Reformulation of Markowitz theorem

Described as a newer version of Markowitz's portfolio theory, the unified 'landscape portfolio platform' is able to predict inflated growth and reduced volatility in an ensemble of stochastically co-varying populations across the landscape.

It was developed by Prof Cang Hui, a bio-mathematician from Stellenbosch University, in collaboration with two researchers from the United States of America, Prof Gordon A Fox, a statistician from the University of South Florida, and Prof Jessica Gurevitch, a well-known ecologist from Stony Brook University.

The theorem was published in the Proceedings of the National Academy of Science (PNAS) today (Monday 6 November 2017) with the title 'Scale-dependent portfolio effects explain growth inflation and volatility reduction in landscape demography'.

Prof Hui says the collaboration started after Profs Fox and Gurevitch visited South Africa in 2014 as Fellows of the Stellenbosch Institute for Advanced Studies (STIAS).

"Initially we were looking for ways to quantify population demographics of invasive species on a larger scale in order to make it more relevant to management," he explains.

At that stage, most demographic work had been carried out on a few populations and at local scales.

But the idea to use the Markowitz theorem was completely serendipitous: "I often go to the library and browse a section of books. That day I was in the economics and statistics section when my eye caught a book on the portfolio theory of financial investment. That is where the idea then came to use Markowitz's theorem as the corner stone."

By combining concepts from landscape ecology and Markowitz portfolio theory, they developed the landscape portfolio platform to quantify and predict the behaviour of multiple stochastic populations across spatial scales. As a case study, they used a 35 year time series on gypsy moth populations, covering about 350,000 square kilometres.

The landscape portfolio platform, however, is applicable to any situation where subsystems fluctuate with a certain level of synchrony, from trade analysis in stock market to sudden outbreaks of pathogens and invasive species.

Prof Hui says while the current article took an invasive moth species as case study, the new theorem is applicable to the financial world, ecologists working on regional scale invasions or threatened species, as well as any biologist working with time-series data.

Prof Hui and co-researchers are now working on expanding the platform to allow the differentiation of system stochasticity and external noise in driving portfolio inflation.