The Equity Premium Puzzle, Ambiguity Aversion, and Institutional Quality
Author: Mr. Abbas Mirakhor and Mr. S. Nuri Erbas

Contributor Notes

Author’s E-Mail Address: serbas@imf.org; amirakhor@imf.org
Publication Date:
01 Sep 2007
eISBN:
9781451867947
ISBN:
9781451867947
Language:
English
Keywords:
WP; equity premium; stock return; asset return; return differential; equity returns up; stock market return; mature market; bond return; equity return; safe asset return
Download PDF (359.6 KB)

With cross-section data from 53 emerging and mature markets, we provide evidence that equity premium puzzle is a global phenomenon. In addition to risk aversion, equity premium may reflect ambiguity aversion. We explore the sources of equity premium using some pertinent fundamental independent variables, as well as the World Bank institutional quality indexes and other proxies for the degree of ambiguity in the sample countries. Some World Bank and other indexes are statistically significant, which indicates that a large part of equity premium may reflect investor aversion to ambiguities resulting from institutional weaknesses.

Abstract

With cross-section data from 53 emerging and mature markets, we provide evidence that equity premium puzzle is a global phenomenon. In addition to risk aversion, equity premium may reflect ambiguity aversion. We explore the sources of equity premium using some pertinent fundamental independent variables, as well as the World Bank institutional quality indexes and other proxies for the degree of ambiguity in the sample countries. Some World Bank and other indexes are statistically significant, which indicates that a large part of equity premium may reflect investor aversion to ambiguities resulting from institutional weaknesses.

I. Introduction

The equity premium puzzle (EPP) is the differential between return to equity and return to safe assets in excess of the premium that can be explained on the basis of a reasonable degree of risk aversion.2 In addition to relative volatility and risk aversion, some macroeconomic fundamentals can explain the return differential, such as consumption smoothing, liquidity constraints, financial sector development, age composition of investors, and differences between the tax rates applying to equity earnings and safe asset returns. After accounting for the impact of such fundamentals on equity and safe asset returns, the observed differential between the two returns may still be large to the extent that it implies an extreme degree of risk aversion, which is empirically unsupported.3

Financial markets pose many unknown and unknowable risks that cannot be exhaustively parsed through analysis of data under the simplifying assumptions of efficient market theories. In general, financial markets exhibit Knightian uncertainty rather than precisely quantifiable risk.4 Knightian uncertainty, or ambiguity, implies that the probabilities and payoffs associated with most investments are not known with precision. When ambiguous and risky economic prospects are compared, decision makers exhibit ambiguity aversion. Since the seminal contribution by Ellsberg (1961), ambiguity aversion has been documented in numerous experimental studies. There is a growing literature—prominently, cumulative prospect theory—that challenges the basic axioms of expected utility theory, which provides the theoretical context in which EPP is posited (Appendix II).

The paper makes two main contributions. First, it proposes ambiguity aversion as a possible explanation for EPP.5 If markets perceive equity returns as more ambiguous than safe asset returns, then, in addition to a risk premium, markets pay an ambiguity premium on equity, making the observed equity premium larger. Second, while data from a few mature markets have been examined, we are not aware of studies that have documented EPP across a large sample of countries.6 The questions remain whether EPP is a global phenomenon and whether it prevails both in emerging and mature financial markets. Using a sample of 53 countries, comprising 29 emerging and 24 mature markets, the paper shows that EPP is a global phenomenon. Institutional quality may have a significant impact on the degree of uncertainty surrounding equity returns. The paper examines the possible impact of ambiguity aversion on equity premium by using the World Bank institutional quality indexes, as well as some other indexes, as proxies for the degree of uncertainty.7 The correlation tests and regression results indicate statistically significant correlations between equity premium and some uncertainty proxies. To the extent institutional quality reflects on uncertainty, ambiguity aversion can explain a significant portion of the large equity premium across the sample countries.

The paper is organized as follows. In Section II, we present some vital observations on equity premium, stock return and safe asset return for the periods 1996–00, 2001–05, and 1996–05. Section III provides a simple example that sheds light on the impact of uncertainty on equity premium. Section IV presents an overview of the data used and correlation tests. Section V presents regression methodology and results. Section VI concludes.

II. Equity Premium is a Global Phenomenon

A. Description of Data and Measurement

The overall period under consideration is 1996–05, which is a relatively short period. It is chosen on the basis of data availability in most emerging markets, where stock markets have become more active and have grown significantly only within the last decade. Also, the World Bank institutional quality indexes and most other indexes used are available only for this period. However, a ten-year period is long enough to facilitate robust inferences because it allows for market adjustments that distinguish longer-term market trends from temporary fluctuations in asset returns.

The real equity premia and stock and safe asset returns are presented in Table 1, with supplementary information shown in Table 2; also see Charts 1 and 2. The real stock market return is calculated as the yearly percentage change in the stock market index that is obtained by dividing the nominal stock market index by the CPI index. The real safe asset return is calculated as the nominal return minus CPI inflation.8 The real equity premium is calculated

Chart 1.
Chart 1.

Equity Premium, Stock Market and Safe Asset Return in the Sample Countries, 1996–05

Citation: IMF Working Papers 2007, 230; 10.5089/9781451867947.001.A001

Chart 2.
Chart 2.

Average Equity Premium, Stock Market and Safe Asset Return, Yearly Country Sample Averages, 1996–05

Citation: IMF Working Papers 2007, 230; 10.5089/9781451867947.001.A001

Sources: Table 2; Country specific data available from the authors.
Table 1.

