*4.4. Seasonality*

Cross-sectional seasonality is a relatively new phenomenon described by Heston and Sadka (2008) and later confirmed by several other authors in international markets (Heston and Sadka 2010; Keloharju et al. 2016). What Heston and Sadka (2008) found is that the stocks with a high same-month average return in the past tend to outperform stocks with a low same-month return in the past. Notably, Keloharju et al. (2016) extend this evidence to country equity indices. They find that this seasonal return pattern is admittedly weaker than in other asset classes but still visible. The tertile of countries with the highest same-month return outperform the tertile of the markets with the lowest same-month return by 0.48% (t-stat = 2.20). Notably, the markets with the highest average return in the remaining months underperformed the markets with the lowest other-month return by −0.36% (−1.66). Consistent findings were also presented in a later paper by the same authors (Keloharju et al. 2019), but, again, the statistical significance was low. The phenomenon has also been verified in early data samples by Baltussen et al. (2019b).<sup>1</sup>

#### *4.5. Long-Run Reversal*

The long-term reversal at the firm level dates back to the seminal study of De Bondt and Thaler (1985), who provided convincing evidence that stocks with a poor (good) performance over the previous 3–5 years tend to produce high (low) returns in the future. Further studies demonstrated that the effect is not only robust, but also pervasive, driving the returns on individual stocks globally (Baytas and Cakici 1999; Blackburn and Cakici 2017), futures (Lubnau and Todorova 2015), currencies (Chan 2013), and commodities (Bianchi et al. 2015; Chaves and Viswanathan 2016). Notably, the effect is also present in country equity indices.

<sup>1</sup> Note that this article focuses only on cross-sectional seasonality. Apart from this, there is some evidence that the equity indices demonstrate some monthly calendar patterns in the time series, for example in Keppler and Xue (2003) or Bouman and Jacobsen (2002).

**Index-level evidence.** The first evidence of the long-term reversal effect was provided by Kasa (1992) and Richards (1995, 1997). These authors based their research usually on limited samples of developed markets and demonstrated that indices with low (high) long-term performance significantly outperform in the future. The results were later confirmed with larger and longer samples by Kortas et al. (2005), Balvers et al. (2000), Balvers and Wu (2006), and Shen et al. (2005). Gharaibeh (2015) corroborated the long-term reversal phenomenon in the Middle East market indices, and Spierdijk et al. (2012) confirmed the findings in study periods exceeding a century. The strategy works well for 36–60-month sorting periods, and Malin and Bornholt (2013), who develop so-called "late stage" contrarian strategies, experiment also with skipping the most recent 12 months as in Fama and French (1996). Finally, Smith and Pantilei (2015) develop a simple mean-reversion-based strategy, which they called "Dogs of the Word". The technique assumes buying in five countries with the worst performance over the last year and holding them for five years. The strategy proves profitable both in indices and single-country ETFs. Smith and Pantilei (2015) argue that "assuming a five-year holding period, such a portfolio would have produced compounded annual returns of 10.39%", exceeding the profits on the global passive equity portfolios. In the years 1997–2012 their strategy implemented with the ETFs of the worst-performing countries outperforms the MSCI All Country World Index (MSCI ACWI) by 246 bps, delivering a higher Sharpe ratio and net of ETF expenses.

**Sources of long-run reversal.** Although there is no consensus on the source of long-run reversals, the existing studies offered some potential explanations. Richards (1997) considers whether the contrarian profits may stem from risk-differentials but finds no support for this hypothesis. He argues that no evidence suggests that loser-index returns are riskier in terms of their volatility or exposure to the world equity market returns. Cooper et al. (2019) link some similar patterns to global macroeconomic risks.

The winner-loser reversals profits are larger among the smaller countries than in the larger markets, so there may be an element of a "small-country effect", but still this phenomenon does not fully explain the long-term reversal effect (Zaremba and Umutlu 2018).

Another option is that the long-run reversal is just a statistical artifact and that its returns were purely period specific. Indeed, country-level long-term reversal tends to be very volatile and unstable over time, but its robustness over very long periods casts doubt on such an explanation (Spierdijk et al. 2012). Furthermore, Malin and Bornholt (2013), who employ longitudinal analysis, argue that the mean-reversion effect is present even in the post-1989 sample despite the absence of visible contrarian profits for the developed markets.

