CHIMERICA AND EXPECTED RETURN OF US STOCKS
Jasmine Z. Yu† ‡ EDHEC Business School Nice, France
November 2017
* I thank Professor Abraham Lioui and Professor Rene Gracia, both are professors at the Finance, Law and Accounting Department of EDHEC Business School for their dissertation advice. I also thank Professor Stefano Marmi of Scuola Normale Superiore (SNS) for factor data made available on his website and Tracy Wu from China Stock Market & Accounting Research (CSMAR) for annual report information. Jasmine Z. Yu is PhD in Finance Candidate at EDHEC Business School. The author’s correspondence is, email: [email protected]. Address: EDHEC Business School, 393, Promenade des Anglais BP3116 06202 Nice cedex 3 – France. Phone: + 1 646 338 8638.
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CHIMERICA AND EXPECTED RETURN OF US STOCKS
Abstract
This paper develops a scorecard to proxy for “Chimerica” and to measure the anomalous return associated with US firms’ overseas expansion in Greater China. Based upon ‘Chimerica’, the symbiotic relation between the People’s Republic of China and the United States of America, this paper uses a variety of approaches, some of which return-based such as regression analysis and Fama MacBeth estimation while others, fundamental- based such as Claus/Thomas earnings analysis, and illustrates little success in proving that the US stock market has actually rewarded companies for doing business in China. The Chimerica premium was about 0.43% per annum from 2006 to 2010. Sector portfolios based on forward-looking analyst forecasts could deliver more dramatic Chimerica premium at 1-2%. However, results are mixed and not always consistent across approaches, especially after advanced econometric modelling and testing. Down-market protection seems to stand out though, for the higher Chimerica-scored companies and proves the benefit for global diversification of revenue streams in periods of market stress.
Keywords: Chimerica, multi-factor model, abnormal earnings, and Fama-Macbeth method, model misspecification, model specification test
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1 Introduction
The holy grail in investment management is all about consistently outperforming the capitalization-weighted market benchmarks. Practitioners have long been implementing investment strategies grounded in academic research. But active management is a zero- sum game, i.e. aggregate outperformance and underperformance cross out. If everyone is reading the same award-winning academic research and following the same investment strategies, why not everyone outperforms? The most renowned academic research in finding cross sectional predictability in stock returns probably belongs to Fama and French (1992) who found the three factors, market, size and book-value-to-market (B/M) capture the variation in average stock returns. Cahart (1997) subsequently discovered the price momentum factor while Fama and French (2015) illuminated firm profitability and investment pattern are factors that also drive stock returns. Other firm-characteristics-based and market-based factors, include liquidity (Acharya and Pedersen, 2005, and Ibbotson 2013) have been found by academic researchers. And now these factors have inundated the field of smart beta investing. Composite trading strategies —going long high-expected-return stocks and short low-expected-return stocks are devised to take advantage of some of the findings. However, results have been mixed. Lewellen (2015) found that many of the factors had turned out to be insignificant predictors of return after testing 15 characteristic-based factors. Other researchers (Hou et al., 2017) used a large data library of 447 anomalies to test and only found 286 (64%) anomalies insignificant at the 5% level. Imposing the t- cutoff of three raises the number of insignificance to 380 (85%). The explanations that researcher gave oftentimes have to do with increased ease of trading and improved market micro-structure. For example, Chordier et al. (2014) found that increased liquidity and trading activity associated with attenuation of prominent equity return anomalies due to increased arbitrage. Average returns based on prominent anomalies halved after
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decimalization. Policies that stimulate liquidity and reduce trading cost improve capital market efficiency. My paper belongs to the strand of research that strives to identify anomalies or factors that predict returns. Unlike other pure firm-based characteristics, the anomaly I try to explain has a macro bent and is inspired by a set of profound geopolitical and socioeconomic influences that are the most prevalent in the last decade. The influences that gave rise to the factor will undoubtedly rise and fall with the changes in the macro environment, such as government policies leading to prosperity, war or peace. That’s what makes investing so interesting because it’s dynamic – what worked in the past may or may not work in the future. Of course, any new anomaly found should be subject to rigorous econometric testing held to the highest standard. Chimerica is a new word coined by historian Niall Ferguson and economist Moritz Schularick (2007) In the article ‘Chimerica” and the Global Asset Market Boom published in International Finance, they described the following relationship - cheap exports by Chinese companies to America allow the Chinese to accumulate large currency reserves that are channelled into purchasing U.S. government securities, which have kept nominal and real long-term interest rates artificially low in the United States. At the same time, China’s provision of cheap labour and the United States’ spending in foreign direct investment have allowed American companies to reinvent themselves by selling to Chinese consumers (Ferguson 2008). This paper seeks to prove that the US equity market recognizes the Chimerica factor1 but does not necessarily always price those American companies possessing higher China exposure with higher stock price. Lower expected returns provide insurance against bad times. In the investment community, there has long been the notion that in order to escape from the slow growth of the developed markets and to benefit from emerging markets’ phenomenal growth, an investor may not need to chase the very volatile emerging markets stocks but should consider instead select exposure to global companies
