates of conventional gilts and forward rates of index-linked gilts. I have used manually calculated discrete breakeven rates for the first four years in the graph above to blend the short end of the curve into the instantaneous forward curve provided by the BoE. Using instantaneous and discrete rates in the same forward curve is an approximation but likely reasonably precise for our purposes which deal with relatively large effects on the order of a percentage point. Another differences is that the BoE derives its forward rates from a curve-fitting model that estimates and smoothes the outcome for all rates simultaneously, while I have iteratively calculated spot rates and forward rates in the usual way starting with short maturities. Data for UK gilts are from Fixed Income Investor. Because not all maturities are exist at any point in time, some maturities of interest must be estimated. To line up maturities of traded index-linked gilts and maturities of conventional gilts, I have linearly interpolated the nearest spot rates for each spot curve. The resulting breakeven rates in Figure 1 for the first four years are discrete annual rates. All calculations below use one-year forward rates and assume that gilt-based breakeven rates are a proxy for RPI. This assumption may not be precise because of changes in the underlying inflation measure used for index-linked gilts.

The effects of capping pension increases at 2.5% per year are shown in Figure 2 below. The upper curve shows the nominal value of an accrued pension that is inflated at the breakeven inflation rate. After 20 years, for example, the nominal value is 1.83 times the pension accrued today. At 40 years, the nominal value of £1 today is £2.72. The lower curve shows the nominal value when inflation adjustments are capped at 2.5% per year. In that case, the nominal value at the 20-year mark is 1.64, and the nominal value after 40 years is 2.44.

The two nominal pension curves in Figure 2 can be compared to find the value of a pension under the 2.5% cap relative to an uncapped pension. Figure 3 shows the result of dividing the lower curve in Figure 2 by the upper curve. Relatively high breakeven rates in the near future cause the values of capped and uncapped pension to diverge quickly. A capped pension that pays out in 10 years is worth about 92% of the uncapped pension. A capped pension promised in 20 years is worth about 90%. At 40 years, the relative value is still 90% because breakeven rates are below the 2.5% cap for maturities greater than 20 years. In other words, switching a pension with uncapped inflation adjustments to one with a 2.5% cap is associated with a 10% loss for a pension that is accrued today and pays out in 20 years’ time. Depending on a person’s distance to retirement, this value will be different The calculation also assumes that all pensions are received as a lump sums at the maturity date. However, a stream of future pensions can be modelled as a weighted sum of lump sums with different maturities.

Limitations

Pension contributions today vs tomorrow

The analysis above only applies to pensions accrued today. Tomorrow’s breakeven rates may be different, and an analyis like the one above would need to be carried out every time a pension is accrued to evaluate the difference between a capped and an uncapped pension. This option-like behaviour of the inflation cap for future pension contribution is why an inflation cap has a value even though it may not currently be binding. If it were not binding today, then the above analysis would not show a cost of the inflation cap, but only because it is not looking in the future in this sense. The cap still has a cost because even if it’s not binding today, it may be binding tomorrow, which represent an economic benefit to the pension scheme (i.e. a cost to scheme members). This cost adds to the cost shown above.

RPI, CPI, CPIH

Breakeven inflation rates may be underestimated if estimated forward rates already take into account the switch to an RPI calculation that is closer to the current CPIH from the year 2030. CPIH, which includes housing costs, is lower than RPI and more in line with CPI. In other words, the negative adjustment of 0.75% to bring RPI breakevens in line with CPI assumed above may be too large for values from February 2030.

Credit risk

Comparing UK gilts to USS pensions assumes that both have the same credit risk. This may or may not be the case. A pension promised by the USS may be worth more or less than the equivalent amount invested in an index-linked gilt. A pension backed by a diversified portfolio of international assets may be less risky with respect to expected real returns than one invested purely in gilts. Using index-linked gilts to hedge the USS’s liabilities may be attractive from an inflation-tracking point of view, but it comes at the cost of linking the fate of the USS to that of the UK government debt and may also forgo attractive (real) returns elsewhere.

