The Importance of Mathematics in Pensions

Celebrating International Day of Mathematics

Today is the International Day of Mathematics. It is also Pi Day. Perhaps it is no coincidence then – as today is also my birthday – that I ended up being an Actuary (and now Pensions Trustee) with a degree in mathematics!

Maths is essential in the world of pensions. It is integral to the work undertaken by pensions professionals, from actuaries and administrators to the fund managers and financial advisers. That doesn’t mean, however, that everyone who works in pensions is a mathematician! Being a Pensions Trustee, I now do less of the everyday “pensions maths” than I once did in my actuarial role. However, I now rely on our pension scheme advisers to understand and interpret the many mathematical concepts required to allow us to manage our pension schemes effectively.

How mathematics shapes pension schemes

Pensions are built up over a long period of time and then, in many cases, paid for a number of years in retirement. This significant length of time creates a large number of uncertainties, for example:

• For how many years will a pension be paid?

• How much do you need to save now to provide that pension in the future?

• What return will be received on the money saved in your pension?

The aim is to ensure that sufficient funds are set aside now to provide a pension far into the future. That’s where the wonder of mathematics comes into play!

Actuarial mathematics: Predicting the future

Actuarial maths involves the use of statistics and probabilities to predict future trends in investment returns and life expectancies, for example. This provides an estimation of how much a pension scheme’s investments will grow over time, and for how long a pension will be paid. Present value calculations are used to determine the time value of money – if a pension payment of £X is required in the future, how much do we need to hold now, taking into account the expected period of time before £X is payable and the anticipated investment returns and price inflation expected over that period?

Stochastic modelling: Managing pension scheme risks

Stochastic modelling can then be used to model a large number of different scenarios, both economic (e.g. different investment returns) and demographic (e.g. different life expectancies). This allows the likelihood of outcomes to be considered, helping trustees and sponsoring employers to understand the level of risk associated with their pension scheme. 

For defined benefit pension schemes, members’ pensions are based on a defined formula at retirement. Pension scheme administrators use that formula to calculate the pension due to each individual. Whilst much of that is now automated through sophisticated administration systems, the individual administrators still use their mathematical knowledge to check calculations and ensure formulae are being applied correctly.

Do you need to be a mathematician to work in pensions?

Mathematics flows through almost every aspect of pensions. Over the years, more and more tools have been developed to assist pensions professionals apply complex (and not so complex) mathematical principles in their everyday roles. You don’t need to be Pythagoras, Fibonacci or Alan Turing to work in the world of pensions, but a basic grasp of mathematics is helpful!