Average Equity Premium, Stock Market and Safe Asset Return in the Sample Countries, 1996–00, 2001–05, 1996–051

article image
Source: Authors’ estimates; Appendix I.

Period averages are calculated as the sample average of individual country averages for each period; σ is standard deviation. Because of missing data during 1996-97 for some emerging market countries, the period averages in this table slightly differ from those that can be calculated from Table 2, and equity premium may not exactly equal to the difference between stock market return and safe asset return in 1996-2000.

Table 2.

Average Equity Premium, Stock Market and Safe Asset Return in the Sample Countries, 1996–05

(in percent)1

article image
Source: Authors’ estimates; Appendix I, Tables 1,2.

Period averages that can be calculated from this table may slightly differ from the period averages presented in Table 1 because of missing data for some countries during 1996-97. Percent change real stock market index is calculated on the basis of the nominal index divided by CPI. Real return safe asset is calculated as the nominal return minus CPI inflation.

as the difference between the real stock market and safe asset returns; it excludes dividend yield because reliable data on dividend yield in most emerging markets are not available; including dividend yield, equity premium may be significantly higher.

B. Main Observations

EPP is a global phenomenon. During 1996–05, average equity premium is substantial in both mature and emerging markets, ranging from 7.5 to 10.5 percent. These magnitudes are comparable to or in excess of the premia reported by Mehra and Prescott (1985) and Mehra (2003) for some mature markets (ranging from 3.3 to 8.0 percent in selected periods).

Equity premium is higher in emerging markets. During 1996–05, equity premium is 3 percent higher in emerging markets than in mature markets. However, during 1996–00, equity premium in emerging markets is (nearly) zero, while it is close to 14 percent in mature markets. This performance is reversed during 2002–05, as the premium in emerging markets jumps to 20.5 percent, while it declines by more than 12 percent to 1.5 percent in mature markets. The 19 percent difference between equity premium in emerging and mature markets during 2001–05 is remarkably large. This is the period during which emerging markets started attracting large capital inflows and experienced large stock markets gains and market development, following the recovery from the Southeast Asia crises which severely depressed stock returns in some of the sample countries. The increase in equity premium in emerging markets during 2001–05 is due to the fourfold jump in equity return, while

safe asset return is half of that observed during 1996–00. Similarly, in mature markets, the decline in equity premium reflects mainly the decline in equity return by more than 13 percent, while the decline in safe asset return is only about 1 percent.

Volatility. Stock return across the sample shows greater variation (as measured by σs in Table 1) than safe asset return both in emerging and mature markets, which justifies risk premium on equity. The variation in both stock market and safe asset returns in emerging markets is significantly greater than the variation in mature markets.

Equity return and safe asset return correlations. Simple regression results in Table 3 indicate that equity return is positively correlated with safe asset return in the whole sample and in mature markets, while this correlation is not statistically significant in emerging markets.

Table 3.

Equity Premium, Stock Market Return, and Safe Asset Return, Sample Correlations1

article image
Source: Authors’ estimates.

Simple regressions based on the 1996-2005 country averages, using Yi =c0 + c1Xi, where Yi is the vector of independent variables and Xi is the vector of dependent variables (1996-2005 country averages); i = 1, 2, …, 53.

The main determinant of equity premium is stock return in both emerging and mature markets (Table 3, Chart 1).

Equity premium over time. The robustness of inferences over time is limited by the small sample size. Nevertheless, the following observations are illuminating: (a) during 1996–05, the volatility of equity and safe asset returns (as measured by σp in Table 1) appears to be higher in emerging markets than in mature markets; (b) simple regression results indicate a significant negative correlation between stock return and safe asset return in emerging markets but those returns are not significantly correlated in the whole sample or in mature markets (Table 4); (c) the main determinant of equity premium over time is stock return in both emerging and mature markets (Chart 2); however, in emerging markets, simple regressions indicate a significant negative correlation between equity premium and safe asset return, which is consistent with the significant negative correlation between stock return and safe asset return (Table 4).

Table 4.

Equity Premium, Stock Market Return, and Safe Asset Return Correlations over the Period 1996–051

article image
Source: Authors’ estimates.

Simple regressions based on the 1996-2005 country averages, using Yt =c0 + c1 Xt, where Yi is the vector of independent variables and Xi is the vector of dependent variables (1996-2005 country averages); t = 1996, 1997, …, 2005.

III. Ambiguity and Equity Premium

We now turn to the discussion of why ambiguity aversion is instrumental in explaining EPP. We do not intend to produce a formal portfolio model and our main focus is an empirical investigation of EPP across the sample countries. The discussion in this section will be limited to a simple example of the possible impact of uncertainty on equity premium.

A. An Example

We use cumulative prospect theory (CPT), originally developed by Kahneman and Tversky (1979, 1992).9 According to CPT, the decision maker’s probability assessment of a prospect is subjective. Suppose there is a safe prospect that requires an investment of $Y and pays a return in the amount of $C, so the rate of return on the safe prospect is C/Y. A risky investment in which $Y can be invested is expected to pay $R with probability p; let w(p) denote the subjective probability assessment of the investor. The utility from the return is defined by the function U(.), U’ > 0, which obeys the risk aversion assumption, U” < 0, and, U(0) = 0.10 The expected utility from the payoff to the risky asset is w(p)U(R). For the risk averse investor to be indifferent between the safe and the risky asset, R must be greater than C. We can calculate R, the certainty equivalent of the risky prospect, from the inequality U(C) ≤ w(p)U(R) as

R=U−(U(C)w(p));R≥C,(1)

where U— is the inverse of the utility function U(.). The minimum rate of return on the risky investment that is acceptable to the risk averse investor is R and (R-C)/Y ≥ 0 is the risk premium.11 Except for the subjective probability weighting, the foregoing results are the same as those that follow from expected utility theory (EUT).

