July 2014: Richard 'Jerry' Haworth - The Parrondo paradox

The Parrondo paradox1
... two ugly parents can have beautiful children... 2

There is a “head-scratcher” called Parrondo’s paradox which is worth a peek at.

The Parrondo's paradox was a name coined in the 1990s by physicist Juan Manuel Rodriguez Parrondo to show this counterintuitive probabilistic phenomenon in repeated decision making under uncertainty. It shows how two losing games when alternated either in sequence or randomly, can turn into a winning one.

How is this possible? By switching between the two games, a ratchet-like accumulation of wins occurs. Swapping from one game to another traps the wins before subsequent repetitions can start the inevitable decline in that particular strategy. The sequence of swapping does not matter!

This paradox is ubiquitous in nature and life. If you jiggle a bag of mixed nuts, the bigger Brazil nuts end up on the surface despite the obvious gravitational pull. Genetics too is all about losing individually in order for the species to win. Etc, etc. What makes this interesting is the ratchet-like exit methodology which is eerily similar to that which we employ at 36 South. By exiting on a ratchet we harvest the option positions much in the same way the Parrondo paradox games do.

The departure from the paradox though is that we take individual value propositions in options which idiosyncratically are WINNING propositions and combine them into a portfolio which can perform in a variety of market environments (even in a falling volatility environment as we can scoop on directional plays), i.e. both bull and bear, calls and puts.

We buy enough time to be right and we wait for movement or volatility. One side will by definition lose whilst the other is winning, also very similar to the Parrondo paradox concept. In this way the volatility causes one part of the portfolio and then the other to be profitable. However, the profits are harvested before they are given back assuming the moves are large enough, locking in decent performance. This is all merely “interesting” and yes, the ability to generate decent performance is good but there are hundreds if not thousands of funds that can do this.

What is truly unique about this strategy is that it generates its best performance during times of high uncertainty and volatility, a time normally associated with falling asset prices. A time when most other funds are normally performing badly. Therefore, this is an ideal diversifier in a portfolio.

It is rare and unique to find a strategy which a) has positive expected returns and b) tends to come into its own at the time you need it, i.e. when all your other investments are falling in tandem.

Correlation, the third arrow of portfolio management, was devilishly hard to predict and take advantage of… until now.

And all because two losing strategies can be combined to create a winning one. Yes, two ugly parents CAN have a beautiful child!



1 Bogomolny, A. Cut The Knot! An interactive column using Java applets. Parrondo Paradox [online] June 2001. Available at http://www.cut-the-knot.org/ctk/Parrondo.shtml [Accessed on 11th August 2014].

2 Zeilberger, D. 1998 Response to the Award of the 1998 Steele Prize [online] January 1998. Available http://math.nist.gov/opsf/personal/wilfzeil.html [Accessed on 11th August 2014].