1 Chimerica factor and China exposure are used synonymously in this paper.
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who are well positioned to capture labour participation and rising consumer spending in developing countries and should expect to be handsomely rewarded by the capital markets (Sterling, 2010). Indeed, rather than confining our thinking and research to nation-state boundaries, nowadays we need to consider the implications of globalization, a new but ubiquitous macroeconomic phenomenon which has existed since the beginning of the 1990’s. The emergence of the developing economies has posed the challenging question whether they have made developed equities more attractive or instead they have crowded out and diverted limited capital for investment. Therefore, the input for analysis needs to be expanded beyond the traditional standalone national statistics. The case study in this paper is “Chimerica” – the two countries which some believe are becoming more like a single economic entity. Their unique relationship has become the axis of the world economy – everything from interest rates to inflation to the global imbalances in trade and finances (Karabell, 2009). In more recent years, Ferguson (2015) argued that the 2008 Global Financial crisis didn’t lead to a Sino-American divorce, despite mutual accusations of monetary manipulation. Instead, like any couple who spend long enough in each other’s company, the Chimericans grew ever more alike. China took steps to make its economy less state-led and export-driven, and more market-led and consumption- driven. China’s economy became dangerously reliant on easy money and mounting debt, and prone to bubbles, beginning with urban real estate. Given the ‘Chimerica’ macro picture, I strive to examine its impact at the micro firm level and see if this macro factor has translated into being an anomaly that global investors can exploit. I selected 100 largest US companies that were perceived to be the most “global” to test the concept of Chimerica. I analyzed these companies’ historical returns in the period between 2006 and 2010 and researched their annual reports in order to understand at the firm level, how these companies may have interacted with China. In order to implement these methodologies, I develop a “scientific” scorecard approach to consistently evaluate a US company’s extent to which their business is
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exposed to Greater China, i.e. the mainland, Hong Kong, Macau and Taiwan. The scorecard uses a point system that considers the Chinese elements reflected in the American company’s publicly available financial disclosures, for example, revenue, cost, SG&A expense, operating and investing cash flows, etc. These US companies are then ranked in accordance to their overall scores. Inspired by factor and style investing, I tried to approximate the Chimerca factor by subtracting returns of the high Chimerica scored company from returns of the low Chimerica scored companies. Then I used a range of techniques that includes basic characteristic sorting, regression analysis, Fama Macbetch estimation to advanced econometrics for statistical testing. Besides historical returns, I also focused on company fundamentals and made good use of a large quantity of stock analyst forecasts to arrive at a forward-looking view in understanding the efficacy of the Chimerica factor. Since the identification and articulation of major investment styles by William Sharpe (1978), investment style analysis has gone beyond the realms of active vs. passive management and techniques of market timing vs. security selection. Investment Style Analysis (Ibbostson and Kim, 2012) and Claus/Thomas (CT hereafter, 2001) are used to test Chimerica as an anomaly, in addition to the well-known market, size and value factors (Fama and French, 1992, 2008). Pioneered by William F. Shapre (Fama and Macbeth, 1973) , benchmark style cross-sectional analysis is historical return-based. It primarily utilizes portfolio sorts and ordinary least squares and general least squares regressions which focus on portfolio characteristics. Claus/Thomas approach is fundamental-based utilizing analyst earnings and growth estimates. This approach projects individual stock return using current market price and analysts’ quarterly earnings forecasts which are arrived from company-specific qualitative and quantitative variables known today. Consistent results drawn from combining returns-based and fundamental-based methodologies are intending to make the conclusion in this paper more robust. Fama Macbeth procedure ignores the estimation errors in betas, advanced econometrics around extensions to the traditional beta pricing models are applied,
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including allowing for serial correlation in the underlying market factors and adjusting for small sample bias (Shanken, 1992), using t-statistic that incorporates asymptotic distributions under model misspecification (Jagannnathan and Wang, 1998), comparison of the OLS and the GLS estimators, though GLS is often more precise but also biased (Shanken, Zhou, 2007), and employing the sample cross-sectional regression (CSR) R2 as a measure of model performance versus the typical adjusted R2 (Kan, Robotti and Shanken, 2013). Also, a t-statistic of 3.0 is being applied as Chimerica is observed purely on an empirical basis and thus requires a higher hurdle to clear (Harvey & Liu, 2016). Harvey’s and Liu’s method of purging out systematic factor risks and allowing for the possibility of time-series and cross-sectional dependence is also followed. The technique accommodates a wide range of test statistics and can be used for both asset pricing tests based on portfolio sorts as well as tests using individual asset returns. I have found that the premium associated with the Chimerica factor was around 43 bps per annum on a historical basis through back-testing. The Chimerica factor could potentially enhance return. And this is positive. However, the more China-exposed American companies tended to withstand down markets better. There’s a varying degree of success in statistical testing of the Chimerica factor, generally with sorting technique outperforming regression techniques and forward-looking quartile and sector portfolios having demonstrated success. On a fundamental forward-looking basis, the impact of Chimerica was felt strongest in the sector portfolio construction, with an average 1-2% premium on an annual basis. The rest of the paper is organized as follows. Section 2 Scorecard and Data introduces how I build the scorecard, stock universe, time period chosen and the key results revealed by the scorecard. Section 3.1 focuses on return differences of the US stocks ranked into four quartiles based on size, style and Chimerica scores. Equal- weighted quartile and half portfolios are formed to analyze risk and return characteristics of Chimerica scorecard, size and value/growth styles. It is revealing that stocks of highly scored companies tended to do well during the 2007-2008 US stock market downturn in
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the midst of the Global Financial Crisis. Section 3.2 Chimerica factor is formally identified by having returns of highly scored (i.e. first quartile) stocks subtracted from returns of lowly scored (4th quartile) stocks. This factor is then used as an independent variable in the CAPM and Fama-french 3-factor frameworks to test for statistical significance. Returns of 10 Chimerica-scored portfolios and 10 industry/sector portfolios are regressed against Fama-French three factors and the Chimerica factor. Section 3.3 Fama Macbeth Estimation is used to test if Chimerica drives portfolio returns and also attempts to price how much return we would expect to receive for a particular beta exposure to the Chimerica factor. Various advanced and innovative econometrics methods are applied to illuminate the efficacy of the Chimerica factor. Section 3.4 Systematic factor returns as expressed in Fama-French three factors are purged from Chimerica so the study the Chimerica factor as a standalone factor. Portfolios are purged from traditional factors and regressed on Chimerica or Chimerica itself purged from other factors. Section 4 Thomas/Claus methodology produces expected returns by stock analyst. It also tests the significance of the long/short portfolio forecast returns and long/short GICS sector portfolio forecast returns. Section 5 Conclusion summarizes research findings and highlights direction for future research relating to the subject.
2 Scorecard and Data
The sample for this research is the 100 largest US companies in terms of market capitalization, i.e. constituents of the S&P 100 index (Bloomberg Ticker: OEX Index). This seems to be an appropriate sample representing the largest American enterprises that are likely to have the willingness and resources to do business aboard. Their disclosures and corporate governance are among the highest quality and at the same time, their stocks are also the most liquid and widely held. Index constituents from June 2004 to June 2010 were picked up and six years of data were compiled for the analysis of this paper.