Under CPT, it is possible to posit an ambiguous prospect as a compound lottery.12 Suppose a prospect is expected to pay off, if two events occur in succession. This prospect pays $A if both Event I and Event II occur, otherwise the payoff is zero; the probability of Event I occurring is q, and the probability of Event II occurring is z.13 To compare the ambiguous prospect, A, to the risky one, R, assume that p = qz. According to EUT, the investor’s assessment of the ambiguous prospect would be exactly the same as his assessment of the risky prospect. This is because the compound lottery involving Events I and II can be reduced to a simple lottery under the reduction axiom of EUT. According to CPT, however, the expected utility from the ambiguous prospect is assessed as w(q)w(z)U(A). Under the CPT assumptions on the subjective probability weighting, w(.), it is possible to show that w(p) = w(qz) ≥ w(q)w(z) (Appendix II). Using the inequality w(p)U(R) ≤ w(q)w(z)U(A), and applying the same operations and arguments leading to (1), the value of A for which the investor would be indifferent between A and R is

A=U−(w(p)w(q)w(z)U(R));A≥R≥C.(2)

Therefore,

A−CY=A−RY+R−CY.(3)

where (A-C)/Y is the total equity premium in percentage terms, and (A-R)/Y is the ambiguity premium in excess of the risk premium, (R-C)/Y.

From data, we observe (A-C)/Y. Since EUT does not differentiate between risk and uncertainty, in the EUT framework, the observed return differential (A-C)/Y is attributed to only to risk premium but, for risk premium, EUT predicts (R-C)/Y. In the literature based on EUT, the differential (A-C)/Y is deemed too large relative to (R-C)/Y to be explained by a justifiable degree of risk aversion, and hence the equity premium puzzle. However, if we take into account ambiguity aversion, the observed return differential may not be too large for empirically supportable degrees of ambiguity and risk aversion.

Simple simulations in Table 5, based on specifications for Equations (1)-(3), as well as on a specification for the CPT probability weighting function, indicate that ambiguity premium can significantly augment the magnitude of equity premium (see Appendix II). For relatively small changes in the behavioral parameter values (probability weighting parameter, θ) and, risk aversion parameter, θ), it is possible to generate high equity premiums.

Table 5.

Simulations for Equity Premium (in percent)

article image
Source: Authors’ simulations.

Of course, the impact of CPT subjective probability weighting and ambiguity on equity premium remains to be tested in a formal asset pricing model.14

B. Discussion

The example above posits that the greater the number of events that lead to the outcome, the smaller is the probability assessment of the payoff. Under uncertainty, investors tend to assign lower subjective probabilities to payoffs than they do under risk.15 When the time dimension is introduced, uncertainty becomes easier to put in a more realistic context. In the case of the uncertain asset in our example, it is easy to surmise that the two events are happening over time (Event I at time t and Event II at time t+1).

Equity returns involve more layers of uncertainty and decision making than safe returns over space and time. Importantly, bond cash flows are known with certainty, while corporate cash flows and earnings are difficult to predict. Profitability of a corporation depends on more layers of information flows and decisions (events) than the return on bonds, such as the corporation’s market share, innovative capacity, managerial prowess, as well as the prospects for such factors over time. Each layer of uncertainty and its interaction with the other layers need to be assessed by markets and this requires greater specialized knowledge. A corporation may have a comfortable niche in the market now but there may be concerns about its ability to make profitable innovations over time. Innovations, if and when they are made, may or may not catch on, they may prove more or less easy to imitate by competitors, and so on.16 This is a familiar description of a riskier asset that an investor—particularly a professional investor—has in mind while making a portfolio decision but there is a fundamental difference. The additional layers of uncertainty, especially over time, underline the impossibility for even a specialized investor of predicting all possible events—some unknown, some unknowable—and their impact on equity return with precision. Summers (1993) underlines that market prices do not necessarily reflect only rational assessments of the fundamentals. Schiller (1993) concurs that stock prices are highly ambiguous; in addition to fundamentals, stock price movements may reflect unquantifiable factors such as suggestibility and group pressure, diffusion of opinions, social movements, and even fashions and fads.17 Corporate fortunes exhibit the type of uncertainty examined by Frank Knight in his Risk, Uncertainty and Profit (1921, 2002). Broadly, Knight’s main argument is that return to investment is return to uncertainty rather than quantifiable (therefore, diversifiable) risk; so is return to equity, reflecting varying degrees of uncertainty. Safe assets, mainly government bonds, however, have fewer layers of uncertainty and are generally subject to fewer number of possible events that lead to their final payoff.

