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:
![](ccr5.gif">
<P>
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.<P>
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).<P>
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.<P>
<H3>Results-Credit Risk Models</H3>
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.<P>
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.<P>
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)
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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