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The starting point was to develop a systematic approach to measure how a US stock is exposed to China. I define China exposure as US company generating revenue through sales activities in China, and/or generating profit through investing activities in China, and/or just having prospecting activities in China. It includes activities primarily on Chinese mainland but due to increasing economic integration, it also includes Taiwan and Hong Kong in the analysis of certain companies depending where these companies’ China headquarters and activities are based. A scorecard containing 15 elements of operational and strategic significance is devised to measure the exposure at the company level. Take Intel Corporation (ticker: INTC) in 2010 as an example. Intel was scored on the below elements with 1 or 0 to represent binary yes/no answers except for sales estimates which are in percentage terms. Intel’s total score in 2010 was 14. Disclose Sales % of Growth Source Ticker S&D Sales/ R&D Manufacture Estimate Total Market Material Profitability INTC 1 1 1 1 1 1 1 1
> 500 Chinese >5 AR Total Hire Invest Location Sub/JV Cont'd Employees Yrs Disclosure >3 Score INTC 1 1 1 1 1 0 1 14
Scorecard Definition: 1 Sales and distribution. Company has this sales and distribution activity in China
2 Company financial statements disclose sales and/or profit from China
3 Company management and/or investment analysts estimate company sales in China (in percentage)
4 Disclosed or estimated sales in China as a percentage of total
5 Company management and/or investment analysts assert that China is the firm's growth opportunity 6 Company performs research and development activity in China
7 Company has manufacturing activity in China
8 Company sources materials locally for their manufacturing activities
9 Company hires locally in China
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10 Company currently employs over 500 people in China
11 Company management and/or investment analysts disclose and/or estimate investment amount in China 12 Company has operated in China for over 5 years
13 Company has country wide operations or representative offices in China
14 Company has subsidiaries and/or joint ventures in China
15 Company’s annual report mentioned China at least three times
In terms of the time periods chosen for the scorecard, Karabell (2009) points out that Chimerica finally came into formal existence in 2004 after China’s accession into the WTO in 2001. Since it took firm’s long-term planning and execution to break into China’s market, the scorecard captures gradual developments and is not assumed to change drastically year over year. Six annual scorecards were created. They reflect constituent companies within the S&P 100 index and their cumulative efforts to build out their Chinese operations. The time span chosen (2004-2010) includes the 2008 Global Financial Crisis when stock markets across the world tumbled and the hypothesis of diversified global revenue streams providing stability was put to test. Similar to Investment Style Analysis (Ibbotson and Kim, 2012), the methodology of the study consisted of a two-part algorithm for the selection (prior) year and the performance (current) year. For each selection year (June 30, 2004-June 30, 2009), I examined the top 100 US stocks in the S&P 100 Index by market capitalization in beginning of June. The scorecard is also created in accordance to the company annual report disclosure published before June 30 of each year. In each of the performance years (June 30, 2004 – June 30, 2010), the portfolios selected were equally weight at the beginning of each year and passively held. Delisting of any kind (e.g. liquidations, mergers) caused the position to be liquidated and held as cash for the remainder of the performance year. I recorded returns at the end of the performance year for each selection-year portfolio so that the portfolios were “identifiable before the fact”. The rationale for equally-weighted portfolio rather than market capitalization- weighted portfolio is two-fold. First, to follow the exact same method in Investment Style
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Analysis set out by Ibbotson and Kim (2012). And second, to avoid the outcome of having mega-cap stocks dominate the analysis. The biggest stock in the S&P 100 index was 41 times larger than the 100th stock in 2010 in terms of market capitalization while the total market capitalization of the top-decile companies in the S&P 100 index was 19 times larger than that of the bottom-decile companies. The scorecard indicates that generally the larger the company size, the higher the score. In fact, when two companies are scored the same on the 15 elements, the larger of its size, the higher is its rank. The top quartile most China exposed companies are on average twice bigger than the bottom quartile companies with the least China exposure. Intuitively, the bigger the US firm, the harder for them to find domestic growth opportunities and the more pressure to expand globally. The clear exception in the top quartile was Avon Products Inc. which has had a very successful Chinese franchise since its entry in China in the 1990’s. Though not one of the largest companies by market cap, both its overall average and the median scores increased by 15-16% from 2007 to 2010 reflecting increased financial disclosure, market intelligence and sell-side research coverage available over time and the significance of these companies’ China activities. [Table 1 about here.] Table 1 shows American companies’ exposure to China has increased over the time period covered in the study. In 2010, 88 of the S&P 100 companies or 91% of the market capitalization have China exposure, compared to 77 companies or 86% of the market capitalization three years ago. Direct revenue from China has also increased across all sectors since 2007, ranging from 2% to 47% of total revenues. The technology sector has the most China exposure in terms of market capitalization. This in part reflects the outsourcing practices of many American multinationals as well as China’s status as the world’s factory where the Chinese workers assemble popular consumer electronics that are sold across the developed world (e.g. Apple Inc.). The consumers and industrial sectors contain the largest number of firms that do business in China with the highest China related revenue. These sectors have benefited from increasing Chinese consumer
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spending and the vast infrastructure projects that contributed to China’s phenomenal GDP growth. The least number of companies are in the heavily regulated sectors, such as financial services (e.g. regional banks) and utilities. While these companies may be more inward-looking, this is also due to Chinese government’s unwillingness to open up these sectors for foreign competition. Largely impacted by the 2008 Global Financial Crisis, the financial sector saw a major drop of 3% in market capitalization in 2010 while all other sectors’ China exposure has increased over time in market capitalization terms. Overall, the market capitalization of financial services firms in 2010 has still not recovered to the pre-crisis level.
3 In Search of Chimerica Factor The objective of this section is to isolate systematic factors such as market, size and style from the Chimerica factor and test for factor effectiveness of the Chimerica factor on a standalone basis. It strives to answer the question if the Chimerica factor produces the effect of enhancing or reducing corss-section of stock returns.
3.1 Chimerica vs. Size and Style
I start with comparing return differences in the time period chosen. Stocks are ranked into 4 quartiles based on size, style (value/growth) and Chimerica scores. Equal-weighted portfolios are formed for each quartile. This is similar to the approach used in the Ibbotson and Kim paper (2012). [Table 2 about here.] Table 2 reports the annualized arithmetic mean, geometric mean and standard deviation of returns for each equal-weighted quartile portfolio with respect to size, style and Chimerica score. While most research in academic finance is done on arithmetic returns, the geometric returns are reflective of realistic investor experience over time.