It is possible to extend this insight to the behavior of equity premium across countries that exhibit varying degrees of uncertainty in the Knightian sense. In addition to generally quantifiable risks associated with observable economic fundamentals, such uncertainty reflects institutional quality. The fundamentals that can be quantified with a reasonable degree of precision include growth, capital market development, debt level, inflation, and so on. The factors that are more difficult to quantify include policymakers’ track record and the credibility of their commitment to robust macroeconomic management and policies, as well as effectiveness of government policies. Institutional factors play an important role in maintaining policy commitments and effective implementation, and a stronger institutional environment makes commitments more credible. Institutional strength also plays an important role in determining the quality of litigation and settlement of business disputes, quality of taxation and expenditure, regulation, investor protection, enforcement of property rights and protections against expropriation by the state, and the integrity of available economic data. Control of corruption and regulatory quality reflect on corporate costs, as well as on the quality of corporate governance. Similarly, the extent of political stability and rule of law have an impact on many unquantifiable and subjectively evaluated business risks. Those factors, evaluated on a subjective basis by respondents from different countries, are embedded in the World Bank institutional quality (and other) indexes, which have significant and intuitively appealing effects on investor decisions and profitability.18 Greater uncertainty emanating from institutional weaknesses may have a significant impact on economic outcomes, including asset returns.19

In this vein, Stulz (2005) argues that the “twin agency problem” is important in explaining why country-specific attributes can outweigh the fundamentals in the determination of financial flows and rates of return.20 The twin agency problem refers to corporate insider discretion and state ruler (government) discretion in expropriating rents from investors, which can deter investment and wide stock market participation, and result in higher equity returns. A preponderance of insider discretion implies weaker rules that govern state and corporate behavior. Due to restrictions on freedoms to disseminate accurate information, and lack of transparency and accountability, rules may not be widely known or understood by decision makers; if they are, their enforcement may also be subject to discretionary inconsistencies through corruption. In such an environment, the uncertainty emanating from discretionary insider decisions is hardly quantifiable and possible outcomes are hardly predictable with precision. Thus, the twin agency problem emanating from institutional weaknesses is directly connected to ambiguity. As underlined in the literature, institutions have two fundamental effects. First, they provide the right (or wrong) incentives to invest (e.g., protection against expropriation by the twin agents) (North, 1991, 1994). Secondly, they reduce (or increase) ambiguity over space and time by excluding some outcomes or events (e.g., discretionary rent-seeking by the twin agents through corruption) (Erbaş, 2004). The second effect indicates a negative correlation between the degree of ambiguity and institutional strength. La Porta and others (1998) examine a fundamental institutional factor, legal rules, and their historical origins and enforcement for the protection of equity holders. They provide evidence for a negative correlation between the concentration of equity ownership and investor protection, based on a sample of mature and emerging markets (closely approximating our sample). If investor protection is low, small investors may be less willing to hold shares. This implies that, if the relative size of small investors is large in an economy, lack of wide participation in the stock market may push equity returns up and safe asset returns down, and thus result in a high equity premium.

Guiso and others (2005) present evidence that equity market participation is negatively correlated with attitudes of trust across countries. They define trust as the subjective probability of being cheated by equity issuers (corporate boards and managers), as well as by the institutions that facilitate and regulate stock market participation (brokerage houses, hedge funds, regulatory and supervisory bodies). This probability is partly determined by the characteristics of the financial system, including the quality of investor protection and its enforcement. Survey data from some industrial countries indicate that low trust significantly accounts for low equity market participation, as well as for the low share of wealth invested in equity. If low trust results in lower equity holdings, on the firms’ side, more firms will be reluctant to broaden their shareholder base and, combined with low demand for equity, this results in lower stock market development. The implication for equity premium is that low trust can result in high equity premium because low trust tends to lower investment in equity, thereby increasing equity return, and, low trust tends to increase investment in safe assets, thereby decreasing safe asset return.

There is experimental evidence that decision maker preferences depend not only on the degree of uncertainty but also on the source of uncertainty; this is known as source dependence in the literature (Fox and Tversky, 1995; Tversky and Wakker, 1995). Decision makers tend to prefer bets on events they are particularly knowledgeable about to making bets on events on which they are not, even when the events they are knowledgeable about are ambiguous.21 However, an ambiguous prospect becomes less attractive when decision makers become aware that more knowledgeable decision makers are also evaluating the same prospect. Thus, investor trust in the actions of more knowledgeable decision makers (corporate insiders; rating agencies), and their trust in the institutional checks and balances (government insiders) on such actions can play an important role in the determination of the extent of stock market participation and equity premium.

The same factors are also at play in the determination of (the relatively) safe asset returns; by the same logic, unquantifiable uncertainties should have an impact on safe asset returns in the same direction.22 For example, sovereign bonds exhibit inflation and exchange rate uncertainty. As observed in many countries, it is possible to reduce inflation and exchange rate uncertainty by issuing inflation-indexed and foreign currency-indexed bonds. To a great extent, having to issue inflation-indexed bonds or to borrow in foreign currency reflects weakly credible policies to maintain inflation and exchange rate stability. If a bond is indexed to the U.S. dollar, uncertainty about the exchange rate between the U.S. dollar and the domestic currency is eliminated, although uncertainty about the exchange rate between the U.S. dollar and, for example, the yen remains. However, opting for U.S. dollar-denominated bonds is a manifestation of the market judgment that the uncertainty of the US$/¥ exchange rate is smaller. This reflects fundamentals but, at the same time, it reflects a more credible institutional stance (or a less uncertain source), for example, the market belief that the institutions (budgetary discipline; central bank independence; regulatory quality) in the United States or Japan will not permit a sudden reversal of monetary policy to spur high unanticipated inflation. As a result, foreign currency-denominated bonds tend to have lower interest rates and longer term structures. Alternatively, those desirable foreign borrowing terms might be achieved by establishing a track record of credible inflation targeting, which serves to reduce uncertainty surrounding inflation and exchange rates. A reasonably narrow band for targeted inflation excludes possible inflation rates (events) outside that band.23 If this policy proves successful by establishing a credible track record, the benefits of a more credible monetary policy may be reaped because uncertainty about inflation rate is reduced. For such a policy rule to prove successful and durable, it needs to be supported by strong institutional checks and balances, such as political consensus about basic macroeconomic policies, central bank independence, accurate data dissemination, and so on. This is institutional strength.

