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Risks 2018, 6(4), 128; https://doi.org/10.3390/risks6040128

Article
The Fundamental Equity Premium and Ambiguity Aversion in an International Context
1
Department of Financial Market, School of Banking, University of Economics, Ho Chi Minh City 800010, Vietnam
2
Department of Banking and Finance, Faculty of Business Administration, University of Trier, Trier 54296, Germany
3
Department of Finance and Economics, School of Management, Xi’an Polytechnic University, Xi’an 710048, China
*
Author to whom correspondence should be addressed.
Received: 2 August 2018 / Accepted: 17 October 2018 / Published: 6 November 2018

Abstract

:
Stocks are riskier than bonds. This causes a risk premium for stocks. That the size of this premium, however, seems to be larger than risk aversion alone can explain the so-called “equity premium puzzle”. One possible explanation is the inclusion of a degree of ambiguity in stock returns to account for an additional ambiguity premium, whose size depends on the degree of ambiguity aversion among investors. It is, however, difficult to test this empirically. In this paper, we compute the first firm-level estimation of equity premium based on the internal rate of return (IRR) approach for a total of N = 28,256 companies in 54 countries worldwide. Using a survey of international data on ambiguity aversion, we find a strong and robust relation between equity premia and ambiguity aversion.
Keywords:
equity premium puzzle; ambiguity aversion; uncertainty aversion

1. Introduction

The equity risk premium puzzle is one of the classic puzzles in finance. Going back nearly three decades, Mehra and Prescott (1985) found that historical average returns on equity on the U.S. stock market from 1889 to 1978 (90 years) far exceeded the average returns of short-term debt, corresponding to basically riskless assets. While the difference would be a natural consequence of risk aversion, the authors argued that the sheer size of this difference could be explained only by a much higher level of risk aversion than what is usually measured in decision experiments.
In the meantime, many possible explanations for this puzzle have been proposed, for example consumption-based generalized expected utility (Epstein and Zin (1991); Constantinides (1990); Abel (1990); Campbell and Cochrane (1999)), rare and disastrous events (Rietz (1988); Mehra (1988); Barro (2005)), idiosyncratic income shocks, (Constantinides and Duffie (1996)), liquidity limitations (Bansal and Coleman (1996)), borrowing constraints (Constantinides et al. (2002)), tax reasons, (McGrattan and Prescott (2003, 2005)), survivorship bias (Brown et al. (2012)), the relative volatility of stocks and bonds (Asness (2000)) and measurement errors and poor consumption growth proxies (Mankiw and Zeldes (1991); Ait-Sahalia et al. (2004)). Further discussion is found in some excellent surveys of this work, such as Kocherlakota (1996); Cochrane (1997); Mehra and Prescott (2003); Mehra (2006). All of these approaches, however, are capable of explaining only parts of the puzzle.
Therefore, recent research has concentrated on behavioral factors contributing to an explanation of the equity premium. The two most convincing theories are based on myopic loss aversion (Benartzi and Thaler (1995); Barberis and Huang (2006)) and ambiguity aversion (Chen and Epstein (2003); Barillas et al. (2009); Gollier (2011)).
The myopic loss aversion theory interprets the high amount of equity risk premium with loss aversion, as defined by prospect theory (Kahneman and Tversky (1979); Tversky and Kahneman (1992)), coupled with a myopic view of an investor who evaluates the returns of his/her portfolio on a short-term basis (e.g., annually), while in fact investing for a long-term goal (e.g., for retirement). Since in the short-term, the loss probability of stocks is relatively high, investors request a larger risk premium.
The explanation based on ambiguity aversion starts from the observation that return distributions of stocks are not well known by investors. Therefore, not only does risk aversion, but also ambiguity aversion make stocks unattractive. However, this should be distinguished from models on uncertainty, which can be observed from market data. Since the world is full of uncertainty, this additional ambiguous factor adds an extra premium over the premium for a risky asset. Uncertainty can refer to model uncertainty, probability uncertainty (Camerer and Weber (1992); Mukerji and Tallon (2001)) or political uncertainty (Pástor and Veronesi (2012, 2013)). Additionally, information quality helps to understand the equity premium (Epstein and Schneider (2008)).
However, the investors’ attitudes toward ambiguity, not the ambiguity itself, causes the ambiguity premium. Ambiguity aversion is therefore crucial for this effect. It has been modeled as an additional behavioral factor beyond risk aversion to contribute to the equity premium (Abel (1989); Abel (2002); Chen and Epstein (2003); Klibanoff et al. (2005); Barillas et al. (2009); Gollier (2011); Ju and Miao (2012)). However, it is hard to test this hypothesis empirically, since it is difficult to distinguish ambiguity from simple risk. An ambiguous situation for one investor might be a risky situation for another investor whose has better a priori knowledge. Even assuming its theoretical feasibility, measuring ambiguity from market data is a complicated task (Izhakian (2012)), and so is investigation of the interaction effect of ambiguity aversion associated with ambiguity on the ambiguity premium in asset pricing models.
Beyond that, one remaining critical problem is the fact that data on the equity risk premium is highly heterogeneous and often inconsistent: different methodologies and in particular very different time horizons are used for the analyses. While in the U.S. time series can go back more than 100 years, in countries that only recently have established financial markets (e.g., in South East Asia, South America or Eastern Europe), time series can be as short as 10 years. Additionally, it would be very helpful to have an estimate that can not only be established at the country level, but actually at the firm level, since this would allow researchers to include various firm level controls that are otherwise necessarily missing in a countrywide comparison.
In our paper, we follow the idea of Fama and French (1999) to consider every firm as an investment project. In other words, we treat an investment into the firm as buying the firm at the beginning of the investment period by acquiring all of its assets. We subsequently retrieve all the positive earnings from its operations and funding all its outflows during the time frame. Finally, we sell the firm at the end to realize our gains. The internal rates of return from the above investments are (on average) the implied returns that investors require when making their decisions to invest money in the companies. It remains to subtract the risk-free returns from the returns of the above investment to obtain an estimate for the equity risk premium. Applying this approach on the Osirisdatabase1results in the equity premia estimations for N = 28,256 companies in 54 countries over the world.
In order to test empirically the ambiguity aversion hypotheses, we also need data on ambiguity aversion and other potentially behavioral determinants in different countries. Such data have been collected by the INTRAsurvey (Rieger et al. (2015); Rieger et al. (2017)). Rieger et al. (2015) and Rieger et al. (2017) show that there is a substantial amount of between-country variation in variables measuring risk preferences and ambiguity aversion. If this relates to the dispersion of the equity premia worldwide beyond other risk factors, ambiguity aversion might play an additional role in accounting for the equity premium.
Cultural finance is a growing field of research that is currently attracting more and more attention. Like “law and finance”, “cultural finance” plays the role of a complimentary part of “behavioral finance”, which is based on the idea that cultural norms may explain some aspects of bounded rationality. Recent arguments yield a persuasive prediction that cultural characteristics indeed influence the decisions of individual investors. To our knowledge, there is not yet a solid model linking cultural factors to market anomalies, but only some empirical evidence from international research, such as overconfidence momentum returns (Chui et al. (2010)), risk attitudes and the value premium (Chui et al. (2012); Caliskan and Hens (2017))2, as well as uncertainty avoidance and the equity premium (Rieger and Wang (2012)). However, how to precisely define cultural factors and how they influence investors’ choices are still open problems. We study in this paper the impact of these cultural dimensions, together with ambiguity aversion on the equity premium with the aim to shed some new light on this potential connection.
This paper is structured as follows: In Section 2, we review some representatively related literature. Section 3 describes our methodology and reports our estimations of the fundamental equity premium. Section 4 discusses the possibility of applying regression methodology in our international context. Section 5 reports our tests on the ambiguity aversion hypothesis empirically and studies also the impact of cultural dimensions. Afterwards, we conclude and propose some further discussions in Section 6.

