Better Beta Is No Monkey Business

Patrick Rudden

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. This makes perfect sense to me, but says more about infinity than it does about monkeys.

In his seminal book, A Random Walk Down Wall Street, Burton Malkiel argued that a blindfolded monkey throwing darts at a newspaper’s financial pages could select a portfolio that would do just as well as one carefully selected by the experts. This makes little sense to me: why does the monkey have to be blindfolded? Monkeys can’t read.

Unblindfolded, however, Malkiel’s monkey may make perfect sense. In a recent paper,1 Rob Arnott et al show that the legendary dart-throwing monkey would produce a portfolio with a substantial value and small-cap bias that would have historically outperformed the cap-weighted index. Such a portfolio, therefore, might have done just as well as one built by non-monkey experts.

Leaving monkeys (blindfolded or not) aside, the research conclusion is an important one. What it shows is the limitation of cap-weighted indices where the size of a constituent is a function of share price. Such indices by construction put more emphasis on stocks with high prices and less emphasis on stocks with low prices. They will favor components whose prices have risen the most.

This concentration risk is often unintended. And it creates risks that can be bad for your wealth when investors stampede out of crowded positions, causing violent market swings. As my colleague, Dave Barnard, points out in a recent paper,2 the technology sector ballooned to more than 29% of the S&P 500 in 2000 (Display). Over the next two years, the sector lost more than half its value. Similarly, Japanese stocks lost about a third of their value in the two years after their weight in the MSCI World Index peaked at 44% in late 1989. Similar trends played out in the energy sector in 1980 and in financials in 2007, at the peak of the credit bubble. 

Today’s favorite market theme lies in so-called safety stocks—particularly, in the US, those with high dividend yields. At their peak in September 2012, stocks with high dividend yields had a 44% weight in the S&P 500, their largest weight since 1970 and far above their 35% average.

Cap-weighted index funds have their virtues. They can provide low-cost exposure to an asset class and, typically, they are easy to buy and sell.

But we believe that any approach which loosens the connection between weight and price is likely to have a performance edge. For example, investors could permit some increase in tracking error or create smarter-beta benchmarks based on equal-, value- or risk-weighted components, and with explicit mechanisms designed to avoid concentration risk. These solutions might be slightly more expensive than a typical passive index, but we think it’s a price worth paying to avoid the risks of a pure, cap-weighted approach. And it’s probably a better idea than giving a monkey some darts and a copy of the FT.

1. “The Surprising ‘Alpha’ from Malkiel’s Monkey and Upside-Down Strategies,” Arnott, Hsu, Kalesnik and Tindall in Journal of Portfolio Management, Summer 2013, Vol. 39, No. 4: pp. 91-105

2. “The Case for Integrated Wealth Management,” David Barnard, AllianceBernstein, July 2013

The views expressed herein do not constitute research, investment advice or trade recommendations and do not necessarily represent the views of all AllianceBernstein portfolio-management teams.

Patrick Rudden is Portfolio Manager, Dynamic Diversified Portfolio at AllianceBernstein.



  1. Interesting. Just wondering, in your analysis, what do you categorize as “High Dividend-Yield” stocks?

    • Patrick Rudden

      We define high dividend-yield stocks as stocks with a yield 0.5 standard deviation higher than the market average.

  2. I see these kind of arguments all the time; they are all the same and ignore the 800 pound dart-throwing monkey in the room: that passive investing beats almost every active manager over time. Moreover, as intelligent as this man sounds, his argument is not with me: it”s with Fama, Sharpe, et al, all of whom won Nobel prizes in financial research in economics – research that was published for years and years in the top peer-reviewed journals. To simply make an intelligent argument on a website, online or in a magazine falls way short. This particular argument above opens the door for smart beta ETF investing, where people pick and choose which sectors look undervalued or ripe for above average returns, and then change the weighting from cap based to whatever they forecast may be better. Again, this is just the strategy mutual funds have tried for years and over time it underperforms. And even when a manager outperforms an associated index, as Sharpe has shown, there is absolutely no evidence of causation to show there was any skill involved – it was all luck…which takes us back to the 800-pound monkey in the room.

    • Patrick Rudden

      Investors who don’t believe active management can outperform or don’t believe they can identify an outperforming active manager ex ante should invest passively. Of course, investing passively also requires two active decisions: what is the universe of securities I am going to invest in and how should I weight them. There is a growing body of academic work (published in peer-reviewed journals) which shows that weighting by something other than price has historically outperformed cap-weighting. The intuition behind these results is that severing the connection to price implicit in cap-weighting means you avoid buying more of things that are expensive versus cheap. It is also the case that “fundamentally-weighted” indexes have tilted towards smaller cap and value and so may simply be capturing the historic small cap and value premiums. The debate goes on.

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