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For example, when a stock declines by 50% in one year, it takes more than 50% return in the next year to break even. Whereas arithmetic returns would be zero in this case. The annualized geometric mean is the compound annual return realized by the portfolios over the period, which, unlike arithmetic mean, is not diminished by the variability of returns. For the time period chose (June 30 2004 – June 30 2010), size effect was the most prominent, i.e. returns were in a uniformly descending order. Small-size 4th quartile companies outperformed large-size 1st quartile companies by 4.70%. In terms of style effect, returns of quartile portfolios were less consistent, however, the bottom half of growth stocks outperformed the top half of value stocks by 0.63%. The most growthy 4th quartile companies outperformed the most value 1st quartile companies by 3.11%. That growth stocks outperformed value stocks in those six years chosen including the 2008- 2009 financial crisis is a not a surprise. Because returns of bank stocks, a major “value” sector substantially declined in the period chosen, though the value factor tends to outperform the growth factor over much longer periods of time. In terms of Chimerica score, returns of quartile portfolios were also not in a uniform sequential order. It’s worth noting that the lowly Chimerica scored 4th quartile companies outperformed highly scored 1st quartile companies by 0.43% on an empirical basis before statistical test for significance. Geometric returns in the table are shown as reference but not analyzed, primarily because both the index constituents and the Chimerica scoring change year over year, disallowing continuously compounding of the same stocks. To summarize, smaller capitalization, growthier stocks and stocks with less exposure to China are shown to have delivered higher returns in those six years. The reason why US growth stocks outperformed value stocks is because the period chosen has incorporated 2008-2009, the Global Financial Crisis when bank stocks which are normally categorized as value stocks underperformed. As a parallel comparison, Chinese growth stocks also outperformed value stocks during this period of time. Another interesting observation is that lowly-scored companies tended to have higher volatility than highly-scored companies. High Chimerica means more diversified global business
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exposure, and hence, the realized returns associated with these companies were less volatile. [Table 3 about here.] Table 3 examines calendar year stock performance based on Chimerica scores and put stocks into high- to low-scored quartiles. Chimerica premium has been most of the time positive. Lowly scored companies in quartile 4 outperformed highly scored companies in quartile 1 most predominantly in 2004 by 18.07% and to a less extend, in 2006 by 3.50%. Both years registered “banner” returns of double digits. Chimerica premium in most of the calendar years was negative. However, stocks of high Chimerica- scored companies in quarter 1 did particularly well ex post in crisis years 2007 and 2008 outperforming the lowly scored companies in quartile 4 by 2.25% and 6.82% respectively. Through those six years chosen, the top half of high Chimerica-scored companies actually underperformed the bottom half of low Chimerica-scored companies by 2.76%, though the highly-scored companies in the 1st quartile outperformed the lowly-scored 4th quartile companies by 0.43%. This seems to be consistent with the concept that overall lower expected returns provide insurance against bad times. Fundamentally, stocks with more diversified global revenue streams, e.g. Chimerica in this case, weathered the storm of 2007-2008 better as the Financial Crisis had a larger impact on US domestic oriented stocks (i.e. companies with low Chimerica scores). Take calendar years of 2007 and 2008 as examples when these stocks delivered negative double-digit returns. In 2007, high Chimerica-scored first quartile companies outperformed the second quartile companies, second-quartile companies outperformed third quartile companies and third quartile companies outperformed thosed in the fourth quartile. I observed the same results in calendar year 2008. Among the many probable explanations, one could argue without testing for statistical significance that the diversification benefit from overseas revenue and profit streams of the first quartile companies with high Chimerca scores indeed seems to stand out in times of acute crisis. Of course, these observations were empirical and are subject to statistical significance tests.
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The next question we ask is whether the Chimerica effect is distinct from the existing well-established size and style effects. We constructed double-quartile portfolios that combined Chimerica score with each of the size and style quartile portfolios. In other words, is investing in Chimerica stocks equivalent to investing in small stocks or growth stocks? [Table 4 about here.] Table 4 reports the annual arithmetic mean return, geometic mean return and standard deviation of returns, as well as the average number of stocks, for each intersection portfolios. The arithmetic mean return is the simple average of returns while the geometric mean return is the time-weighted or compounded annual return that is generally lower than the arithmetic mean return.The strongest Chimerica effect resides with small stocks and followed by big stocks, with the premiums of the Chimerica factor at 3.17% and 1.43% respectively while big and smaller stocks did not exhibit positive Chimerica premiums. Across the smaller stock quartile, big stock quartile and bigger stock quartile, the top half of high Chimerica-scored stocks returned less than the bottom half of low Chimerica-scored stocks. Only in the small stock quartile, the bottom half of low Chimerica-scored stocks returned more than the top half of high Chimerica-scored stocks, indicating Chimerica premium. The Chimerica effect does not present uniformity across all size quartiles, though the Chimerica effect is found to be so high and negative with big stocks. The conclusion from Table 4 seems to be that even though the size premium was observed in the time period chosen (Table 2), the Chimerica premium did not coexist with the size premium and probably operated independently. Only two out of four size quartiles (Small and Bigger) existed Chimerica premiums. Certainly, statistical significance has not been tested here. [Table 5 about here.] Similarly, to address the question of how the Chimerica effect differs from style of value or growth, we constructed equally weighted double-sorted portfolios on Chimerica scores and the earnings-to-price ratio (E/P). Table 5 reports the annual return results for
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the 16 value/growth and Chimerica portfolios. Except for the high value quartile portfolio where lowly-scored stocks in the 4th quartile outperformed highly-scored stocks in the 1st quartile by 2.53%, all other style portfolios, mid value, mid growth and high growth showed opposite results. The value premium is strongly negative, apart for the mid high scores. There is also the lack of consistency across the style quartile portfolio in testing the Chimerica scores. Chimerica effect seems to be the least plausible with style portfolios. From the results of tables 4 and 5, it seems to be possible to justify Chimerica differs from each of the established size and style factors for the time period chosen. We do not observe much synergistic effect when combining low Chimerica scores with other factors. It is unclear that Chimerica can be mixed with the higher-performing small-size or growth portfolios for the time period tested. Therefore, Chimerica seems to warrant more analysis, independent of investment style analysis.
3.2 Chimerica as a Factor
This section focuses on expressing Chimerica as a factor, i.e. a series of long-short portfolio returns. I constructed monthly returns of a long-short portfolio in which the returns of the bottom quartile portfolio (lowest Chimerica scored companies) were subtracted from the returns of the top quartile portfolio (highest Chimerica scored companies). This series represents the Chimerica factor as the dependent variable and then is regressed on market, size and style factors. The market, size and value/growth style factors were defined by Fama-French and extracted from the Dartmouth University website (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html). It’s important to note that the definition of these factors do not correspond to those on Tables 2, 3, 4 and 5 as the universes of stocks, time periods chosen and the groupings are different, though sorting is the basic tool being employed across all tables. [Table 6 about here.]