Experimental studies indicate that ambiguity aversion is sensitive to comparative ignorance (Fox and Tversky, 1995). This means that ambiguity aversion is driven by the comparison of prospects. In the case of equity premium, ambiguity aversion emanates from the comparison of stock and safe asset returns. The same comparison is relevant between emerging markets and mature markets for both stocks and bonds. It is possible, therefore, that ambiguity aversion, emanating from market comparisons of stocks to bonds and comparisons of emerging markets to mature markets, plays a significant role in the determination of equity premium. In the comparison of prospects in emerging and mature markets, perceptions of relative institutional strength can be particularly important.24

As noted, when the time dimension is considered, ambiguity is placed in a more realistic context. Since investment in financial instruments is a forward-looking phenomenon, greater ambiguity over time reflects on equity premium, as well as on the differences between equity premia in emerging and mature markets (Table 1). Over time, institutions play an important role in reducing uncertainty by establishing rules for dealing with events that can be anticipated with varying degrees of precision and events that cannot be foreseen (North, 1994). Knight (2002) stresses that basic market institutions evolve to deal with uncertainty.25 Strong institutions make future policy responses to unforeseen events more easily predictable or less ambiguous, which may also reflect on the degree of volatility. Hale and others (2006) present evidence that institutional quality (better shareholder and creditor rights) lowers the probability of financial crises; higher probability of crises increases stock market volatility; and, deeper markets are less volatile than thinner markets. Those authors conclude that institutional weaknesses increase the variance of stock returns, which may contribute to the spread between stock and safe asset returns; thus, institutional factors may have significant explanatory power in deconstructing EPP.

Finally, it should be highlighted that our example is based on the comparison of only pure-gain prospects. Modeling ambiguity with mixed prospects involving both gains and losses under CPT may have greater power in explaining asset return behavior over time.26

IV. Examination of Data and Cross-Correlations

The comparison of emerging and mature markets has revealed some important differences between the two samples. To a significant degree, those differences may reflect differences in institutional quality. A comparison of data in mature and emerging markets is provided in Table 6, which summarizes the independent variables chosen to explain equity premium across the three samples during the three periods we examine. The fundamental independent variables are chosen on the basis of the factors examined in the literature; the institutional quality indexes are proposed as proxies for the degree of uncertainty.

Table 6.

Summary of Variables in the Sample Countries

article image
Sources: IFS; World Bank; Heritage Foundation; World Federation of Exchanges; Bureau of International Statistics (BIS); U.S. Census Bureau, International Database; Appendix I, Tables 1, 2.

Rate of growth of GDP in constant 2000 U.S. dollars.

In percent of GDP.

(Ct/Yt - Ct-1/Yt-1), where C is private consumption and Y is GDP.

πt-πt-1, where πt is CPI inflation, πt = (CPIt - CPIt-1)/CPIt-1.

Statutory corporate income tax rate divided by statutory personal income tax rate (2005 data only).

Percent of population above forty.

1996-2000 (1996, 1998, 2000); 2002-2005; 1996-2005 averages only; higher value indicates higher (better) ranking. Overall index is the simple average of individual indexes.

We first explore the extent of cross-correlation between the variables by calculating the Pearson Product Moment Correlation Matrix.27 The results are presented in Table 7. As confirmed by the results in Table 3 above, equity premium is mainly determined by stock return. The correlation between stock return and safe asset return is not significant at the 5 percent level. However, during 1996–05, the results indicate a positive correlation between stock and safe asset returns at about 7 percent level of significance in the whole sample and mature markets (the t values shown in parentheses in Table 7), which is corroborated by the results in Table 3.

Table 7.

Summary of Statistically Significant Cross-Correlations between Independent and Dependent Variables (t statistics)

article image
Source: Authors’ estimates.

Equity premium and stock return are positively correlated with real growth, indicating plausibly that higher return to equity investment is associated with higher growth. A negative correlation is indicated between real growth and safe asset return in emerging markets during 2001–05. On average, real growth in emerging markets during 2001–05 is one percent higher than growth during 1996–00 and, while stock return increases sharply during 2001–05, safe asset return declines significantly. Relatively more attractive equity investment might have driven safe asset return down in emerging markets during 2001–05.

Equity market capitalization is used as a proxy for financial market development and depth, along with bond market capitalization. The mature market averages for both variables are two or more times higher than the emerging market averages. A negative correlation between stock return and the level of equity market capitalization seems plausible because a more developed equity market enables less costly portfolio adjustments and better arbitrage and risk diversification, which can result in a decline in stock returns.28 However, the tests do not indicate a statistically significant correlation between equity premium or stock return and equity market capitalization. This result may reflect the impact of the large decline in equity premium along with stock returns in mature markets during 2001–05, even though equity market capitalization remained high (Tables 1 and 6).

It is also plausible that higher bond market capitalization tends to lower bond return, induce a substitution of stocks for bonds, and result in lower stock return. The reverse argument is that lower bond market capitalization may drive up bond return along with stock return. For the whole sample, the correlation between bond market capitalization and stock return is negative during 2001–05; however, the correlation is positive during 1996–00. During 1996–00, bond market capitalization and stock return are high in mature markets but they are much lower in emerging markets; high bond market capitalization and high stock return in mature markets appear to dominate, resulting in a positive correlation between those two variables in the whole sample. But during 2001–05, bond market capitalization increased by a large margin in mature markets relative to 1996–00, while stock return declined sharply, which may explain the negative correlation between those two variables for the whole sample. Also during 2001–05, there is a positive correlation between bond-market capitalization and safe asset return in emerging markets, but a negative one in mature markets. In emerging markets, safe asset return declined, while stock return rose sharply during 2001–05; along with the significant increase in bond market capitalization, the increase in stock return may have had a positive impact on safe asset return so that the decline in safe asset return was less, and hence the positive correlation between bond market capitalization and safe asset return. Similarly, in mature markets, the significant increase in bond market capitalization, along with the sharp decline in stock return, may have resulted in a decline in safe asset returns, and hence the negative correlation.