Further explanations point to behavioral mispricing that cannot be arbitraged away for many reasons, including cross-border flow limitations. The behavioral overreaction hypothesis is also consistent with the link to the momentum effect (Richards 1997; Balvers and Wu 2006; Malin and Bornholt 2013).

#### *4.6. Price Risk*

The relationship between the risk measures calculated on the basis of prices and future returns on stocks has been a controversial and intensively researched topic in recent years. On the one hand, early theoretical models sugges<sup>t</sup> that systematic risk should positively correlate with future returns in the cross section, and some early studies seem to produce consistent evidence (Sharpe 1964; Black et al. 1972; Fama and MacBeth 1973; Blume 1970; Miller and Scholes 1972; Blume and Friend 1973). Similarly, the stock-specific risk should also be either positively correlated or unrelated, depending on market integration (Levy 1978; Tinic and West 1986; Merton 1987; Malkiel and Xu 1997, 2004). However, the empirical evidence mounting over the past two decades documents a contrary phenomenon—the so called low-risk anomaly. The high-risk firms tend to underperform the low-risk firms on the risk adjusted basis, both when the risk is understood as a systematic risk or an idiosyncratic risk (Frazzini and Pedersen 2014; Ang et al. 2006, 2009). The effect is usually explained with the combination of behavioral biases and limits to arbitrage (Blitz et al. 2019). Notably, some other measures of price-based risk, such as value at risk, display a rather positive than negative relationship with future returns in the cross section (Bali and Cakici 2004).

**Market beta.** The risk-return relationship at the country level is also far from obvious and depends strongly on risk measures. The first studies bring weak evidence on the pricing on systematic risks, especially in emerging markets (Harvey 1991, 1995; Harvey and Zhou 1993). In one of the first studies, Harvey (1995) finds no relationship between beta and future returns across 20 emerging markets. In addition, more recent studies by Estrada (2000) and Bali and Cakici (2010) lead to similar conclusions. Nonetheless, the seminal study of Frazzini and Pedersen (2014) demonstrates that on a risk-adjusted basis, low-beta indices outperform high-beta indices, and the e ffect is confirmed by Berrada et al. (2015). Hedegaard (2018) also corroborates the low-beta e ffect in developed and emerging market indices, demonstrating additionally that it is partially predictable by past market returns.

**Idiosyncratic risk.** The country-level examinations display no evidence of the low-idiosyncratic risk anomaly, which is similar at the firm level. The majority of the studies find either a positive relationship or no significant relationship between idiosyncratic (or total) volatility and expected country returns in the cross section. Bali and Cakici (2010) compute total and idiosyncratic volatility measures of di fferent asset pricing models based on estimation periods ranging from one to six months and find a positive relationship. On the other hand, articles by Umutlu (2015, 2019), Liang and Wei (2019), and Hueng and Ruey (2013) show either very weak on unreliable links between idiosyncratic or total volatility and future returns in the cross section. The pricing of similar measures of price risk has been also considered by Bekaert and Harvey (1995), Estrada (2000), and Hueng (2014).

**Other definitions of risk.** Several studies examined other definitions of price risk. Some of them documented significant relationships, while others were less successful. Hollstein et al. (2019) investigate the pricing of tail risk in international stock markets. They find that both local and our newly computed global tail risk strongly predict global equity index excess returns. Sorting equity market countries into portfolios by their tail risk generates sizable excess returns across various holding periods. Arouri et al. (2019) examine the role of jump risk. Umutlu and Bengitöz (2017) o ffer a similar metric based on return range. Finally, Atilgan et al. (2019) test the forecasting power of several measures of downside risk, i.e., downside beta, tail beta, value at risk, and expected shortfall, but find no consistent evidence of return predictability.

#### *4.7. Non-Price Risks*

Besides the measures of risk derived from price behavior discussed in the previous section, numerous studies explore the role of alternative definitions and source of risk. The logic behind these studies is the following: if the country-specific risk matters for country-level asset pricing, what actually is this country-specific risk? Can it be conceptualized and captured more precisely with some alternative measures?