2. Related Literature

2.1. Measurements of Equity Premia

We first summarize briefly the three widely-accepted approaches of estimating the equity premium3: the historical equity premium, the required premium from surveys and the implied equity premium. All these methods have strengths and weaknesses, but they share the common limits of a survivor bias and the aggregation problem, as will be discussed below.
The original and most natural approach is the historical equity premium. Proposed in the seminal paper of Mehra and Prescott (1985), the idea of comparing the actual returns on stocks over a long time period with the actual returns on a risk-free asset (usually long-term bonds or T-bills) to ascertain the difference on an annual basis as a proxy for the “historical” equity premium is straightforward and easy to replicate. Despite its wide application, the divergence in equity premia between different estimation periods and the general bounded robustness of this approach limits the applicability of this method.
Other concerns are the need for a precise definition of a risk-free proxy and the choice of a representative stock market index. Both treasury-bills and bonds cannot exclude systematic risks, while the return on a single market index clearly does not represent the stock market as a whole; also, whether using a geometric average or an arithmetic average predicts different equity premia, even on the same data and for the same investigation parameters.
All approaches for the estimation of the equity premium, including our approach, share two potential problems: the survivor bias and aggregation problems. First, only data at a country level have been studied, which leads to very few data points. The selection bias of using only data on listed companies (which show to some extent “the survival of the fittest” and tend to outperform other firms in the market) results in a positive return. There is also an “aggregation problem” that the index has to reflect the overall returns of the whole stock market, which requires the broadest coverage and has to be weighted according to stocks’ market capitalization. Last but not least, the exogeneity of the equity premia leads to greater difficulties if one wishes to investigate the equity premia in an international comparison.
The second widely-accepted approach is the “required equity premium” from surveys. It seems natural to ask investors directly about the expected returns they demand when investing in stocks. The survey subjects may range from individual investors (Shiller (2000)), institutional investors, professionals, managers (Graham and Harvey (2015)), to academics (Welch (2000); Fernandez et al. (2017)). However, the participants in stock markets are very diverse. One of the challenges is to find a subset of investors that best represents the aggregate market. A sub-problem of that is to overcome the well-documented errors in the prediction of the survey subjects, such as narrow framing, the anchoring effect or overconfidence4. A specific investor/fund manager or other individuals in charge of investment decisions also have their own knowledge, experience and inside information. This means that their actions are driven by those behavioral errors and consequently lead to disagreement in the subjectively required equity premia. Since these components are often inaccurately predicted, the aggregation of those might not be particularly reliable.
The last method to be discussed is the implied equity premium. This method is most closely related to the “fundamental” approach that we apply in this paper. To prove that investing in stocks yields better payoffs than investing in other risk-free assets, the key components of the average equity premium, the rate of return from firm investments, need to be estimated. If we know a priori the duration in years of a firm’s high growth rate as N, the expected free cash flows to equity (potential dividends) per year t as E( F D F E t ), the expected rate of return of equity investors as k e and the stable growth rate (after year N) as g N , we can estimate the implied rate of return with the following formula:
V a l u e o f e q u i t y = E ( F C F E t ) ( 1 + k e ) t + E ( F C F E N + 1 ) ( k e g n ) ( 1 + k e ) N
The above equation is the basic NPV formula to solve k e , given the potential dividends and the current price. The subtraction of a risk-free rate generates a more precise estimation. However, the assumption of a constant growth rate, a contrarian N and a forecasted g raises concerns about the accuracy of this methodology. Again, no guarantee on the representativeness of the country-wide aggregation rate of return is given.
All of these obstacles seem to suggest that it would be helpful to have an estimate that can not only be established at the country level, but actually at a firm level, since it would allow researchers to include various firm-level controls that are otherwise missing, especially in a country-wide comparison. Such an alternative approach is taken by the internal rate of return (IRR), which was initially used by Fama and French (1999) for a similar purpose5. Its advantages are, as pointed out above, that it is computable at a firm level and also computable on shorter time series. Its disadvantage is that it is rather difficult to compute, because, in order to obtain a worldwide sample, one needs accounting data of good quality for a sufficiently large number of companies worldwide. Fortunately, the Osiris database nowadays provides exactly such data. We describe our methodology and report the estimation results in Section 3.

2.2. Ambiguity Aversion to Explain the Equity Premium

Ambiguity as introduced in the seminal work by Knight (1921), in which Knightian uncertainty is defined as a situation in which some events do not have an obvious probability assignment. The experimental relevance of this distinction between risk and uncertainty was first introduced through the Ellsberg paradox (Ellsberg (1961)), whereby people would rather choose to bet on the outcome of an urn with 50 red balls and 50 blue balls than to bet on the one with 100 balls, but for which the distribution of blue or red balls is unknown. The behavior of preferring risky choices over ambiguous choices is, therefore, ambiguity aversion.
In later literature, attitudes toward ambiguity and the degree of ambiguity were mixed in some axiomatizations (Gilboa and Schmeidler (1989); Epstein and Miao (2003)), but they are two different concepts in other works (Ghirardato et al. (2004); Klibanoff et al. (2005)). While attitudes toward ambiguity (ambiguity aversion) can be measured with data from experiments in the setting of the above-mentioned Ellsberg paradox, other works argue that the degree of ambiguity can be observed directly from the market data (Izhakian (2012) and the references therein). However, behaviorists maintain a skeptical view on the direct measurement of ambiguity: the distinction between risk and ambiguity exists in the mind of the decision maker, rather than in the data. Thus, only attitudes toward ambiguity can be observed, rather than the ambiguity that influences the decisions of agents (Chen and Epstein (2003); Barillas et al. (2009); Gollier (2011)).
Intuition suggests that the effect of ambiguity aversion adds to those of risk aversion: the effect reduces the demand for ambiguous assets and acts as an extra risk aversion. Then, the equity premium is the sum of two positive terms, one for risk aversion and the other for ambiguity aversion (Chen and Epstein (2003)). However, definitions of ambiguity aversion differ among scholars, such as the aversion toward model misspecifications in robust control asset pricing (Hansen et al. (1999)) or the aversion towards the unknown probability distribution of contingent events (Mukerji and Tallon (2001)). In line with this, the most widely-known theory, the smooth ambiguity model (Klibanoff et al. (2005, 2009)), succeeds in separating ambiguity and ambiguity attitudes to form the preference foundations for introducing ambiguity as an additional (risk) factor. Investors require a premium for their compensation for risks, but also an ambiguity premium for additional ambiguity. In theoretical models, this is proven to hold under some specific conditions (Gollier (2011)). Ambiguity aversion implies an increased implicit risk, not necessarily an increase in risk aversion. The increasing implicit risk reduces the risk-free return, thereby leading to a larger equity premium.

3. The “Fundamental” Equity Premium

To estimate the equity premium with the fundamental approach, we treat every firm as a project. In other words, we consider the investment as buying a firm at the beginning by acquiring all its assets, subsequently retrieving earnings and funding outflows. At the end, we sell the firm to realize returns. The IRR from this investment is the objective return, given the condition that investors had enough initial money to buy the whole company at the beginning and to sponsor all the outcomes (e.g., investments and operational costs). The equity premia aggregated at the country level can then be used as a proxy for the required equity premia under the assumptions of the law of large numbers.
More precisely, we use the following accounting items to estimate the IRRs: the book capital of a firm in year t is defined as the sum of long-term debt plus short-term debt and book equity, where book equity is the sum of total assets, minus total liabilities, plus deferred tax. The cash earnings in year t are computed by adding earnings before extraordinary items and depreciation.
Investment in year t is measured as the change in book capital of the firm between year t 1 and t. To increase the number of observations, we set the value of long-term debt, short-term debt and the value of net cash flow to zero when there are missing values6. This modification is suggested by Fama and French (1999) and has been proven to work well for real-life data.
A natural concern is the accounting regulation in different countries investigated, but this has been addressed by the global detailed format in Osiris. Raw data are presented in the company’s country-specific and regional accounting standards. The accounts are further condensed, and the format presentations are synchronized across the different templates in the global detailed and global formats. These standardized formats enable users to follow the account logic while maintaining a high level of data transparency and accuracy7.
Technically, the IRR8 is the discount rate r c solving from the following formula:
0 = I C 0 + t = 1 T 1 X t I t ( 1 + r c ) t + F C T + ( X T I T ) ( 1 + r c ) T ,
where I C 0 is the book value of a firm’s assets at the beginning of the investment period, X t is the cash earnings of a firm in year t, I t is the gross investment of a firm in year t, F C T is the book value of a firm’s assets at the end of the investment period, T is the number of years of the investment period, c denotes book values and t is the summation index.
Formula (2) is the standard expression of the IRR of an investment project. The ideal cases in which we have all the accounting variables for the whole period of 10 years from OSIRIS are infrequent, whereas the cases in which firms entering and exiting the data in durations of less than 10 years are more frequent. Thus, the time indexes of the IRR formula have to be adjusted to match these time spans.
We have to apply the following method to utilize the best information available from OSIRIS: firstly, the IRR formula requires firm values at time zero, firm values at time T (the end of an investment period) and yearly information about incomes and investments. Secondly, firms with at least two consecutive years of data availability are then selected. Thirdly, an investment subperiod is named as a run from year t to year t + i , in which i is the number of consecutive years. Lastly, the firm value at the beginning of a run I C t equals the book capital of this firm in that year, while the firm value at the end of the run F C t + i has to be adjusted by the net cash flow (i.e., earnings minus investments). The largest number of years in a run is nine, and the smallest number is two. Numerical examples of the IRR methodology are illustrated in Table 1.
The next step is to create a 10-year investment period from 2001 to 2010 to apply the IRR formula to estimate the equity premia9. After computing the IRR for a large number of companies, we then remove outliers10 and check the consistency of our results by comparing the country-aggregated IRRs with the equity premia approximated by other methodologies.
Applying this method yields reasonably-sized estimates for the equity premium (Table 2). The median equity premia range from 0.94% (Denmark) to 7.75% (The Netherlands) in Europe; 4.46% (Argentina) to 13.82% (Cayman Islands) in the Americas; 4.14% (Jordan) to 11.86% (United Arab Emirates) in the Middle East; 3.04% (Indonesia) to 15.05% (Vietnam) in Asia; and 9.55% (Morocco) to 16.33% (South Africa) in Africa. Interestingly, the equity premium in the U.S. is 9.93%, which is very close to some recent estimations of the equity premia (reviews can be found in Damodaran (2013); Rieger and Wang (2013) and the references therein). Intuitively, the equity premium that we measure for a single country is, strictly speaking, not an equity premium, but just one instance of a required return by investors. On average, however, this corresponds to the equity premium.
To the best of our knowledge, this is the first international estimation of firm-level equity premia. The results confirm that the equity premium exists and is not merely an artifact of previously applied country-level methods. There is a certain payoff applying this approach, since the values do not necessarily reflect long-term data; however, the (necessary) short-term series expand our world sample and keep the consistency of our international comparison.