Like equity and bond market capitalization, credit to private sector in mature markets is about two times larger than it is in mature markets. This variable is used as a proxy both for liquidity availability to investors and financial market development. Overall, credit to private sector shows a negative correlation with equity premium and stock return. This is a plausible result because greater availability of liquidity can stimulate greater investment in stocks and result in a decline in stock return. In addition, along the lines of the arguments by La Porta and others (1998), credit to private sector can also be interpreted as an indicator of the degree of confidence and transparency in the financial system, reflecting better lender protection, greater availability of reliable credit information, and better enforcement of laws. If so, then the negative correlation between credit and equity premium and stock return also indicates less uncertainty in the financial system, which reduces the ambiguity premium and results in lower equity premium. It is worth highlighting that both credit to private sector and institutional quality ratings in mature markets are much higher than they are in emerging markets (Table 6).

If financial instruments that can be used for consumption smoothing are accessible by a greater segment of the population, then consumption volatility is likely to be lower. Therefore, greater investment in such instruments to reduce consumption volatility can be expected to drive down their returns. At the same time, however, if the return on such instruments tends to move in the same direction as income and consumption, then the return needs to be higher to cover for volatility risk. Lagged consumption, which is used as a proxy for the degree of consumption volatility, shows a positive correlation with safe asset return only in mature markets during 2001–05; this means the greater the consumption volatility, the higher is the safe asset return. In mature markets, consumption volatility is (nearly) zero during 2001–05; stock return declines sharply and safe asset return declines by more than one percent. Consequently, the positive correlation between safe asset return and lagged consumption during 2001–05 may reflect the positive correlation between stock and safe asset returns in the mature markets sample (Table 3); that is, higher consumption volatility is associated with higher return on safe assets to cover the risk of a decline in safe asset returns.

Unanticipated inflation shows a remarkable decline in emerging markets, reflecting the overall decline in inflation; in mature markets, it is negligible.29 Reflecting the decline in inflation in the sample, the estimated unanticipated inflation (πt − πt-1) is negative (Table 6). Unanticipated inflation is negatively correlated with equity premium and stock return, as well as safe asset return. This result appears plausible because it indicates that asset returns are vulnerable to the uncertainties surrounding inflation. To the extent inflation is anticipated, investors hedge against it by requiring commensurate nominal returns; but to the extent investors are wrong in their inflation expectations, actual returns are high when unaticipated inflation is low, and returns are low when unaticipated inflation is high. However, it should also be noted that this result may also reflect the biases in the way we calculated real stock and safe asset returns (Section II.A).

Tax ratio (CIT/PIT) in emerging markets is significantly higher than it is in mature markets. It shows a positive correlation with stock return but a negative correlation with safe asset return. This result can be expected because a higher corporate tax burden (CIT) tends to increase gross stock return in order to make the net stock return attractive relative to bond return that is subject to a lower tax burden (PIT).

Data indicate that populations are significantly older in mature markets than in emerging markets. On average, the share of population over forty years of age in mature markets exceeds the same share in emerging markets by 17–18 percent. This comparison underscores that, in mature markets, older wealth holders are the more pivotal investors in equity markets. An older population—with higher and more stable income and smaller liquidity constraints that are compatible with more established jobs—is likely to have a higher share of equity income. Thus, for an older population, equity income volatility has a larger impact on total income volatility, therefore, a higher stock return is necessary to cover for higher volatility. It can be expected that, if the share of older cohorts is large in total population, then stock return and equity premium are likely to be high. Hence, a positive correlation may be posited between age composition and stock return. Age composition shows a positive correlation with equity premium and stock return during 1996–00, however, the correlation turns negative during 2001–05, reflecting mainly the impact of mature markets. This sign reversal between periods may be explained by factors other than age; in mature markets, stock return declined sharply during 2001–05, even though the share of the population above forty rose.

The World Bank institutional quality indexes rank mature markets significantly higher than emerging markets. The rankings for either sample do not show a significant variation between the two subperiods under consideration. The institutional quality indexes are used as proxies for the degree of uncertainty across the sample countries. Our main prior argument concerning the correlations between equity premium, stock and bond returns and the institutional quality indexes is that the higher the institutional quality, the lower is ambiguity. This logic implies that higher institutional quality should reduce ambiguity premium and result in lower stock and safe asset returns. Although the impact on equity premium is ex ante indeterminate, since stock return is the main determinant of equity premium, a negative correlation between equity premium and institutional quality indexes can be posited. However, along with reducing uncertainty, institutional quality also has incentive effects (e.g., strong property rights; investor protection). Thus, higher institutional quality may stimulate larger and longer-term investments with significantly higher returns. So, while less ambiguity may serve to lower the asset returns, greater incentives to invest may serve to increase equity returns. Consequently, a positive correlation between stock return and institutional quality is also quite plausible. For the whole sample, the tests show a significantly negative correlation between the World Bank indexes and equity premium during the periods 2001–05 and 1996–05. This result provides strong support to our hypothesis that higher institutional quality reduces ambiguity and results in lower stock return, and hence in lower equity premium. On the other hand, the correlations are positive during 1996–00; this indicates that higher institutional quality is associated with in higher equity premium in that period, which may be due to the incentive effect of institutional quality. Real growth is at the same level in both samples during 1996–00, and equity premium is near zero in emerging markets but it is high in mature markets; high equity premium in mature markets, which rank higher in institutional quality, dominates the near zero equity premium in emerging markets, which rank lower in institutional quality. Consequently, during this period, high equity premium and stock return are associated with high institutional quality, hence the positive correlation. But during 2001–05, equity premium and stock return are high in emerging markets and low in mature markets, and high equity premium and stock return are associated with low institutional quality, and, hence the negative correlation between equity premium and all of the World Bank indexes. It may be argued that, when stock market activity picked up in emerging markets during 2001-05, markets added a significant ambiguity premium to stock returns. For the whole period 1996–05, the negative correlation persists between equity premium and stock return and most institutional quality indexes, which supports our hypothesis.

