19/12/16: Market Anomalies and Data Mining: Some Pretty Tough Love from Data

Investment anomalies (or in other words efficacy of exogenous factors in determining abnormal returns to investment) are a matter of puzzle for traditional investment analysis. In basic terms, we normally think about the investment as an undertaking that offers no ‘free lunch’ - if markets are liquid, deep and, once we control for risk factors, taxes and transaction costs, an average investor cannot expect to earn an above-market return. Put differently, there should be no ways to systematically (luck omitting) beat the market.

Anomalies represent the case where some factors do, in fact, generate such abnormal returns. There is a range of classic anomalies, most commonly known ones being Small Firms Outperform, January Effect, Low Book Value, Under-dogs or Discounted Assets or Dogs of the Dow, Reversals, Days of the Week, etc. In fact, there is an entire analytics industry built around markets that does one thing: mine for factors that can give investors a leg up on competition, or finding anomalies.

One recent paper have identified a list of some 314 factors that were found - in the literature - to generate abnormal returns. As noted by John Cochrane: “We thought 100% of the cross-sectional variation in expected returns came from the CAPM, now we think that’s about zero and a zoo of new factors describes the cross section.”

A recent paper published by NBER and authored by Juhani Linnainmaa and Michael Roberts (see link below) effectively tests this Cochrane’s proposition. To do this, the authors “examine cross-sectional anomalies in stock returns using hand-collected accounting data extending back to the start of the 20th century. Specifically, we investigate three potential explanations for these anomalies: unmodeled risk, mispricing, and data-snooping.” In other words, the authors look into three reasons as to why anomalies can exist:

1. Unmodeled risk reflects the view that some of risk premium paid out in the form of investment returns is not captured by traditional models of risk-return relations;
2. Mispricing reflects the view that markets’ participants routinely and over long run can misplace risk; and
3. Data-snooping view implies that anomalies generate returns in the historical data that do not replicate in forward-looking implementation because these anomalies basically arise from ad hoc empirical data mining.

The authors argue that “each of these explanations generate different testable implications across three eras encompassed by our data: (1) pre-sample data existing before the discovery of the anomaly, (2) in-sample data used to identify the anomaly, and (3) post-sample data accumulating after identification of the anomaly.”

In their first set of tests, the authors focus on profitability and investment factors, because prior literature shown that “these factors, in concert with the market and size factors, capture much of the cross-sectional variation in stock returns.”

Finding 1: the authors “find no statistically reliable premiums on the profitability and investment factors in the pre-1963 sample period… Between 1963 and 2014, these factors average” statistically and financially significant returns on average of “30 and 25 basis points per month, respectively.”

Finding 2: “The attenuations of the investment and profitability premiums in the pre-1963 data are representative of most of the other 33 anomalies that we examine. Just eight out of the 36 (investment, profitability, value, and 33 others) earn average returns that are positive and statistically significant at the 5% level in the pre-1963 period.

Finding 3: All of the measures of abnormal returns used in the study generate premiums that “decrease sharply and statistically significantly when we move out of the original study’s sample period by going either backward or forward in time.” In other words, anomalies tend to disappear or weaken every time the authors significantly broaden time horizon beyond that which corresponds to the time horizon used in the original study that uncovered such an anomaly.

As authors note, “these findings are consistent with data-snooping as the anomalies are clearly sensitive to the choice of sample period."

How? "...If the anomalies are a consequence of multidimensional risk that is not accurately accounted for by the empirical model (i.e., unmodeled risk), then we would have expected them to be similar across periods, absent structural breaks in the risks that matter to investors. Similarly, if the anomalies are a consequence of mispricing, then we would have expected them to be larger during the pre-discovery sample period when limits to arbitrage, such as transaction costs, were greater.”

But there is a note of caution due. “Our results do not suggest that all return anomalies are spurious. The average in-sample anomaly earns a CAPM alpha of 32 basis points per month (t-value = 10.87). The average alpha is 13 basis points (t-value = 4.42) per month for the pre-discovery sample and 14 basis points (t-value = 4.06) for the post-discovery sample. Although these estimates lie far below the in-sample numbers, they are highly statistically significant.”

The kicker is that “investors, however, face the uncertainty of not knowing which anomalies are real and which are spurious [or due to data mining], and so they need to treat them with caution. …because data-mining bias affects many facets of returns—averages, volatilities, and correlations—it is best to test asset pricing models out of sample," or absent such opportunity (perhaps due to tight data) - by selecting a model / factor that "is able to explain half of the in-sample alpha".




Full paper: Linnainmaa, Juhani T. and Roberts, Michael R., The History of the Cross Section of Stock Returns (December 2016). NBER Working Paper No. w22894. https://ssrn.com/abstract=2880332

14/2/2014: Buffett's Alpha Demystified... or not?

Warren Buffett is probably the most legendary of all investors and his Berkshire Hathaway, despite numerous statements by Buffett explaining his investment philosophy, is still shrouded in a veil of mystery and magic.

The more you wonder about Buffett's fantastic historical track record, the more you ask whether the returns he amassed are a matter of luck, skill, unique strategy or all of the above.