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It’s worth pointing out that the means of these factors, size, style and Chimerica in Panel A of Table 6 do not match those in Table 2. First, the prior table specifically reports on the universe of 100 largest US stocks during the period from June 2004 to June 2010 whereas Table 6 uses Fama-French factor data as input from the Dartmouth University database. These Fama-French factors are value-weighted, as opposed to equally-weighted factors reported on Table 2. Second, the data in the Table 2 uses June- June 12-month annualized returns as input while Table 6 is based on monthly returns. Due to dividend compounding, Chimerica-scored quartile portfolio returns slightly varied with the mean of the Chimerica factor at 9 bps in Table 6 vs. 43 bps on Table 2. Panel A of table 6 reports that the means of all Fama-French factor returns and the Chimerica factor returns were positive. Other than the market factor and stlye factors, returns of size and Chimerica factors were positively skewed. The variation of factor returns, as measured by standard deviation is the highest for market return (3.07%), followed by style (2.71%), size (2.35%) and Chimerica (2.11%). The minimum of all factor returns is also the lowest for the market factor, which was over two to three times as big as other factors’ minimums. The Global Financial Crisis strongly explained this large negative factor returns of market and style (Value). On the maximum factor return side, market and style factor returns were again the largest, reflecting the strong rebound experienced by the same factors post crisis. Panel B shows the average of 10 Chimerica decile portfolios that has arithmetic return of 0.12% per annum. Though the returns of the 10 portfolios are not in a uniform ascending order, we do observe that higher scored Chimerica portfolios generally underperform less scored portfolios, with a 0.10% of premium for the average of Portfolio 6-10 minus the average of Portfolio 1-5. Interesting to note that higher returns are associated with higher volatility. However, returns for Portfolio 6-10 are all negatively skewed while returns for Portfolio 1-5 are less negatively skewed. Panel C shows the returns for the 10 industry sector portfolios. All sectors had positive mean returns. The return dispersion is narrow within a range of 1.31%, with the energy sector returning the highest 1.37% and the Telecommunication Communication sector the lowest 0.06%.
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Returns of most industry sector portfolios are negative skewed. Consumer discretionary, financials and materials sectors are exceptions though their positive skewness is only in the narrow range of 0.07-1.14%. The materials sector experiences the highest drawdown at -29.98% while it also enjoys the highest draw-up at +54.54%. Next, as a further quest for the anomalies, I use the CAPM framework, regressing
Chimerica long-short factor return (Rit) on the excess returns of the US market (RMt).
Monthly and arithmetic returns are used in the creation of the Chimerica long-short factor. I follow Fama-French’s definition of “the market” where they use all NYSE, Amex and Nasdaq firms. And market return is value-weighted. Risk free rate (Rft) is obtained from Kenneth R. French’s website.
푅 , = α+ 훽 푅 − 푅 + 휖 (1)
In the standard Fama-French three-factor model, the long-short Chimerica factor is regressed on the long market portfolio and the long-short size and value portfolios. Kenneth French’s website also provides factor returns.
푅 , = α+ 훽 푅 − 푅 + 푠 푆푀퐵 +ℎ 퐻푀퐿 + 휖 (2)
[Table 7 about here.] Table 7 presents the time-series regression analyses, with Chimerica factor as the explained variable and using the individual Fama-French three factor, market, size and style and combined three factors as independent variables. On the one-factor regressions, none of the market, size or style factor explain the Chimerica factor. The adjusted r-squares are very low at 0.00%, -0.01% and -0.01% respectively. Similarly, none of the t-stats for the market, size and style factors has reached the statistically significant level. Using Fama-French three factors combined, the adjusted r-square of the regression
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does not improve at all. Alpha is negative and statistically insignificant. The beta coefficient for the market factor is negative while the beta coefficients for size and style factors are positive. Results from this table seem to indicate that Chimerica is indeed an anomaly, that neither the individual Fama-French three factors or the Fama-French three- factor model can explain it well. [Table 8 about here.] Table 8 presents results of cross section analyses on the portfolio sorts. Panel A are 10 Chimerica portfolios sorted by Chimerica score, using market, size, style as explainable factors and Chimerica-sorted portfolio returns as explained factor. The purpose is the assess if the three factors explain majority of the return variation. Any left alpha is something that Chimerica can potentially explain. The alphas in 6 out of 10 portfolios are positive. The adjusted r-squares are all very high ranging from 79-89% and the t-stats for alphas in 9 portfolios are insignificant, except for Portfolio 5. This indicates the general effectiveness of the Fama-French three-factor model in explaining the Chimerica anomaly in a portfolio setting. Here the market is defined as the 10 portfolios, as opposed to the broad market such as the S&P 500 index. T-statistics for the market factor in particular are very high in excess of 17.0 for all ten portfolios, surpassing the new standard of t-statistic greater than 3 for a higher hurdle to clear for market prices of risk (Harvey and Liu, 2016). Panel B shows cross section results of the ten industry sector portfolios. Again, the Fama-French 3-factor model is meaningful in explaining most of the industry sector portfolios, with the minimum adjusted R2 at 29% for the telecommunications sector portfolio while the maximum at 88% for the industrials portfolio. The industrials sector portfolios show statistically meaningful alpha. The market factor also dominates the other two factors in explaining industry/sector portfolio results across the board. Results from both Table 7 and Table 8 seem to conclude that the Chimerica factor in general cannot be fully explained by the Fama French individual factors and combined
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model both on a standalone basis and in portfolio settings. On a historical basis, there were more successes with certain sector or scored portfolios.
3.3 Fama Macbeth Estimation
Fama Macbeth factor premium estimation is a two stage analysis (Fama and Macbeth, 1973). The first stage involves a set of regressions equal in number to the number of assets being tested. Stage two is a set of regressions equal in number to the number of time periods. According to Hsu (2007), the first stage regressions are a set of time series regressions of each asset’s returns on the factors, and Stage 2 tells us the premium awarded to each factor exposure.
푅 , = 훼 + 훽 , 푅 − 푅 + 훽 , 푆푀퐵 + 훽 , 퐻푀퐿 +
훽 , 퐿푀퐻 + 휖 ,
푅 , = 훼 + 훽 , 푅 − 푅 + 훽 , 푆푀퐵 + 훽 , 퐻푀퐿 +
훽 , 퐿푀퐻 + 휖 ,
푅 , = 훼 + 훽 , 푅 − 푅 + 훽 , 푆푀퐵 + 훽 , 퐻푀퐿 +
훽 , 퐿푀퐻 + 휖 , …
푅 , = 훼 + 훽 , 푅 − 푅 + 훽 , 푆푀퐵 + 훽 , 퐻푀퐿 +
훽 , 퐿푀퐻 + 휖 , Excess returns of each stock or portfolio across the time period chosen are used as dependent variables. Independent variables as defined in Section 3.2 are market excess return, size (small minus big), style (high minus low) and Chimerica (low score minus high score).