4. Data on Ambiguity Aversion and the Empirical Approach

4.1. Data on Ambiguity Aversion and Risk Preferences

In order to find empirical evidence for the ambiguity aversion hypothesis, we need data on ambiguity aversion and risk preferences in different countries. The INTRA survey (Rieger et al. (2015); Rieger et al. (2017)) shows that there is a substantial amount of between-country variation in variables measuring risk preferences and ambiguity aversion. If this relates to the dispersion of the equity premia worldwide beyond other risk factors, ambiguity aversion might play an additional role in accounting for the equity premium.
The first experimental design to capture the ambiguity-averse attitude is the well-known Ellsberg paradox (Ellsberg (1961)). By recording choices of decision makers between alternative lotteries with precise and imprecise probabilities, Ellsberg (1961) determines a preference for known risks over unknown risks. The degree of ambiguity aversion can be measured experimentally with minor modifications in the settings of the original lottery selection game. In the INTRA survey, ambiguity aversion is measured by the percentage of participants who chose the unambiguous lottery in each country, using an Ellsberg paradox-type question as follows. These data are then aggregated at a country level to determine a proxy for the average ambiguity aversion of individual investors in a country. Therefore, a higher value means more ambiguity aversion.
Please imagine the following offers and mark your choice.
In an urn, there are 100 balls with three colors (red, yellow and blue); 30 balls are red, whereas the remaining 70 consist of yellow and blue balls.
30 balls70 balls
RedYellowBlue
Imagine a ball is drawn randomly from the urn. You are offered the following two lotteries. Which lottery would you prefer?
A. If the color of this ball is red, you win $100; otherwise, you win nothing
B. If the color of this ball is yellow, you win $100; otherwise, you win nothing.
(A preference for Option A points to a significant amount of ambiguity aversion).
Similarly, we use the relative risk premium (RRP) parameters from the INTRA as proxies for risk preferences. The RRP11 is measured in the two domains: gains and losses. According to the prospect theory, losses have more emotional impact than an equivalent amount of gains. The RRP is positive when a person is risk averse and negative when a person is risk-seeking. A large RRP means more risk aversion (or less risk-seeking).
Connecting investors’ preferences to the equity premium requires us to overcome the critique of the representativeness of our countrywide aggregation. Thanks to home bias (Coval and Moskowitz (1999)), investors tend to hold local stocks in the majority. For instance, French and Poterba (1991) empirically report the domestic ownership share in 1990 of the world’s five largest stock markets to be 92.2% (U.S.), 95.7% (Japan), 92% (U.K.), 79% (Germany) and 89.4% (France). This tendency to prefer local stocks is due to institutional barriers to foreign investments, transaction costs (Black (1974); Stulz (1981)) and tax reasons (French and Poterba (1991))
While we do not assume that ambiguity aversion of average investors corresponds exactly to that measured in the INTRA study, the relative differences between countries should be reflected by the relative differences between investors of companies from the respective countries12. For instance, it might be the case that participants of the INTRA study in Vietnam and Germany have higher ambiguity aversion than average investors in their respective countries, but given that the participants in Vietnam have a higher ambiguity aversion than those in Germany, the result nevertheless suggests that investors in Vietnam are likely to have a higher ambiguity aversion than investors in Germany. That this relative difference is consistent with the INTRA study data is relevant for our empirical result. A precise value of ambiguity aversion of investors would be nice to know, but the elicitation method in the INTRA survey in any event does not allow us to obtain precise quantitative data on the amount of ambiguity aversion.
Since preference variables from INTRA are the results of the aggregation among individual investors, a possible criticism is that institutional investors might outperform individual investors. However, the majority of investors, especially in emerging markets, are individuals (DeBondt (1998)). Even when that is not the case, in a world of institutional investors such as pension, mutual and hedge funds, managers investing others’ money often exhibit interests aligned with those of their clients (Haigh and List (2005)). In fact, our estimation of investors’ preferences in INTRA proves a good proxy to model a representative investor in every country in the sample. Matching INTRA data with our estimations of equity premia results in N = 25,748 companies in 35 countries for our final investigation (Table 3).

4.2. Regression Models and Controls

We apply the weighted regression as follows:
w i E P i , j = α i + w i A i β 1 i + w i C i β 2 i + ϵ i
where E P i , j is the equity premium of firm j in country i and A i is the vector of ambiguity aversion and/or other risk factors. C i is the vector of controls, and w i is the weight, which equals the ratio of the number of companies in a country over the total number of companies in the sample, while ϵ i is the error term. As robustness checks, we apply regressions using the down-weighting outlier methodology, as introduced in Street et al. (1988). This helps to create a smoother dataset by assigning case-by-case weights associated with every extreme case. However, for international data, an outlier in one country could be the normal case in the sample of another region. This approach increases the explanatory power (high R-squared), but reduces the effects of global-wide dispersion in our investigated variables.
Controls have been selected with care. For firm-specific risks, we use the beta of a stock (Ben-Zion and Shalit (1975)) (computed using the last one-year returns in reference to the market indexes), the volatility (Bekaert and Wu (2000)) (over the last 360 trading days13), the log of a firm’s leverage ratio (Ben-Zion and Shalit (1975)), the number of analysts following a stock (Harris and Marston (2001)) and the past one-year’s cumulative stock return (Graham and Harvey (2005)). Those variables are available from the OSIRIS database.
The effects of market-wide determinants and country-level factors (Ferson and Harvey (1994); Lombardo and Pagano (2006)) are controlled by proxies representing information quality, transparency, institutional environment and government policies. To overcome collinearity, we report only results in regressions with selected macroeconomics factors as controls. In particular, all our regressions are tested using the Collin tests (Belsley et al. (2005)).
We use the log of gross domestic product (GDP) per capita, log of the ratio of stock market capitalization to GDP, log of the GDP growth rate and the economic freedom index as macroeconomic controls. For robustness checks, the investor protection index, market efficiency index and the Gini index are investigated, as well as the LLSV14-type variables (details in Appendix A), which control for the relationship between law, institutional system and finance, and all may have some impact on the equity premium.
Since our data are unique, we integrate additional behavioral variables from other international surveys. One of these is the proportion of participants who describe themselves as risk-seeking or risk averse in the World Value Survey15, and the uncertainty avoidance index (UAI) from Hofstede (2001), which is more closely related to ambiguity aversion. This index captures the extent to which a society can tolerate an uncertain or ambiguous situation. Last but not least, the cultural indexes of Hofstede are investigated to shed light on the relationship between the equity premium and cultural determinants. Intuitively, one may infer that the UAI is associated with risk attitude, but Hofstede (2001) has emphasized that “uncertainty avoidance does not equal to risk avoidance”. Moreover, Rieger et al. (2015) also demonstrated that ambiguity aversion differs from Hofstede’s UAI.

5. Empirical Tests on Ambiguity Aversion and the Equity Premium

5.1. Key Results

We begin our investigation by using equity premium as the dependent variable and other potential determinants as the independent components of the weighted least squares regressions. Starting with only firm-level controls, we investigate our ambiguity-aversion measure together with other macroeconomics factors in turn (Table 4). Our evidence supports the additional role of ambiguity aversion beyond other risk preferences to account for the equity premia (Table 5). The coefficients of ambiguity aversion are significantly negative in all of our models, that is the equity premia are lower in countries where investors are ambiguity averse, which is in line with Gollier (2011). Even though the intuition suggests that ambiguity aversion plays an additional role beyond risk aversion to explain the equity premium puzzle (Hansen et al. (1999); Chen and Epstein (2003)), this is not true (Rothschild and Stiglitz (1971); Fishburn and Porter (1976); Gollier (1995); Abel (2002); Athey (2002)) or holds only under some specific conditions16. Ambiguity aversion increases the implicit risk, not necessarily the risk aversion. Generally speaking, the ambiguity premium, i.e., the interaction term between ambiguity aversion and ambiguity, plays this additional role beyond risk premium in the modern asset pricing formula. The impossibility to measure ambiguity from our data prevents us from testing the effects of this interaction term between ambiguity aversion and ambiguity on the equity premium.
In the next step, we attempt to test cultural factors, in particular Hofstede (2001)’s individualism collectivism index (IDV) and UAI. All the four behavioral dimensions might have effects, but we focus more on the above-mentioned two factors, because they have been shown previously to affect financial markets (Kwok and Tadesse (2006); Beugelsdijk and Frijns (2010)). The feasible approaches have been applied on momentum returns (Chui et al. (2012)), value premium (Chui et al. (2012); Caliskan and Hens (2017)), foreign equity holdings of institutional investors (Anderson et al. (2011)) and, similarly, in the field of cultural behavioral finance (Lucey and Dowling (2013)).
According to Hofstede (2001), the individualism dimension reflects the degree to which individuals address themselves as unique and independent, or alternatively, as integrated into groups. However, because the individualism index is the result of an aggregation of cultural values, it is difficult to imply a direct link from cultural norms to investors’ risk attitudes. On the one hand, individualism is positively related to overconfidence and self-attribution bias (Chui et al. (2010)): investors in more individualistic countries tend to see themselves as better than others, which leads to overweighting their own trading skills and private information, and consequently, more risk-seeking. This eventually causes excess noise-trading and, therefore, higher equity premia. On the other hand, the “cushion hypothesis” (Hsee and Weber (1999)) proposes the opposite: the strong social network in a collectivistic (i.e., low individualism) society provides a “cushion” against potential financial catastrophe and, therefore, induces less risk-averse behavior. Our empirical results slightly support the first of these ideas by finding positive significant coefficients of the IDV in all our models (Table 6).
The second cultural dimension that we investigate is the UAI, which is to some extent related to our ambiguity aversion. This dimension expresses the degree to which the members of a society feel comfortable with uncertainty or ambiguity. In the original definition by Hofstede (2001), uncertainty avoidance measures how a society deals with the fact that “the future can never be known: should we try to control the future or just let it happen?”. Uncertainty avoidance is a much more general concept than ambiguity aversion itself. In our tests, the effects of uncertainty avoidance on the equity premium are weak and negative, suggesting a need for further investigation before any implication can be drawn (Table 7).
Two possible concerns are the possibility of collinearity between cultural variables with ambiguity aversion and the strong effect of ambiguity aversion in joint models with other macroeconomic and cultural characteristics. We check these issues by removing ambiguity aversion from the above-mentioned models after the collinearity tests. However, the results remain similar and, therefore, are not reported.

