What are the implications for this approach if we take structural factors into account that encourage a home bias? Australia, for example, offers tax incentives applicable only to local investors, so their citizens earn higher returns than foreign investors do holding the same stocks. Brazil accomplishes the same thing by imposing additional taxes on foreign investors.
Would it make sense for foreigners to weight each country using a market cap adjusted to reflect only non-local holdings?
KRF: Although there are several ways to think about these issues, one useful perspective is Bob Merton's intertemporal capital asset pricing model. Suppose investors can hedge consumption risk or currency risk by overweighting their own stock market. Australians overweight Australia, Americans overweight the US, etc. The net effect on prices depends on the ability of assets to hedge specific risks, the desire of various investors to hedge those risks, and the relative wealth of various investors.
If all investors knew all tastes, wealth, and underlying cashflow distributions perfectly, it is unlikely that anyone would want to put their foreign investments in the pure foreign market portfolio. Take a simple case in which Japanese investors can hedge their consumption risks with Japanese stocks, but local consumption is not correlated with any other local market. Then Japanese investors want to overweight Japan. If we ignore the impact of the Japanese investors, no other investors would have a home bias. But we can't ignore Japan. From everyone else's perspective, Japanese investors have screwed up the world portfolio. They have bid up asset prices in Japan and driven down expected returns. As a result, all other investors want to underweight Japan. (Of course, this is good because if Japanese investors overweight Japan, other investors must underweight it.)
The Japanese effect will be reduced and possibly reversed if we assume all investors can hedge with their own markets. But it is highly unlikely that everyone will just cancel everyone else perfectly. In other words, it is highly unlikely the foreign market portfolio will be ideal for all investors.
Taxes and other frictions that affect domestic and foreign investors differently will also push people away from a market portfolio. Franking credits in Australia, for example, give local investors a higher after-tax return than foreign investors—even if the foreign investors don't pay taxes. Thus, if everything else is the same, foreigners should underweight Australia. Similarly, foreigners should underweight countries that are particularly likely to expropriate their investments, perhaps because of the possibility of war or because the judicial system favors local investors. It seems next to impossible, however, to measure the relative hedging demands of all investors and to construct the specific foreign portfolio for each investor that accounts for all of the interactions.
EFF: This question is a brain twister, and any answer is likely to be only partly correct, at least in real-world situations. The best I can do is lay out some of the issues.
There is one clean answer to the question, but it only applies under totally unrealistic assumptions. Let's start there and then introduce the complications that cloud the issues.
Suppose there are no taxes, and all markets are equally open to investors in all countries. Suppose in addition there is complete purchasing power parity. This means that the ratio of the prices of any two goods (for example, apples and oranges) is the same in all countries, and the exchange rate for the currencies of any two countries is just the ratio of the prices of any good in the two countries. Under these assumptions, investors in all countries face exactly the same investment opportunities, that is, the same probability distributions of real payoffs on assets and portfolios.
In this oversimplified world, the value-weight (which means cap-weighted) global market portfolio is a default portfolio in the sense that it is one of the "multifactor efficient" portfolios in all the multifactor asset pricing models of Bob Merton's ICAPM. The global market portfolio is a legitimate starting point for the investment decisions of all investors.
This does not necessarily mean that any investor chooses to hold the market portfolio. For example, as Ken points out, investors in a given country may have strong preferences for the consumption goods produced in their country (for example, French wines and cheeses). If local assets provide better hedges against uncertainty about the relative prices of local goods, the result can be home bias in portfolio holdings, even in a world of completely open markets and complete purchasing power parity.
In the simple scenario we are discussing, we can identify other default multifactor efficient portfolios, potentially one for each country. If all investors choose multifactor efficient portfolios, the portfolio obtained by aggregating the portfolios of investors in a given country is multifactor efficient. (Portfolios of multifactor efficient portfolios are multifactor efficient.) For a given country, this aggregate portfolio is the portfolio of the assets, local and global, held by the country's investors. Following the arguments above, the portfolio may have a substantial home bias. Moreover, the international component of the portfolio may not be a portfolio of foreign market portfolios, and it may not cap-weight individual foreign markets. This is not a problem if we have access to the domestic and foreign asset holdings of domestic investors, which means we can identify the portfolio. There is a real sense in which this portfolio is the natural starting point for the investors of a country since it is what they in aggregate hold.
Now let's introduce the complications. Lots of papers show that purchasing power parity does not hold (at least in the short run) and relative prices of consumption goods are not the same in all markets. Moreover, as noted in the question, in some markets, locals and foreigners face different taxation of investment returns, and even within a local market different local investors face different tax rates on investment returns. These and other frictions affect optimal portfolio decisions in ways that may be impossible to describe without all the details about the frictions and the tastes of individual investors (an impossible task). Thus, once we drop the unrealistic assumptions of the simple scenario above, it becomes difficult to say anything concrete about optimal portfolios.
One can argue that asset pricing theory always makes unrealistic assumptions, which are irrelevant if a model does a good job describing observed average returns. True, if one is only concerned with describing average returns. But this argument does not imply that a simplified model can be used as a prescription for optimal portfolios. Here one must face the implications of real world frictions in international investment.
One might argue that the effects of all frictions are captured by the aggregate portfolio of local and foreign assets held by the investors of a country. This is, in a limited sense, true, and it is reasonable to argue that this portfolio is a starting point for investment decisions (perhaps the best we can do). But there are caveats. Within a country, there are taxable and non-taxable investors, and if the data are available, it makes more sense to start with separate aggregate portfolios for the two groups, which also seems a reasonable starting point. There are real problems, however, because not all taxable investors face the same tax rates. Etc. Etc.
In the end, faced with all the frictions in local and international investing, some simple advice for investment advisors may be best. The fundamental consideration is that the portfolio chosen should be highly diversified. If you think market prices are correct, you do not want risk that can be avoided through diversification. Various considerations due to the interplay of frictions, risk-return tradeoffs, and investor tastes for risk may then lead you to tilt the portfolio toward domestic assets, low or high-tax assets, small stocks, value stocks, etc. But if the portfolio chosen is highly diversified, it is likely to be close to multifactor-efficient, which is the desirable end result for all portfolio decisions.
Eugene Fama and Ken French are members of the Board of Directors of the general partner of, and provide consulting services to Dimensional Fund Advisors LP.