The second AGNOSTIC Paper on agnostic fundamental analysis.1Two times “agnostic” in one sentence, isn’t this lyrically brilliant? As promised last week, this is the international out-of-sample test where the authors apply their methodology to stock markets around the world.
- Part 1: Agnostic Fundamental Analysis in the US
- Part 2: Agnostic Fundamental Analysis around the World
- Part 3: Agnostic Fundamental Analysis with Modern Statistical Tools
Since the methodology is indeed almost identical, I will not cover it again and rather focus on the international sample and the results. I therefore recommend to read this series chronologically and to start with last week’s post.
Everything that follows is only my summary of the original paper. So unless indicated otherwise, all tables and charts belong to the authors of the paper and I am just quoting them. The authors deserve full credit for creating this material, so please always cite the original source.
Data and Methodology
The international sample consists of 25,731 stocks from 36 countries and ranges from April 1993 to September 2016. Most of the firms come from the US (9,112) and Japan (4,249). Other “large” countries are Korea (7% of firms), China (6%), and France (5%). As you can see from these names, the sample covers both developed and emerging markets. In addition to that, the sample period is four years longer than in the original US study. Thereby, the authors not only tests their methodology in other geographies but also beyond the original sample period.
The authors get their data from Datastream and Worldscope, two high-quality databases. Similar to the methodology in the US-paper, they exclude the Financial Services industry and all companies with a stock price below $5. The authors also explicitly mention that their database is free from survivorship, backfill, restatement, and look-ahead bias. This is of course very important and the authors achieve this with quite conservative assumptions. For example, they use annual fundamentals to avoid hypothetical trading on information that wasn’t available at the respective point in time.
Except for some minor adjustments due to data availability, the agnostic fundamental analysis is essentially similar to the US paper. The authors use 21 variables from the balance sheet, income statement, and cash-flow statement to explain the market capitalization of firms at the end of each month.2This is slightly less than in the US paper where they use 28. The fitted values of these regressions are again the peer implied fundamental values. The percentage deviation between the current market capitalization and this estimated “fair” value represents the mispricing signal for each stock.
A further detail worth mentioning is that the authors run those regressions separately within each country. Although it appears reasonable, this assumption is actually not that clear. On the one hand, stocks compete globally for investors’ money3If I don’t find an attractive US stock but one in Japan, why should I go with the less attractive US stock if I don’t have to? and fundamental analysts typically consider global peers when evaluating stocks. On the other hand, each country has its particularities and the current tastes of investors may be different across countries. In addition to that, accounting standards differ between countries and a Chinese balance sheet is probably not directly comparable with an American one. From this perspective, it makes sense to look at each country separately.
Similar to last week, the absolute values of the mispricing signal are not really meaningful and the authors again just use them to sort stocks into quintiles. The table above presents summary statistics about some characteristics for each quintile across different regions. Within both the United States and World (excl. U.S.), undervalued companies tend to be smaller, have lower betas, and score worse on momentum. The absolute numbers are of course slightly different but overall, these results go into a very similar direction.
Important Results and Takeaways
Undervalued stocks outperformed overvalued stocks – also globally
Similar to last week, I will start with statistics on “raw” returns. The following table presents monthly averages for the quintile portfolios across different regions. Starting with the United States, the results are considerably weaker than in the original study. The average return spread (Q5-Q1 Undervalued-Overvalued) decreased to 0.2606% for equal-weighted and to 0.2255% for value-weighted portfolios. The authors don’t comment on it specifically but I suspect that this is because the different sample period of the two papers. Also note that the monthly difference is not even statistically significant for the United States in this paper. While this is unsatisfying for investors, it is very consistent with the idea that strategies tend to perform worse after they have been discovered and published.4This is the so called “alpha decay”. For more details, check the well-known McLean & Pontiff (2016) paper.
