Joseph Mariathasan: Discount rates and error margins

‘You can only manage what you can measure’ is a fundamental plank of any management approach – but if too much credence is given to the measurements themselves without understanding their limitations, it can create chaos.

One of the more revealing actuarial jokes I have heard (told to me by an actuary), was the story of an actuary standing next to a farmer who was surveying the sheep grazing in his fields. “How many sheep do you think I have?” asked the farmer. The actuary, after a few moments’ thought, answered: “1,007.” 

The farmer looked astonished and asked the actuary how on earth he was able to get a precise answer so quickly. To which the actuary answered: “It was quite simple, you must have around 1,000 in that field in the distance, and you have seven sheep in the field next to us, so adding them together gives a thousand and seven.”

That type of thinking perhaps underlies many of the issues relating to liability-driven investment (LDI) and the concept of matching estimated long-term liabilities with expensive risk-free bonds.

Valuing pension fund liabilities based on index-linked gilt yields is useful as an accounting device. It is a mathematical exercise based on two assumptions: Firstly, that a government-backed risk-free yield is the correct rate to discount future liabilities. Secondly, there is an implicit assumption that all pension funds can match liabilities exactly using the index-linked gilt market. What the valuation is not is an economic truth.

The second assumption is patently not true given that the size of the pension fund liabilities is four times that of the total index-linked market: The size of the UK index-linked gilt market is around £400bn (€452bn) while the UK’s defined benefit pension schemes have a combined liability of around £1.6trn.

Therefore the idea that the methodology for providing an accounting valuation of pension fund liabilities should be the basis for the strategy used to manage them cannot be sensible either. It is impossible for all pension funds to be able to acquire enough index-linked gilts to be able to do so. The reason why index-linked real yields are negative is because of demand from schemes under pressure to match estimated liabilities with expensive bonds with exact cashflows, irrespective of the price. The strategy suffers from, as the actuary in the sheep joke, the lack of incorporation of error margins.

The ‘present value’ calculation of liabilities incorporates a number of estimates, each of which has its own error margin. As any physicist knows, these error margins need to be published along with the measurement itself. If error margins in liabilities are large, then adopting an approach of approximate matching using asset classes such as equities and other assets aimed at producing high long-term absolute returns with given levels of risk may be more sensible than investing in bonds with precise cashflows to match liabilities with much more imprecise cashflows.

Investors may be better off (even in an LDI context) with approximate matches that are cheap, rather than purchasing expensive and precisely tailored cashflows via sovereign debt to match liability streams that are themselves only imperfectly defined.

The idea that LDI is purely a risk management problem needs to take this into account. The controversies over schemes such as the Universities Superannuation Scheme can then be understood as at least partly arising from a collision between an accounting methodology designed for book-keeping and economic realities.

Sometimes measurements can be misleading. Focusing on solutions based on flawed measurements is bit like the story of the actuary found on his knees searching round a lamp post in the middle of the night. When asked by a passer-by what he was doing, he replied that he was searching for his phone which he had dropped in the fields opposite. When asked why he was therefore looking under the lamp post, he replied: “Because there is more light here.”

If analysis and management of financial issues requires a rigorous scientific approach, then understanding the flaws, assumption failures and error margins in measurements is a pre-requisite. Otherwise, you may be scrambling around where there appears to be light, but you won’t find what you are looking for.

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