Expected Returns and Volatility in 135 Countries

Claude B. Erb
First Chicago Investment Management Co., Chicago, IL

Campbell R. Harvey
Duke University, Durham, NC 27708
National Bureau of Economic Research, Cambridge, MA

Tadas E. Viskanta
First Chicago Investment Management Co., Chicago, IL

ABSTRACT

We analyze expected returns and volatility in 135 different markets. We argue that country credit risk is a proxy for the ex-ante risk exposure of, particularly, segmented developing countries. We fit a time-series cross-sectional regression using data on the 47 countries which have equity markets. These regression predict both expected returns and volatility using credit risk as a single explanatory variable. We then use the credit rating data on the other 88 countries to project hurdle rates and volatility into the future. Finally, we calculate for each country, the expected time in years, given the forecasted country risk premium and volatility, for an investor to break even and double the initial investment - with 90% probability.

Introduction

The idea of this paper is to develop a simple country risk model that can be used to establish hurdle rates for emerging country investments. Importantly, these rates are appropriate for markets which are segmented in the sense that the same risk project receives the same expected return irrespective of domicile. The model uses Institutional Investor's country credit ratings. We establish rates which represent investments which mimic the average risk within each country. These hurdle rates are forward looking. In addition, we calculate expected volatilities for each of the countries. Combining the expected hurdle rate with the expected volatility, we develop two measures of payback which are directly related to the literature in statistics on "hitting time." We calculate the time in years necessary to recover the investment with 90% probability. We also calculate the number of years necessary to double the investment with 90% probability.

To ensure the widest possible dissemination of our methodology, we have established a country risk homepage:

../../Country_Risk

This site includes the most recent estimates of the expected returns for 135 countries as well as the associated hitting time measures.

Measures of Country Risk in Developed Markets

There are remarkably diverse ways to calculate country risk and expected returns. The risk that we will concentrate on is risk that is "systematic." That is, this risk, by definition, is not diversifiable. Importantly, systematic risk will be rewarded by investors. That is, higher systematic risk should be linked to higher expected returns.

A simple, and well known, approach to systematic risk is the beta of the Sharpe (1964), Lintier (1965) and Black (1970) Capital Asset Pricing Model. This model was initially presented and applied to U.S. data. The classic empirical studies, such as Fama and MacBeth (1973), Gibbons (1982) and Stambaugh (1982) presented some evidence in support of the formulation. This model was brought to an international setting by Solnik (1974a,b, 1977). The risk factor is no longer the U.S. market portfolio but the world market portfolio.

The evidence on using the beta factor as a country risk measure in an international context is mixed. The early studies find it difficult to reject a model which relates average beta risk to average returns. For example, Harvey and Zhou (1993) find it difficult to reject a positive relation between beta risk and expected returns in 18 markets. However, when more general models are examined, the evidence against the model becomes stronger. Harvey (1991) presents evidence against the world CAPM when both risks and expected returns are allowed to change through time. Ferson and Harvey (1993) extend this analysis to a multifactor formulation which follows the work of Ross (1976) and Sharpe (1982). Their model also allows for dynamic risk premiums and risk exposures.

The bottom line for these studies is that the beta approach has some merit when applied in developed markets. The beta, whether measured against a single factor or against multiple world sources of risk, appears to have some ability to discriminate between expected returns. The work of Ferson and Harvey (1994, 1995) is directed at modeling the conditional risk functions for developed capital markets. They show how to introduce economic variables, fundamental measures, and both local and world wide information into dynamic risk functions. However, their work only applies to 21 developed equity markets. What about the other 114 countries?

Country Risk in Developing Markets

One might consider measuring systematic risk the same way in emerging as well as developed markets. Harvey's (1995) study of emerging market returns suggests that there is no relation between expected returns and betas measured with respect to the world market portfolio. A regression of average returns on average betas produces an R-square of zero. Harvey documents that the country variance does a better job of explaining the cross-sectional variation in expected returns.

Bekaert and Harvey (1995a) pursue a model where expected returns are influenced by both world factors (like a world CAPM) and local factors (like a CAPM which holds only in that country). They propose a conditional regime switching methodology which allows the country to evolve from a developing segmented country to a developing country which is integrated in world capital markets.

