Academic journal article International Journal of Business

Optimal International Diversification with Constraints

Academic journal article International Journal of Business

Optimal International Diversification with Constraints

Article excerpt


Many authors have well documented the gains from international diversification. Grubel (1968), Levy and Sarnat (1970), Lessard (1973) and Solnik (1974a) have shown how international diversification can provide lower return variances than those achievable by only the domestic market. Eun and Resnik (1988) have proved that international portfolio diversification outperform purely domestic portfolios (U.S.) even when taking exchange risk into account. However, as illustrated by Cooper and Kaplanis (1994) and French and Porterba (1991), individuals invest significantly much more in their respective domestic financial markets. This phenomenon is the so-called "home bias".

According to Stulz (1981), taxes on foreign asset investments can induce such bias. Solnik (1974b) and Stulz (1983), Adler and Dumas (1983) argue that home inflation risk can increase the demand for domestic assets. When investing in international markets, typically the investor must take account of all financial asset returns, of the domestic and foreign interest rates and also of exchange rates. Such problem has been previously studied for example by Solnik (1974a,b), Noetzlin and Solnik (1982), Adler and Dumas (1983) and related problems have been examined by Lessard (1983), Odier and Solnik (1993) or Campbell (1991). Uppal (1993) examines also the effect of consumption goods on the home bias.

As underlined in Coppeland and Weston (1988): "From the purely financial point of view, investors, whether they be firms or individuals, ought to consider the possibility of expanding their investments beyond the geographical limits of their own countries, if only because of the greater number and diversity of investment possibilities available." For example, Europeans are markedly under-diversified in international terms with regard to what would be an theoretical optimal portfolio or compared with the current practice of investors in other countries.

Additionally, some specific constraints may appear when determining the optimal portfolio. This is due to many "frictions": for example, information problems which imply additional costs, limited access to markets ... and exchange risk. Chiou (2009) examines for example the benefits of the optimal international diversification for a U.S.A. investor under various portfolio constraints. He suggests that introducing lower and upper weighting bounds may reduce but not completely eliminate the international diversification benefits (see also Bekaert and Urias, 1996; De Roon et al., 2001; Harvey 1995; Li et al., 2003; Pastor and Stambaugh, 2000; Wang, 1998) for no short selling conditions). Therefore, they emphasize that international diversification of investors must be examined according to specific investment constraints. This is precisely the purpose of the paper that is decomposed as follows.

Section II briefly recalls the main equilibrium relations between interest and exchange rates of Frachot (1995), for affine and lognormal models. In Section III, we solve (2) the international portfolio optimization problem with convex constraints, using results of Cvitanic and Karatzas (1992). In Section IV, we illustrate the general result for the two-country case.


A. International Stock Markets

In this paper, asset prices, domestic and foreign interest rates as well as exchange rates are assumed to be exogenous: the investor is a price taker. The investor's portfolio is assumed to be denominated in domestic numeraire. Therefore, returns on foreign investments depend both on asset returns denominated in foreign currencies and on exchange rates. For example, from the point of view of an American investor, it is convenient to express foreign currencies as costing so many dollars.

Denote by [S.sup.0] the domestic stock and by [S.sup.j], j? {1, ..., n - 1} the foreign stocks, which are [m.sup. …

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