Infinite Monkey-Business and Splitting the Atom

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Published on August 15, 2018

| 7 min read

David Schofield, President, International Division


It seems that just about any systematic approach to constructing equity portfolios beats the poor old cap-weighted index, as numerous entertaining articles and papers over the last few years have pointed out.1

Monkey Business Blog-1Amongst many other methods, analysts have used (hypothetical) dart-throwing monkeys to generate random portfolios, the Scrabble™ scores of stock tickers, equally-weighted portfolios, as well as the usual factor-based and other popular smart-beta approaches. They all seem to outperform the market in the long run. Even the inverse of the chosen weighting schemes appear to do better, in some cases by yet more than the “parent” weighting scheme! What on earth is going on here? A new study by Intech® in conjunction with academia provides a deep and universal explanation for this phenomenon.2

Traditional Explanations

The conventional explanation of this superficially surprising phenomenon is that it all comes down to factor exposures. The ubiquitous risk factors, especially the “Big 4” (market, size, value and momentum), have been adopted by many investment practitioners and finance academics as the basic components sufficient to explain portfolio performance.

Once it has been established that a portfolio’s relative return can be explained by the presence of such factor exposures, no further explanation is thought to be necessary, or even possible as it is thought that the factors cannot be further decomposed.

Factors are considered the “atoms” of attribution, the ultimate particles of portfolio performance.

The atom was once believed to be the ultimate particle of matter that could not be split. But its nameAtom (Greek = ‘indivisible’) turned out to be a little premature, as we have known since the late 19th century that the atom can indeed be further decomposed into various sub-atomic particles, providing one has the right equipment to detect them.

Similarly, we can now demonstrate that the relative performance of the various systematic, naïve portfolios mentioned above can be broken down in a decomposition that is deeper than the conventional factor explanation, and what’s more it is universal for all portfolios. It explains why these portfolios really outperform.

Fortunately, it was not necessary to build a new Large Hadron Collider in order to establish this result. A simple experiment using the mathematics of Stochastic Portfolio Theory as the lens with which to examine the results was sufficient.

Decomposing Portfolio Returns

It’s been known since the early 1980s that the long-term growth rate of a portfolio is comprised of two elements: 1) average stock growth rate and 2) excess growth rate. You can see immediately from this decomposition that a portfolio’s growth rate is, remarkably, greater than the average growth of its parts by an amount called the “Excess Growth Rate.”3



The Experiment

The excess growth rates of portfolios can vary a lot depending on their construction and the following experiment illustrates this point. We used the top 1000 U.S. stocks by size from 1964 to 2012.4 We simulated the performance of several systematically-constructed portfolios chosen to be representative of those studied in the literature and then broke the performance down into the two components outlined above.5



Eagle-eyed readers will have noticed that column 1 is not the exact sum of columns 2 and 3. This is due to the inevitable inaccuracies that arise from computing a covariance matrix, required in the calculation of the Excess Growth Rate. These small differences do not change the table’s qualitative conclusion that the Excess Growth Rate explains most of the differences in the portfolios’ returns.


Key Observation: Diversification Matters

The average stock growth rates for all of the portfolios, including the cap-weighted, were extremely similar and did not explain the variation in performance between the portfolios.

The source of most of the variation in the portfolios’ performance is the excess growth rate; this depends only on stocks’ variances and covariances, and is of a similar order of magnitude for the better-diversified portfolios as the stock’s growth rates themselves.

Notice the portfolios that outperformed. All three were more diversified than the cap-weighted portfolio, improving portfolio efficiency. They shared buy-low, sell-high characteristics. The one portfolio that was by design less diversified than the cap-weighted portfolio (Large Cap Overweight) underperforms because it creates buy-high, sell-low trades.

Rebalancing Unlocks the Opportunity

Portfolios do not outperform or underperform because their stocks have inherently higher or lower returns; rather, they are better (or less well-) diversified. Capturing this opportunity requires buy-low, sell-high rebalancing trades.

Rebalancing is vital for preserving the gains from diversification. To keep the compound return high, it’s necessary to redistribute capital away from the previously successful investment to the other investments. The relationship between diversification and rebalancing is symbiotic when it comes to capturing excess growth: you can’t have one without the other.

Learn More

Intech founder, Dr. E Robert Fernholz, members of the current Intech leadership team and Johannes Ruf, PhD, of the London School of Economics recently co-authored a more in-depth paper on this topic, “Diversification, Volatility and Surprising Alpha.” You can access the paper by clicking the image below.

1. E.g. “The Surprising Alpha from Malkiel’s Monkey and Upside-Down Strategies.” Arnott, Hsu, Kalesnik and Tindall. Journal of Portfolio Management (Summer 2013).

2. “Diversification, Volatility, and Surprising Alpha.” Banner, Fernholz, Papathanakos, Ruf and Schofield (2018).

3. For the gory mathematics behind this, see “Diversification, Volatility, and Surprising Alpha.” Banner, Fernholz, Papathanakos, Ruf and Schofield (2018).

4. This time period was chosen to mirror the original experiment.

5. Trading costs were not included; dividends were reinvested.

The information expressed herein is subject to change based on market and other conditions. The views presented are for general informational purposes only and are not intended as investment advice, as an offer or solicitation of an offer to sell or buy, or as an endorsement, recommendation, or sponsorship of any company, security, advisory service, or fund nor do they purport to address the financial objectives or specific investment needs of any individual reader, investor, or organization. This information should not be used as the sole basis for investment decisions. All content is presented by the date(s) published or indicated only, and may be superseded by subsequent market events or other reasons. Although the information contained herein has been obtained from sources believed to be reliable, its accuracy and completeness cannot be guaranteed.

The simulated performance results shown have been compiled solely by Intech, have not been independently verified, and are presented for illustrative purposes only. The simulated results are hypothetical, not real, and have many inherent limitations. They do not reflect the results or risks associated with actual trading or the actual performance of any portfolio, and have been prepared with the benefit of hindsight. Therefore, there is no guarantee that an actual portfolio would have achieved the results shown. In fact, there will be differences between simulated and actual results. No investor should assume that future performance will be profitable, or equal to the results shown.

In no circumstances should the hypothetical results be regarded as a representation, warranty, or prediction that investors will achieve or are likely to achieve the results displayed or that investors will be able to avoid losses. The simulated results reflect the reinvestment of dividends and other earnings, but do not reflect the deduction of advisory fees, trading costs, and other expenses.

Past performance of live and simulated data is no guarantee of future results. Investing involves risk, including fluctuation in value, the possible loss of principal and total loss of investment. There are numerous other factors related to the markets in general or to the implementation of any specific trading strategy, which cannot be fully accounted for in the preparation of simulated performance results, all of which can adversely affect actual trading results.