The Bekaert and Harvey (1995a) is very promising and they have applied this idea to the cost of capital estimation for individual securities in emerging markets [see Bekaert and Harvey (1995b).] However, all of the estimation is calibrated using the data for only the 20 developing markets collected by the International Finance Corporation.

It is straightforward to estimate a relation (the "reward for risk") between, say, a beta and expected return. The cost of capital is obtained by multiplying this reward for risk times the beta. The beta is measured by analyzing the way the equity returns covary with a benchmark return. What if there is no equity market? That is, even if we estimate the risk premium using the 47 countries where data is available, we have no way of using the reward for risk because we do not have betas for many of the developing economies' markets -- because the equity market does not yet exist.

Alternative Risk Measures

We start our exercise with the requirement that the candidate risk measure must be available for all 135 countries and it must be available in a timely fashion. This eliminates risk measures based solely on the equity market. This also eliminates measures based on macroeconomic data that is subject to irregular releases and often dramatic revisions. We focus on country credit ratings.

Our country credit ratings source is Institutional Investor's semi-annual survey of bankers. Institutional Investor has published this survey in its March and September issues every year since 1979. The survey represents the responses of 75-100 bankers. Respondents rate each country on a scale of 0 to 100, with 100 representing the smallest risk of default. Institutional Investor weights these responses by its perception of each bank's level of global prominence and credit analysis sophistication [see Shapiro (1994) and Erb, Harvey and Viskanta (1994, 1995)].

How do credit ratings translate into perceived risk and where do country ratings come from? Most globally-oriented banks have credit analysis staffs. Their charter is to estimate the probability of default on their bank's loans. One dimension of this analysis is the estimation of sovereign credit risk. The higher the perceived credit risk of a borrower's home country, the higher the rate of interest that the borrower will have to pay. There are many factors that simultaneously influence a country credit rating: political and other expropriation risk, inflation, exchange-rate volatility and controls, the nation's industrial portfolio, its economic viability, and its sensitivity to global economic shocks, to name some of the most important.

The credit rating, because it is survey based, may proxy for many of these fundamental risks. Through time, the importance of each of these fundamental components may vary. Most importantly, lenders are concerned with future risk. In contrast to traditional measurement methodologies which look back in history, a credit rating is forward looking.

Our idea is to fit a model using the equity data in 47 countries and the associated credit ratings. Using the estimated reward to credit risk measure, we will forecast "out-of-sample" the expected rates of return in the 88 which do not have equity markets.

Model

We fit our model using equity data from 47 national equity markets. Morgan Stanley Capital International (MSCI) publishes 21 of the indices, and the International Finance Corporation (IFC) of the World Bank publishes the other 26 indices. We view the MSCI national equity indices as developed market returns and the IFC indices as emerging market returns. Our sample begins in September 1979 and ends in March 1995. Twenty-eight of the country indices existed at the beginning of this analysis. We added country indices to the analysis during the month that they were first introduced by either MSCI or the IFC. A list of the countries included in the equity analysis and the inclusion date for each country index is also provided in Table 1 along with some summary statistics.

The equity returns presented in Table 1 are calculated in U.S. dollars. This is especially appropriate in the segmented developing markets where the evidence in Liew (1995) suggests that purchasing power parity closely holds. There are a wide range of average returns and volatility in this sample. Some of the most extreme average returns are found in the newly added markets (Poland and Hungary). Unfortunately, there is only a short sample of equity returns available for these countries.

Table 1 also presents the correlation with the world portfolio calculated over the full sample and over the last five years. The beta with respect to the world market index is also presented. This beta is an appropriate ex ante measure of risk if:

Even in this group of 47 equity markets, there are strong reasons to believe that conditions three and four do not hold.

We estimate the following linear model

where R is the semi-annual return in U.S. dollars for country I, CCR is the country credit rating which is available at the end of March and the end of September each year, t is measured in half years and epsilon is the regression residual. We estimate a time-series cross-sectional regression by combining all the countries and credit ratings into one large model. In this sense, the coefficient is the "reward for risk." Consistent with asset pricing traditions, this reward for risk is world-wide -- it is not specific to a particular country.