Examinations of the country-specific risks as determinants of future market-level performance are found in the earliest studies of cross section of country returns and date back to the 1990s (Ferson and Harvey 1994a, 1994b; Erb et al. 1995, 1996a; Bekaert et al. 1996). Some of these studies focus on just one type of risk, such as credit risk or political risk, while others examine several categories or exposures to them (Ferson and Harvey 1994a; Erb et al. 1996a; Harvey 2004). The types of considered country specific risks could be categorized into several broad classes.

**Credit risk.** Country credit risk (sovereign risk, default risk) belongs among the best-established predictors of future returns. Not only has it been extensively documented by practitioners, it is also widely employed by practitioners in models of cost of equity. A widely used database in Damodaran (2019) advocates using country risk premia based on local sovereign ratings. Erb et al. (1995) employ measures of credit risk calculated on the basis of the Institutional Investor Semiannual Survey of Bankers and demonstrate that the credit risk is priced in the country equity premium. In a later study, the same authors show how the credit risk could be used to estimate risk premia for 135 di fferent countries—even those without developed stock markets (Erb et al. 1996b). More recent research confirms these early findings with different measures of credit risk. Avramov et al. (2012) use quantified credit ratings for 75 countries in the period 1989–2009. They show that the high credit risk tercile outperforms the stocks in the countries in the low credit risk tercile by 0.57% monthly. Zaremba (2016) further corroborates these findings by using the Economist Intelligence Unit sovereign risk indicator calculated by its Country Risk Service. Having examined 74 countries for the years 1999–2015, Zaremba arrives at a qualitatively similar return on a tertile differential portfolio of 0.50% per month.

**Political risk.** The political risk is another category of risk that has been examined since the beginning of studies of the cross section of country returns (Erb et al. 1996a; Diamonte et al. 1996). The political risk is most frequently measured with the Political Risk Index, which constitutes a component of the International Country Risk Guide calculated by the PRS Group.<sup>2</sup> In general, the studies find that the political risk is positively related to the expected returns in the cross section. (Erb et al. 1996a; Dimic et al. 2015; Lehkonen and Heimonen 2015; Vortelinos and Saha 2016). Bilson et al. (2002) show that the political risk is more strongly priced in emerging markets rather than in developed ones. Consistently with this, Diamonte et al. (1996) concentrate on changes in political risk and demonstrate that average emerging market returns in countries experiencing declining political risk exceed those of emerging markets experiencing growing political risk by approximately 11% per quarter. In contrast, the analogous return for developed markets amounted to only 2.5%. Furthermore, Zaremba (2016) show that country-risk pricing is stronger in emerging and—in particular—frontier markets. Dimic et al. (2015) explore this difference further and show that while composite political risk is priced in all the types of stock markets (i.e., developed, emerging, and frontier), the role of individual components varies across countries. For example, governmen<sup>t</sup> action is a common source of risk in all market categories, but the impact of governmen<sup>t</sup> stability is unique to frontier equities.

Recent studies offer some further insights into the effect of political risk. Pagliardi et al. (2019) propose an international capital asset pricing model that accounts for the political risk. The model explains up to 77% of cross-sectional returns, outperforms some other benchmark models, and has a good predictive power. Gala et al. (2019) offer two new politics and policy risk factors and demonstrate that markets with lower politics and policy rankings produce higher average returns. They also offer some long-short strategies, which are argued to produce returns exceeding 12% per year with a corresponding Sharpe ratio of 0.59.

**Other non-price risks.** While credit risk and political risk seem to be the most intensively researched categories, other studies also consider alternate types of risks, such as economic and financial risks (Erb et al. 1996a), macroeconomic and political risks and uncertainty (Chang et al. 2017; Rapach et al. 2005), or expropriation risk (Dahlquist and Bansal 2002). Lee (2011) empirically tests the liquidity-adjusted asset pricing model of Acharya and Pedersen (2005) at the global level. The latter provide evidence that liquidity risk is priced internationally, independently of other risks. Additional analyses of country-level risk are also performed by Suleman et al. (2017).

#### *4.8. Other Predictors*

In this section, we review an array of less known predictors that have been discovered and examined in recent years.