Inflation and other pension rules

This analysis only looks at the effects of inflation. If other changes to the pension are to be modelled alongside the inflation cap, effects should be treated multiplicatively. For example, if the accrual rate drops by 12%, and the cost of the inflation cap is 10%, then the combined effect would be 1-(1-12%)×(1-10%)=1-0.792=20.8%.

In summary, there are reasons to believe that the economic cost to scheme members is greater than shown in the analysis above.

## Estimating the value of an inflation-capped pension from market data

November 1, 2021

The University Superannuation Scheme (USS) is planning to introduce a cap of 2.5% for inflation adjustments to its members’ accrued pensions. The effect of this cap is to increase new accrued pension benefits in line with official consumer prices (CPI) but only up to 2.5% per year. If inflation runs hotter than 2.5%, that year’s pension increase will be limited to 2.5%.

To evaluate such a proposal, it would be useful to know the effect such an inflation cap would have on expected pensions. One way to obtain such an estimate is to simulate future paths of inflation using historical data as shown in an earlier post. Another option is to use market data from UK government inflation-linked bonds. Why these bonds? Pensions accrued by USS members (or any other defined-benefit pension scheme) can be interpreted as assets that promise a real payoff at the pension date (i.e., a lump sum) or a stream of real payoffs from the pension date (i.e., a pension). The real value of this payoff is known, and the nominal value depends only on UK inflation rates.

A link to UK inflation rates can also be found in inflation-linked bonds. UK index-linked gilts have payoffs linked to the retail price index (RPI), a feature that makes them almost ideal for comparisons against CPI-linked pensions. So-called breakeven inflation rates can be estimated from the market prices of these instruments. The breakeven rate is defined as the future inflation rate that would make the value of a conventional bond equal to that of an inflation-linked one. It is is the difference between the nominal yield on a fixed-rate bond and the real yield on an inflation-linked bond of similar maturity and credit quality. For a comparison against an inflation cap, we need inflation rates by year in the future and then adjust them for the expected difference between RPI and CPI. The Bank of England (BoE) publishes implied forward inflation rates, which approximate an RPI breakeven rate. Historically, RPI has been about 0.75% higher than CPI. Once this long-run difference is subtracted from estimated breakeven rates, the cap of 2.5% can be subtracted to obtain a loss estimate per year. These losses relative to a pension that has been increased according to CPI can then be summed up or multiplied (depending on whether we work with instantaneous or discrete rates) for the entire planning horizon.

The forward curve of implied CPI inflation rates on 29 October 2021 is shown in Figure 1. It is obtained, essentially, from yield differences between UK index-linked gilts and conventional gilts, adjusted for the long-run difference between CPI and RPI. For example, the CPI inflation expected for next year (year 1) is 4.7%. The annual inflaton expected in five years’ time is about 3.1%. Inflation is expected to be above the 2.5% cap for the next 20 years. To be precise, actual future inflation is expected to be lower than the corresponding breakeven inflation rate, because the estimated breakeven rate consists of the expected inflation plus a premium for inflation risk, which compensates for variations in future inflation rates. However, for owners of an inflation-linked asset such as a defined-benefit pension, this risk premium is a yield component of this asset and cannot be ignored.