5.2. Robustness Checks

To test for robustness, we employ a new group of control variables that may have effects on the return distributions, which are well documented in the literature. We add the Investor Protection Index and Market Efficiency Index from the Global Competitiveness Report 2010 by the World Economic Forum and the Gini index as controls for the development of a country’s stock market. Other firm-level factors remain unchanged. Further tests are implemented by collecting LSSV-type variables, such as the rule of law (LaPorta et al. (1998)), investor protection index (LaPorta et al. (2000)) and self-dealing regulations (Djankov et al. (2008)). In addition, ambiguity aversion remains a significant contributor in tests with or without controlling for risk-preference parameters (Table 8 and Table 9).
The second robustness test we employ is the robust regression for down-weighting outliers (Street et al. (1988)). An algorithm is applied in the first step to form the case-by-case weight for every extreme case, with the aim of minimizing the sum of a less rapidly increasing function of the residuals. The next step is to run a weighted least squares regression with these case-by-case weights, which yields robust results, since all the outliers are down-weighted to create smoother data. This approach helps to minimize the sum of residuals to the lowest extent, which results in a significantly high R-squared. However, this case-by-case weighting approach bypasses the country effect of those extreme values, which is captured successfully by the case-by-country weighting methodology.
In all regressions, the effect of ambiguity aversion remains significant (with a high R-squared (Table 10 and Table 11). As previously mentioned, the down-weighting methodology smooths out all the country effects, and therefore, it is not appropriate to interpret the regression coefficients in the usual way. However, the strong explanatory power of ambiguity aversion on the equity premia is robust, as can be observed by its statistical significance, which is at the 1% level in all models.

6. Conclusions

The main contribution of this research is to provide rigorous empirical evidence supporting the approach of ambiguity aversion in explaining the equity premium puzzle. Intuitively, the interaction effect of ambiguity and ambiguity aversion causing an ambiguity premium beyond the risk premium must be the central object. Given the current data and results, we can conclude only that ambiguity aversion has an impact on the equity premium. Theoretical models suggest that ambiguity aversion can explain the equity premium puzzle, but our current data are insufficient to estimate the proportion of equity premium that can be explained by it.
A further interesting aspect of our research is the significant impact of cultural differences on the size of the equity premium. The cross-country differences in investors’ preferences can be translated into a systematic distribution of the equity premia worldwide.
Our research, based on a large international database, is the first to understand the equity premium at a level beyond country aggregation. Since it is difficult to connect preferences and behavior at the individual level, our results suggest some initial causal effects, which could be investigated in more detail in future research in the field of cultural finance.

Author Contributions

Writing, original draft preparation, M.H.N. Review and editing, S.Y. Supervision, M.O.R.

Funding

This research was funded by the University of Economics, the HCMCscholarship, the MOET, the Project 322 scholarship and the University of Trier “Studentabschluss-Stipendien” scholarship.

Conflicts of Interest

The authors declare 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; nor in the decision to publish the results.

Appendix A

Table A1. List of control variables.
Table A1. List of control variables.
Variables DescriptionsSources
(1) Firm level controls
Beta of stock The last 1-year beta of stockOSIRIS
Stock volatility The stock’s volatility (the last 360 trading days)OSIRIS
Leverage ratio Log of (long-term debt/market capitalization)OSIRIS
Analysts The number of analysts following a stockOSIRIS
Past stock return Log of the last 1-year cumulative returnOSIRIS
(2) Country aggregate controls
GDP per capita Log of GDP per capitaWorld Development Indicators 1
Stock market capitalization Ratio of the stock market capitalization to GDPWorld Development Indicators
GDP growth rate Log of annual GDP growth rateWorld Development Indicators
Economic freedom A series of 10 economic measurements (World Heritage)Economic Freedom Index 2
Gini index The index measures the equality of income distributionWorld Bank 3
Market efficiency index Index of market efficiency by the World Economic ForumThe Global Competitiveness Report 4
Investor protection index Index of minority investor protection by the World Economic ForumThe Global Competitiveness Report 5
(3) LLSV-type variables
Rule of law (0–10) Rule of law (0–10)LaPorta et al. (1998)
Eff. of the jud. system Efficiency of the judicial system (0–10)LaPorta et al. (1998)
Corruption Corruption index (0–10)LaPorta et al. (1998)
Accounting standard Accounting standard indexLaPorta et al. (1998)
Anti-director index (0–6) Measure of shareholder protectionLaPorta et al. (2000)
Creditor right (0–4) Creditor rights protectionLaPorta et al. (2000)
Anti-self-dealing index Legal protection of minority shareholdersDjankov et al. (2008)