**Fund flows.** Srimurthy et al. (2019) offer a new country asset allocation approach based on fund flows. The authors find reliable positive returns on a strategy that goes long in the countries that have attracted indirect investment via equity fund flows and short in the countries that have not. The effect is independent of some other well-established return predictors, such as size or momentum.

**Economic freedom**. Several studies explore the role of economic freedom for the future stock market returns. Stocker (2005) was, most probably, the first to try to examine this relationship. Having examined the returns on developed and emerging markets in the years 1975–2002, he demonstrates

<sup>2</sup> For details, see https://www.prsgroup.com/explore-our-products/international-country-risk-guide/.

that the rate of increase in economic freedom is directly related to equity returns. He also develops an investment strategy based on this phenomenon, which earns attractive investment returns. Similar evidence is provided by Smimou and Karabegovic (2010), who concentrate on MENA markets. Finally, Stocker (2016) corroborates his own earlier results. He documents that the index of economic freedom provides incremental information about future returns that have low correlation with value, momentum, and size factors. Stocker (2016) christens the abnormal returns from investing in low economic freedom countries "the price of freedom".

**News**. Calomiris and Mamaysky (2019) develop a new classification methodology for using the content and context of news to forecast the performance of 51 equity markets. They consider issues such as topic-specific sentiment, frequency, and unusualness (entropy) of word flow. They demonstrate significant predictive abilities of the news flow for returns, volatilities, and drawdowns, particularly for longer (one-year) horizons. The effect is more pronounced in emerging markets.

**Analyst recommendations**. There are numerous studies of the predictive power of analysts' recommendations for individual stock returns (Kothari et al. 2016), but Berkman and Yang (2019) are the first to consider a country-level parallel. The authors digest analysts' reports from 30 countries for the years 1994–2015 to demonstrate that the aggregate recommendation score helps to predict international stock market returns. The country-level recommendations make it possible to predict future aggregate cash flow and returns. A country-allocation strategy based on the insights of Berkman and Yang (2019) yields an approximate abnormal return of 1% per month.

**Asset growth.** The role of asset growth for future returns on individual stocks has become well known since Cooper et al. (2008); it was even incorporated in some popular recent factor pricing models (Fama and French 2015; Hou et al. 2015). Wen (2019) checked whether any similar effect exist at the country level. The author provides convincing evidence that aggregate asset growth constructed from bottom-up data negatively predicts future market returns across the G7 countries. This information about future performance is not captured by other measures of investment growth and macroeconomic variables.

**Growth of government debt.** Using a set of 77 countries and data from World Development Indicators, Wisniewski and Jackson (2018) document a negative association between increases in the central governmen<sup>t</sup> debt-to-GDP ratio and stock index returns, expressed in U.S. dollars. The authors estimate that raising the debt ratio by one percentage point decreases the stock returns by between 39 to 95 basis points. Wisniewski and Jackson (2018) explain this phenomenon with an upward pressure on private interest rates, which appears to signal a greater tax burden in the future.

**Democracy.** Lei and Wisniewski (2018) explore the role of democracy, proxied with the Political Right Index calculated by the Freedom House. Having researched a sample of 74 countries for the years 1975–2015, they conclude that, compared with autocracies, democratic states are characterized by higher returns despite displaying lower volatility risk. Lei and Wisniewski (2018, p. 1) offer three potential explanations of this effect: "First, the strength of investor protection under authoritarian leaders is relatively weak, making capital holders more vulnerable to expropriation. Second, our findings appear to be partly attributable to investors' sentiment that is driven by media reports. Last but not least, autocracies appear to hinder the development of pension funds, suppressing thereby the demand for stocks."

**Gravity.** Bae (2017) documents an interesting linkage between performance of different countries, namely, large countries lead returns of small countries, and this predictability decreases with geographical distance of the two countries. The effect could be translated into a long-short strategy producing about 10% risk-adjusted return per annum, which is not explained by the well-established return predictors.

**Interest rates.** Hjalmarsson (2010) investigates several potential predictors of future stock returns. The empirical results demonstrate that short-term interest rate and the term spread are fairly robust predictors of stock returns in developed markets. In contrast, Hjalmarsson (2010) finds no robust and

consistent evidence of predictability by earnings or dividend yields. Consistent evidence is provided by Charles et al. (2017).