V. Regression Methodology and Results

A. Regression Methodology

We propose the following general model: Y = f(X1, X2, X3, …), where the dependent variable Y is the vector of values in, respectively, the equity premium, stock returns, or, the safe asset returns sample; Y = (y1, y2, …, y}, with j denoting a country. As we have argued above, some independent variables may have an impact on equity and safe asset returns in the same direction and, therefore, their impact on equity premium may be ambiguous. Thus, there is merit in regressing equity and safe asset returns on the independent variables separately because this allows us to identify whether equity premium is affected primarily through the equity channel or the safe asset channel. The independent variables X1, X2, X3, … are the vectors of the variables shown in Table 5. All variables, including the dependent variables, are normalized as vij =(xij − μi)/σi, where xij is the observation for variable i in country j; μi is the sample mean; and, σi is the sample standard deviation for variable i, so that Xi ={vi1, vi2, …, vi53}. We run the following regression:

Yi=c0+∑i=1kciXi+ui,(4)

where ui is a random error term that is assumed to obey the properties of multiple regression.

B. Regression Results

The regression results excluding the World Bank indexes are presented in Table 8. The results including the World Bank indexes are presented in Table 9. We focus on the results on equity premium.

Table 8.

Summary of Statistically Significant Regression Results Excluding Uncertainty Proxies 1

article image
Sources: Authors’ estimates; Appendix III, Tables 1-3.

Coefficient values. Statistically significant results at least at the 10 percent level are presented. The results that are statistically significant at the five percent level or better are highlighted.

Table 9.

Summary of Statistically Significant Regression Results Including Uncertainty Proxies 1

article image
Source: Authors’ estimates; Appendix IIITables 4-6.

Coefficient values. Statistically significant results at least at the 10 percent level are presented. The results that are statistically significant at the five percent level or better are highlighted. The regression sample sizes are the same as those shown in Table 8.

Results Excluding the World Bank Indexes

First, we examine regression results excluding the World Bank indexes in order to make a judgment on the robustness of the fundamentals in explaining equity premium. Regression results show that most independent variables have high explanatory power at the 5 percent or higher level of significance. Independent variables have an impact on equity premium mainly through stock return. As indicated by the correlation test, regression results show that equity premium is positively correlated with real growth. Although not supported by the correlation tests, regression results indicate a negative correlation between equity premium and equity market capitalization in 2001–05, which is plausible in view of the arguments in the previous section. Contrary to the indication of the correlation tests, regression results show no significant correlation between equity premium and bond market capitalization. As expected, regressions results indicate a negative correlation between equity premium and credit to private sector. In contrast to the correlation test result for mature markets, equity premium shows a negative correlation with lagged consumption during 2001–05. However, as argued earlier, consumption smoothing through access to stock market by a significant segment of the population could result in a decline in stock return. This result may also reflect the fact that, while consumption volatility is lower during 2001–05 relative to 1996–00, equity premium and stock return are higher (Table 6). Regression results also show that equity premium is negatively correlated with unanticipated inflation and it is positively correlated with tax ratio, as indicated by the correlation tests. Finally, equity premium is positively correlated with age composition, as suggested by the correlation tests.

Results Including the World Bank Indexes

We now turn to the regression results including the World Bank indexes to see if the fundamentals continue to have significant explanatory power and to compare the significance of the World Bank indexes to the fundamentals; the results are presented in Table 9. The fundamentals continue to have significant explanatory power and most World Bank indexes are equally significant. At the 5 percent (or higher) level of significance, equity premium is correlated with real growth, equity market capitalization, credit to private sector, tax ratio, and age composition; the signs of those correlations are the same as those in Table 8. Relatively less significant correlations (at 6 to 10 percent level) are indicated between equity premium and bond market capitalization, as well as lagged consumption.

Compared to the fundamentals, most World Bank indexes have equally significant explanatory power for equity premium. Equity premium is negatively correlated with voice and accountability, government effectiveness, and political stability. The negative correlations support our hypothesis that greater institutional strength results in less uncertainty, reduces the ambiguity premium, and hence the equity premium. A significant positive correlation is indicated between equity premium and rule of law, which may be attributable to incentive effects. It is interesting to note that the significance of the World Bank indexes mainly emanates from emerging markets. In those markets, equity premium shows a greater variation within the sample (Table 1). Furthermore, the World Bank indexes also show a greater variation in the emerging markets sample.30 Institutional quality matters in the determination of equity premium in emerging markets.

