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IV. Regression Tests for Country Returns
Since the global portfolios are highly diversified, they provide sharp perspective on the
CAPM’s inability to explain the international value premium, and on the improvements provided by a two-factor model. In contrast, portfolios restricted to individual countries are less diversified and their returns have large idiosyncratic components (e.g., Harvey, 1991). As a result, asset pricing tests on country portfolios are noisier than tests on global portfolios. But the country portfolios have an advantage. Since most of the country portfolios are small fractions of the global portfolios (table I), and since all have large idiosyncratic components, there is no reason to think we induce a linear relation between average return and risk loadings by the way we construct the explanatory portfolios.
Thus, the country portfolios leave plenty of room for asset pricing models to fail.

A. The CAPM versus a Two-Factor Model
In an international CAPM, all expected returns are explained by slopes on the global market return. Table V shows estimates of the CAPM time-series regression (1) that attempt to explain the returns on three separate sets of country portfolios that include, respectively, the market, high book to-market (HB/M), and low book-to-market (LB/M) portfolios of our 13 countries. We group country portfolios by type (rather than doing joint tests on all portfolios and countries) to have some hope of power in formal asset pricing tests.

Like Solnik (1974), Harvey (1991), and others, we find little evidence against the
international CAPM as a model for the market returns of countries. The GRS test of the hypothesis that all the intercepts in the CAPM regressions for the country market portfolios are 0.0 produces an F-statistic, 1.12 (p-value = 0.34), near the median of its distribution under the null. The low book-tomarket portfolios of the countries are also consistent with an international CAPM. The GRS p-value for the LB/M portfolios (the probability of a more extreme set of intercepts when the CAPM holds) is 0.932. Results not shown confirm that an international CAPM is also consistent with the average returns on the country growth portfolios formed on E/P, C/P, and D/P.

Confirming the global portfolio results in table IV, however, table V says that the international CAPM cannot explain the high average returns on the country value portfolios. For the high book to- market (HB/M) portfolios, the average of the intercepts from the CAPM regressions is 0.48% per month. The GRS test produces an F-statistic of 2.20, which cleanly rejects (p-value = 0.01) the hypothesis that all the intercepts are 0.0. The results (not shown) for value portfolios formed on E/P, C/P, and D/P are similar.

Table V shows that a two-factor model that describes country returns with the global market return and the spread between the global high and low book-to-market returns, H-LB/M, does a better job on the country value portfolios. The average intercepts drop from 0.48 in the CAPM regressions to explain the HB/M returns of countries to 0.11 in the two-factor regressions. The p-value for the test of whether all the intercepts are 0.0 rises from 0.01 in the CAPM regressions to 0.72 in the twofactor regressions. Results not shown confirm that, unlike the CAPM, the two-factor regressions also capture the average returns on country value portfolios formed on E/P, C/P, and D/P.

There is an interesting pattern in the way the country portfolios load on the international
distress factor in table V. Not surprisingly, every country’s HB/M value portfolio has a positive slope on the global value-growth return, H-LB/M. Every country’s HB/M portfolio also has a larger slope on the global H-LB/M than its LB/M portfolio. What is surprising is that except for the U.S., Japan, and Sweden, every country’s LB/M portfolio has a positive slope on the global H-LB/M return. In other words, the growth portfolios of ten of the 11 smaller markets load positively on the international distress factor. Similarly, in the two-factor regressions to explain the market returns of the countries, only the U.S. and Japan have negative slopes on the global value-growth return. The H-LB/M slopes for the market portfolios of the 11 smaller markets are all more than 1.0 standard error above 0.0, and seven are more than 2.0 standard errors above 0.0. In short, measured by
sensitivity to the global H-LB/M return, the 11 smaller markets tilt toward return behavior typical of value stocks.

Finally, a caveat is in order. Country returns have lots of variation not explained by global
returns. The average R2 in the two-factor regressions for the countries is only about 0.35. As a result, the two-factor regression intercepts are estimated imprecisely, so our failure to reject international two-factor pricing for the country portfolios may not be impressive. But we do not, in any case, mean to push a two-factor model too hard. Additional risk factors are likely to be necessary to describe average returns when, for example, the tests are extended to small stocks. Like the more precise tests on the global portfolios in table IV, however, the tests on the country portfolios in table V do allow us to conclude that the addition of an international distress factor provides a substantially
better explanation of value portfolio returns than an international CAPM.

B. Global Risks in Country Returns
The hypothesis that an international CAPM or ICAPM explains expected returns around the world does not require security returns to be correlated across countries. International asset pricing just says that the expected returns on assets are determined by their covariances with the global market return (CAPM and ICAPM) and the returns on global MMV portfolios needed to capture the effects of priced state variables (ICAPM). But covariances with these global returns (and the variances of the global returns themselves) may just result from the variances and covariances of asset returns within markets; that is, covariances between the asset returns of different countries may be
zero.0 Still, it is interesting to ask whether the global market and distress risks that seem to explain country returns arise in part from covariances of returns across countries.

For direct evidence on the local and international components of country portfolio returns,
we decompose the variances of the global M-F and H-LB/M returns into country return variances and the covariances of returns across countries,
(3)

where wi is the weight of country i in the global portfolio and Ri is the return for the portfolio of country i. If there were no common component in returns across countries, the covariances in (3) would contribute nothing to the global variance. At the other extreme, with perfect correlation of returns across countries, the contribution of the covariances depends on country weights and variances. Using the average country weights for 1975-1995, country covariances would then account for about 75% of the variances of the global M-F and H-LB/M returns. In fact, international components (the covariances in (3)), are 53% of the variance of the global M-F return, and 20% of the variance of the global H-LB/M return. Thus, although country-specific variances account for 80% of the variance of the global H-LB/M return, both the global market return and the global valuegrowth return contain important international components.

The correlations between country returns in table VI provide perspective on these
calculations. Not surprisingly, the correlations of the excess market returns of the 13 countries are all positive (the average is 0.44), and much like those of earlier studies. Given the estimates of (3), it is also not surprising that the correlations of the value-growth (H-LB/M) returns of the countries are smaller. The average is only 0.07, but three quarters of the correlations (59 of 78) are positive. The correlations of the country H-LB/M returns with the global H-LB/M return tend to be larger. This is due in part to the diversification of the global H-LB/M return, but it also reflects the fact that the global return is constructed from the country returns.

From an asset pricing perspective, the important point is that the lower correlation of the HLB/ M returns of the countries does not result in low volatility for the global H-LB/M return; the global value-growth premium is not an arbitrage opportunity. The standard deviation of the global H-LB/M return, 10.02% per year, is about two-thirds that of the global market return, 15.65%. The lower volatility of H-LB/M is also associated with a smaller average premium, 7.60%, versus 9.47% for M-F. And the Sharpe ratio for H-LB/M (mean/standard deviation) is 0.75, well within striking distance of the Sharpe ratio for M-F, 0.61.