Shrödinger’s Pension Fund

I’ve been planning to write a blog on this topic for some time. It was the title of my session at the 2011 Actuarial Profession Pensions Conference and a topic that I am passionate about. I guess the place to start is with some quantum mechanics and Shrödinger’s cat…

Shrödinger’s Cat

Shrödinger’s cat is a reasonably famous thought experiment from 1935 (NB: as it was just a thought experiment no cats were actually injured!). The idea is as follows:

– get a box
– add some poison released by an atomic timer (such that the time of its release is random)
– put a cat inside
– seal the box

Then ask the question “Is the cat dead or alive?”

The quantum mechanics answer is that the cat is both dead and alive at the same time. It is only when you open the box that its actual state is determined.Zombie cat

This is of course nonsense as a cat cannot be dead and alive. And in fact Schrödinger agreed. It was a classic “reductio ad absurdum” (a reduction to the absurd) designed to show how bizarre applying quantum mechanics principles to real world objects is.

So how does this relate to pensions?

Well, if we modify the experiment slightly and put an employer in a box we can then ask the question “is the employer solvent or insolvent?”. In the same way as a cat can’t be dead and alive, an employer cannot be both solvent and insolvent at the same time.

A further modification. What if we put an employer with a defined benefit pension scheme in the box and ask the question “what level should we fund the scheme to?”. We know there are 2 states that the employer could be in so these are the 2 states we should consider when funding a scheme.

This is unfortunately not how UK pensions regulation works. The Pensions Regulator lives in a quantum mechanical world of scheme funding and sees a continuum of schemes from those with strong employers to those with weak employers. Trustees are told1 to set their funding target taking into account this strength with higher targets required for weaker employers.

There are two key problems with this. Firstly, what happens when a strong employer becomes weaker? In this sort of scenario it is unlikely it suddenly has more money available to increase the funding level. Such demands could even make the employer weaker still and be a catalyst for its demise. Secondly, and related to this, strong employers can fail too! Who predicted the fall of Lehman Brothers and failure of Woolworths? Is it acceptable for members to receive a lower proportion of their benefits because we thought the employer was stronger than others?

Taking this approach to pension scheme funding is as nonsensical as a dead and alive cat!

So what approach should be used? To answer this we need to go back to the 2 possible outcomes for the employer and look at what this implies for the pension scheme…

Assume the employer is insolvent

In this case there is no additional money available to fund the pension scheme and, to wind it up and secure benefits with an insurance company, the full buy-out insurance liability will be required. On the assumption that the employer will be insolvent, we need to ensure the scheme is funded to this buy-out level.


If this was the approach taken for funding defined benefit pension schemes then no schemes would ever be setup. The cost of funding the benefits at this level would significantly outweigh the perceived benefits from employees. An employer may as well just pay extra salary.

This approach to funding, although appealing from a security point of view, does not ultimately lead to an efficient way of providing pensions.

Assume the employer is solvent

If the employer is solvent until the last pension benefit is paid then (ignoring unfunded arrangements that would be even better!) it is most efficient for it to hold the best estimate of the amount of money it needs today to pay benefits in the future as and when they fall due i.e. taking into account best estimate expectations of returns on assets.

By doing this there is no opportunity cost of tying up capital. Benefits can also potentially be provided cost effectively meaning employees are able to access something they really value.


If the funding regime took this approach then if an employer did become insolvent, there would not be enough money to secure benefits for all members leading to reductions. We therefore need a mechanism to address this and provide protection to members.

Interestingly enough, at the same time as introducing the current funding regulations such a solution was also launched:

Pension Protection Fund


To sum up my conclusions:

– The way schemes are currently funded does not make sense
– There are only really 2 ways to tackle scheme funding as an employer can only be solvent or insolvent
– Working on an insolvency assumption leads to no pension schemes
– Assuming solvency and funding to a best estimate level is therefore the answer
– Security needs to be addressed and the PPF is perfect for this

I will write more on why the PPF is perfect for this (or at least why it should be) another day!

1 – Notably they are told this by the Pensions Regulator rather than UK pensions law – see more here: Taking things too far