*The importance of knowing the errors in any measurement is not just critical for the pilots of low-flying planes, Joseph Mariathasan warns*

Mathematics lies at the heart of modern finance and its applications to investment. But there is a fundamental difference between the way pure mathematicians would approach the use of mathematical models to describe the world outside the lecture theatre and the approach adopted by physicists.

Many of the current ills of the financial market can be placed at the doors of the mathematicians who tried to apply mathematical rigour to the financial world, assuming the same success could be achieved as that seen in the physical world. The errors of this have been described very well in books such as *The Black Swan* by Nassim Nicholas Taleb.

One of the clearest things I still remember from my undergraduate lectures in experimental physics is that, when it comes to the measurement of any quantity, the estimate of the error associated with the measurement is just as important as the measurement itself. In simple terms, if you measure the height of a building as 34.5 metres, it is as important to know whether the error in the measurement is plus or minus 20 meters or plus or minus 0.2 meters.

The importance of knowing the errors in any measurement is not just critical for the pilots of low-flying planes. It has a fundamental importance in the management of financial assets and liabilities, and it appears to have been ignored often.

The reason for this is quite simply that, whilst experimental physicists can claim to have a deep knowledge of mathematics (two-thirds of my first-year lectures were in mathematics), much of the application of mathematical techniques to finance has been undertaken by mathematicians for whom the whole idea of error margins appears to be an alien concept. The effects can be seen throughout the financial world.

For pension funds, the effects of this can be seen in the way a mathematician and an experimental physicist might approach a typical problem such as calculating a liability-driven investment (LDI) strategy. Typically, an actuary with a pure mathematics background would state that, as of the moment of calculation, the liabilities are precisely £1,543,456,000 based on his models, and this value changes by the minute in the light of market movements in government bonds. Asset allocation decisions in the form of precisely matching cashflows should be based on this and continuously rebalanced in the light of any mismatches that appear with time. This would lead to frequent rebalancing decisions, with all the costs that would entail.

A physicist, on the other hand, would come up with the answer that the best estimate for liabilities is a figure of £1.5bn, plus or minus £100m, reflecting factors such as uncertainties in mortality rates, the appropriate risk-free government bond yield and so on. The figure, together with the error associated with it, should be the basis on which asset allocation and any hedging decisions are made. Moreover, this figure and the error associated with it are likely to remain relatively stable, and so little rebalancing would be justified. Clearly, the financial and economic consequences of the two approaches are likely to be very different!

The economic reality is there are large uncertainties in a valuation due to inherent uncertainties in the maturity profile of the pension liabilities, for example, and also in the actual future risk-free bond yields that are the basis for any form of discounting. Current government bond yields clearly do not represent an unbiased estimate for future government bond returns, with the effects of quantitative easing and the artificial demand stimulated by the effect of rigid LDI approaches to matching. Using government bond yields to discount pension fund liabilities may be useful for accountants and as a shorthand, but the calculated discounted value of the liabilities represents an estimate not an absolute truth.

The reality is that any economic valuation of a pension fund’s liabilities has an error margin built into it. The size of that is of critical importance since it effectively determines whether expensive approaches using risk-free government bond portfolios to match liabilities make any sense at all. 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, than purchasing expensive and precisely tailored cashflows via sovereign debt to match liability streams that are themselves only imperfectly defined. This is particularly so when core euro-zone bonds are offering negative yields.

Unless there is a proper appreciation of error margins in the valuations of assets and liabilities, pensions funds may be like the pilot of the low-flying plane at night who has been given some measurements of the buildings he is flying over but no has appreciation of the error margins in the heights. Perhaps it is time for the mathematicians to move aside and let the experimental physicists take the lead in applying mathematics to an imperfect world!

*Joseph Mariathasan is contributing editor at IPE*

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