Gamesmanship and seasonality in U.S. stock returns

Ackert, Lucy F.; Athanassakos, George Article Gamesmanship and seasonality in U.S. stock returns Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Ackert, Lucy F.; Athanassakos, George (2021) : Gamesmanship and seasonality in U.S. stock returns, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 14, Iss. 5, pp. 1-11, https://doi.org/10.3390/jrfm14050206 This Version is available at: https://hdl.handle.net/10419/239622 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Journal of Risk and Financial Management Article Gamesmanship and Seasonality in U.S. Stock Returns Lucy F. Ackert 1,* and George Athanassakos 2   Citation: Ackert, Lucy F., and George Athanassakos. 2021. Gamesmanship and Seasonality in U.S. Stock Returns. Journal of Risk and Financial Management 14: 206. https://doi.org/10.3390/jrfm14050206 Academic Editor: Ruipeng Liu Received: 31 March 2021 Accepted: 23 April 2021 Published: 3 May 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1Department of Economics and Finance, Michael J. Coles College of Business, 560 Parliament Garden Way, Kennesaw, GA 30144, USA 2Ivey Business School, Western University, 1255 Western Road, London, ON N6G 0N1, Canada; [email protected] *Correspondence: [email protected]; Tel.: +1-470-578-6111 Abstract: We re-examined the seasonal pattern in the excess returns of highly visible American firms. In contrast to the seasonality for risky, less visible firms, we found that highly visible stocks display return seasonality that shows the opposite trend. Fund managers are prone to gamesmanship, putting downward pressure on prices for highly visible firms at the beginning of the year, which is reversed later with buying pressure. Due to the bonus culture, fund managers start the year by buying small, risky stocks in order to beat benchmarks. Once targets are met, they adjust toward visible, less risky stocks to lock in returns, providing them with a seasonal returns pattern opposite to that of small firms. A re-examination is warranted because the world has become increasingly globalized, and some argue that managers’ incentives are aligned with investors due to increased scrutiny. We used analyst following as a proxy for visibility and examined the seasonal pattern for 1997–2018. Though the anomaly was first reported twenty years ago, it persists in recent data. Rational investors may be limited in their ability to arbitrage mispricing because institutional investors who drive the market are self-interested. Future research may examine the seasonal pattern in countries with more stringent regulation of financial professionals or with high-frequency data. Keywords: financial analysts; gamesmanship; window dressing; agency considerations; institutional investors JEL Classification: G11; G12 In the light of the scanty evidence presented here, it can readily be seen that forecasts predicated upon seasonal movements alone, completely ignoring the customary cycle and trend analysis, have an extremely high probability of success. Certainly, the seasonal curve is well worth watching when formulating actual investment policy. (Wachtel 1942) 1. Introduction Economist and investment banker Sidney Wachtel recognized that the “December to January seasonal rise” in stock prices presents a trading opportunity for investors. Wachtel further notes that selling for tax purposes at the year end could be a driving force behind return seasonality. However, as Ackert and Athanassakos (2000) argue, tax-loss selling cannot explain why we observe different seasonal patterns in the returns for small, little known stocks and those of large, highly visible firms. To understand this seasonal difference, we need to consider the behavior of professional mutual fund managers and the structure of their incentives. Institutional investors are clearly important participants in securities markets. As remuneration is typically tied to the performance of the managed portfolio, a mutual fund manager’s goal is to end the year with strong performance. To look strong at the end of the year, the manager adds risky, potentially high-return securities at the start of the year and J. Risk Financial Manag. 2021,14, 206. https://doi.org/10.3390/jrfm14050206 https://www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2021,14, 206 2 of 11 then moves toward lower risk, well-known, and visible securities toward the year end. By following this strategy, the manager earns the year-end performance bonus that is hoped for and investors see solid returns and portfolio holdings in visible, highly regarded, and lower risk assets at the end of the year. In the following section, we review the evidence of a number of persistent return patterns that are driven by mispricing (Heston and Sadka 2008;Keloharju et al. 2016, 2021). As is well documented, the stocks of small, more risky firms earn high returns, on average, in January when demand for these stocks is high (e.g., (Banz 1981;Blume and Stambaugh 1983;Keim 1983)). As the year progresses, prices for small, risky stocks are bid up, and returns fall. In contrast to the seasonality reported for small firms, stocks of highly visible firms display return seasonality that shows the opposite trend, as documented by Ackert and Athanassakos (2000). In this paper, we re-examine the seasonal pattern in excess returns for highly visible stocks. As the behavior was first reported over twenty years ago, surely the observed seasonal patterns will have evaporated if markets are efficient and the incentives of fund managers are aligned with investors. Today, markets are quite globalized. Furthermore, re-visiting seasonality is important as recent commentary suggests that strategic portfolio rebalancing among fund managers for self-interested purposes has “pretty much disappeared completely ever since state regulators and the SEC cracked down on the practice in 2001 and 2008” (Institute of Business & Finance 2021) Here, we ask whether, as this quote suggests, managers have evolved so that conflicts of interest no longer impact the portfolio management behavior of professional fund managers. The remainder of this paper is organized as follows. Section 2provides a review of the related literature. Section 3describes the sample construction and provides summary information. Sections 4and 5report the primary and supplemental results. Section 6 contains a discussion of the results and concluding remarks. 2. Literature Review The January effect, a seasonal pattern in the returns for small stocks, has been documented by a number of studies including Banz (1981); Blume and Stambaugh (1983); Keim (1983); Haug and Hirschey (2006); and Keloharju et al. (2016). Finance academics believe that asset markets are efficient, so that prices reflect all available information. In such case, no trading strategy using public information could consistently generate abnormal returns. Yet, seasonal return patterns uncovered by researchers in recent years, including the Monday effect (Fishe et al. 1993;Athanassakos and Robinson 1994;Chiah and Zhong 2019), day-of-the-month effect (Booth et al. 2001;Kunkel et al. 2003;Singh et al. 2021), Holiday effect (Cao et al. 2009;Brockman and Michayluk 2010;Robbins and Smith 2019), and Halloween effect (Bouman and Jacobsen 2002;Jacobsen and Marquering 2008;Zhang and Jacobsen 2021), have called this belief into question. Some researchers report that not all anomalies are robust (Linnainmaa and Roberts 2018;Harvey and Liu 2019), though other evidence suggests that these return patterns are driven by mispricing and are quite persistent (Heston and Sadka 2008;Keloharju et al. 2016,2021). For small, more risky firms, high returns are observed in January as demand for such stocks is high due to bonus-chasing portfolio rebalancing and gamesmanship by professional portfolio managers. This behavior causes prices to be bid up at the start of the year. Over the year, as professional portfolio managers lock in the desired performance, they adjust away from small, risky stocks, and these stocks’ returns fall over the year. In contrast to the seasonality reported for small firms, stocks of highly visible firms display return seasonality that shows the opposite trend (Ackert and Athanassakos 2000). Due to gamesmanship and window dressing, the stocks of large, visible firms experience selling pressure at the beginning of the year and buying pressure toward the end. In fact, Ma et al. (2019) report that the majority of their sample mutual funds compensate managers using a bonus scheme rather than a fixed salary. Furthermore, 79% of the funds explicitly tie the manager’s bonus to the fund’s investment performance. In addition to aiming to clinch a bonus, a manager may engage in window dressing to provide a positive image to J. Risk Financial Manag. 2021,14, 206 3 of 11 investors by systematically rebalancing portfolio holdings over the year after locking in desired returns (Haugen and Lakonishok 1988;Lakonishok et al. 1991;Ortiz et al. 2015). Gamesmanship and window dressing are tactics fund managers use to gain a psychological advantage and provide a winning strategy that assures a performance-based bonus. To this end, the manager adds risky, potentially high-return securities at the start of the year and then gravitates toward lower risk, well-known, and visible securities toward the year end to lock in a Christmas bonus. With this strategy, the manager earns the desired bonus, and investors see solid returns and portfolio holdings in visible, highly regarded, and lower risk assets at the end of the year. This paper re-examines reported seasonality in excess returns for highly visible stocks. As Ackert and Athanassakos (2000) argue, the incentives of fund managers can explain the seasonal patterns in small, little known stocks as well as those that are large and highly visible. At the beginning of the year, institutional investors add small, less visible stocks to their portfolios, and these stocks experience abnormally high returns due to buying pressure. As the year progresses, fund managers rebalance away from small stocks leading to selling pressure and lower returns. In contrast, at the beginning of the year, highly visible stocks have low returns that adjust up as institutional investors adjust toward these stocks after achieving targeted returns. A large body of research provides evidence consistent with the seasonal impact of fund manager behavior on both stock and bond returns (e.g., (Ng and Wang 2004;Morey and O’Neal 2006;Ortiz et al. 2012)) . It has been twenty years since Ackert and Athanassakos (2000) first reported the seasonal pattern in returns for visible stocks. If investors are rational, surely smart traders will have taken advantage of this opportunity, eliminating systematic excess returns. If an anomaly is due to mispricing, it should not persist. McLean and Pontiff (2016) argue that after the academic publication of a predictable pattern in returns, investors should learn about the anomaly. On average, they find that return predictability falls by 58% after publication in an academic outlet. More recently, Jacobs and Müller (2020) report that the United States is the only nation with a reliable decline in predictability after publication, with high arbitrage costs limiting the ability to eliminate mispricing in other countries. As compensation schemes tied to fund performance are still widely used, self-interested behavior among managers may remain undeterred by smart investors. Gamesmanship and window dressing are fund manager behaviors that may persist. 3. Data Description We obtained the number of analysts following a firm, forecasted earnings, actual earnings, and the standard deviation of earnings estimates from the Institutional Brokers Estimate System (IBES) for each month from January 1980 through December 2018. Here, we report results for the later time period, January 1997 through December 2018, because our goal is to re-examine the results of Ackert and Athanassakos (2000) whose data end in 1996. We repeated all analyses reported subsequently with data from January 1980 through December 2018, and inferences were unchanged. These results are available upon request. Though our sample ends in 2018, we believe our results reflect the long-term American experience. However, we recognize that the economic upheaval of 2019–2020, with the black swan effect of COVID-19, led to a sharp reduction in inflation and interest rates, which may have impacted the seasonal patterns. The final sample for 1997–2018 (1980–2018) includes 24,280 (30,831) monthly observations for 549 (692) unique companies representing 63 industries classified by the two-digit Standard Industrial Classification (SIC) code. The two-digit code is the last non-zero Standard Industrial Classification (SIC) code found in a specific security’s name structure in CRSP’s database. We obtained data on prices, returns, and market values from the CRSP NYSE/AMEX database. The data included in the final sample passed through several filters, described below. (1) The IBES database includes analysts’ consensus forecasts for at least twelve consecutive months starting in January of the forecast year and ending in December. J. Risk Financial Manag. 