"Buffett’s Alpha" by Andrea Frazzini, David Kabiller, and Lasse H. Pedersen (NBER Working Paper 19681 http://www.nber.org/papers/w19681, November 2013) shows that "looking at all U.S. stocks from 1926 to 2011 that have been traded for more than 30 years, …Berkshire Hathaway has the highest Sharpe ratio among all. Similarly, Buffett has a higher Sharpe ratio than all U.S. mutual funds that have been around for more than 30 years." In fact, for the period 1976-2011, Berkshire Hathaway realized Sharpe ratio stands at impressive 0.76, and "Berkshire has a significant alpha to traditional risk factors." According to the authors, "adjusting for the market exposure, Buffett’s information ratio is even lower, 0.66. This Sharpe ratio reflects high average returns, but also significant risk and periods of losses and significant drawdowns."

According to authors, this begs a question: "If his Sharpe ratio is very good but not super-human, then how did Buffett become among the richest in the world?"

The study looks at Buffett's performance and finds that "The answer is that Buffett has boosted his returns by using leverage, and that he has stuck to a good strategy for a very long time period, surviving rough periods where others might have been forced into a fire sale or a career shift. We estimate that Buffett applies a leverage of about 1.6-to-1, boosting both his risk and excess return in that proportion."

The conclusion is that "his many accomplishments include having the conviction, wherewithal, and skill to operate with leverage and significant risk over a number of decades."


But the above still leaves open a key question: "How does Buffett pick stocks to achieve this attractive return stream that can be leveraged?"

The authors "…identify several general features of his portfolio: He buys stocks that are
-- “safe” (with low beta and low volatility),
-- “cheap” (i.e., value stocks with low price-to-book ratios), and
-- high-quality (meaning stocks that profitable, stable, growing, and with high payout ratios).
This statistical finding is certainly consistent with Graham and Dodd (1934) and Buffett’s writings, e.g.: "Whether we’re talking about socks or stocks, I like buying quality merchandise when it is marked down"  – Warren Buffett, Berkshire Hathaway Inc., Annual Report, 2008."


Of course, such a strategy is not novel and Ben Graham's original factors for selection are very much in line with it, let alone more sophisticated screening factors. Everyone knows (whether they act on this knowledge or not is a different matter altogether) that low risk, cheap, and high quality stocks "tend to perform well in general, not just the ones that Buffett buys. Hence, perhaps these characteristics can explain Buffett’s investment? Or, is his performance driven by an idiosyncratic Buffett skill that cannot be quantified?"

The authors look at these questions as well. "The standard academic factors that capture the market, size, value, and momentum premia cannot explain Buffett’s performance so his success has to date been a mystery (Martin and Puthenpurackal (2008)). Given Buffett’s tendency to buy stocks with low return risk and low fundamental risk, we further adjust his performance for the Betting-Against-Beta (BAB) factor of Frazzini and Pedersen (2013) and the Quality Minus Junk (QMJ) factor of Asness, Frazzini, and Pedersen (2013)."

And then 'Eureka!': "We find that accounting for these factors explains a large part of Buffett's performance. In other words, accounting for the general tendency of high-quality, safe, and cheap stocks to outperform can explain much of Buffett’s performance and controlling for these factors makes Buffett’s alpha statistically insignificant… Buffett’s genius thus appears to be at least partly in recognizing early on, implicitly or explicitly, that these factors work, applying leverage without ever having to fire sale, and sticking to his principles. Perhaps this is what he means by his modest comment: "Ben Graham taught me 45 years ago that in investing it is not necessary to do extraordinary things to get extraordinary results." – Warren Buffett, Berkshire Hathaway Inc., Annual Report, 1994."


There is more to be asked about Warren Buffett's investment style and strategy. "…we consider whether Buffett’s skill is due to his ability to buy the right stocks versus his ability as a CEO. Said differently, is Buffett mainly an investor or a manager?"

Authors oblige: "To address this, we decompose Berkshire’s returns into a part due to investments in publicly traded stocks and another part due to private companies run within Berkshire. The idea is that the return of the public stocks is mainly driven by Buffett’s stock selection skill, whereas the private companies could also have a larger element of management."

Another 'Eureka!' moment beckons: "We find that both public and private companies contribute to Buffett’s performance, but the portfolio of public stocks performs the best, suggesting that Buffett’s skill is mostly in stock selection. Why then does Buffett rely heavily on private companies as well, including insurance and reinsurance businesses? One reason might be that this structure provides a steady source of financing, allowing him to leverage his stock selection ability. Indeed, we find that 36% of Buffett’s liabilities consist of insurance float with an average cost below the T-Bill rate.


So core conclusions on Buffett's genius: "In summary, we find that Buffett has developed a unique access to leverage that he has invested in safe, high-quality, cheap stocks and that these key characteristics can largely explain his impressive performance. Buffett’s unique access to leverage is consistent with the idea that he can earn BAB returns driven by other investors’ leverage constraints. Further, both value and quality predict returns and both are needed to explain Buffett’s performance. Buffett’s performance appears not to be luck, but an expression that value and quality investing can be implemented in an actual portfolio (although, of course, not by all investors who must collectively hold the market)."

Awesome study!