Skip to content

Is math behind passive investing wrong?

November 7, 2016


For many investors, the superiority of passive investing over active investing is axiomatic.

And why not?

Study after study has demonstrated that only a small portion of actively managed funds beat their benchmarks over long time frames. A recent Wall Street Street Journal article, “The Dying Business of Picking Stocks,” noted that while 66% of mutual funds and ETFs are currently actively managed, this figure is down from 84% 10 years ago.

For many investors, the move into passive investing is simply another form of short-term performance chasing, but for others, the move is much more strategic and backed by persuasive logic. For example, back in 1991, William Sharpe published “The Arithmetic of Active Management,” which laid out the challenges faced by the active-management industry.  Mr. Sharpe argued the market is made up of two kinds of investors: 1) passive investors, who hold the market-cap weight of every stock in the market, and never trade, and 2) active investors, who individually hold portfolios that differ from the market, and actively trade.

Mr. Sharpe’s “arithmetic” concluded the following: 1) passive investors earn market returns, and 2) active investors play a zero-sum game–for every winner there is an offsetting loser. The implications are profound for active investing because after deducting management fees, active investors must underperform passive investors, on average. The natural conclusion is for investors to simply punt on higher fee active management and invest all their capital in ultra-low-cost passive strategies.

Mr. Sharpe’s logic is compelling, but I think the assumptions underlying the conclusions are not grounded in reality.

recent essay by Druce Vertes at the CFA Institute, and more formal research by NYU Professor Lasse Pedersen, suggests that Mr. Sharpe’s conclusions might be incorrect. Dr. Pedersen offers a very powerful critique in a new white paper entitled, “Sharpening the Arithmetic of Active Management.” Dr.  Pedersen argues Mr. Sharpe’s arithmetic relies on the faulty assumptions that the market never changes and passive investors never need to trade.

Objectively, these assumptions are false: The market is not static, as new firms are created through IPOs, new shares are issued or repurchased, and indexes are reconstituted all the time. Additionally, passive investors must sometimes rebalance their portfolios, for instance to raise cash or reinvest dividends. In short, passive managers must, and do, trade with active investors.

As evidence for the need of passive investors to trade, Dr. Pedersen cites the case of a theoretical passive investor in 1927, who never trades. After 10 years, this investor owns only 60% of the market. And this ongoing market turnover is persistent: The average turnover for all equities from 1926 through 2015 was a whopping 7.6% per year. Last year, the Vanguard 500 Index Fund reported turnover of 10%. Clearly, the assumption that passive investors never need to buy and sell is false. And this mechanical need to trade opens passive investors up to exploitation by active investors.

But newly “passive” investors are only making matters worse by trading well beyond what they are required to do to maintain their passive exposure to an ever-changing market mix. The advent of cheap, liquid ETFs has increased trading activity. For example, in a recent essay titled “ETFs may actually make weak players weaker,” the author analyzed Morningstar data from the past five  years, and found that ETF investors massively underperformed the very ETFs in which they were invested. These “passive” investors weren’t passive by any stretch of the imagination–they were active investors trading passive vehicles, providing opportunities for more sophisticated investors to exploit.

Mr. Sharpe’s arithmetic relies on an assumption that passive investors never trade and simply buy and hold forever. This is an unrealistic assumption that thoughtful market commentators and researchers are now criticizing.  The necessary trading required by passive investors to remain passive, and unnecessary trading by so-called passive investors trying to “time” the market with passive ETFs, change, in my opinion, Mr. Sharpe’s conclusions:  1) passive investors pay indirect fees to active investors for liquidity, and 2) active investing is no longer a zero-sum game.

The implications are more reasonable and reflect what we see in the marketplace: Passive investors no longer eat a completely free lunch, active investing still plays a role in the market, and a handful of puzzling societal problems associated with excessive passive investing no longer pose a problem for financial economists. A triple win-win-win insight.

Wesley R. Gray (@alphaarchitect) is the CEO and CIO of Alpha Architect, a quantitative asset manager based near Philadelphia.

From → Uncategorized

Leave a Comment

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: