A simple game for investors: How would you play?

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Some years ago, financial author and advisor, Bill Schultheis, devised a simple game to illustrate the difficulty faced by investors who try to outguess the stock market and the utility of knowing the odds of success. The game called “Outfoxing the Box” is discussed in his book, The Coffee House Investor. (Hat tip to Larry Swedroe, the Director of Research at BAM Alliance, for reminding his readers of this overlooked gem.)

The game looks like this:

The premise is simple. The nine boxes represent possible returns on your investment portfolio which will be guaranteed for your lifetime.

The first rule of the game is that you can choose to play or not. If you choose not to play, you will be assigned the middle box which represents a lifetime investment return of 10 percent. That figure approximates the long-term annualized return of stocks over the past 100 years. If you choose to play, another return from the boxes will be assigned to you randomly as a guaranteed lifetime return.

You quickly note that of the remaining eight possible returns, four are better than 10 percent and four are worse. That gives you a 50 percent chance of a better than market return and a 50 percent chance of worse than market return. You also note that the average of all the possible returns is 10 percent, the same return you would receive if you chose not to play the game. What is the utility of deciding to play?

The market return is simply the average return of all investors, at least before taxes and expenses. What is the utility to investors of trying to achieve better than market returns? You might be skillful or lucky enough to extract a better than average return from the market, or you might be less skillful than you thought and underperform the market. Is the game worth playing?

Several advisors, including author Larry Swedroe, who have presented the game to their clients report that almost without exception, clients prefer to take the 10 percent and opt out of the game. Most participants prefer to take the 10 percent rather than risk what is essentially a coin toss in the search for more upside. These are interesting results, but they are anecdotal and hardly a rigorous study.

The actual data is even more daunting for investors. For over twenty years, S&P Dow Jones Indices has scored the performance of fund managers against their relevant market benchmark. Their scoring, known as the SPIVA Report (S&P Index v. Active), shows that over periods of ten years and longer, most fund managers under perform their benchmark. Over 15 years and longer, around 80% or more of managers across virtually all asset categories underperform their benchmark.

The SPIVA Report considers the performance of thousands of individual funds against their relevant benchmark. What happens when we look at the performance of a portfolio holding multiple funds? Most individual investors own multiple funds – ten or more is quite common.

A study published in 2013 showed that the odds of a portfolio of ten actively managed funds outperforming a portfolio of ten comparable index funds is about 1 in 10. Remember, an index fund simply aims to match as closely as possible the returns of a particular market benchmark, such as the S&P 500 Index. Not only did 90 percent of actively managed portfolios underperform a portfolio of ten index funds, but the average underperformance (.90%) was much greater than the average outperformance (.30%) of the 10 percent of portfolios that outperformed.

The data confirms the hunch of most investors who decline to play Bill Schultheis’ game, which is simply a metaphor for the market. The high probability option is to refuse to play and instead accept the returns the market has to offer.

Let’s acknowledge that there may be good reasons to decide to play the game in the sense of being a more active investor as opposed to an index focused investor. You may have socially minded goals for your portfolio and maximizing returns may not be your primary objective. You may believe that you have the knowledge to extract better returns from the market. You may be willing to take on greater risk in the search for better than market returns by carving out a limited portion of your portfolio for more individualized security selection.

All fine, provided that you are aware of the potential risks and challenges of betting against the market. The high probability approach is to decline to play the game – that is, to accept the market returns. If you choose to do otherwise, do so as an informed investor. If you are working with an advisor, the game may prompt an interesting discussion about your current approach to investing.

David Peartree JD, CFP® is an investment advisor with Brighton Securities Capital Management. This column is a collaborative work by David Peartree and Patricia Foster, Esq. Patricia Foster is a securities law attorney with substantial experience advising members of the financial services industry. The information in this article is provided for educational purposes and does not constitute legal or investment advice.