As the real estate industry looks to learn from the fallout of covid-19, one issue which should be at the top of the list is to recognise the glaring mathematical limitations in the traditional performance measurement models. Engineering a solution is important; as with high value thresholds and illiquidity, investment decisions cannot be easily changed when we experience an extreme risk event – unlike completing marketable liquid asset classes.

Currently, the performance of commercial property is principally measured by recognised mathematical models of return (mean) and risk (standard deviation). These statistical approaches provide the backbone for many in the investment community to compare performance across asset classes, and importantly the foundation for leading investment strategies: risk-adjusted returns, capital asset pricing models and modern portfolio theory.

There is increasing evidence (see Nassim Taleb’s work) that while the application of the standard deviation model works well under stable conditions, the formula fails when stable assumptions cease to hold and extreme volatility occurs, as demonstrated by the recent severe pricing swings associated with the global financial crisis (GFC) and now as we begin to see the impact of covid-19.

In defining normal distribution on a bell curve, the possibilities of unpredictable large deviations (outliers) are simply marginalised, because data typically over-samples the good times and under-samples the bad ones. These extreme events far from the centre of the distribution are more frequent than a normal distribution would predict. This creates a so-called ‘fat-tailed’ distribution profile. Past research on Australian real estate data shows that the normal bell curve distribution underestimates actual extreme values both by frequency and extent, by a very significant 30% for the outermost data point.

As measures of extreme risk provide skewed distribution, there is evidence that Power Law (also known as the Pareto Distribution) may be a more appropriate model to measure fat-tailed distributions. This technique is becoming more popular in applications of extreme value theory as it overcomes many of the shortcomings of traditional financial stress-testing (value at risk) models.

Mandelbrot (1982) provided the origin of modern Power Law research as he examined the inconsistency of the orthodox theory of finance and developed new approaches to identify performance vulnerability to severe risk. He developed fractal geometry, (the term ‘fractal’ is from the Latin for ‘broken’) and in subsequent years fractal scaling application covering Power Law was recognised to have the fundamental qualities to cover the higher probabilities of extreme values as experienced in the financial markets.

In practical terms, conventional distribution calculations are best suited for a data series that exhibits mild and well-behaved randomness, as the difference between each point and the mean is squared and so leads to an equitable scattering of points evenly around the mean. Power Law, on the other hand, utilises fractal patterns which can relate intensity to frequency and so is more suited for data series that can exhibit irregular large movements. Such Power Law formulae are used in science, for example; seismologists use mathematical models that show the intensity of earthquakes varying in accordance with Power Law.

While scalable laws do not yet yield precise results, past Australian research shows the Cubic Power Law model to be an extremely robust method to identify the performance of an investment to the vulnerability to severe disruption, where extreme values are more common than a normal distribution implies. On the outermost data point, Cubic Power Law detailed a more realistic one-in-42-year event compared with an improbable one-in-313-year event provided by a standard bell curve distribution on the Australian real estate data.

In summary, modelling techniques for estimating measures of tail risk provide challenges and have been shown to go beyond conventional traditional risk management practices, which bring a relatively narrow and constrictive definition. On this evidence, analysis of extreme downside risk based on a Cubic Power Law model should form a key part of the property investment decision-making process and be included in the property investment manager’s toolkit.

Measuring extreme risk and the likelihood of ruin is the first step in analysing and dealing with risk both in the real estate asset class and portfolio context. This should now be a research priority as there is evidence that current quantitative property decision-making systems do not properly take into account extreme downside risk determinants which are increasing by magnitude, frequency and impact.

A covid-19 wake-up call.

You can contact David Higgins at david.higgins@bcu.ac.uk

Further reading

Higgins D, 2015, “Defining the Three Rs of Commercial Property Market Performance: Return, Risk and Ruin”, Journal of Property Investment and Finance, vol. 33, issue 6, pp481-493