References

  1. Abel, Andrew B. 1989. Asset Prices Under Heterogeneous Beliefs: Implications for the Equity Premium. Philadelphia: Rodney L. White Center for Financial Research, pp. 32–58. [Google Scholar]
  2. Abel, Andrew B. 1990. Asset prices under habit formation and catching up with the Joneses. The American Economic Review 80: 38–42. [Google Scholar]
  3. Abel, Andrew B. 2002. An exploration of the effects of pessimism and doubt on asset returns. Journal of Economic Dynamics and Control 26: 1075–92. [Google Scholar] [CrossRef]
  4. Ait-Sahalia, Yacine, Jonathan A. Parker, and Motohiro Yogo. 2004. Luxury goods and the equity premium. The Journal of Finance 59: 2959–3004. [Google Scholar] [CrossRef]
  5. Anderson, Christopher W., Mark Fedenia, Mark Hirschey, and Hilla Skiba. 2011. Cultural influences on home bias and international diversification by institutional investors. Journal of Banking & Finance 35: 916–34. [Google Scholar]
  6. Asness, Clifford S. 2000. Stocks versus bonds: Explaining the equity risk premium. Financial Analysts Journal 56: 96–113. [Google Scholar] [CrossRef]
  7. Athey, Susan. 2002. Monotone comparative statics under uncertainty. The Quarterly Journal of Economics 117: 87–223. [Google Scholar] [CrossRef][Green Version]
  8. Bansal, Ravi, and Wilbur John Coleman. 1996. A monetary explanation of the equity premium, term premium, and risk-free rate puzzles. Journal of Political Economy 104: 1135–71. [Google Scholar] [CrossRef]
  9. Barberis, Nicholas, and Ming Huang. 2006. The loss aversion/narrow framing approach to the equity premium puzzle. National Bureau of Economic Research. [Google Scholar] [CrossRef]
  10. Barillas, Francisco, Lars Peter Hansen, and Thomas J. Sargent. 2009. Doubts or variability? Journal of Economic Theory 144: 2388–418. [Google Scholar] [CrossRef]
  11. Barro, Robert J. 2005. Rare events and the equity premium. Technical Report: National Bureau of Economic Research 22: 133–36. [Google Scholar]
  12. Bekaert, Geert, and Guojun Wu. 2000. Asymmetric volatility and risk in equity markets. The Review of Financial Studies 13: 1–42. [Google Scholar] [CrossRef]
  13. Belsley, David A., Edwin Kuh, and Roy E. Welsch. 2005. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. Hoboken: John Wiley & Sons. [Google Scholar]
  14. Ben-Zion, Uri, and Sol S. Shalit. 1975. Size, leverage, and dividend record as determinants of equity risk. The Journal of Finance 30: 1015–26. [Google Scholar] [CrossRef]
  15. Benartzi, Shlomo, and Richard H. Thaler. 1995. Myopic Loss Aversion and the Equity Premium Puzzle. The Quarterly Journal of Economics 110: 73–92. [Google Scholar] [CrossRef][Green Version]
  16. Beugelsdijk, Sjoerd, and Bart Frijns. 2010. A cultural explanation of the foreign bias in international asset allocation. Journal of Banking & Finance 34: 2121–31. [Google Scholar]
  17. Black, Fischer. 1974. International capital market equilibrium with investment barriers. Journal of Financial Economics 1: 337–52. [Google Scholar] [CrossRef]
  18. Breuer, Wolfgang, and Benjamin Quinten. 2009. Cultural Finance. Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1282068 (accessed on 5 November 2018).
  19. Brown, Stephen J., William N. Goetzmann, and Stephen A. Ross. 2012. Survival. The Journal of Finance 50: 853–73. [Google Scholar] [CrossRef]
  20. Caliskan, Nilufer, and Thorsten Hens. 2017. Value and patience: The value premium in a dividend-growth model with hyperbolic discounting. In Swiss Finance Institute Research Paper No. 13-32. Geneva: Swiss Finance Institue. [Google Scholar]
  21. Camerer, Colin, and Martin Weber. 1992. Recent developments in modeling preferences: Uncertainty and ambiguity. Journal of Risk and Uncertainty 5: 325–70. [Google Scholar] [CrossRef]
  22. Campbell, John Y., and John H. Cochrane. 1999. By force of habit: A consumption-based explanation of aggregate stock market behavior. The Journal of Political Economy 107: 205–51. [Google Scholar] [CrossRef]
  23. Chen, Zengjing, and Larry Epstein. 2003. Ambiguity, risk, and asset returns in continuous time. Econometrica 70: 1403–43. [Google Scholar] [CrossRef]
  24. Chui, Andy. C. W., Sheridan Titman, and K. C. John Wei. 2010. Individualism and momentum around the world. The Journal of Finance 65: 361–92. [Google Scholar] [CrossRef]
  25. Chui, Andy C. W., Sheridan Titman, K.C. John Wei, and Feixue Xie. 2012. Explaining the value premium around the world: Risk or mispricing? Working paper. Available online: http://www.sfm.url.tw/20thSFM/pdf/CompletePaper/025-627822826.pdf (accessed on 10 August 2018).
  26. Cochrane, John H. 1997. Where is the market going? Uncertain facts and novel theories. National Bureau of Economic Research. [Google Scholar] [CrossRef]
  27. Constantinides, George M., and Darrell Duffie. 1996. Asset pricing with heterogeneous consumers. Journal of Political Economy 104: 219–40. [Google Scholar] [CrossRef]
  28. Constantinides, George. M., John B. Donaldson, and Rajnish Mehra. 2002. Junior can’t borrow: A new perspective on the equity premium puzzle. The Quarterly Journal of Economics 117: 269–96. [Google Scholar] [CrossRef]
  29. Constantinides, George M. 1990. Habit formation: A resolution of the equity premium puzzle. Journal of Political Economy 98: 519–43. [Google Scholar] [CrossRef]
  30. Coval, Joshua D., and Tobias J. Moskowitz. 1999. Home bias at home: Local equity preference in domestic portfolios. The Journal of Finance 54: 2045–73. [Google Scholar] [CrossRef]
  31. Damodaran, Aswath. 2013. Equity Risk Premiums (ERP): Determinants, Estimation and Implications—The 2012 Edition. World Scientific Series in Finance Managing and Measuring Risk 5: 343–455. [Google Scholar]
  32. De Bondt, Werner F. M. 1998. A portrait of the individual investor. European Economic Review 42: 831–844. [Google Scholar] [CrossRef]
  33. Djankov, Simeon, Rafael La Porta, Florencio Lopez-de-Silanes, and Andrei Shleifer. 2008. The law and economics of self-dealing. Journal of Financial Economics 88: 430–465. [Google Scholar] [CrossRef][Green Version]
  34. Ellsberg, Daniel. 1961. Risk, ambiguity, and the savage axioms. The Quarterly Journal of Economics 75: 643–669. [Google Scholar] [CrossRef]
  35. Epstein, Larry G., and Jianjun Miao. 2003. A two-person dynamic equilibrium under ambiguity. Journal of Economic Dynamics and Control 27: 1253–88. [Google Scholar] [CrossRef]
  36. Epstein, Larry G., and Martin Schneider. 2008. Ambiguity, information quality, and asset pricing. The Journal of Finance 63: 197–228. [Google Scholar] [CrossRef]
  37. Epstein, Larry. G., and Stanley E. Zin. 1991. Substitution, risk aversion, and the temporal behavior of consumption and asset returns: An empirical analysis. Journal of Political Economy 99: 263–86. [Google Scholar] [CrossRef]
  38. Fama, Eugene F., and Kenneth R. French. 1999. The corporate cost of capital and the return on corporate investment. The Journal of Finance 54: 1939–67. [Google Scholar] [CrossRef]
  39. Fernandez, Pablo, Javier Aguirreamalloa, and Luis Corres Avendaño. 2017. Market Risk Premium Used in 82 Countries in 2012: A Survey with 7192 Answers. In IESE Business School Working Paper No. WP-1059-E. Barcelona: IESE Business School. [Google Scholar]
  40. Ferson, Wayne, and Campell R. Harvey. 1994. An exploratory investigation of the fundamental determinants of national equity market returns. In The Internationalization of Equity Markets. Chicago: University of Chicago Press, pp. 59–147. [Google Scholar]
  41. Fishburn, Peter C., and Burr R. Porter. 1976. Optimal portfolios with one safe and one risky asset: Effects of changes in rate of return and risk. Management Science 22: 1064–73. [Google Scholar] [CrossRef]
  42. French, Kenneth R., and James M. Poterba. 1991. Investor diversification and international equity markets. American Economic Review 81: 222–26. [Google Scholar]
  43. Ghirardato, Paolo, Fabio Maccheroni, and Massimo Marinacci. 2004. Differentiating ambiguity and ambiguity attitude. Journal of Economic Theory 118: 133–173. [Google Scholar] [CrossRef][Green Version]
  44. Gilboa, Itzhak, and David Schmeidler. 1989. Maxmin expected utility with non-unique prior. The Quarterly Journal of Economics 18: 141–53. [Google Scholar]
  45. Gollier, Christian. 1995. The comparative statics of changes in risk revisited. Journal of Economic Theory 66: 522–35. [Google Scholar] [CrossRef]
  46. Gollier, Christian. 2011. Portfolio choices and asset prices: The comparative statics of ambiguity aversion. The Review of Economic Studies 78: 1329–44. [Google Scholar] [CrossRef]
  47. Graham, John R., and Campbell R. Harvey. 2005. The long-run equity risk premium. Finance Research Letters 2: 185–94. [Google Scholar] [CrossRef]
  48. Graham, John R., and Cambell R. Harvey. 2015. The Equity Risk Premium in 2015. Working paper. Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2611793 (accessed on 5 November 2018).
  49. Haigh, Michael S., and John A. List. 2005. Do professional traders exhibit myopic loss aversion? An experimental analysis. The Journal of Finance 60: 523–34. [Google Scholar] [CrossRef]
  50. Hansen, Lars Peter, Thomas J. Sargent, and Thomas D. Tallarini. 1999. Robust permanent income and pricing. Review of Economic Studies 66: 873–907. [Google Scholar] [CrossRef]
  51. Harris, Robert S., and Felicia Marston. 2001. The market risk premium: Expectational estimates using analysts’ forecasts. Journal of Applied Finance 11. Available online: https://ssrn.com/abstract=285557 (accessed on 5 November 2018). [Google Scholar]