2021,14, 206 4 of 11 (2) At least three individual forecasts determine the consensus forecast of earnings per share per month. (3) The company’s fiscal year ends in December. We excluded firms with non-December year ends to ensure appropriate intertemporal comparisons over our cross-section (Givoly 1985). (4) The CRSP NYSE/AMEX database includes price, raw, and beta excess returns, and shares outstanding information. We compounded daily returns for each firm using holding period and excess returns to compute monthly returns. The CRSP daily excess return is the excess of the daily return above the return on a portfolio of stocks with similar risk. Benchmark portfolios are defined using portfolio rankings determined by beta values (beta excess return) for the entire population of firms included in the CRSP database. Table 1presents summary information for the overall sample. Panel A reports sample statistics for quartiles based on the standard deviation of analysts’ forecasts scaled by price ( σ (FEPS)), and Panel B reports information for quartiles based on market value (MV). Ackert and Athanassakos (1997) report that analysts’ earnings forecasts are too optimistic for firms in highly uncertain information environments, where uncertainty is measured using the standard deviation of earnings forecasts. However, when uncertainty is low, analysts’ forecasts are more accurate. As these authors show that strategies based on uncertainty can generate abnormal returns, we examined whether differences arise across the level of uncertainty. In addition, because the January seasonal is reported to be related to firm size, in Panel B of Table 1, we report summary information by market value quartile (Keim 1983). Table 1. Summary statistics: The table reports summary information for our sample which includes data from January 1997 through December 2018. In addition to full sample information, Panel A provides sample statistics for quartiles based on the standard deviation of analysts’ forecasts scaled by price ( σ (FEPS)), and Panel B reports information for quartiles based on market value (MV). First, the table reports the number of analysts following sample firms as reported in the IBES database. Next, the table reports on forecasted and actual earnings, σ(FEPS), stock price, and market value (in millions of dollars). Panel A: Means for the Full Sample as Well as Quartiles Determined by the Standard Deviation of Analysts’ Earnings Forecasts Scaled by Price (σ(FEPS)). Overall Q1 (Low) Q2 Q3 Q4 (High) Number of analysts 30.59 31.09 31.26 30.00 30.00 Forecasted earnings USD 2.77 USD 2.71 USD 3.12 USD 2.60 USD 2.65 Actual earnings USD 2.69 USD 2.69 USD 3.04 USD 2.57 USD 2.47 σ(FEPS) 0.0250 0.0048 0.0111 0.0193 0.0663 Price USD 40.32 USD 49.19 USD 45.09 USD 39.15 USD 27.37 Market value USD 25,445 USD 46,918 USD 27,524 USD 16,817 USD 9749 Panel B: Means for Quartiles Determined by Market Value. Q1 (Low) Q2 Q3 Q4 (High) Number of analysts 24.34 USD 31.81 USD 34.06 USD 32.31 Forecasted earnings USD 0.98 USD 2.49 USD 3.13 USD 4.55 Actual earnings USD 0.84 USD 2.47 USD 3.00 USD 4.54 σ(FEPS) 0.0197 0.0185 0.0189 0.0110 Price USD 22.02 USD 36.69 USD 44.06 USD 59.25 Market value USD 2029 USD 6112 USD 14,630 USD 80,684 The statistics reported in Table 1indicate that the average following is substantial for the overall sample and each uncertainty ( σ (FEPS)) and MV quartile. Overall, our sample firms are followed by almost 31 professional financial analysts, on average. Forecasted earnings exceed actual earnings in all cases, consistent with the large body of research that reports analyst optimism about the earnings for firms they follow (e.g., (Ali et al. 1992)). For the low-uncertainty quartile, analyst optimism is 2 cents, on average, whereas for the J. Risk Financial Manag. 