This model forces a linear relation between credit rating and expected returns. Intuition suggests that a linear model may not be appropriate. That is, as credit rating gets very low, expected returns may go up faster than a linear model may suggest. Indeed, at very low credit ratings, such as the Sudan, it may be unlikely that any hurdle rate is acceptable to the multinational corporation considering a direct investment project.

We present two alternative formulations which capture the potential nonlinearity at low credit ratings. The first model is a log-linear model, i.e. the natural log of the CCR is used in the regression (log model). The second model uses the inverse of the CCR (risk model) We call this last model the risk model because a high factor implies a higher risk. Whereas in the other models, a higher factor implies a lower risk. These alternative models are

In the linear model and the log model, the slope coefficient should be negative implying a higher credit rating is associated with lower average returns. In the risk regression, the slope coefficient should be positive.

We are also interested in any differences in the reward for risk across different markets. We estimate augmented versions of these models. The log model is:

This superscripts D and E denote emerging and developed markets respectively. The model allows for different rewards for credit risk depending on the type of market.

Finally, we fit the identical specifications to explain the variance of the returns over the period:

where sigma is the unconditional standard deviation of the monthly returns six months after the credit rating is observed.

Results-Beta Risk and Total Risk Models

Figure 1 presents the average returns five years following the observation of a beta coefficient against the beta. There is no significant relation between beta and average return. The regression equation suggests that the slope is negative but insignificant. This implies that higher beta risk carries lower expected returns - which does not make much economic sense. Hence, this particular model, while potentially a useful paradigm for developed markets, is potentially problematic when applied to emerging markets. This extends the results of Harvey (1995) to a broader cross-section of countries.

We also estimated a conditional beta model which follows Shanken (1990) and Ferson and Harvey (1991, 1995). The model is:

where the asterisk denotes the log demeaned credit rating. This interaction term tells us the impact of credit rating on the risk. The last two columns in Table 1 report the slope coefficients. While the coefficient on the interaction term is negative in 33 of the 47 markets (lower credit rating means higher risk), it is clear that this formulation is insufficient to explain the return patterns in the developing markets.

Figure 2 presents the average returns five years following the observation of a standard deviation against the beta. There is a weak positive relation observed here. Higher standard deviation is associated with higher returns. This is particularly the case among the emerging equity markets and is consistent with the economic model proposed in Bekaert and Harvey (1995a).

As mentioned earlier, both of these models are problematic when going to the other 88 countries. In those countries, there is no way to estimate a beta coefficient or volatility. Even if significant coefficient were obtained, however, this framework is problematic because data on the determining attribute (equity risk) is not available for a broader set of countries.

Results-Credit Risk Models

Table 2 present the regression results for the three credit risk models. In all of the models in panel A, the slope coefficients are significantly different from zero and the correct sign. Indeed, it is difficult to distinguish the fits of the different models. In this case, a graphical analysis is helpful. Figure 3 graphs the fitted values of the regression equations in Panel A and extends the fitted values to credit ratings lower than the ones observed in our sample.

There are a number of observations from this graph. First, even within the sample of equity returns, the linear model does not seem appropriate. The fitted values for the highest rated countries (like Switzerland) are too low compared to the average returns. The fitted values for the lowest rated countries are also too low. This is immediate evidence of nonlinearity.

Both the log and risk model appear to capture this nonlinearity. The difference between the two models is most evident at the very low credit risk points. In this region, the risk model gives much higher fitted values. It is difficult to judge the model in this region because we are in "no man's land". That is, there are no observations of the dependent variable available for a reasonableness check. However, this is a problem that we inevitably face when trying to estimate the cost of capital for all countries in the world.

It turns out that the split sample regression offers little compared to the full sample regression. The coefficients on the credit rating variable for developed countries and the credit rating variable on the developing countries is indistinguishable. In addition, the amount of variance explained, adjusted for the number of regressors, is lower with the augmented model. The fitted values are presented in Figure 4. Notice that the log model (fit on the developed country returns) and extended to the emerging returns is very similar in to the model estimated on the emerging market returns. This analysis suggests that the reward for credit risk is not different across emerging and developed markets.