The more general point is that, through the uncertainty and incentive effects, equity premium is significantly correlated with institutional quality, at least, as significantly as it is correlated with the fundamentals. To the extent institutional quality reflects on ambiguity, a strong case can be made for a significant correlation between equity premium and ambiguity.31

Regressions With Other Uncertainty Proxies

We use a number of other proxies for uncertainty, which are explained in Appendix III, Table 7. Data availability restricts regressions to the period 1995–06. We only present the results for which a significant correlation is indicated between equity premium, stock return, and safe asset return, and the uncertainty proxy used.32 The significant regression results are presented in Table 10 (also see Appendix III, Table 8).

Table 10.

Summary of Statistically Significant Results for other Uncertainty Proxies, 1996–051

article image
Source: Authors’ estimates; Appendix III, Tables 7, 8.

Coefficient values. See Appendix III, Table 7 for the description of the variables reported in this table. Results that are significant at 5 percent or better are highlighted.

The Heritage Foundation index rankings are valued such that a lower (worse) ranking is assigned a high index value and higher (better) ranking is assigned a low index value; the same is true for the World Bank Enterprise Surveys. Equity premium is positively correlated with government intervention (Heritage) and infrastructure (World Bank) indexes, which is plausible. This result indicates greater degree of government intervention results in higher equity premium; similarly, less satisfactory infrastructure results in higher equity premium. Both factors imply higher uncertainty in the business environment.

On the other hand, equity premium is positively correlated with the index that measures the degree of confidence in various social and political categories. The index is constructed (by the authors) such that a higher value indicates higher confidence ranking. Therefore, the positive correlation between equity premium and the confidence index may be attributable to the incentive effects of greater confidence, that is, higher social confidence may stimulate investment in riskier areas with higher returns, which results in higher stock return.33

VI. Conclusions

Equity premium puzzle is a global phenomenon that is present in both emerging and mature markets. The impact of the fundamentals on equity premium is mainly through stock return because stock return is the dominant determinant of equity premium.

Institutional quality indexes play as significant a role as the fundamentals in the determination of equity premium. Equity premium and stock return have a significantly negative correlation with the World Bank indexes for voice and accountability, political stability and government effectiveness. Similarly, greater government intervention (Heritage) and less satisfactory infrastructure (World Bank) indicate higher equity premium. We interpret these results as an indication of institutional quality reflecting on unquantifiable uncertainty or ambiguity. We argue that lower ambiguity results in a decline in equity premium. The same effect may be posited for safe asset returns, however, safe assets display less ambiguity than equity across the countries in the institutional quality spectrum. This observation is supported by the result that there is no statistically significant correlation between safe asset returns and the World Bank institutional quality indexes.

In the case of two World Bank institutional quality indexes, rule of law and control of corruption, as well as in the case of the confidence indexes (World Values Survey), we find significantly positive correlations with stock return and equity premium. A plausible case can be made for a positive correlation. It is intuitively appealing that better rule of law and better control of corruption induce greater social trust, which makes the investment environment more stable and predictable, and levels the playing field. This creates incentive effects and serves to induce greater innovation and longer-term, higher-yield investments, which might not have been undertaken in a less politically stable and more corrupt environment. Consequently, higher rankings in those areas are associated with higher stock return, and hence with higher equity premium.

Interestingly, the results also indicate that institutional quality indexes are significant in emerging markets but not in mature markets. On average, mature markets are ranked significantly higher by the World Bank institutional quality indexes; furthermore, the emerging markets sample shows a significantly greater variation (as measured by the sample standard deviation) than the mature markets sample.34 These observations help explain why institutional quality indexes are significant in the emerging market regressions. They also lend support to Stulz’s (2005) point that “the reason why countries matter is that finance is critically affected by twin agency problems” (p. 1633). Evidently, institutional quality shows a greater variation in emerging markets, reflecting significantly on perceptions of risk and ambiguity, so that stock returns are significantly affected by the institutional quality ranking of the countries.

As Benartzi and Thaler (1995) underline, “the equity premium is a puzzle within the standard expected utility maximizing paradigm” (p. 90). Within that paradigm, the theories that have attempted to explain this puzzle have proposed some quantifiable fundamentals. The theories that relax the assumptions of the expected utility paradigm (e.g., incorporating nonexpected utility preferences; rank dependent utility; subadditive probability weighting) seem to fare better in explaining EPP. However, the literature has not focused on an important aspect of behavior under uncertainty, namely, ambiguity aversion. Ambiguity aversion may be instrumental in explaining the observed equity premium, which seems too large under expected utility theory. Without a formal portfolio model, we propose that uncertainty can be modeled using cumulative prospect theory, according to which equity premium can be decomposed into two conceptual parts, risk premium and ambiguity premium. Thus, when ambiguity aversion is taken into account, a significant part of the premium can be attributed to unquantifiable uncertainty or ambiguity. The empirical results support our main hypothesis that unquantifiable uncertainty plays an important role in the determination of equity returns. Safe assets, on the other hand, appear to exhibit less ambiguity, and this is the fundamental reason why markets see them as relatively safer than equity. To the extent that institutional quality is a good proxy for the degree of ambiguity in an economy, a strong case can be made that ambiguity aversion significantly augments equity premium and explains a large part of the equity premium puzzle.

For future research, a time-series analysis of the impact of ambiguity on assets returns across countries would be illuminating. Importantly, the relative significance of risk and ambiguity aversion in the determination of asset returns could provide important clues on the dynamics of financial markets, and perhaps even on the processes of decision making in ambiguity that underlie the onset of financial crises.35

Appendix I.

Table 1.

Data Sources for Stock Market Indexes

article image
Memorandum item:Equity market capitalization data sources are Datastream; S&PIFC Emerging Markets Database; and World Federation of Exchanges.