  52. Hofstede, Geert. 2001. Culture’s Consequences: Comparing Values, Behaviors, Institutions and Organizations Across Nations. Thousand Oaks: Sage Publications, ISBN 0-8039-7323-3. [Google Scholar]
  53. Hsee, Christopher K, and Elke U. Weber. 1999. Cross-national differences in risk preference and lay predictions. Journal of Behavioral Decision Making 12: 165–79. [Google Scholar] [CrossRef]
  54. Izhakian, Yehuda. 2012. Ambiguity Measurement. Working paper 12-01. New York: New York University. [Google Scholar]
  55. Ju, Nengjiu, and Jianjun Miao. 2012. Ambiguity, learning, and asset returns. Econometrica 80: 559–91. [Google Scholar] [CrossRef][Green Version]
  56. Kahneman, Daniel, and Amos Tversky. 1979. Prospect theory: An analysis of decision under risk. Econometrica: Journal of the Econometric Society 47: 263–91. [Google Scholar] [CrossRef]
  57. Klibanoff, Peter, Massimo Marinacci, and Sujoy Mukerji. 2005. A smooth model of decision making under ambiguity. Econometrica 73: 1849–92. [Google Scholar] [CrossRef]
  58. Klibanoff, Peter, Massimo Marinacci, and Sujoy Mukerji. 2009. Recursive smooth ambiguity preferences. Journal of Economic Theory 14: 930–76. [Google Scholar] [CrossRef]
  59. Knight, Frank H. 1921. Risk, Uncertainty and Profit. Boston: Houghton Mifflin Company. [Google Scholar]
  60. Kocherlakota, Narayana R. 1996. The equity premium: It’s still a puzzle. Journal of Economic Literature 34: 42–71. [Google Scholar]
  61. Kwok, Chuck Y., and Solomon Tadesse. 2006. National culture and financial systems. Journal of International Business Studies 37: 227–47. [Google Scholar] [CrossRef]
  62. La Porta, Rafael, Florencio Lopez-de-Silanes, Andrei Shleifer, and Robert W. Vishny. 1998. Law and finance. Journal of Political Economy 106: 1113–55. [Google Scholar] [CrossRef]
  63. La Porta, Rafael, Florencio Lopez-de-Silanes, Andrei Shleifer, and Robert W. Vishny. 2000. Investor protection and corporate governance. Journal of Financial Economics 58: 3–27. [Google Scholar] [CrossRef][Green Version]
  64. Lombardo, David, and Marco Pagano. 2006. Legal determinants of the return on equity. In Corporate and Institutional Transparency for Economic Growth in Europe. Bingley: Emerald Group Publishing, pp. 235–70. ISBN 0-08-044665-5. [Google Scholar]
  65. Lucey, Brian M., and Michael Dowling. 2013. Cultural behavioral finance in emerging markets. In Emerging Markets and the Global Economy: A Handbook. Cambridge: Academic Press. [Google Scholar]
  66. Mankiw, N. Gregory, and Zeldes Stephen P. 1991. The consumption of stockholders and nonstockholders. Journal of Financial Economics 29: 97–112. [Google Scholar] [CrossRef][Green Version]
  67. McGrattan, Ellen R., and Edward C. Prescott. 2003. Average debt and equity returns: Puzzling? The American Economic Review 93: 392–97. [Google Scholar] [CrossRef]
  68. McGrattan, Ellen R., and Edward C. Prescott. 2005. Taxes, Regulations, and the Value of US and UK Corporations. The American Economic Review 72: 767–96. [Google Scholar]
  69. Mehra, Rajnish, and Edward C. Prescott. 1985. The equity premium: A puzzle. Journal of Monetary Economics 15: 145–61. [Google Scholar] [CrossRef]
  70. Mehra, Rajnish, and Edward C. Prescott. 1988. The equity risk premium: A solution? Journal of Monetary Economics 22: 133–36. [Google Scholar] [CrossRef]
  71. Mehra, Rajnish, and Edward C. Prescott. 2003. The equity premium in retrospect. In Handbook of the Economics of Finance. Amsterdam: Elsevier B.V., vol. 1. [Google Scholar]
  72. Mehra, Rajnish. 2006. The equity premium puzzle: A review. Foundations and Trends in Finance 2: 1–81. [Google Scholar] [CrossRef]
  73. Mukerji, Sujoy, and Jean-Marc Tallon. 2001. Ambiguity aversion and incompleteness of financial markets. Review of Economic Studies 68: 883–904. [Google Scholar] [CrossRef]
  74. Pástor, Lubos, and Pietro Veronesi. 2012. Uncertainty about government policy and stock prices. The Journal of Finance 67: 1219–64. [Google Scholar] [CrossRef]
  75. Pástor, Lubos, and Pietro Veronesi. 2013. Political uncertainty and risk premia. Journal of Financial Economics 110: 520–45. [Google Scholar] [CrossRef]
  76. Ramsey, Philip H., and Patricia R. Ramsey. 2007. Optimal trimming and outlier elimination. Journal of Modern Applied Statistical Methods 6: 355–60. [Google Scholar] [CrossRef]
  77. Rieger, Marc O., and Mei Wang. 2012. Can ambiguity aversion solve the equity premium puzzle? Survey evidence from international data. Finance Research Letters 9: 63–72. [Google Scholar] [CrossRef]
  78. Rieger, Marc O., Mei Wang, and Thorsten Hens. 2013. International evidence on the equity premium puzzle and time discounting. Multinational Finance Journal 17: 149–63. [Google Scholar] [CrossRef]
  79. Rieger, Marc O., Mei Wang, and Thorsten Hens. 2015. Risk preferences around the world. Management Science 61: 637–48. [Google Scholar] [CrossRef]
  80. Rieger, Marc Oliver, Mei Wang, and Thorsten Hens. 2017. Estimating cumulative prospect theory parameters from an international survey. Theory and Decision 82: 567–96. [Google Scholar] [CrossRef]
  81. Rietz, Thomas A. 1988. The equity risk premium a solution. Journal of monetary Economics 22: 117–31. [Google Scholar] [CrossRef]
  82. Rothschild, Michael, and Joseph Stiglitz. 1971. Increasing risk II: Its economic consequences. Journal of Economic Theory 3: 66–84. [Google Scholar] [CrossRef]
  83. Shiller, Robert J. 2000. Measuring bubble expectations and investor confidence. The Journal of Psychology and Financial Markets 1: 49–60. [Google Scholar] [CrossRef]
  84. Street, James O., Raymond J. Carroll, and David Ruppert. 1988. A note on computing robust regression estimates via iteratively reweighted least squares. The American Statistician 42: 152–54. [Google Scholar]
  85. Stulz, Rene M. 1981. On the effects of barriers to international investment. The Journal of Finance 36: 923–34. [Google Scholar] [CrossRef]
  86. Tversky, Amos, and Daniel Kahneman. 1992. Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5: 297–323. [Google Scholar] [CrossRef][Green Version]
  87. Welch, Ivo. 2000. Views of financial economists on the equity premium and on professional controversies. Journal of Business 73: 501–37. [Google Scholar] [CrossRef]
1
“OSIRIS is a fully integrated public company database and analytical information solution. The database provides financial, ownership, news, ratings, earnings and stock data for the world’s publicly listed companies. The industrial company financial data on OSIRIS is provided by World’Vest Base (WVB) and five regionally specialized providers; Korea Information Service (KIS), Teikoku Databank (Japan), Huaxia International Business Credit Consulting Company (China), Reuters (USA) and Edgar Online (USA)” (Osiris Data Guide).
2
A recent summary can be found in Table 3 in Breuer and Quinten (2009).
3
We do not mention here the traditional definitions of equity premia derived from asset pricing models (CAPM, APTand others). An excellent review can be found in Damodaran (2013).
4
In brief, investors usually overvalue themselves (overconfident), pay more attention to the recent fluctuations of some specific stocks in their portfolio (narrow framing) and use past information as reference points (anchoring effect). This explains the common positive magnitudes of the required equity premia and the tight bounds of those estimations.
5
They used accounting and stock data in the U.S. for the period of 1950 to 1966. Their measurements were in the order of six to seven percent in real terms, which is close to the compound year returns of stocks for the same period.
6
We have to replace 2438 observations of deferred tax, 5196 observations of extraordinary items, 1921 observations of short-time debt and 1162 observations with long-term debt with zero. This constitutes in total less than 7% of the overall observations. This trade-off makes sense, since we can include more firms, but our methodology still maintains the consistency of the estimated IRRs.
7
“The industrial financials on Osiris from World’Vest Base, Multex, KIS, Teikoku and Huxia are collected through direct company contact and directly from the original annual reports issued by the companies. The regional accounting practices are retained with the use of the Anglo(mostly used for American, English and Nordic companies), Hybrid (mostly used for European companies) and Continental (mostly used for Asian and Australian companies) templates, which present differing Spreadsheet formats. Accuracy is retained in the Global detailed and Global formats as the accounts are further condensed and the format presentations are synchronized across the three industrial templates” (Osiris data guide) (http://www.otago.ac.nz/library/pdf/OSIRISDataGuide.pdf).
8
Fama and French (1999) propose two concepts: IRRs on costs and IRRs on values. In the first term, the initial investment is to acquire the firm at its market value, while booked costs are used in the second. The same argument is applied to the values at the end of the investment period. In this section, we apply only nominal values following the “money illusion” assumption in which investors usually deal with nominal values in practice (Benartzi and Thaler (1995)). Consequently, the use of book values better captures the “fundamental” corporate returns by excluding all trading risks in stock markets. Thus, such data perfectly fit our international comparison.
9
