Arborbridge wrote:TUK020 wrote:I fear that I do not understand the chain of reasoning.
A rise in interest rates will increase the rate of return on a long term gilt.
For a gilt already owned, it does not do this by increasing the interest payment. It does it by reducing the price of the gilt.
How does this reduce the deficit?
I can see a long term effect when the bond matures, the money can be recycled into a new bond at a higher interest rate. But I fail to see how increasing interest rates magically cuts the pension deficit.
What am I missing?
As Dod says, it is nothing to do with the price of the bonds being discussed here, but the liability as determined by teh actuaries to the BT pension fund - and that liability in turn is heavily dependent on the gilt rate. Mixing the fact that BT are issuing a bond with the gilt rate in the same disussion led to the misunderstanding.
I think TUK020's problem may well be to do with understanding why the liability as determined by the actuaries is heavily dependent on the gilt rate. So perhaps an explanation is in order...
Suppose I had to pay you say £10k per year for say the next 20 years. To make the obligation concrete and the formulae as simple as possible, I'll assume that I have to pay the entire £10k for each year at the start of the year. Assuming I can find investments with a completely safe rate of return of R% per year, how much capital would I have to have in those investments to be able to meet my obligation?
Well, the first year's payment is due immediately, so I have to have £10k available to meet it. And the second year's payment is due in one year's time, so to meet it, I have to have the sum that will grow to £10k after being invested for one year at a return rate of R%. That multiplies the sum by (1+R/100), so I have to have £10k / (1+R/100) available now to be able to make that payment after investing it for a year. And the third year's payment is due in two years' time, so I similarly need to have £10k / (1+R/100)^2 available now to be able to make that payment after investing it for a couple of years. And so on, right up to the 20th year's payment, which requires £10k / (1+R/100)^19 available now. And so to meet my obligation to make all 20 years' payments, I need to have the sum of all those amounts available now, i.e.
£10k + £10k/(1+R/100) + £10k/(1+R/100)^2 + ... + £10k/(1+R/100)^18 + £10k/(1+R/100)^19
That formula is a bit cumbersome, but I can simplify it if I set r = 1/(1+R/100) - it becomes:
£10k + £10k * r + £10k * r^2 + ... + £10k * r^18 + £10k * r^19
Or:
£10k * (1 + r + r^2 + ... + r^18 + r^19)
There's a further simplification available. If r=1, then that's just £10k * (1+1+1+...+1), with 20 1's in the second part), so £10k*20 = £200k. Otherwise, we'll leave the sum (1 + r + r^2 + ... + r^18 + r^19) unchanged if we multiply it by 1-r and then divide it by 1-r (this doesn't work if r=1 because the multiplication produces 0, and then the division produces the indeterminate 0/0). But the multiplication produces:
(1-r) * (1 + r + r^2 + ... + r^23 + r^24) = (1-r) + (r-r^2) + (r^2-r^3) + ... + (r^18-r^19) + (r^19-r^20)
= 1 - r + r - r^2 + r^2 - r^3 + ... + r^18 - r^19 + r^19 - r^20
= 1 - r^20,
since the - r and + r cancel each other out, as do the - r^2 and + r^2, and so on up to the - r^19 and + r^19. So the division then produces (1-r^20)/(1-r), and so the capital I need to meet my obligation to make all 20 years' payments is £200k if r=1 and otherwise £10k * (1-r^20)/(1-r).
Now add one small-but-significant complication: rather than the payment obligation starting immediately, suppose it starts in N years' time (and then continues for 20 years after that). In that case, the capital I require reduces, because I get N years of growth at R% to build it up to the amount determined by the formulae in the last paragraph. That growth multiplies the capital by (1+R/100)^N, so the capital required at the start is divided by that, or equivalently multiplied by r^N. So the capital required is £200k if r=1 and otherwise £10k * r^N * (1-r^20)/(1-r)
Now look at how this changes as R and N change - for each value of R, the safe rate of return, we need to calculate r = 1/(1+R/100) and then calculate the required capital. Doing that for a selection of values for R and N:
The point of all this is that this is roughly the situation a pension fund faces about the capital they require with respect to someone who is entitled to a £10k flat pension from the age of 65 if they are currently aged 65, 50, 35 or 20 for the last four columns respectively, assuming they live to age 85, and that it is very sensitive to changes in the safe rate of return, especially for the younger future pensioners - e.g. the last column shows that a 0.5 percentage point decrease in the safe rate of return can add about 30% to the amount of capital required now for safe funding of the 20-year-old's future pension.