Expressed in matrix form, the regression for Rn would look as follows:
푅 = 퐹훽 + 휖 (4)
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Where Rn is a n × 1 vector of excess returns, F is a 1 × (m + 1) matrix of factors where all elements in the first column are 1, βn is a (m+ 1) × 1 vector of factor loadings where all elements in the first row are the intercept αn, and ɛn is a n × 1 vector of error terms. n is the sample size of asset returns and T is the number of periods. Upon completing (4), we know how each stock’s or portfolio’s return is affected by each factor. To calculate factor premiums for each factor, we run a set of cross sectional regression. 훽 , the unobservable factor loading is the estimated for 훽 of each asset for each factor, i.e. market, size, style and Chimerica that are empirically estimated factor loadings. 푅 , = 훼 + 훾 , 훽 , + 훾 , 훽 , + 훾 , 훽 , + 훾 , 훽 , + 푒 푅 , = 훼 + 훾 , 훽 , + 훾 , 훽 , + 훾 , 훽 , + 훾 , 훽 , + 푒 … 푅 , = 훼 + 훾 , 훽 , + 훾 , 훽 , + 훾 , 훽 , + 훾 , 훽 , + 푒
Expressed in matrix form, the regressions for Rt 푅 =β 훾 (5)
Where Rt is an n × 1 vector of average asset returns, 훽 is an n × (m + 1) vector of factor loadings where all elements in the first column are 1, and ɤis an (m+ 1) × 1 vector of factor premia where all elements in the first row are the intercept .
T-statistics on 훾 terms are used to gauge if 훾 estimated is statistically significant and different from zerio. This is the gamma estimated in the second stage. 훾 푗 (6) ϒ,푗/√
∂ϒ, Is the standard deviation of 훾 , term.
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Statistical inference with Fama Macbeth method is typically conducted under the assumption that the models are correctly specified, i.e., expected returns are exactly linear in asset betas. This can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. As mentioned in the Introduction Section, various econometric methods (Shanken, 1992, Jagannathan and Wang, 1998 and Shanken, Kan, Robotti, 2013) and subsequent statistics are further analysed on the cross section results. [Table 9 about here.] First, on the Chimerica-scored portfolios purged from one, three and four factors, the initial observation is on the adjusted R2 s of Ordinary Least Square method for one- factor (market), three-factor (market, size and style) and four-factor (including Chimerica) models have improved with the additional factor inclusion from 23%, 27% to 35%. The addition of the Chimerica factor increased explanatory power by 8%. The loadings of these factors in market price of risk and covariance are positive for the market factor and Chimerica factor while negative for size and style. None of the t-statistics is significant though. The set of t-tests include Fama MacBeth test (tFM, 1973), Shanken test (ts, 1992),
Jagannathan and Wang test (tjw, 1998) and the Kan, Robotti and Shenken test (tkrs, 2013). The Shanken test aims at correcting errors in variables, the Jagannathan and Wang test assumes correctly specified models and the Kan, Robotti and Shenken test accounts for model misspecification. On the market prices of risk (ϒs) and covariance risk (λs), Table 9 shows that the Fama-Macbeth t statistic (tFM) and Shanken t statistic (ts) for the ϒs in 1- factor, 3-factor and 4-factor models are exactly the same. Yet, when correcting for the error in variables and model misspecification, this is no longer the case. The t-stats for covariance risk, λs are different across all tests. One can reject the null when testing the cross sectional adjusted R2 is equal to 1, as the small p-values indicate statistical significance. This is consistent with the very large standard error of the sample R2 in excess of 1.0 for one-factor, three-factor and four-factor models respectively. The pricing errors are also high. The statistic csrt, which is an approximate F-test of model specification
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shows 0.19, 0.13 and 0.12 for one-factor, 3-facotr and 4-factor models. These results seem to indicate one-factor, three-factor and 4-factor models don’t explain well enough excess returns of the 10 Chimerica-scored portfolios under the Ordinary Least Squared function. It seems to indicate that there is no Chimerica in a statistically significant way for this set of US stocks sorted in 10 portfolios ranked by Chimerica scores. [Table 10 about here.] Table 10 shows results of the same tests under General Least Square methodology. The GLS function eliminates heteroskedasticity in the error term and thus represents a higher statistical hurdle to clear whereas the OLS function assumes normal distributed residuals We see less dramatic enhancement with the inclusion of the Chimerica factor in the 4-factor model as the adjusted R2 has increased from less than 1% for the one-factor model, to 28.8% in the Fama-French three factor model and eventually 29.0% in the 4-factor model. The factor loadings for the market factor are positive whereas they are negative for size, style and Chimerica factors. Again, none of the t- statistics is significant, except for tFM associated with the style factor. The p-value for cross section of adjusted R2 equal to 1 is small so we can reject the null. Standard error, csrt and p-value for model misspecification are relatively low. Even though these results again indicate that one-factor, three-factor and 4-factor models don’t explain excess returns of the 10 Chimerica-scored portfolios well, the model seems to be better specified under GLS when compared to those under the OLS function. [Table 11 about here.] [Table 12 about here.] Tables 11 and 12 summarize the results for the 10 sector/industry portfolios, repeating the same tests for the same 1-factor, 3-factor and 4-factor models in OLS and GLS settings. The Chimerica factor has more explanatory power in explaining this set of returns. The adjusted R2 increases from 45%, 48% to 57% in OLS and 3%, 4% and 5% in GLS for 1-factor, 3-factor and 4-factor models respectively.