Technical note on Figure 1: Inflation forward rates provided by the BoE do not include the first two years, which must be estimated separately. This can be done by first estimating spot rates for index-linked gilts and conventional gilts separately, calculating forward rates based on these spot rates, and then calculating breakeven inflation rates as the difference between forward rates of conventional gilts and forward rates of index-linked gilts. I have used manually calculated discrete breakeven rates for the first four years in the graph above to blend the short end of the curve into the instantaneous forward curve provided by the BoE. Using instantaneous and discrete rates in the same forward curve is an approximation but likely reasonably precise for our purposes which deal with relatively large effects on the order of a percentage point. Another differences is that the BoE derives its forward rates from a curve-fitting model that estimates and smoothes the outcome for all rates simultaneously, while I have iteratively calculated spot rates and forward rates in the usual way starting with short maturities. Data for UK gilts are from Fixed Income Investor. Because not all maturities are exist at any point in time, some maturities of interest must be estimated. To line up maturities of traded index-linked gilts and maturities of conventional gilts, I have linearly interpolated the nearest spot rates for each spot curve. The resulting breakeven rates in Figure 1 for the first four years are discrete annual rates. All calculations below use one-year forward rates and assume that gilt-based breakeven rates are a proxy for RPI. This assumption may not be precise because of changes in the underlying inflation measure used for index-linked gilts.The effects of capping pension increases at 2.5% per year are shown in Figure 2 below. The upper curve shows the nominal value of an accrued pension that is inflated at the breakeven inflation rate. After 20 years, for example, the nominal value is 1.83 times the pension accrued today. At 40 years, the nominal value of £1 today is £2.72. The lower curve shows the nominal value when inflation adjustments are capped at 2.5% per year. In that case, the nominal value at the 20-year mark is 1.64, and the nominal value after 40 years is 2.44.

The two nominal pension curves in Figure 2 can be compared to find the value of a pension under the 2.5% cap relative to an uncapped pension. Figure 3 shows the result of dividing the lower curve in Figure 2 by the upper curve. Relatively high breakeven rates in the near future cause the values of capped and uncapped pension to diverge quickly. A capped pension that pays out in 10 years is worth about 92% of the uncapped pension. A capped pension promised in 20 years is worth about 90%. At 40 years, the relative value is still 90% because breakeven rates are below the 2.5% cap for maturities greater than 20 years. In other words, switching a pension with uncapped inflation adjustments to one with a 2.5% cap is associated with a 10% loss for a pension that is accrued today and pays out in 20 years’ time. Depending on a person’s distance to retirement, this value will be different The calculation also assumes that all pensions are received as a lump sums at the maturity date. However, a stream of future pensions can be modelled as a weighted sum of lump sums with different maturities.

LimitationsPension contributions today vs tomorrowThe analysis above only applies to pensions accrued today. Tomorrow’s breakeven rates may be different, and an analyis like the one above would need to be carried out every time a pension is accrued to evaluate the difference between a capped and an uncapped pension. This option-like behaviour of the inflation cap for future pension contribution is why an inflation cap has a value even though it may not currently be binding. If it were not binding today, then the above analysis would not show a cost of the inflation cap, but only because it is not looking in the future in this sense. The cap still has a cost because even if it’s not binding today, it may be binding tomorrow, which represent an economic benefit to the pension scheme (i.e. a cost to scheme members). This cost adds to the cost shown above.

RPI, CPI, CPIHBreakeven inflation rates may be underestimated if estimated forward rates already take into account the switch to an RPI calculation that is closer to the current CPIH from the year 2030. CPIH, which includes housing costs, is lower than RPI and more in line with CPI. In other words, the negative adjustment of 0.75% to bring RPI breakevens in line with CPI assumed above may be too large for values from February 2030.

Credit riskComparing UK gilts to USS pensions assumes that both have the same credit risk. This may or may not be the case. A pension promised by the USS may be worth more or less than the equivalent amount invested in an index-linked gilt. A pension backed by a diversified portfolio of international assets may be less risky with respect to expected real returns than one invested purely in gilts. Using index-linked gilts to hedge the USS’s liabilities may be attractive from an inflation-tracking point of view, but it comes at the cost of linking the fate of the USS to that of the UK government debt and may also forgo attractive (real) returns elsewhere.

Inflation and other pension rulesThis analysis only looks at the effects of inflation. If other changes to the pension are to be modelled alongside the inflation cap, effects should be treated multiplicatively. For example, if the accrual rate drops by 12%, and the cost of the inflation cap is 10%, then the combined effect would be 1-(1-12%)×(1-10%)=1-0.792=20.8%.

In summary, there are reasons to believe that the economic cost to scheme members is greater than shown in the analysis above.