2021,14, 206 5 of 11 high-uncertainty quartile, average optimism is 18 cents. Interestingly, analyst optimism has declined significantly over time. In comparison, Ackert and Athanassakos (2000) report an average optimism of 86 cents for their high uncertainty quartile. In Panel B, we also observed, not surprisingly, that larger firms as measured by MV are associated with higher analyst following, lower σ(FEPS), and higher stock prices, on average. From Table 1, we can see that, consistent with expectations, our sample includes many large firms. This is expected, given that firms that are widely followed by analysts tend to have larger market capitalization. Importantly, however, a significant number of our highly visible sample firms are of small to moderate size. Of course, there is no single definition of small and medium capitalization, and the definitions change from year to year. For a reference point, we look to the Standard and Poor’s classifications. Prior to 20 February 2019, the S&P SmallCap600 (MidCap400) indices included firms with market capitalizations of USD 450 million to 2.1 billion (USD 1.6 billion to 6.8 billion). For the capitalization eligibility criteria before and after 20 February 2019 (S&P Global 2021). In fact, approximately one-half of our sample of highly visible firms fall into the small to mid-sized range. 4. Results We estimated the following pooled cross-sectional, time series model to examine the seasonal pattern in returns for highly visible firms: Ri,t=α0+ 12 ∑ j=2 αjDj,t+ei,t(1) where α0 is the sample average January return, R i,t is the time treturn for firm i, and D j,t is a dummy variable taking the value of one for month j, and zero otherwise. The estimate of the coefficient of each dummy variable, αj , measures the difference is return for month j from the return in January. Table 2reports OLS regressions for raw returns for our sample of highly followed firms over the January 1997 through December 2018 time period. We used Pooled OLS because it obtains unbiased estimates when attributes are constant through time. Other approaches, such as Generalized Methods of Moments, might be used in future research if concern about unbiasedness arises (Ferson and Harvey 1992). Table 2reports estimates of the seasonal dummy variables as represented by Equation (1) for the full sample as well as for quartiles based on the standard deviation of analysts’ forecasts scaled by price ( σ (FEPS)). In the table, we report t-statistics below each coefficient estimate and the final two rows report F-tests and χ2 -tests of the null hypothesis of no difference in medians across months. Asterisks of *, **, and ** indicate significance at the 10%, 5%, and 1% level, respectively. Both the F-statistics and χ2 -statistics indicate strong seasonality in returns. However, unlike Ackert and Athanassakos (2000), for the raw returns, we did not observe the typical seasonal pattern in returns, with high returns in January and adjustment down over time. Instead, Table 2indicates a lower return in January as compared to other months, though the coefficient for the January dummy is only significant for the highest uncertainty quartile and not for the overall sample. There is some significant adjustment upward, particularly in the first four months of the year across all uncertainty quartiles and the overall sample. This pattern was also observed in the seasonal pattern for raw returns across market value quartiles (not tabulated, but available upon request). As these are raw returns, though, we do not know whether the abnormal pricing leads to predictable trading opportunities. Thus, we turn to excess returns. J. Risk Financial Manag. 2021,14, 206 6 of 11 Table 2. Tests for monthly seasonal effects in raw returns with uncertainty quartiles. The table reports of OLS regressions for our sample of raw returns, which includes data from January 1997 through December 2018. The table reports estimates of seasonal dummy variables for the full sample as well as for quartiles based on the standard deviation of analysts’ forecasts scaled by price ( σ (FEPS)). t-statistics appear below each coefficient estimate with asterisks indicating statistical significance. The final two rows report F-tests and χ2 -tests of the null hypothesis of no difference across months. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. Month Overall Q1 (Low) Q2 Q3 Q4 (High) January −0.0036 (−1.04) 0.0086 (1.58) 0.0077 (1.18) −0.0054 (−0.79) −0.0259 (−3.07) ** February 0.0163 (3.36) *** 0.0117 (1.52) 0.0011 (0.12) 0.0167 (1.73) 0.0360 (3.01) ** March 0.0407 (8.40) *** 0.0122 (1.59) 0.0245 (2.67) ** 0.0482 (5.00) *** 0.0795 (6.64) *** April 0.0477 (9.84) *** 0.0247 (3.22) ** 0.0331 (3.60) *** 0.0505 (5.25) *** 0.0837 (7.00) *** May 0.0084 (1.73) −0.0036 (−0.46) −0.0004 (−0.05) 0.0115 (1.20) 0.0266 (2.22) * June −0.0021 (−0.43) −0.0147 (−1.92) −0.0102 (−1.11) −0.0031 (−0.32) 0.0205 (1.72) July −0.0029 (−0.61) −0.0137 (−1.78) −0.0058 (−0.63) −0.0048 (−0.50) 0.0132 (1.10) August −0.0032 (−0.65) −0.0249 (−3.24) ** −0.0151 (−1.65) −0.0027 (−0.28) 0.0314 (2.62) ** September 0.0154 (3.18) ** −0.0015 (−0.19) 0.0077 (0.84) 0.0154 (1.60) 0.0410 (3.43) *** October 0.0074 (1.53) 0.0056 (0.73) −0.0065 (−0.71) 0.0031 (0.33) 0.0278 (2.32) * November 0.0049 (1.01) 0.0037 (0.48) −0.0124 (−1.34) −0.0012 (−0.13) 0.0300 (2.50) * December 0.0079 (1.63) 0.0063 (0.82) 0.00001 (0.01) 0.0034 (0.35) 0.0223 (1.86) F-statistic 23.3777 *** 6.2017 *** 4.9402 *** 7.8823 *** 8.3862 *** χ2-statistic 1611.00 *** 412.42 *** 400.64 *** 410.27 *** 393.16 *** Table 3reports OLS regressions for excess returns for our sample of highly followed firms with estimates of the seasonal dummy variables for the full sample and quartiles based on the standard deviation of analysts’ forecasts scaled by price ( σ (FEPS)). Excess returns are computed using portfolio rankings indicated by beta, as explained in Section 2 of the paper. As Ackert and Athanassakos (1997) argue that strategies based on uncertainty have the potential to generate abnormal returns, we examined whether seasonal differences arise across the level of uncertainty. Asterisks of *, **, and ** indicate significance at the 10%, 5%, and 1% level, respectively. As with raw returns, the F-statistics and χ2 -statistics indicate strong seasonality in excess returns. Here, as in Ackert and Athanassakos (2000), we observed that the typical seasonal pattern of high returns in January that adjust down over time is reversed. The estimates reported in Table 3indicate a significantly lower return in January as compared to other months for the full sample, as well as the third and fourth uncertainty quartiles, with adjustment upward over most of the year. The pattern is consistent across uncertainty quartiles, though not always statistically significant. We repeated all analyses for market value quartiles, and inferences were unchanged. These results are not tabulated but are available upon request. J. Risk Financial Manag. 2021,14, 206 7 of 11 Table 3. Tests for monthly seasonal effects in excess returns with uncertainty quartiles. The table reports of OLS regressions for our sample of excess returns, which includes data from January 1997 through December 2018. The table reports estimates of seasonal dummy variables for the full sample as well as for quartiles based on the standard deviation of analysts’ forecasts scaled by price ( σ (FEPS)). Excess returns are computed using portfolio rankings indicated by beta. t-statistics appear below each coefficient estimate with asterisks indicating statistical significance. The final two rows report F-tests and χ2 -tests of the null hypothesis of no difference across months. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively. Month Overall Q1 (Low) Q2 Q3 Q4 (High) January −0.0131 (−4.44) *** −0.0022 (−0.45) −0.0031 (−0.55) −0.0130 (−2.24) * −0.0350 (−4.85) *** February 0.0181 (4.33) *** 0.0111 (1.64) 0.0046 (0.57) 0.0178 (2.18) * 0.0394 (3.85) *** March 0.0206 (4.91) *** −0.0028 (−0.42) 0.0054 (0.66) 0.0265 (3.23) ** 0.0544 (5.32) *** April 0.0187 (4.47) *** 0.0037 (0.54) 0.0064 (0.79) 0.0176 (2.15) * 0.0482 (4.71) *** May 0.0109 (2.60) ** −0.0024 (−0.36) 0.0023 (0.28) 0.0116 (1.42) 0.0329 (3.22) ** June 0.0070 (1.67) −0.0054 (−0.80) 0.0016 (0.20) 0.0050 (0.61) 0.0275 (2.69) ** July −0.0030 (−0.71) −0.0143 (−2.11) * −0.0056 (−0.69) −0.0063 (−0.76) 0.0150 (1.46) August 0.0157 (3.76) *** −0.0036 (−0.54) 0.0056 (0.70) 0.0136 (1.66) 0.0486 (4.75) *** September 0.0221 (5.29) *** 0.0055 (0.82) 0.0155 (1.92) 0.0217 (2.65) ** 0.0467 (4.56) *** October 0.0118 (2.81) ** 0.0093 (1.37) −0.0022 (−0.27) 0.0060 (0.73) 0.0346 (3.37) *** November 0.0006 (0.14) 0.0022 (0.32) −0.0186 (−2.31) * −0.0055 (−0.67) 0.0247 (2.41) * December −0.0020 (−0.47) −0.0040 (−0.59) −0.0101 (−1.25) −0.0051 (−0.62) 0.0116 (1.13) F-statistic 9.8043 *** 2.1204 * 2.3791 ** 3.7718 *** 5.4037 *** χ2-statistic 1622.29 *** 415.45 *** 401.28 *** 412.22 *** 394.88 *** We again documented seasonality in returns for highly visible firms that shows the opposite trend to the seasonality reported for small firms or those with low stock prices. Uncertainty in a firm’s information environment as measured by the standard deviation of earnings forecasts appears to have some importance in this seasonal pattern as it is stronger for firms with greater uncertainty. Ackert and Athanassakos (1997) provide evidence that analysts are more prone to act on their inclinations when greater uncertainty surrounds a firm, a behavior that might also describe fund manager behavior. If fund managers are prone to gamesmanship and window dressing, there is downward pressure on the stock price at the start of the year for highly visible firms, and this pressure reverses as the year progresses. A role for gamesmanship in understanding monthly seasonality seems to rely on annual contracting. Often, it is assumed in the literature that portfolio managers are evaluated on an annual basis. However, Ma et al. (2019) note that 3 years is the most commonly observed evaluation window, though many of their sample managers are evaluated annually. Though a longer evaluation window might seem to weaken our ability to detect an annual seasonal pattern, annual performance is quite important to managers who seek significant end-of-year performance bonuses. In any case, we provide evidence J. Risk Financial Manag. 2021,14, 206 8 of 11 of a very strong seasonal pattern that is consistent with annual seasonality caused by the forces of gamesmanship and window dressing impinging on the behavior of fund managers. 5. Additional Analysis As we noted earlier in this paper, arbitrage costs may be an impediment to efficient pricing in markets (Jacobs and Müller 2020). Rational traders exploit profit opportunities, but if they are constrained by high costs of trading, stocks may remain mispriced. Correlated opinions based on misinformation can move markets (e.g., (Shleifer and Summers 1990)). Stambaugh et al. (2012) examine the role of investor sentiment in explaining stock return anomalies. Their evidence suggests that anomalies are stronger when sentiment is high. In contrast, Hulbert (2019) suggests that when it comes to mutual fund managers and return seasonality, the anomaly could be weaker in good years. In a bull market, driven by positive investor sentiment, fund managers have less pressure to adjust portfolios at the year end. Ortiz et al. (2013) provide evidence that window dressing is more prevalent among Spanish fund managers in bear markets. Whether the seasonal pattern varies across bull and bear markets is a question Ackert and Athanassakos (2000) did not address. To shed light on sentiment and seasonality in returns, we designated 1987, 1990, 2000, 2002, 2008, and 2011 as bear market years, with all other years in the 1986 through 2018 period characterized as bull markets. The timing of bull and bear markets is from the (Dow Theory 2021). For this analysis, we used the sample period from 1980 through 2018 because there are few bear years in recent years. Table 4provides summary information for bull (Panel A) and bear (Panel B) years. For bull market years, we observed higher actual earnings, stock prices, and market values, on average. Interestingly, average analyst optimism is considerably higher in bear market years (USD 0.26), as compared to bulls (USD 0.09). Consistent with Ackert and Athanassakos (1997), we observed that analysts’ earnings forecasts are more optimistic for firms in highly uncertain information environments (Q4), particularly in bear market years. Table 4. Summary statistics for bull and bear years. The table reports summary information for our sample, which includes data from January 1980 through December 2018. In addition to full sample information, Panel A provides sample statistics for bull-market years and quartiles based on the standard deviation of analysts’ forecasts scaled by price ( σ (FEPS)), and Panel B reports information for bear-market years and quartiles based on market value (MV). First, the table reports the number of analysts following sample firms as reported in the IBES database. Next, the table reports on forecasted and actual earnings, σ(FEPS), stock price, and market value (in millions of dollars). Panel A: Means for the Bull-Market Years and Quartiles Determined by the Standard Deviation of Analysts’ Earnings Forecasts Scaled by Price (σ(FEPS)). Overall Q1 (Low) Q2 Q3 Q4 (High) Number of analysts 25.75 26.02 26.59 25.34 25.05 Forecasted earnings USD 2.22 USD 2.24 USD 2.42 USD 2.03 USD 2.20 Actual earnings USD 2.13 USD 2.21 USD 2.31 USD 1.92 USD 2.07 σ(FEPS) 0.0213 0.0038 0.0088 0.0157 0.0579 Price USD 31.80 USD 38.42 USD 35.29 USD 30.31 USD 22.85 Market value USD 16,912 USD 30,476 USD 18,296 USD 11,434 USD 6960