Fitted Expected Rates of Return

The graphs provide fitted expected rates of return the full range of credit rating. Table 3 presents the most recent forecast of expected (annual) returns for 134 countries. These expected returns are presented for the log model. The formula is simple. The natural logarithm of the March 1995 credit rating is multiplied by -10.14 (slope coefficient from Table 2) and added to 52.32 (the intercept from Table 2). This presents a semiannual expected return. This quantity is doubled and is found in Table 3.

In order to calculate hitting times, we need both the ex ante expected return and variance. The results of estimating the volatility models are presented in Table 4. The format is identical to Table 2. Three models are presented. In the final analysis, the log of country credit rating shows the most promise in explaining the cross-section and time-series of semi-annual returns.

There is one difference between the results for the expected returns and the volatilities. There appears to be more of a difference between developed countries and developing countries. Although credit rating is strongly negatively related to expected returns in both groups of countries, the magnitude of the coefficient is greater in emerging markets (-0.0323 versus -0.0285). In economic terms, a ten point drop in credit rating would increase volatility by 6.6% points in a developed market and 7.4%points in an emerging market. Nevertheless, the two coefficients are only one standard error from each other.

Hitting Time

Often potential investors are presented with the net present value of the investment and the internal rate of return. Another useful piece of information is the hitting time. The intuition is as follows. Suppose returns are symmetrically distributed. If you know that expected return on a U.S. investment is 14.8%, what is the probability that 14.8% will be achieved in the first year? The answer is 50%. That is, the expected return is just the mean of the probability distribution and by definition of a symmetric distribution, there is equal probability on both sides. If we were given more information on the distribution, such as the shape of the distribution (normal) and the standard deviation, we could calculate the probability of achieving certain returns over the year.

The idea of hitting time is to fix the probability, the expected returns and the volatility, and to calculate how long it would take to achieve a certain return. We choose two hurdles: break-even and doubling of investment. We ask how long it will take to achieve these hurdles with 90% confidence. We make the assumption that the distribution of data is normal. It is possible to make other assumptions about the distribution of returns. Indeed, it is also possible to use the historical returns as the empirical distribution and by using Monte Carlo methods answer the same question.

The hitting times have a wide range of values depending on the country examined. For example, it takes almost two years for the investment in Afghanistan to break even with 90% confidence. This amount of time may be too long for an investor worried about the potentially volatile downside political and economic risk. On the other hand, the U.S. takes a little over 4 years to break even with 90% probability. One has to wait 16 years for the investment to double in value with 90% confidence.

Other Measures of Risk

There are alternative metrics that can be used to develop volatility and expected returns in these countries. To be useful, the variable must be available for a wide range of countries on a timely basis. Some fundamental variables might include: per capital GDP, the growth in GDP, the size of the trade sector, inflation growth, the change in the exchange rate versus a benchmark, the volatility of exchange rate changes, size of the government sector, the indebtedness of the country, the number of years of schooling, life expectancy, quality of life index, and political risk indices. Using the same technique, a regression model can be fit on the 47 countries and extended to the other 88 countries.

The country credit rating might subsume some of these measures. For example, the correlation between the country credit ratings and the ICRG political risk ratings reported in Diamonte, Liew and Stevens is 88%.

Conclusions

Developing countries represent about 20% of world GDP, 85% of the world population yet only 9% of world equity capitalization. It is reasonable to suppose that these markets will grow in the future -- especially as more countries create new equity markets. This paper provides a method of assessing what to expect in these new markets.

The other contribution of the paper is to examine the investment process. In segmented capital markets, it is not appropriate to use the beta of the country with respect to the world market portfolio as a measure of risk. Indeed, a misapplication of this methodology could lead to gross underestimates of the cost of capital in segmented equity markets.

The method we propose to forecast expected returns and volatility is very simple and parsimonious. Importantly, it is not necessarily the best model for expected returns and volatility. Unfortunately, because of the nature of the problem, there is no way to verify the accuracy of the results until some of the developing countries "emerge" into the MSCI or IFC database.

Acknowledgements

We appreciate the comments of Bernard Dumas who suggested the hitting time approach.

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