The arithmetic of active: a zero sum game?

[3 min read, open as pdf]

• Defining terms is key
• What the Sharpe paper says
• What are the implication for fund pickers

 
The active vs passive debate is nothing new: the first index fund was launched in 1976 to track the S&P 500.
In 1991, Nobel prize winner, William Sharpe (of Sharpe ratio fame), wrote a paper on “The Arithmetic of Active” setting out some of the clichés articulated by active managers, and why, in his view, it’s a zero sum game.

Definition terms is key
Whenever the active vs passive debate kicks off it’s always important to define terms.  If referring to an asset allocation process, we prefer the terms static and dynamic and that’s got nothing to do with the subject of this paper or the claims by index investors that “active” is a zero sum game.  Nor does the “activeness” or otherwise of hedge funds.
The zero-sum game allegation relates to security selection, typically in a long-only context and therefore most relevant to managers of portfolios of securities and/or retail funds.

What the Sharpe paper says
Broadly speaking the Sharpe paper argues that in a closed world of active managers (stock pickers within an asset class), where the opportunity set is the index, for every “star” manager buying and holding the best performing stocks, there is a “dog” manager to whom the worst performing stocks have been sold.  In aggregate, over time, this means the combined performance of both managers is the same as the index less active fees.  This makes it hard for active managers to persistently outperform the index over time, which is evidenced by the SPIVA study.  On this basis, using a fund that delivers performance of the index less passive fees seems like a more efficient way to gain exposure to that opportunity set.

What are the implications for fund pickers
The SPIVA study shows that the ability of active managers to outperform an index persistently varies from market to market depending on the efficiency of that market.  For example, US and Global Equity markets fewer managers manage to outperform.  For UK and Emerging Markets, active managers achieve better results.  The latest SPIVA scorecard can be found here.
We are not against “true active”, but the “arithmetic” is stacked against traditional long-only retail managers when it comes to persistency of alpha.  Incorporating an index based approach where markets are highly efficient, and or where the availability of “true active” managers is rare.
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How to identify “true active” is a topic for another day!