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Local vs. Foreign Returns and Home Bias

An important conceptual issue to keep in mind is that the CAPM suggests that investors hold the (value-weighted) market portfolio. This portfolio should considers all investable assets, domestic and foreign. Consequently, investors should invest not just in the U.S. market, but also in all foreign markets. Of course, even if the CAPM does not hold, thinking about diversification across all possible dimensions—including international—is a good idea.
However, the empirical evidence suggests that investors tend to have strong home bias: U.S. investors tend to overweight U.S. stocks, European investors tend to overweight European stocks, Japanese investors tend to overweight Japanese stocks, and so on. In fact, many investors hold nothing but domestic securities. This home bias holds up even after we adjust for differential transaction costs—and currency.
Currency matters because investment rates of return themselves depend on the currency in which they are earned. For example, Volkswagen AG started 2002 with a price of €52.30 and ended 2002 with a price of €34.50. Therefore, its local currency rate of return was €34.50/€52.30 − 1 ≈ −34% (incorrectly ignoring dividends). But the euro started 2002 at 0.90 $/€ and ended 2002 at 1.05 $/€, a 16.7% appreciation of the euro against the dollar. The Volkswagen shares therefore cost €52.30 · 0.90$/€ ≈ $47.07 and returned €34.50 · 1.05 ≈ $36.23 for a Volkswagen dollar rate of return of −23%. Most U.S. investors in Volkswagen are more concerned with the dollar rate of return; most German investors in Volkswagen are more concerned with their local currency rate of return.