We attempt to increase the IRR estimates by assuming that a firm with data that have missing values during the investigation period can be disparted into a maximum of three runs (consecutive years). The IRRs from these runs are then aggregated to estimate an IRR for a specific firm. However, this does not work since the IRRs cannot yield estimated results due to a lack of data points.
10
We drop the top and bottom 1% percent of observations, as is standard in this field (Ramsey and Ramsey (2007)). In addition, we remove countries that have less than 30 companies in order to improve the representativeness of sampling, thereby excluding 64 countries and 491 companies out of the sample.
11
For a more detailed description of the survey, please refer to Rieger et al. (2015).
12
Cross listing and foreign ownership could be issues if the aim is to estimate precisely the equity premia acquired by local investors. However, firm-level data on ownership structures are difficult to find. Moreover, the relative differences of equity premia across countries, not their absolute values, are the main subjects of our investigation in accordance with the variation in investors’ preferences. This could be improved in further research, provided that more data are available.
13
The 360-day volatility as of a specific date is the unbiased standard deviation of the 359 most recent logarithmic daily returns, multiplied by an ‘annualization’ factor (which is 260, since there are 260 working days in a calendar year) (OSIRIS definition).
14
Rafael La Porta, Florencio Lopez-de-Silanes, Andrei Shleifer and Robert Vishny (LaPorta et al. (1998, 2000)); Djankov et al. (2008)).
15
16
As indicated in Gollier (2011): if the distribution of the returns of the equity market is ambiguous and agents bias their beliefs towards the one with the smallest expected utility, i.e., ambiguity aversion, the sufficient conditions for an increase in ambiguity aversion to reduce the demand for the risky asset, i.e., an increase in the equity premium, are the following: (1) the marginals (priors) can be ranked by first-order stochastic dominance, and relative risk aversion is less than unity; (2) the marginals can be ranked by Rothschild and Stiglitz’s increase in risk, and relative prudence is positive and less than two; and (3) the marginals can be ranked by second-order stochastic dominance and central dominance. In this case, a reduction in the return on an asset has a substitution effect and a wealth effect. The wealth effect may induce an increase in the ambiguous asset demand in the same way as the Giffen goods in consumption theory, consequently an increase in the equity premium. However, the existence of the Giffen goods is quite rare and not well documented in the literature. Ambiguity aversion increases the implicit risk of the uncertain assets, but does not necessarily affect the risk preference of investors. In the counter example of Gollier (2011), the more ambiguity averse, the less the equity premium.
Table 1. Numerical examples of the internal rate of return (IRR) methodology.
Table 1. Numerical examples of the internal rate of return (IRR) methodology.
Company ACompany BCompany CCompany D
31 December 2001−1.104.830 −183.174
31 December 2002203.821 −5.310
31 December 2003−197.944 −3.022.000142.967
31 December 2004−490.045 −252.000
31 December 2005−662.773 628.000
31 December 2006435.908−73.653252.000
31 December 2007−38.6881.9754.627.000
31 December 2008−511.8062.218
31 December 2009462.479−8.246
31 December 20104.591.151107.112
IRR12%9%15%−13%
The cash flows to estimate IRRs are formed as follows: the initial value of each run equals the book capital of the firm and starts with a negative value; the middle terms are net cash flows (i.e., earnings minus investments); and the end-run value equals the book capital of the firm plus the net cash flow of the end-run year. The currency unit is U.S. dollars. These values are extracted from real data, but company names are hidden.
Table 2. Fundamental equity premia across countries.
Table 2. Fundamental equity premia across countries.
No.CountryFirmsObs.ERPsSDNo.CountryFirmsObs.ERPsSD
Western Europe Middle East
1Austria584685.57%120.1%29United Arab Emirates3521711.86%17.3%
2Belgium967055.88%16.9%30Israel36418965.68%11.1%
3Switzerland1198476.04%12.5%31Jordan1218924.14%8.3%
4Cyprus783607.23%215.8%32Kuwait9055611.21%50.4%
5Germany48934653.26%13.3%33Oman927198.19%96.5%
6Denmark583910.94%9.6%34Saudi Arabia704428.98%11.6%
7Spain986034.75%11.1%
8Finland1018665.83%8.8% Far East and Central Asia
9France56439766.63%25.5%35Bangladesh9929410.20%23.2%
10U.K.107564496.30%49.6%36China223614,5486.36%12.4%
11Greece20013031.66%8.7%37Hong Kong1238567.34%8.6%
12Ireland503366.98%12.3%38Indonesia722783.04%6.9%
13Italy19713193.29%9.5%39India275614,5835.01%11.4%
14Netherlands987477.75%9.8%40Japan243517,7693.02%6.1%
15Norway985645.65%9.9%41Korea (South)128881437.48%19.4%
16Portugal382741.46%8.3%42Sri Lanka1588357.14%12.3%
17Sweden26516047.29%20.1%43Malaysia67248655.48%9.2%
18Turkey22811085.16%15.1%44Philippines1267136.79%12.7%
45Pakistan34716976.16%136.6%
South and Central America 46Singapore52732569.02%11.1%
19Argentina815494.66%15.1%47Thailand40927717.78%9.1%
20Bermuda54340577.12%17.1%48Taiwan141391046.86%11.7%
21Brazil30318486.35%58.6%49Vietnam15541715.06%18.2%
22Chile693664.73%136.3%
23Cayman Islands657379313.82%47.5% Africa
24Mexico835185.43%13.6%50Egypt154106513.77%12.0%
25Peru1237375.54%33.5%51Kenya3418112.23%20.4%
26Virgin Islands (British)581948.80%18.4%52Morocco342339.55%9.2%
53Nigeria8439911.25%115.6%
North America 54South Africa212136616.33%13.4%
27Canada259613,5961.50%383.5%
28U.S.572736,0899.93%249.1%
Table 3. Equity premia, ambiguity aversion and risk preferences.
Table 3. Equity premia, ambiguity aversion and risk preferences.
CountryNumber of CompaniesERPsRRPAmbiguity Aversion
GainsLosses
Argentina814.66%0.74−0.340.59
Austria585.57%0.65−0.630.39
Australia13443.61%0.65−0.440.48
Belgium965.88%0.66−0.350.72
Canada25961.50%0.77−0.330.63
Switzerland1196.04%0.78−0.450.57
Chile694.73%0.67−0.170.68
China22366.36%0.56−0.350.67
Germany4893.26%0.84−0.540.47
Denmark580.94%0.64−0.170.59
Spain984.75%0.72−0.230.60
Finland1015.83%0.73−0.320.46
France5646.63%0.54−0.430.54
U.K.10756.30%0.72−0.490.61
Greece2001.66%0.66−0.770.59
Hong Kong1237.34%0.93−0.720.64
Ireland506.98%0.86−0.530.48
Israel3645.68%0.83−0.630.58
India27565.01%0.68−0.540.82
Italy1973.29%0.80−0.350.53
Japan24353.02%0.76−0.540.62
South Korea12887.48%0.55−0.390.58
Mexico835.43%0.93−0.720.62
Malaysia6725.48%0.64−0.810.59
Nigeria8411.25%0.69−0.600.65
Netherlands987.75%0.44−0.170.57
Norway985.65%0.74−0.460.46
New Zealand817.95%0.67−0.640.53
Portugal381.46%0.61−0.290.60
Sweden2657.29%0.65−0.210.50
Thailand4097.78%0.60−0.520.80
Turkey2285.16%0.63−0.180.62
Taiwan14136.86%0.66−0.540.67
USA57279.93%0.78−0.430.42
Vietnam15515.06%0.67−0.330.70
Table 4. Regression results for the equity premium and ambiguity aversion.
Table 4. Regression results for the equity premium and ambiguity aversion.
(1)(2)(3)(4)(5)
Model 1Model 2Model 3Model 4Model 5
Ambiguity aversion−1.88 ***−2.53 ***−1.88 ***−2.08 ***−0.77 ***
(0.762)(0.877)(0.695)(0.763)(0.286)
GDP per capita0.00 **
(0.000)
GDP growth rate −0.05 **
(0.022)
Stock market capitalization 0.00 ***
(0.000)
Economic freedom 0.03 ***
(0.009)
Beta of stock0.19 **0.08 **0.14 **0.17 **0.06
(0.087)(0.052)(0.069)(0.078)(0.043)
Stock volatility0.00−0.000.020.020.03 *
(0.019)(0.04)(0.019)(0.018)(0.020)
Leverage ratio−0.03 **−0.03 **−0.03 **−0.03 ***−0.03 ***
(0.012)(0.014)(0.013)(0.012)(0.009)
Analysts−0.01−0.00−0.01−0.01−0.01
(0.004)(0.003)(0.004)(0.004)(0.004)
Past stock return−0.02−0.001−0.02−0.02−0.00
(0.012)(0.012)(0.012)(0.012)(0.011)
Anti-director index−0.24 ***−0.24 ***−0.27 ***−0.33 ***
(0.078)(0.081)(0.090)(0.109)
Rule of law−0.36 **−0.07−0.05−0.16 **
(0.163)(0.038)(0.036)(0.070)
Anti-self-dealing index1.53 ***1.46 ***1.42 ***1.40 ***
(0.513)(0.490)(0.473)(0.467)
Creditor right index−0.13 ***−0.15 ***−0.14 ***−0.15 ***
(0.044)(0.050)(0.045)(0.050)
Judicial efficiency index0.09 **0.20 ***0.17 ***−0.01
(0.039)(0.074)(0.066)(0.023)
Constant0.84 ***0.94 **0.97 ***0.41 **0.58 ***
(0.294)(0.332)(0.341)(0.175)(0.186)
Observations11,17611,17611,17611,17615,424
R-squared1.19%1.00%0.98%1.12%0.18%
Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.10.
Table 5. Regression results for the equity premium, ambiguity aversion and risk preferences. RRP, relative risk premium.
Table 5. Regression results for the equity premium, ambiguity aversion and risk preferences. RRP, relative risk premium.
(1)(2)(3)(4)(5)
Model 1Model 2Model 3Model 4Model 5
Ambiguity aversion−2.98 ***−3.42 ***−3.08 ***−3.30 ***−0.71 ***
(1.104)(1.206)(1.130)(1.201)(0.261)
RRP gains0.36 *0.57 *0.55 **0.280.44 **
(0.207)(0.298)(0.273)(0.195)(0.184)
RRP losses1.11 ***1.35 ***1.20 ***1.34 ***0.23 ***
(0.407)(0.486)(0.441)(0.490)(0.079)
GDP per capita0.30 **
(0.149)
GDP growth rate −0.11 ***
(0.037)
Stock market capitalization 0.00 **
(0.000)
Economic freedom 0.03 ***
(0.012)
Beta of stock0.18 **0.100.20 **0.26 **0.10 *
(0.084)(0.063)(0.091)(0.112)(0.055)
Stock volatility−0.02−0.06 *−0.02−0.030.03
(0.023)(0.031)(0.022)(0.024)(0.018)
Leverage ratio−0.04 ***−0.04 **−0.04 ***−0.04 ***−0.03 ***
(0.015)(0.015)(0.014)(0.013)(0.009)
Analysts−0.01 *−0.00−0.01 *−0.01 **−0.01 *
(0.005)(0.003)(0.005)(0.007)(0.004)
Past stock return−0.01−0.00−0.01−0.020.00
(0.013)(0.014)(0.012)(0.012)(0.012)
Anti-director index−0.29 ***−0.28 ***−0.32 ***−0.41 ***
(0.097)(0.102)(0.113)(0.146)
Rule of law index−0.39 **−0.27 ***−0.21 **−0.13 **