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Looking at market prices of risk (ϒs) and covariance risk (λs) for the 10 sector/industry portfolios, one can see the factor loadings for market price of risk and covariance are negative for all factors, except the market factor. This means that Chimerica is detractive in explaining excess returns. Again, none of the t-stats are statistically significant across both the OLS and GLS functions and across market prices of risk and covariances. The p-values are relatively small so one can reject the nulls that the cross section of adjust R2 is equal to 1. Standard errors are higher under OLS, nonetheless they are not small under GLS either. The csrt’s are relatively small for both OLS and GLS, ranging from 0.15 for the one-factor model, 0.14 for the three-factor model and 0.10 for the 4-factor model. The p-values for model misspecification in OLS are in the range of 0.28 to 0.41. What we can conclude from these two tables is that one-factor, three-factor and four-factor models do not explain the 10 sector/industry portfolios. These are similar results drawn from table 9 and table 10. Chimerica does not exist in 10 sector/industry portfolios. [Table 13 about here.] In quest for the efficacy of the Chimerica factor, I run cross section regression of excess returns on combining the 10 Chimerica score-sorted portfolios and 10 sector/industry portfolios. Tables 13 shows the results under the OLS function. The adjusted R2 continues to increase within the inclusion of additional factors. It goes up from 39% in the one-factor model, to 42% in the three-factor model to 43% in the four- factor model. Under OLS, factor loadings are negative for size, style and Chimerica factors while positive for the market factor. The t-stats for all factors across the board continue to be low and do not reach the statistical significance level. Low p-values allow us to reject the nulls that the adjusted R2 is equal to 1 and high p-values allow us to accept the nulls that the adjust R2 is equal 0. Standard errors, csrt’s and p-values for model misspecification are high. Again, one-factor, three-factor and four-factor models do not explain the excess returns of the combined 10 Chimerica-scored portfolios and 10 sector/industry portfolios.
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[Table 14 about here.] As expected, the adjusted R2 under GLS has substantially increased with the incorporation of Chimerica factor from less than 1%, 6.8% to 7.1% under 1-factor, 3-factor and 4-factor models. None of the factors have significant t-statistics. The factor loadings for market and Chimerica factors are positive while they are negative for size and style factors. The p-values are small so to reject the nulls that the cross section adjusted R2 is equal to 1. Standard errors, csrt’s and p-values for model misspecifications are smaller under GLS and hence, indicate a better model fit under GLS. But they have not reached the statistical significance level to indicate that the one-factor, three-factor and four- factor models can explain the excess returns of the combined 10 Chimerica-scored portfolios and 10 sector/industry portfolios. These statistics from Table 13 and 14 seem to again indicate that there’s no Chimerica in these combined portfolios.
3.4 Chimerica and the Cross Section
Since the Chimerica factor is developed purely based on empirical experience based on Furgerson and Schularik (2006), rather than derived from First Principles, it is subject to the “purging” exercise, in which the underlying systematic risk exposure to Chimerica is separated to ascertain that it is meaningful on a standalone basis. The intuitive explanation could be that investors want unadulterated domestic US exposure that is distinct from Chinese macroeconomic risk and thus reward the least Chinese exposed stocks, the highest return. Another plausible explanation could be domestic US dollar- based investors who are dominating the US stock market like to chase faster growth American companies, of which are less Chinese exposed. Then the question becomes about avoiding any confounding effects. The tools in this section are portfolios (10 chimerica-scored portfolios and 10 industry/sector portfolios) purged from three systematic factors, namely the market, size and style (value vs. growth) factors. [Table 15 about here.]
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Next, I run cross-sectional regressions of (purged) excess returns on 10 Chimerica-scored portfolios purged from traditional Fama-French three factors and regress on Chimerica or Chimerika itself purged from factors. Tables 15 shows the results under the OLS function from a cross sectional analysis when the test assets are the 10 Chimerica-scored portfolios. The loadings (both covariances and betas) are computed over the whole sample and used at each single period to compute the market prices of risk according to Fama-Macbeth (1973). Both the Chimerica-scored portfolios and the factors have been purged from three Fama-French factors. The sign has been positive for both Chimerica and Chimerica New factors and the t-statistics have not
2 been meaningful across all tests such as tFM, tS, tJW, and tKRS. The adjusted R s are small, at 6.6% for both factors. One can reject the null as suggested by the low p-value when testing that the cross sectional adjusted R2 is equal to one. In the same token, one accepts the null that this sample metric is equal to 0. The standard error of the sample R2s are small at 15.2% and 14.8% respectively for both factors while csrt is small for Chimerica factor (0.23) but bigger for Chimerica New factor (0.40). The p-values for model misspecification are at 0.14 and 0.01 respectively. It’s disappointing that these results are inconclusive for the Chimerica and Chimerica new factors. [Table 16 about here.] Table 16 reports results of GLS function performed on the cross-sectional regressions of (purged) excess returns on 10 Chimerica-scored portfolios purged from traditional Fama-French three factors and regress on Chimerica or Chimerika itself purged from factors. The R2 is so small that it’s tempting to throw away these results and models right away. The signs of the factor loadings are positive for Chimerica and negative for Chimerica new factor after purge. But unfortunately, none of the t-stats is meaningful. [Table 17 about here.] Next, I run the cross-sectional regressions of purged excess returns on 10 industry/sector portfolios purged from traditional Fama-French three factors and
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regress on Chimerica and Chimerica itself purged from factors. Table 17 reports results from the OLS function. The signs for both Chimerica and Chimerica new are negative, indicating value addition of the factor. The adjust R2’s are much lower less than 1% when compared to those derived from the 10 Chimerica-scored portfolios. However, none of the t-stats has reached the statistical significance level, even though p-value for adjust R2 equal to 1, standard errors, csrt’s and p-values for model misspecification have been low. [Table 18 about here.] Table 18 reports the results from GLS function performed on the cross-sectional regressions of purged excess returns on 10 industry/sector portfolios purged from the traditional Fama-French three factors and regress on Chimerica and Chimerica itself purged from factors. The signs for loadings of market price of risk and covariance have turned positive, indicating how unstable the factors and the models are when switching from the OLS function to the GLS function. The adjusted R2 is close to zero and none of the t-statistics is significant. There’s not much again in this set of analysis. [Table 19 about here.] Finally, I run cross sectional analysis on the expanded opportunity set, i.e. combined 10 Chimerica-scored portfolios and 10 sector/industry portfolios purged from traditional Fama-French three factors and regress on Chimerica and Chimerica itself purged from other factors. Table 19 reports very low adjust R2s of less than 1%. The signs for loadings are positive. All t-stats for both Chimerica and Chimerica New are insignificantThe p-values for cross sectional adjusted R2 equal to 1 is small so we can reject the null. The csrt’s are big. Again, the results did not lead to much research finding. [Table 20 about here.] Tables 20 reports results from the GLS function performed on the cross section of the expanded opportunity set, i.e. combined 10 Chimerica-scored portfolios and 10 sector/industry portfolios purged from traditional Fama-French three factors and
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regress on Chimerica or Chimerka itself purged from other factors. Results from this table have a bit more different from those in the prior tables. First of all, the adjusted R2s are negative, indicating the inability of Chimerica factor and new Chimerica factor after purge to explain combined 10 Chimerica-scored portfolios and 10 inustry/sector portfolios results. Second, the signs for the loadings of market price of risk and covariance have turned positive. Third, none of the t-stats is meaningful. Fourth, the p- value is very small so one can reject the null that the cross section adjusted R2 equal to 1. Finally, csrt’s are of decent size while standard errors are relatively large and p-values for model misspecification are small. In summary, Chimerica is an anomaly not explained by the traditional CAPM or Fama-French three-factor models. However, in portfolio settings, both the time series and cross-sectional analysis on the purged and unpurged basis have not led to the finding of much explanatory power of the Chimerica factor in explaining excess returns of 10 Chimerica-scored portfolios, 10 sector/industry portfolios or the combined 10 Chimerica- scored portfolios and 10 sector/industry portfolios. There’s not a single meaningful t- statistics. This means that the Chimerica effect could have existed on an empirical basis but it’s very difficult if not impossible to put it to rigorous scientific tests.
