“The Loser’s Game” is the title of a paper written by Charles D. Ellis and published in the January-February 1995 issue of Financial Analysts Journal. On the fifth page of this article, Ellis provides one of the most devastating equations for active investors. The following is a long quote from this article as he talks about investing moving from a Winner’s Game to a Loser’s Game.
“The new ‘rules of the game’ can be set out in a simple but distressing equation. The elements are these:
- Assume equities will return an average nine percent rate of return. [9% was about right at the time.]
- Assume average turnover of 30 percent per annum.
- Assume average costs–dealer spreads plus commissions–on institutional transactions are three percent of the principal value involved. [This is likely high in today's market.]
- Assume management and custody fees total 0.20 percent.
- Assume the goal of the manager is to outperform the averages by 20 percent.
[ It was necessary to clean up some of the decimal errors in Ellis' equation. ]
Solve for “X”: (X x .09) – [30 x (.03 + .03)] – (0.20) = (120 x .09)
X = {[30 x (.06)] + (0.20) + (120 x .09)}/.09
X = (1.8 + 0.20 + 10.8)/.09
X = 12.8/9 = 142%
“In plain language, the manager who intends to deliver net returns 20 percent better than the market must earn a gross return before fees and transactions costs (liquidity tolls) that is more than 40 percent better than the market. If this sounds absurd, the same equation can be solved to show that the active manager must beat the market gross by 22 percent just to come out even with the market net.”
“In other words, for the institutional investor to perform as well as, but no better than, the S&P 500, he must be sufficiently astute and skillful to ‘outdo’ the market by 22 percent. But how can institutional investors hope to outperform the market by such a magnitude when, in effect, they are the market today? Which managers are so well staffed and organized in their operations, or so prescient in their investment policies that they can honestly expect to beat the other professionals by so much on a sustained basis?”
Here is the equation, with data, if the investor only wants to match the market.
X = [ 30 x .06 + .2 + 9 ]/.09 = 122% or the 22% Ellis talks about in the above paragraph.
Now let’s enter the numbers that are closer to the Passive Portfolio I’ve worked with for over seven years.
X = [ 10 x .02 + .2 + 9 ]/.09 = 104.4% or 4.4% is needed to perform better than the market. This is still a difficult hurdle, but manageable if one skews a portfolio toward small-cap and value oriented investments.
Photograph: Corfu street restaurant – Greece
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