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
Amongst 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
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 name (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 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.
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 may access the paper 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.
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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.
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