To celebrate the World Cup, our resident “sports reporter” (yes, apparently we now have a sports beat) draws on the Beautiful Game to make a point about CAPM…

By: Miran Ahmad, AllAboutAlpha.com Editorial Board

With the World Cup upon us and all eyes turned to South Africa, I could not help but think of how the sport loved by millions around the world is secretly teaching us about finance. So from the blog that brought you “What US College Basketball Can Teach Us About Survivorship Bias” and “What NASCAR Can Teach Us About Return Persistence” comes the next installment: What the World Cup Can Teach Us about Modern Portfolio Theory. Now what in the world does soccer (a.k.a. football, but for purposes of this article will be referred to as soccer) have in common with finance?  Surprisingly, a lot if you know where to look.

South Africa is playing host to 32 qualifying teams in the 2010 FIFA World Cup. On any given team, there are a handful of coaches and approximately 20-25 soccer players. We know that players who make their team during one World Cup may not make the team during the next World Cup. Also, each player specializes in a particular skill, including scoring (strikers/forwards), ball control (midfielders) and/or defending (defenders and goalie), all of which contribute to the overall success of the team. With few restrictions, each country is free to strategize and create a team with what they believe is the best combination of strikers, midfielders and defenders. One team may pay particular attention on midfielders while another may focus primarily on strikers.

You can see the connection between FIFA, finance and modern portfolio theory.   What if we replace coaches with investment managers, teams with portfolios and players with assets before we revisit the facts. We learn from modern portfolio theory that investment managers (coaches) create a portfolio (team) that maximizes return while minimizing risk by specifically selecting assets (players).

Ever present in financial prospectuses is the mantra past performance does not guarantee future success. Additionally, academic research has shown the importance on two aspects of the asset selection process: the number of assets to include and the characteristics of assets themselves in a portfolio context. First, the number of assets chosen in a portfolio reduces the overall risk of the portfolio; however, risk reduction deteriorates as the number included becomes larger. Like the number of players on a soccer team, having 20-25 well chosen assets greatly reduces overall risk with additional assets not really contributing much to risk reduction as evinced by data below from E.J. Elton and M.J. Gruber’s historic study (described here on Wikipedia) .

More recently, Dr. Lokanandha Reddy Irala and Prakash Patil’s study “Portfolio Size and Diversification” illustrate similar risk reducing results when increasing portfolio size.

Second, not all the assets perform the same role or share similar characteristics. Some assets may be focused on growth (strikers), some on capital preservation (midfielders) while others characterized as defensive (defenders/goalie). How these assets work with another in a portfolio context is more important than how these assets perform individually. In fact, risk reduction is maximized when assets have negative correlations with one another. How?  As correlation (denoted PAB) drops from +1 to -1, the 3rd term of the equation becomes negative and lowers overall portfolio variance.

And lastly, each investment manager is free to create a portfolio independent of the opinions of others. A fundamental aspect of the Modern Portfolio Theory and the Capital Allocation Line (CAL) is the ability of people to disagree on the risk/return composition of their portfolio. Unlike CAPM and the Capital Market Line (CML) that assume investors universally agree on the market risk/return expectations, CAL allows more optimistic views to have higher reward/risk ratios.

And there is another potential similarity between World Cup soccer/football and portfolio management.  With approximately 200 sovereign countries, it is interesting to see how only 32 teams qualified to play in this year’s World Cup, perhaps a case of “sampling bias”?  Who knows.

Whether you are picking teams for the office pool or stocks in the fund portfolio, there is alpha  in keeping your finance goggles on even while watching this year’s World Cup. Sometimes alpha can be found properly dining on tail risk, or in this case, maybe alpha can be found just by remembering the basics. Generate positive returns by minimizing trading and research costs low by only selecting 20 to 25 players/assets needed to achieve diversification while avoiding the law of diminishing returns. Alpha can come by properly conducting due diligence to ensure that you know who will be on your team and what their specific contribution overall will be or by keeping in mind that how players work with each other (correlation) is more important than how they perform by themselves. So next time your boss yells at you for watching soccer on company time, just show him what the World Cup can teach him about Modern Portfolio Theory.

(Ed: For more on using sports to help explain portfolio management also check out: “Alpha Generation in the NFL” and “Why The Search for Alpha is More Like Baseball Than Mining.”)