Information theory as a tool to improve individual pensions: The Chilean case

•Application of techniques developed for statistical physics to economics.•Analysis of the evolution of individual capitalizations.•Use of mutability to establish the differences among agencies.•Use of sensitivity to detect the appropriate instances for actions.•Examples showing how to increase profits avoiding loses.

We review the Chilean Pension System (CPS) under an entirely new prism: the fluctuation of the capitalization funds measured by means of information theory, which is achieved by the application of the recently proposed data compressor wlzip. We begin by explaining the basics of the CPS at the time we review its economical performance during the period 2003–2012. The share value and its return or profitability are the main indicators used in the introductory analysis. Then we use wlzip to recognize regimes for fluctuations of the share values of the different funds and agencies, by means of the indicator known as mutability in a way similar to what mutability achieves in the case of magnetic transitions. It turns out that mutability recognizes the onset of fluctuations of the markets. This fact combined to the variations of returns allows us to define a very sensitive parameter which we call sensitivity. It has been shown that sensitivity is able to anticipate large variations of the share values with several days of advance, thus allowing clients to switch their investments to a safer fund avoiding capital losses. A simulation is conducted to show the huge differences that could have happened during the crises in 2008 and 2011: using information provided by wlzip it is possible to obtain better profits and obtain better pensions in the long run.