Can 10 million monkeys outperform the index?

October 28, 2016 | Last updated on October 28, 2016
4 min read

Factor-based or smart-beta ETFs use static strategies in their attempt to outperform capitalization-weighted benchmarks. These ETFs are typically more expensive than their passive cousins. Do they actually outperform?

10 million monkeys

Professors Andrew Clare, Nick Motson and Steve Thomas (Cass Business School, City University of London, 2013) examined factor-based equity strategies in two papers.

They populated portfolios by picking from the largest 1,000 U.S. stocks annually (1968 to 2011) and randomly weighting them, simulating 10 million monkey picks.

The resulting portfolios were then categorized into eight characteristics (see Chart 1), and almost every one of those monkey portfolios outperformed the cap-weighted index. The study was hailed as a rigorously proven challenge to the popular cap-weighted passive investing movement. But given Prof. Sharpe’s position (see “Does alpha exist?”), how could this be?

The portfolios have a small-cap bias and are commission-free, explaining part of the result. What worked best were risk-controlled strategies: risk efficiency (downside deviation weighted), low volatility and equal risk (each stock represents 1% of total portfolio risk).

Formula for volatility drag

Volatility drag is equal to 0.5(SD)2, where SD stands for standard deviation.

Chart 2 shows the relative Sharpe ratios of the various alternative strategies. Added to the previous list of risk-controlled strategies are minimum variance portfolios (MVP). Our key observation is that all the better-performing strategies trend toward lower or controlled volatility.

Why controlled volatility?

Albert Einstein identified compound interest as the most powerful force in the universe. Investment professionals understand this, but few understand the impact of volatility on compounding.

Volatility is like kryptonite to the superpowers of compounding. Its impact offers insights into diversification, portfolio growth and protection. The difference between arithmetic and geometric returns, or volatility drag (see “Formula for volatility drag”) is key:

CHART 1: Monkeys’ terminal wealth value and CHART 2: Monkeys’ Sharpe ratios
(risk-adjusted returns)

  • An asset that’s up 10% today and down 10% tomorrow (or vice versa) ends up at 99% of its starting value.
  • An asset that’s up 50% today and down 50% tomorrow (or vice versa) ends up at 75% of its starting value. The higher volatility (50% change) has 25 times the impact of the lower (10%) change.

Volatility impedes compounding, so avoiding volatility makes compounding more effective.

Uncertain factor persistence

Another study of U.S. and international stocks from 1995 to 2015 showed that while smart beta strategies outperform for a period, periods of underperformance lasted between three and nine years. Further, the degree of underperformance varied from 9% to 33%. A study, “Getting smart about beta” by Jason Stoneberg and Bradley Smith, concluded that a market down 30% would achieve smart beta returns of -33% to -40%. One caveat: smart beta static strategies may be successful over a period that we can’t yet see or predict.

Outperforming monkeys

In Chart 3, the green areas show periods of monkey outperformance using a three-year moving average (such smoothing tends to be favourable to alternative strategies). The length of these periods can be deceptive. For instance, 2008-2009 occurred in the middle of an extended period of alternative “outperformance,” but was devastating.

CHART 3: Monkeys beat cap-weighted

Smart beta summary

  • Alpha, in aggregate, does not exist. If some strategies have higher returns for a period, it is at the expense of others with lower returns.
  • Owning a portfolio different than the benchmark will always lead to tracking error and performance different than the index—positive, neutral or negative. But it’s impossible to tell in advance what that difference will be.
  • Under- and overperformance can persist for up to nine years. Can your practice survive?
  • Controlling volatility is the key to success.

All active strategies outperform for a while. Selecting which ones will do so in advance and for how long remains the challenge. Are the higher costs of these strategies worth it? Advisors will have to decide.

Does alpha exist?

RP = βRM + α

A portfolio’s return (RP) is the sum of the broad market’s return (Rm) multiplied by that portfolio’s sensitivity to the market (beta, or β) and a residual return above the market’s return (alpha, or α), a product of market inefficiencies. But does alpha (α) really exist? Returns minus costs equal net returns, according to William Sharpe. Furthermore:

  • average passive return = the market return and average active return = the market return;
  • active costs are higher than passive costs, therefore, passive net returns are higher than active net returns.

In aggregate, if alpha exists for active strategies (like smart beta), it must be negative. But this seems wrong. All smart beta products claim to outperform. The market return at any point in time is fixed, like the number of bananas in a bunch. If a portfolio returns more bananas than average, it is at the expense of another with fewer bananas. Excess returns come only at the expense of others that underperform.