#### *4.9. Further Investment Considerations*

Besides discovering, testing, and explaining di fferent cross-sectional patterns, separate strains of literature examine di fferent practical aspects of country allocation based on market-level cross-sectional patterns. From the practitioners' perspective, two issues seem of particular importance: (1) the influence of trading costs and (2) the timing and selection of di fferent country-allocation strategies.

**Transaction costs.** At the individual stock level, Novy-Marx and Velikov (2016) and Chen and Velikov (2019) demonstrate that transaction costs may have a detrimental impact on the profitability of anomaly-based quantitative strategies, in particular in the case of high turnover anomalies. At the inter-market level, the e ffect could be potentially even worse due to the necessity to move capital across countries. The results may also strongly depend on the implementation method chosen. Nonetheless, several studies document that when implemented with the use of ETFs, the most prominent country allocation strategies may remain profitable. Andreu et al. (2013) examine the momentum e ffect in single-country ETFs. They find that investors are potentially able to exploit the country momentum strategies with an excess return of about 5% per year. They note that the bid-ask spreads on ETFs are markedly below the implied break-even transaction cost levels, so the momentum e ffect could be profitable even after accounting for the trading costs. Finally, Blitz and van Vliet (2008) provide similar evidence extending the asset universe to additional asset classes, and Angelidis and Tessaromatis (2018) put forward analogous arguments also for value and size e ffects.

**Factor timing and selection.** The large number of di fferent potential factor strategies that could be used to allocate money across countries raises the question of factor timing and factor selection. In other words, which strategies could be selected at a given time and how can we predict their performance? Several studies demonstrate significant time-series variation in country-level strategy returns, which can be linked, for example, to macroeconomic variables, sentiment, or liquidity and arbitrage constraints (Asness et al. 2013; Cooper et al. 2019; Ilmanen et al. 2019). Indeed, some papers provide evidence that country-level strategies could be timed. Yara et al. (2018) argue that value spreads, i.e., the di fferences in valuations of long and short sides of the spread portfolios, help to predict their performance. Finally, Ilmanen et al. (2019) compare several well-known anomaly selection strategies from the firm-level universe. In particular, they investigate 12 di fferent timing signals. In general, they find weak and inconsistent evidence of factor timing. The strongest results are found for timing based on inverse volatility and valuation spreads.

#### **5. Concluding Remarks**

Over the last 30 years the asset pricing literature has accumulated remarkable evidence on the predictability of the country equity returns in the cross section. The empirical findings demonstrate numerous cross-sectional patterns in country equity indices. Some of them resemble their stock-level counterparts, such as value, momentum, or seasonality. Others, such as fund flows or political risk, are strictly characteristic for country-level return patterns.

The studies of the cross section of country equity returns use various data sets and di ffering methodologies. Such a situation may lead to inconclusive results and inconsistencies across papers. This highlights the need, therefore, of further standardization of country-level asset pricing studies.

In this article, we attempted to capture possibly the broadest survey of the studies of the country-level returns. Nevertheless, we acknowledge that due to possible omissions the presented picture may be incomplete. Furthermore, an additional limitation of this paper is the reliance on previously published research without any replication or verification of the accuracy of their outcomes.

The current landscape of cross sections of market index returns is growing in sophistication. The number of documented patterns is increasing. Meanwhile, the sources of this massive mispricing remain still largely unknown or not commonly agreed upon. The future studies of the topics discussed

in this paper should focus on pan-anomaly examinations that will try to bring some order into the factor structure of the country equity returns. Perhaps the multiple return predictive signals could be summarized in only several variables. Furthermore, we still need to improve our understanding of the economic mechanisms behind these patterns. Studies focused on the sources of the cross-sectional patterns in country returns would be very valuable. Finally, future investigations should also consider a practical investor's perspective. The questions of implementability, transaction costs, or potential improvements of the trading strategies based on cross-sectional patterns would be highly valuable for market practitioners.

**Funding:** Adam Zaremba acknowledges support from the National Science Centre of Poland. This paper is a part of project No. 2016/23/B/HS4/00731 of the National Science Centre of Poland.

**Conflicts of Interest:** The author declares no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.