Globally and within other regions, however, there is a clear pattern that undervalued stocks outperformed overvalued ones. Depending on the region and weighting-scheme, monthly return spreads reach up to 1.23% (Emerging). Also note that the outperformance is quite consistent over time as undervalued stocks outperformed more than 50% of the time in most regions (sometimes even beyond 60%). Finally, the more sophisticated Theil-Sen regression estimator (final column TS) generated again better results than the simple linear regression within most regions.
Overall, I believe these results are quite reliable out-of-sample evidence for the simple agnostic fundamental analysis. Performance patterns are in-line with the idea of a convergence between price and estimated “fair” values, the return spreads between under and overvalued stocks are sizable, and the results are quite consistent around the globe. In addition to that, the table also reports average returns for all stocks within a region, i.e. the respective equal and value-weighted market portfolio. Remarkably, the Q5 Undervalued portfolio had higher monthly returns than the overall market within all regions. This suggests that agnostic fundamental analysis also “worked” for long-only investors.
Agnostic fundamental analysis yielded significant alpha – globally and against up to 80 factors
As in the US-paper, the authors also benchmark the international portfolios against well-known factor models. The following table shows monthly alphas for equal and value-weighted quintile portfolios across different regions. Depending on the specification, the factor models consider up to 80 known return predictors. So this is really a comprehensive test and way beyond the commonly used benchmarks.
Given that this table contains even more numbers than the previous one, I will again focus on the big picture. Equal-weighted long-short portfolios (Q5-Q1) mostly exhibit statistically significant alpha. Depending on the specific region, the magnitude ranges from 0.2% to more than 1% per month. Those are sizable risk-adjusted returns for a portfolio with almost zero correlation to equity markets. The pattern is even stronger for the more sophisticated Theil-Sen (TS) regression which is less sensitive with respect to outliers. So similar to last week, better methodology appears to be compensated.
For value-weighted portfolio, the results are not as clear and alphas tend to be smaller and less significant. This suggests that the strategy works better with small and mid caps as those stocks receive higher weights in equal-weighted portfolios. With the more sophisticated Theil-Sen methodology, however, alphas for the long-short portfolios are again sizable and mostly statistically significant.
Agnostic fundamental analysis remains profitable after transaction costs
To test if their agnostic fundamental analysis survives in more realistic settings, the authors also look at after-cost performance.5This is a new analysis of the international follow-up and they haven’t done this in the US-paper. They obtain data about commissions, fees, and market impact for each country from Elkins McSherry LLC, a trading-cost consulting firm. They also introduce a Buy-and-Hold version of the strategy with lower turnover and slower rebalancing to mitigate trading costs.6The Buy-and-Hold portfolios are constructed as follows: each month, the authors create a quintile portfolio that remains unchanged for 12 months. The final quintile portfolio is then the average of all overlapping portfolios in the respective month.
The first observation is that monthly rebalancing comes (unsurprisingly) with substantially higher transaction costs. For example, the monthly rebalanced World Q5-Q1 portfolio generated transaction costs of about 0.26% per month. The Buy-and-Hold strategy, in contrast, only comes with costs of about 0.05% per month. This is a substantial reduction of almost 80%.
The second observation is that although net alphas of the long-short portfolio remain positive in all regions except Europe, their magnitude is considerably smaller. So transaction costs are definitely an issue. However, the slower rebalancing of the Buy-and-Hold version appears to be effective. Depending on the region, the long-short Buy-and-Hold portfolios still generated monthly alphas of up to 0.7% after estimated costs. This is quite comparable to the gross-alphas in the previous table. The results therefore suggest that agnostic fundamental analysis remains profitable after costs if the right real-world adjustments are made.
Unfortunately, however, this analysis comes with one important limitation. The authors explain that the trading cost estimates don’t include the cost (and potential impossibility) of shorting. So we unfortunately cannot evaluate if it was indeed possible to (profitably) implement the long-short portfolios in practice.7Shorting is generally more difficult than going long (buying) because you need to find someone who borrows you a share to sell short for an adequate fee. Depending on the situation (remember GameStop in 2021), this is not always possible. Since the net alphas of the long-only Q5 portfolios are considerably smaller than those of the long-short Q5-Q1 portfolios, this remains unfortunately an open issue.