Of course, the pension fund isn't guaranteed that its pensioners and future pensioners will live to exactly age 85, but as long as it has a large number of them, they should average out at around that. And there are all sorts of other complications - increasing lifespans, indexation of pensions, possible future changes to safe rates of return and to pension regulations, the fact that younger future pensioners have probably built up a smaller pension entitlement so far, etc, etc, etc. So the real actuarial calculations are nothing like as simple as those above, and an actuary's job is hugely more difficult and complex than is describable in a post! But the above captures the gist of the problem: small changes in investment rates of return can make big differences to the capital required now to safely cover future pension liabilities, and the further they are in the future, the bigger this effect - e.g. a 0.5 percentage point decrease in investment returns only makes about a 5% difference to the capital required now to cover the future payments to a 65-year-old, compared with the ~30% difference for the 20-year-old. (As an aside, the same effect actually applies to all future liabilities, not just pension liabilities - it's just that pension liabilities are likely to be in the especially distant future and so are particularly affected by it.)
TUK020's point about such effects also affecting asset values is entirely valid, with the equivalent "the further into the future, the bigger" effect being that they apply especially to indefinite-duration or long-duration investments such as shares and long-dated gilts. But if for instance a company has a £10b pension deficit due to its pension scheme having £40b of assets and requiring £50b of assets to safely cover its future pension liabilities, and a 0.5 percentage point drop in the safe rate of return causes both the assets and the asset requirements to increase by 20% (as a very rough round-figure guess as to the average effect across the ages of the future pensioners), then those two figures change to £48b and £60b respectively - and the deficit grows to £12b.
The other big issue in this area is just what the "safe" long-term investment rate of return is. Long-dated gilts are generally reckoned to be the safest form of long-term investments (*) and so the rate of return on long-dated gilts gives a reasonable basis for determining it, which is the basic explanation for the connection between pension deficits and interest rates via long-term gilt rates. In practice, higher rates of return are achievable very safely, and I would certainly expect any well-run pension scheme to do so to at least some extent. As even a small increase in the safe future rate of return assumed by the pension deficit calculation will lead to a big reduction in the capital required, it will produce a big reduction in the pension deficit (note that the value of the pension scheme's assets is not affected by that assumption - it will be affected by the market's assumption about the safe rate of future investment returns, but not by the rate assumed in the pension deficit calculation). So companies have a strong incentive to assume as high a safe rate of investment returns in the pension deficit calculation as they can to keep the calculated pension deficits low - and correspondingly, governments / regulators have a strong incentive to keep the assumed rate of investment returns down to a figure that really is as safe as reasonably possible. The conflict between those incentives leads to rules about how a pension deficit should be calculated that specify some sort of compromise between the two. The safe rate of return that produces to be assumed by pension deficit calculations may not be the same as what is actually reasonably safely achievable - and as the above illustrates, even small differences can produce quite major differences in the calculated pension deficit.
The net result is that pension deficits for defined-benefit pension schemes are the difference between two very large numbers - the actual value of the scheme's assets, and a calculated estimate of what value of assets is required now to meet very long-term liabilities. And the second figure (but not the first) is very sensitive to small changes to the safe investment rate it assumes. That combination of being the difference between two very large figures and one of them being an actual current figure and the other very much an estimate based on long-term interest rates makes them highly volatile.
To make "very long-term" concrete, for an open scheme one might think of the liabilities becoming due an average of ~30 years in the future (assuming it has assets for employees averaging about halfway through an ~40-year working life, and pension payments will need to be paid out of it for pensioners averaging about halfway through an ~20-year retirement). Such long-term forecasts really are very difficult indeed, so I'm not saying that the estimates are being made incompetently, excessively roughly, or anything like that - just that high volatility of the calculated pension deficits (and especially their sensitivity to interest rates) is an inherent aspect of the way they're calculated. (So why not use a better method of calculating them, one might ask... To which the answer is basically that no-one has found one that is better, when judged by the standards of all those involved - employees, companies, regulators and governments - weighted by their influence on the standards.)
For a scheme that has been closed to future accruals (so not just no new members, but also no additions to existing entitlements of existing members), each year that passes makes it that much less long-term and so more accurately forecastable. So the problem can be expected to wind down following the BT pension scheme's closure to future accruals. But only very slowly, and so the small amount of winding-down per year can be expected to be swamped by interest-rate effects for many years to come.
(*) Which doesn't mean absolutely 100% safe - governments can in principle find themselves forced to default - but just that there's nothing safer (and if a situation develops in which the government is forced to default, it's probably one in which all investment bets are off anyway).
Gengulphus