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Evidence Based Investing is Dead. Long LiveEvidence Based Investing! Part 1
September 25, 2017by Adam Butler
Advisor Perspectives welcomes guest contributions. The views presented here do not necessarilyrepresent those of Advisor Perspectives.
Michael Edesess article, The Trend that is Ruining Finance Research, makes the case that financialresearch is flawed. In this two-part article series, I will examine the points that Edesess raised in somedetail. His arguments have some merit. Importantly however, his article fails to undermine the value offinance research in general. Rather, his points serve to highlight that finance is a real profession thatrequires skills, education, and experience that differentiates professionals from laymen.
Edesess case against evidence-based inveesting rests on three general assertions. There is a veryreal issue with using a static t-statistic threshold when the number of independent tests becomes verylarge. Financial research is often conducted with a universe of securities that includes a large numberof micro-cap and nano-cap stocks. These stocks often do not trade regularly, and exhibit largeovernight jumps in prices. They are also illiquid and costly to trade. Third, the regression models usedin most financial research are poorly calibrated to form conclusions on non-stationary financial datawith large outliers.
This article will explore the issues around the latter two challenges. My next article will tackle the p-hacking issue in finance, and propose a framework to help those who embrace evidence-basedinvesting to make judicious decisions based on a more thoughtful interpretation of finance research.
An un-investable investment universe
A large proportion of finance studies perform their analysis with a universe of stocks that is practicallyun-investable for most investors. Thats because they include stocks with very small marketcapitalizations. In fact, the top 1,000 stocks by market capitalization represent over 93% of the totalaggregate market capitalization of all U.S. stocks. This means the bottom 3,000 or so stocks accountfor just 7% of total market capitalization. The median market cap of a stock in the bottom half of themarket capitalization distribution is just over $1billion.
Figure 1. Cumulative proportion of U.S. market capitalization
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Mathematically, only a very small portion of investment capital can be deployed outside the top 1,000or so stocks. Smaller stocks are also much less liquid, with less frequent trading, high bid-ask spreadsand larger overnight volatility. Moreover, these companies tend to trade at low prices, which meanstrading costs are larger for institutions who pay commissions on a per-share basis.
For these reasons, practitioner-oriented studies should include sections on inefficiencies in larger andsmaller companies. And many do. In particular, many of the papers from AQR break down theperformance of anomalies into effects among large (top 30% by market cap), mid (middle 40% bymarket cap) and small (lowest 30% by market cap) companies. The paper The Role of Shorting, FirmSize, and Time on Market Anomalies by Israel and Moskowitz at AQR focused specifically on thistopic. Figure 2 below shows the results for traditional value and momentum factor portfolios for fivedifferent market capitalization buckets from 1926-2011.
Figure 2. Performance of value and momentum factor portfolios conditioned on marketcapitalization
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Source: Israel, R., and T. Moskowitz. The Role of Shorting, Firm Size, and Time on MarketAnomalies. Journal of Financial Economics, Vol. 108, No. 2 (2013)
Many readers may be surprised at the results. The red circles show the long-short factor returns forthe largest 20% of firms by market capitalization. The value factor for the largest capitalization bucketproduced 3.7% excess average annual returns, with a t-stat of just 1.9, which is not quite statisticallysignificant. On the other hand momentum produced 7.49% average annual excess returns with ahighly significant t-stat of 2.95 (more on t-stats below). Regression alphas in green circles were moregrim for large-cap value, with a t-stat of just 1.14, while large-cap momentum has produced over 10%average annual alpha with a very significant t-stat of 4.23 (more on regression below).
The blue circles in Figure 2 examine whether the difference in factor alphas between the lowest andhighest market capitalization buckets are statistically significant. The value factor produced over 10%greater average annual alpha in the smallest capitalization stocks than in large-cap stocks. This is ahighly statistically significant effect, with a t-statistic of 3.21 (top blue circle). In contrast, the differencein alphas between the lowest and highest capitalization buckets was relatively small (2.88%) andinsignificant (t-stat = 1.31) for the momentum factor.
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The analysis in Figure 2 did not account for trading frictions. After accounting for the cost of liquidity,which might be substantial for small-cap stocks, but inconsequential for large-cap stocks, the gapbetween large- and small-cap factor performance would almost certainly close, perhaps significantly. Inaddition, those practitioners who are fond of small- or mid-cap value should feel well validated, asvalue-factor performance is strong and significant for every market capitalization quintile other than thelargest cap stocks.
Investors must be aware of the practical implications of the universe chosen for investment research.Practitioners should focus on observed effects among mid- and large-capitalization stocks, whereresults align more closely with academic findings.
Regression is a blunt tool
Researchers in empirical finance use linear regression to determine whether, and to what extent, aneffect that they are investigating is already explained by previously documented effects. For example,academics use linear regression to determine how well a factor model explains differences in thecross-section of securities prices. Researchers in search of novel return premia use linear regressionto determine how much value a newly proposed factor adds above what is explained by already well-known factors. Advisors, consultants and investors use regression to determine if an active investmentproduct or strategy has delivered significant excess risk-adjusted performance, above what they couldachieve through inexpensive exposure to factor products.
Unfortunately, linear regression is a very blunt tool when it comes to dealing with complex financialdata. The following example will highlight one important reason why. I poached this example from LarrySwedroe's great book, Reducing the Risk of Black Swans (update forthcoming), because it is soperfect and surprising.
Consider two strategies A and B, and their returns over a 10-year period. Their return series is depictedin the table below.
StrategyYear 1Year 2Year 3Year 4Year 5Year 6Year 7Year 8Year 9Year 10
A 12% 8% 12% 8% 12% 8% 12% 8% 12% 8%
B 8% 12% 8% 12% 8% 12% 8% 12% 8% 12%
Both strategies have an annual average return of 10%. Whenever As return is above its average of10%, Bs return is below its average of 10%. And whenever As return is below its average of 10, Bsreturn is above its average of 10%. Thus, regressing strategy As returns on strategy Bs returns overthis period will conclude that they are negatively correlated. Note that they are negatively correlatedeven though they both always produced positive returns.
Now imagine that the same strategies produced the following returns in a different 10-year period.
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StrategyYear 1Year 2Year 3Year 4Year 5Year 6Year 7Year 8Year 9Year 10
A 2 -2 2 -2 2 -2 2 -2 2 -2
B -2 2 -2 2 -2 2 -2 2 -2 2
Over this period, the same strategies have an average annual return of 0%. Perhaps the styles wentout of favor. However, whenever As return is above its average of 0%, Bs return is below its averageof zero. And whenever As return is below its average of 0%, Bs return is above its average of zero.Thus, regressing A on B will render the conclusion that they are negatively correlated.
Now lets string together the two 10-year periods so that we have a 20-year period. Thus, the returnseries looks like this:
Asset A: 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2.
Asset B: 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2.
Recall that both A and B had average returns in the first 10 years of 10%, and average returns of 0%inthe second 10 years. Thus, their average return for the full 20 years in both cases is 5%. Now: Are Aand B positively or negatively correlated?
A closer inspection reveals that, over the full 20-year period whenever As return was above its averageof 5%, Bs return was also above its average of 5%. And whenever As return was below its average of5%, Bs return was also below its average of 5%. Thus, we see that despite the fact that A and B werenegatively correlated over each of the two 10-year periods independently, over the full 20-year periodthey were positively correlated.
This example highlights an omnipresent but rarely discussed challenge with financial time-series.Specifically, that the measured relationship between variables will almost always change dramaticallyacross time. This effect is not isolated to observations over two distinct periods o