Home Bias in Financial Markets: Robust Satisficing with Info Gaps

Abstract

Abstract: The observed patterns of equity portfolio allocation around the world are at odds with predictions from a capital asset pricing model (CAPM). What has come to be called the phenomenon is that investors tend to hold a disproportionately large share of their equity portfolio in home country stocks as compared with predictions of the CAPM. This paper provides an explanation of the home-bias phenomenon based on information-gap decision theory. The decision concept that is used here is that profit is satisficed and robustness to uncertainty is maximized rather than expected profit being maximized. Furthermore, uncertainty is modeled nonprobabilistically with info-gap models of uncertainty, which can be viewed as a possible quantification of Knightian uncertainty. JEL classification: D81, F30, G11, G15 Key words: equity home bias, Knightian uncertainty 1 Introduction The observed patterns of equity portfolio allocation around the world are at odds with predictions from the Capital Asset Price Models (CAPM) of Sharpe [16] and Lintner [13]. What has come to be called the 'home bias' phenomenon is that investors tend to hold a disproportionately large share of their equity portfolio in home country stocks, as compared with predictions of the CAPM. This paper provides an explanation of the home bias phenomenon based on information-gap decision theory. The decision concept which is used here is that profit is satisficed and robustness-to-uncertainty is maximized, rather than expected profit being maximized. Furthermore, uncertainty is modelled non-probabilistically with info-gap models of uncertainty. French and Poterba [6, 7] quantify the magnitude of the home bias for a number of countries and conclude that the size of the home bias is substantial, which led to the terms Home Bias Puzzle or French and Poterba Puzzle. For more details see Jeske [10]. In their calculations, French and Poterba assume that the investor maximizes the expected return decremented with a variance-based risk term. Let w = ([w.sub.h];[w.sub.f])' represent the vector of home and foreign investments, let [??] be the expected returns for home and foreign investments, and let [SIGMA] be the covariance matrix of returns. In the French and Poterba model, w is chosen to maximize U(w) = w'[??] - [lambda]/2 w'[SIGMA]w where [lambda] is chosen to weight the risk term. An extremum of U(w) occurs when [??] = [lambda][SIGMA]w. Let [w.sup.o] denote the observed portfolio weights for a particular country, so that the expected returns consistent with CAPM profit maximization would be [[??].sup.o] = [lambda][SIGMA][w.sup.o]. For the same country, let [w.sup.mc] denote the portfolio weights based on world market capitalization, without any home bias effect. That is, [w.sup.mc.sub.h] is the fraction of the world market capitalization ascribable to the country in question. For example, [w.sup.mc.sub.h] = 0.475 for the US. Without any home bias, one would expect that 47.5% of US investments would be in US assets. The vector of expected returns consistent with the CAPM, based on world market capitalization without home bias, is [[??].sup.mc] = [lambda][SIGMA][w.sup.mc]. French and Poterba observed, for a wide range of countries, that: [[??].sup.o.sub.h] > [[??].sup.mc.sub.h] and [[??].sup.o.sub.f] The returns vectors [[??].sup.o] and [[??].sup.mc] are not observed market values, but rather calculated values which are consistent with the CAPM decision model and observed portfolio weights. If the investor's behavior is rightly modelled by the CAPM theory, then [[??].sup.o] and [[??].sup.mc] can be interpreted as returns vectors which are anticipated or perceived by the investor. Relations (1) imply that investors perceive the domestic assets to perform better, and the foreign assets to perform worse, than the bias-free portfolio would indicate. …