(0.187)(0.103)(0.093)(0.061)
Anti-self-dealing index1.91 ***2.00 ***1.87 ***1.89 ***
(0.641)(0.674)(0.626)(0.634)
Creditor right index−0.10 ***−0.13 ***−0.09 ***−0.13 ***
(0.032)(0.042)(0.029)(0.042)
Judicial efficiency index0.08 *0.14 ***0.09 **−0.29 **
(0.047)(0.055)(0.042)(0.119)
Constant−0.492.53 ***2.30 ***2.48 ***0.35 ***
(0.692)(0.876)(0.812)(0.874)(0.089)
Observations11,17611,17611,17611,17615,424
R-squared1.28%1.36%1.26%1.50%0.22%
Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.10.
Table 6. The equity premia, ambiguity aversion and the individualism index.
Table 6. The equity premia, ambiguity aversion and the individualism index.
(1)(2)(3)(4)(5)
Model 1Model 2Model 3Model 4Model 5
Ambiguity aversion−2.31 ***−2.34 ***−2.19 ***−2.30 ***−0.35 **
(0.874)(0.845)(0.824)(0.860)(0.158)
Individualism Index0.01 ***0.01 ***0.01 ***0.02 ***0.00 ***
(0.003)(0.004)(0.004)(0.005)(0.002)
GDP per capita0.00 **
(0.000)
GDP growth rate −0.12 ***
(0.041)
Stock market capitalization 0.00 **
(0.000)
Economic freedom 0.04 ***
(0.015)
Beta of stock0.22 **0.080.17 **0.26 **0.14 **
(0.095)(0.052)(0.079)(0.111)(0.065)
Stock volatility−0.01−0.04−0.00−0.030.04 *
(0.020)(0.026)(0.019)(0.023)(0.021)
Leverage ratio−0.03 **−0.03 **−0.03 ***−0.03 ***−0.03 ***
(0.013)(0.014)(0.014)(0.013)(0.011)
Analysts−0.01 *−0.00−0.01 *−0.01 **−0.01 **
(0.005)(0.002)(0.005)(0.006)(0.005)
Past stock return−0.02 *−0.01−0.02 **−0.03 **−0.00
(0.012)(0.012)(0.012)(0.013)(0.011)
Anti-director index−0.16 ***−0.14 ***−0.18 ***−0.27 ***
(0.053)(0.052)(0.062)(0.094)
Rule of law−0.61 **−0.35 ***−0.32 **−0.32 **
(0.255)(0.132)(0.136)(0.131)
Anti-self-dealing index1.50 ***1.53 ***1.37 ***1.20 ***
(0.497)(0.510)(0.445)(0.386)
Creditor right index−0.12 ***−0.17 ***−0.11 ***−0.13 ***
(0.039)(0.055)(0.036)(0.045)
Judicial efficiency index0.09 **0.28 ***0.20 **−0.31 **
(0.041)(0.101)(0.076)(0.126)
Constant0.41 **0.33 **0.43 **0.230.04
(0.181)(0.159)(0.183)(0.145)(0.045)
Observations11,16511,16511,16511,16515,413
R-squared1.47%1.39%1.26%1.63%0.33%
Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.10.
Table 7. The equity premia, ambiguity aversion and the uncertainty avoidance index.
Table 7. The equity premia, ambiguity aversion and the uncertainty avoidance index.
(1)(2)(3)(4)(5)
Model 1Model 2Model 3Model 4Model 5
Ambiguity aversion−1.69 ***−1.82 ***−1.62 **−1.68 ***−0.75 ***
(0.650)(0.679)(0.639)(0.645)(0.281)
Uncertainty Avoidance Index−0.00 ***−0.00 ***−0.00 ***−0.00−0.00 ***
(0.001)(0.000)(0.000)(0.000)(0.000)
GDP per capita0.52 **
(0.229)
GDP growth rate −0.08 ***
(0.030)
Stock market capitalization 0.00
(0.000)
Economic freedom 0.02 **
(0.009)
Beta of stock0.21 **0.11 *0.17 **0.22 **0.06
(0.092)(0.059)(0.077)(0.096)(0.043)
Stock volatility−0.00−0.010.020.010.04 *
(0.019)(0.021)(0.018)(0.018)(0.020)
Leverage ratio−0.03 **−0.03 **−0.03 **−0.03 ***−0.03 ***
(0.012)(0.013)(0.013)(0.012)(0.009)
Analysts−0.01−0.00−0.01−0.01 *−0.01
(0.004)(0.002)(0.004)(0.005)(0.004)
Past stock return−0.02−0.01−0.02 *−0.02 *−0.00
(0.012)(0.012)(0.012)(0.012)(0.011)
Anti-director index−0.27 ***−0.26 ***−0.29 ***−0.35 ***
(0.090)(0.088)(0.096)(0.122)
Rule of law−0.36 **−0.040.020.07 ***
(0.176)(0.029)(0.023)(0.023)
Anti-self-dealing index1.60 ***1.66 ***1.62 ***1.55 ***
(0.533)(0.557)(0.534)(0.513)
Creditor right index−0.17 ***−0.19 ***−0.16 ***−0.17 ***
(0.055)(0.062)(0.049)(0.056)
Judicial efficiency index0.19 **0.26 ***0.18 **−0.06
(0.073)(0.094)(0.072)(0.049)
Constant−4.05 **0.72 ***0.75 ***0.67 ***0.62 ***
(1.864)(0.250)(0.254)(0.233)(0.196)
Observations11,16511,16511,16511,16515,413
R-squared1.19%1.13%1.05%1.19%0.19%
Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.10.
Table 8. Regressions with different controls for the equity premia and ambiguity aversion.
Table 8. Regressions with different controls for the equity premia and ambiguity aversion.
(1)(2)(3)(4)
Model 1Model 2Model 3Model 4
Ambiguity aversion−0.95 **−2.20 ***−1.36 ***−1.88 ***
(0.404)(0.852)(0.518)(0.695)
GDP per capita0.21 ***
(0.073)
GDP growth rate −0.78 **
(0.307)
Stock market capitalization 0.03 ***
(0.011)
Economic freedom 0.04 ***
(0.015)
Beta of stock0.060.070.040.16 *
(0.052)(0.056)(0.048)(0.080)
Stock volatility0.040.050.04 *0.03
(0.026)(0.031)(0.027)(0.023)
Leverage ratio−0.05 **−0.06 **−0.05 **−0.05 **
(0.023)(0.028)(0.023)(0.022)
Analysts−0.01−0.01−0.01−0.01 *
(0.005)(0.005)(0.004)(0.006)
Past stock return−0.000.00−0.00−0.01
(0.014)(0.016)(0.014)(0.014)
Investor protection index0.05 ***0.04 ***0.05 ***0.06 ***
(0.018)(0.014)(0.017)(0.022)
Market efficiency index0.06−0.020.18 ***−0.31 **
(0.041)(0.029)(0.063)(0.124)
Gini index0.02 ***0.05 ***0.02 ***0.02 ***
(0.007)(0.018)(0.006)(0.008)
Constant−1.33 ***0.62 *−0.90 ***−1.34 ***
(0.461)(0.323)(0.325)(0.467)
Observations12,32412,32412,32412,324
R-squared0.63%1.07%0.61%0.87%
Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.10.
Table 9. Regressions with different controls for the equity premia, ambiguity aversion and risk preferences.
Table 9. Regressions with different controls for the equity premia, ambiguity aversion and risk preferences.
(1)(2)(3)(4)(5)
Model 1Model 2Model 3Model 4Model 5
Ambiguity aversion−2.85 ***−2.17 ***−1.21 ***−2.17 ***−2.01 ***
(1.083)(0.769)(0.396)(0.771)(0.735)
RRP gains1.69 **1.63 **0.88 **0.440.77 **
(0.771)(0.634)(0.447)(0.394)(0.393)
RRP losses1.67 ***1.49 ***1.86 ***1.16 ***1.36 ***
(0.601)(0.510)(0.691)(0.448)(0.473)
GDP per capita−0.43 **
(0.181)
GDP growth rate −0.08 **
(0.035)
Stock market capitalization −0.00 **
(0.002)
Economic freedom 0.02 *
(0.009)
Beta of stock0.15 *0.130.28 **0.17 **0.15 *
(0.083)(0.083)(0.136)(0.088)(0.084)
Stock volatility0.010.01−0.010.010.01
(0.022)(0.028)(0.028)(0.022)(0.023)
Leverage ratio−0.05 **−0.06 **−0.06 **−0.05 **−0.05 **
(0.022)(0.028)(0.028)(0.023)(0.023)
Analysts−0.01−0.01−0.01 *−0.01 *−0.01
(0.006)(0.006)(0.008)(0.006)(0.006)
Past stock return0.000.02−0.01−0.000.00
(0.016)(0.021)(0.015)(0.018)(0.017)
Investor protection index0.06 ***0.10 ***−0.000.07 ***0.06 ***
(0.019)(0.031)(0.010)(0.023)(0.022)
Market efficiency index0.62 ***0.21 ***0.86 **0.090.30 ***
(0.233)(0.070)(0.340)(0.126)(0.098)
Gini index0.03 ***0.04 ***0.07 **0.04 ***0.04 ***
(0.012)(0.016)(0.029)(0.014)(0.014)
Constant0.94 *−1.99 ***−5.45 **-1.76 **−1.85 ***
(0.518)(0.737)(2.238)(0.687)(0.700)
Observations12,32412,24211,44012,32412,324
R-squared1.18%1.34%1.38%1.13%1.10%
Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.10.
Table 10. Down-weighting outliers for the equity premium and ambiguity aversion.
Table 10. Down-weighting outliers for the equity premium and ambiguity aversion.
(1)(2)(3)(4)
Model 1Model 2Model 3Model 4
Ambiguity aversion−0.10 ***−0.06 ***−0.09 ***−0.04 ***
(0.011)(0.010)(0.011)(0.011)
GDP per capital−0.00 ***
(0.000)
GDP growth rate 0.01 ***
(0.000)
Stock market capitalization 0.00 ***
(0.000)
Economic freedom 0.00 ***
(0.000)
Beta of stock0.01 ***0.01 ***0.01 ***0.01 ***
(0.001)(0.001)(0.001)(0.001)
Stock volatility−0.17 ***−0.17 ***−0.17 ***−0.17 ***
(0.001)(0.001)(0.001)(0.001)
Leverage ratio−0.02 ***−0.02 ***−0.02 ***−0.02 ***
(0.001)(0.001)(0.001)(0.001)
Analysts0.00 ***0.00 ***0.00 ***0.00 ***
(0.000)(0.000)(0.000)(0.000)
Past stock return0.00 ***0.00 ***0.00 ***0.00 ***
(0.000)(0.000)(0.000)(0.000)
Anti-director index−0.03 ***−0.03 ***−0.02 ***−0.03 ***
(0.001)(0.001)(0.001)(0.001)
Rule of law0.02 ***0.02 ***−0.01 ***0.01 ***
(0.003)(0.002)(0.002)(0.002)
Anti-self-dealing index0.01 ***0.02 ***−0.01 ***−0.01 ***
(0.004)(0.004)(0.004)(0.004)
Creditor right index−0.000.00−0.00−0.00
(0.001)(0.001)(0.001)(0.001)
Judicial efficiency index−0.02 ***−0.03 ***−0.02 ***−0.06 ***
(0.002)(0.002)(0.002)(0.003)
Constant0.41 ***0.34 ***0.38 ***0.38 ***
(0.008)(0.009)(0.008)(0.009)
Observations11,17611,17611,17611,176
R-squared68.75%68.70%67.94%67.78%
Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.10.
Table 11. Down-weighting outliers for the equity premia, ambiguity aversion and risk preferences.
Table 11. Down-weighting outliers for the equity premia, ambiguity aversion and risk preferences.
(1)(2)(3)(4)
Model 1Model 2Model 3Model 4
Ambiguity aversion−0.14 ***−0.14 ***−0.17 ***−0.15 ***
(0.013)(0.013)(0.013)(0.013)
RRP gains0.02 **−0.05 ***−0.02 **−0.01
(0.011)(0.010)(0.010)(0.011)
RRP losses0.07 ***0.05 ***0.08 ***0.07 ***
(0.008)(0.008)(0.008)(0.008)
GDP per capita−0.00 ***
(0.000)
GDP growth rate 0.01 ***
(0.000)
Stock market capitalization 0.00 ***
(0.000)
Economic freedom 0.00
(0.000)
Beta of stock0.01 ***0.01 ***0.01 ***0.01 ***
(0.001)(0.001)(0.001)(0.001)
Stock volatility−0.17 ***−0.17 ***−0.17 ***−0.17 ***
(0.001)(0.001)(0.001)(0.001)
Leverage ratio−0.02 ***−0.02 ***−0.02 ***−0.02 ***
(0.001)(0.001)(0.001)(0.001)
Analysts0.00 ***0.00 ***0.00 ***0.00 ***
(0.000)(0.000)(0.000)(0.000)
Past stock return0.00 ***0.00 ***0.00 ***0.00 ***
(0.000)(0.000)(0.000)(0.000)
Anti-director index−0.02 ***−0.02 ***−0.01 ***−0.02 ***
(0.002)(0.002)(0.002)(0.002)
Rule of law0.000.00−0.03 ***−0.02 ***
(0.004)(0.003)(0.003)(0.003)
Anti-self-dealing index0.01 **0.01 ***−0.01 ***0.00
(0.004)(0.004)(0.005)(0.005)
Creditor right index0.000.000.00 **0.00 **
(0.001)(0.001)(0.001)(0.001)
Judicial efficiency index−0.03 ***−0.02 ***−0.02 ***−0.03 ***
(0.003)(0.003)(0.003)(0.003)
Constant0.47 ***0.39 ***0.46 ***0.46 ***
(0.011)(0.011)(0.011)(0.013)
Observations11,17611,17611,17611,176
R-squared69.02%69.05%68.14%68.40%
Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.10.

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