4.0 Chimerica Factor in Fundamental Analysis
After testing if Chimerica has been priced by realized return factor variables of the market, I ask if the Chimerica factor also shows up in the future expected returns forecasted based on company fundamentals.
4.1 Claus/Thomas Analysis
This paper attempts to use a second methodology to prove that the return differential between the highest exposure stocks and the lowest exposure stocks is meaningful and
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recurring so that the anomaly can be employed in practical money management. Claus/Thomas model is used by utilizing analysts’ earnings forecasts. Essentially, the expected return of a stock in the Claus/Thomas model is the equivalent IRR that equates today’s price to analysts’ earnings estimates. Different from the traditional discounted cash flow model and dividend growth model, Claus/Thomas model does not heavily rely on the terminal earnings growth rate provided by equity analysts, which tends to be overly optimistic about earning growth beyond year 5, though their near-term earnings forecast can be rather unbiased. Claus/Thomas model makes good use of the historical book value of the company and their abnormal earnings above the cost of equity. The expected return of a stock, k is derived from the equation below.
푎푒 푎푒 푎푒 푎푒 푎푒 푃 = 푏푣 + + + + + (1 + 푘) (1 + 푘) (1 + 푘) (1 + 푘) (1 + 푘)
푎푒 (1+ 푔 ) + (푘 − 푔 )(1 + 푘 )
Where
푎푒 = 푒 − 푘(푏푣 ) = expected abnormal earnings for year t, or forecast accounting earnings less a charge for the cost of equity, 푘 = expected rate of return on the market portfolio, derived from the abnormal earnings model. k is firm specific and shows up in both denominator and numerator
푒 = earnings forecast for year t,
푏푣 = expected book (or accounting) value of equity at the end of year t. and
푔 = terminal year abnormal earnings growth rate assumed to be equal to expected inflation, which is the difference between the risk-free rate (10-year Treasury) and the yield of 10-year inflation-linked government bonds
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4.2 Equity Premium for S&P 100 Index [Figure 1 about here.] Figure 1 shows the expected returns over risk free rate by Sector/Industry as of March 30, 2007 and March 18, 2010. All sectors are expected to generate positive excess returns in both years, with 2010’s forecast expected returns well in excess of 8% across all sectors. 2010 witnessed the rapid rebound of stock prices post Global Financial Crisis and was one of the banner years in terms of the US stock market return. The sector that declined the most during 2008-2009 was financial services companies. This sector was indeed expected to generate the most excess return, in excess of 10%. This speaks to the powerfulness of the Claus/Thomas model, because we all know now that banks, insurance companies and asset management companies actually did perform the best in 2010. In contrast, the excess returns across all sectors were significantly lower in 2007, all hovering between 1-4%. This again was accurate as the summer of 2007 saw the decline of quant-managed hedge funds that started the subsequent market decline into 2008. Appendix 3contains stock by stock forecast for the S&P 100 companies via Claus/Thomas methodology. Expected returns for each of the S&P 100 stocks for the one year after March 2007 and March 2010 are calculated respectively. These two dates are selected to correspond to the 2010 scorecard and the 2007 scorecard. Analysts’ earnings estimates and company book values are extracted from I/B/E/S (the Institutional Brokers’ Estimate System). To estimate individual expected stock return, the actual fiscal year-end book value of the company disclosed prior to the release of earnings estimate is used. For each company, I/B/E/S provides a number of analyst forecasts. The median of the forecasts is used for each of the next five fiscal years to calculate future abnormal- earnings and future book values. In the few cases where fiscal year 4 and 5 earnings forecasts are not available, these are estimated by extrapolation based on the growth rates derived from fiscal year 2 and 3. As a part of the terminal value calculation, expected inflation is estimated in accordance with the Claus/Thomas model by subtracting the 10-year
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Treasury yield from the yield of 10-year inflation-linked government bonds to proxy the expected inflation. To examine the validity and practical relevance of the Claus/Thomas approach, let’s first have a quick look at the derived expected return for the S&P 100 index, which is the weighted average of individual S&P 100 company returns, according to the index’s value-weighted methodology. The reason that I focus on value-weighted average of expected returns here, rather than equally weighted is to be consistent with the S&P 100 index construction. And the equity risk premium of the index is the difference between the stock expected return and the 3-month T-bill return. The equity risk premium in 2010 for the S&P 100 index is calculated to be at 9.4% while the equity risk premium in 2007 at 2.9%. This huge gap of equity premium (6.5%) in the two selected years is indicative of how cheaply US equity in general had been priced post the 2008 financial crisis relative to its history and relative to bonds. In other words, in looking back and based on valuation, an intelligent investor should have sold US equity in 2007 but should have bought it in 2010.
4.3 Long/Short Portfolios and Testing
Using the same scorecards as in the ex-post analysis, long/short portfolios are created by going long the lowest ranked Chimerica stocks while shorting the highest ranked. Due to the fact that multiple analysts following the same company submit various forecasts, a statistical test that has all analysts input (rather than the median analyst forecast in 3.2) is necessary to determine the significance of forecast return for the long/short portfolios. First, hypothesis test concerning differences between means is used to prove the significance of the result of the long/short portfolio. In other words, the average return of the long side of the portfolio minus the average return of the short side of the portfolio should be statistically significantly from zero assuming normal distribution of returns. The hypotheses are therefore:
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퐻 = 휇 − 휇 =0
퐻 = 휇 − 휇 ≠0
Using monthly returns, the test statistic for a test of the difference between two population means based on analyst earnings estimates is