The degree of market efficiency differs around the world
Apart from validating the results of the original US-study, the actual purpose and idea of this week’s paper is to quantify the degree of market efficiency in stock markets around the world. The idea is simple: the better agnostic fundamental analysis “works” (i.e. the higher the alpha), the less efficient the market. The authors devote an entire section to this idea and examine it in much more detail than I will do here.
The bottom line, however, is quite intuitive. Pre-cost alphas tend to be higher in countries with higher transaction costs, indicating that those markets are indeed less efficient. The authors also stress-test this result by looking at other frictions like short-sale bans and find similar results. Following this argument, the authors mention that markets in Emerging countries and Asia-Pacific tend to be less efficient.
Although, I kept this part rather short, the implications for investors are very important. There is a saying in Poker that in order to win, you don’t need to be the best player but you must pick the easiest table. This also applies to investing. Stock markets are fairly efficient and to outperform in a very competitive space like US large caps, you need to bring a lot to the table (become the best player). In contrast, it is probably less difficult to outperform in a less competitive segment like Emerging markets or small caps.8I deliberately use the term “less difficult” because generating outperformance is never “easy”… The results of the paper are in line with this idea and I think that is quite encouraging.
Conclusions and Further Ideas
I know, there are unfortunately no intuitive charts and graphics in this post-series but only painful tables with a lot of numbers. What is important, however, is that the international numbers point in the same direction as the numbers from the original US-paper. Depending on the region, the agnostic fundamental analysis strategy “worked” even better than in the US, so this is strong out-of-sample evidence. The authors analyzed virtually all tradable stocks so there is not much more one can look at. They also test the returns of their portfolios against up to 80 known factors which is way beyond commonly used benchmarks. So overall, this looks all quite robust and suggests that even very simply forms of fundamental analysis were historically sufficient to generate alpha. On the other hand, the lower out-of-sample alphas for the US also show that the strategy probably doesn’t last forever and requires continuous improvement.
This brings us, once again, to the very simple agnostic valuation methodology. Please note that this is not a critique to the authors. They use basic linear and the more robust Theil-Sen regression to provide a transparent and replicatable academic methodology. There is nothing wrong with that, but as I mentioned several times, the more sophisticated Theil-Sen methodology yielded much better results, probably because it better deals with outliers. So in-line with the idea of competitive markets, more sophisticated methodology appeared to be compensated. The final part of this series will therefore examine a more advanced form of agnostic valuation based on state-of-the-art machine learning models. But more on that next week.
- AgPa #72: Machine-Reading of Private Equity Prospectuses
- AgPa #71: Go Where the Earnings (per Share) Are
- AgPa #70: Equal vs. Market Cap Weights
- AgPa #69: Rebalancing Luck
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|1||Two times “agnostic” in one sentence, isn’t this lyrically brilliant?|
|2||This is slightly less than in the US paper where they use 28.|
|3||If I don’t find an attractive US stock but one in Japan, why should I go with the less attractive US stock if I don’t have to?|
|4||This is the so called “alpha decay”. For more details, check the well-known McLean & Pontiff (2016) paper.|
|5||This is a new analysis of the international follow-up and they haven’t done this in the US-paper.|
|6||The Buy-and-Hold portfolios are constructed as follows: each month, the authors create a quintile portfolio that remains unchanged for 12 months. The final quintile portfolio is then the average of all overlapping portfolios in the respective month.|
|7||Shorting is generally more difficult than going long (buying) because you need to find someone who borrows you a share to sell short for an adequate fee. Depending on the situation (remember GameStop in 2021), this is not always possible.|
|8||I deliberately use the term “less difficult” because generating outperformance is never “easy”…|