NBER WORKING PAPER SERIES ARE FINANCIAL ASSETS PRICED LOCALLY OR GLOBALLY? G.Andrew Karolyi Rene M.Stulz Working Paper 8994 http://www.nber.org/papers/w8994 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge,MA 02138 June 2002 Prepared for the Handbook of the Economics of Finance,George Constantinides,Milton Harris,and Rene M.Stulz,eds.,North-Holland.We are grateful to Dong Lee and Boyce Watkins for research assistance,and to Michael Adler,Kee-Hong Bae,Warren Bailey,Soehnke Bartram,Laura Bottazzi,Magnus Dahlquist, Craig Doidge,Cheol Eun,Vihang Errunza,Jeff Frankel,Thomas Gehrig,John Griffin,Cam Harvey,Mervyn King,Paul O'Connell,Sergio Schmukler,Ravi Schukla,Enrique Sentana,Bruno Solnik,Christof Stahel, Lars Svensson,Linda Tesar,Frank Warnock,and Simon Wheatley for comments.The views expressed herein are those of the authors and not necessarily those of the National Bureau of Economic Research. 2002 by G.Andrew Karolyi and Rene M.Stulz.All rights reserved.Short sections oftext,not to exceed two paragraphs,may be quoted without explicit permission provided that full credit,including notice,is given to the source
NBER WORKING PAPER SERIES ARE FINANCIAL ASSETS PRICED LOCALLY OR GLOBALLY? G. Andrew Karolyi René M. Stulz Working Paper 8994 http://www.nber.org/papers/w8994 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 June 2002 Prepared for the Handbook of the Economics of Finance, George Constantinides, Milton Harris, and René M. Stulz, eds., North-Holland. We are grateful to Dong Lee and Boyce Watkins for research assistance, and to Michael Adler, Kee-Hong Bae, Warren Bailey, Soehnke Bartram, Laura Bottazzi, Magnus Dahlquist, Craig Doidge, Cheol Eun, Vihang Errunza, Jeff Frankel, Thomas Gehrig, John Griffin, Cam Harvey, Mervyn King, Paul O’Connell, Sergio Schmukler, Ravi Schukla, Enrique Sentana, Bruno Solnik, Christof Stahel, Lars Svensson, Linda Tesar, Frank Warnock, and Simon Wheatley for comments. The views expressed herein are those of the authors and not necessarily those of the National Bureau of Economic Research. © 2002 by G. Andrew Karolyi and René M. Stulz. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source
Are Financial Assets Priced Locally or Globally? G.Andrew Karolyi and Rene M.Stulz NBER Working Paper No.8994 June 2002 JEL No.G11,G12,G15 ABSTRACT We review the international finance literature to assess the extent to which international factors affect financial asset demands and prices.International asset pricing models with mean-variance investors predict that an asset's risk premium depends on its covariance with the world market portfolio and, possibly,with exchange rate changes.The existing empirical evidence shows that a country's risk premium depends on its covariance with the world market portfolio and that there is some evidence that exchange rate risk affects expected returns.However,the theoretical asset pricing literature relying on mean-variance optimizing investors fails in explaining the portfolio holdings of investors,equity flows, and the time-varying properties of correlations across countries.The home bias has the effect of increasing local influences on asset prices,while equity flows and cross-country correlations increase global influences on asset prices. G.Andrew Karolyi Rene M.Stulz Fisher College of Business Fisher College of Business Ohio State University Ohio State University 2100 Neil Avenue 2100 Neil Avenue Columbus,OH 43210-1144 Columbus,OH 43210-1144 and NBER stulz 1@cob.osu.edu
Are Financial Assets Priced Locally or Globally? G. Andrew Karolyi and René M. Stulz NBER Working Paper No. 8994 June 2002 JEL No. G11, G12, G15 ABSTRACT We review the international finance literature to assess the extent to which international factors affect financial asset demands and prices. International asset pricing models with mean-variance investors predict that an asset’s risk premium depends on its covariance with the world market portfolio and, possibly, with exchange rate changes. The existing empirical evidence shows that a country’s risk premium depends on its covariance with the world market portfolio and that there is some evidence that exchange rate risk affects expected returns. However, the theoretical asset pricing literature relying on mean-variance optimizing investors fails in explaining the portfolio holdings of investors, equity flows, and the time-varying properties of correlations across countries. The home bias has the effect of increasing local influences on asset prices, while equity flows and cross-country correlations increase global influences on asset prices. G. Andrew Karolyi René M. Stulz Fisher College of Business Fisher College of Business Ohio State University Ohio State University 2100 Neil Avenue 2100 Neil Avenue Columbus, OH 43210-1144 Columbus, OH 43210-1144 and NBER stulz_1@cob.osu.edu
1.Introduction Over the last forty years,financial markets throughout the world have steadily become more open to foreign investors.Yet,most academic research on portfolio choice and asset pricing focuses only on local factors when investigating the determinants of portfolio choice and of expected returns on risky assets.For instance,a vast literature looks at the relation between the U.S.risk premium and the volatility of the U.S.stock market even though in global markets the U.S.risk premium ought to depend at least on the relation between U.S.stocks,a global market portfolio,and possibly exchange rates.In this paper,we examine the lessons from the theoretical and empirical finance literature on the extent to which global factors--i.e.,foreign stock markets and exchange rates--affect asset demands and prices,and on when these factors can be ignored or have to be taken seriously. We start this paper by examining how portfolios would be chosen and asset prices determined in a world where financial markets are assumed to be internationally perfect.In such a world,an asset has the same price regardless of where it is traded and no finance is local.Markets where assets have the same price regardless of where they are traded are said to be integrated,while markets where the price of an asset depends on where it is traded are said to be segmented.In examining the empirical evidence on asset pricing models that assume financial markets to be internationally integrated,a case can be made for studying the cross-section of expected returns without regard for international influences,at least for large markets like the U.S.But,the case for ignoring international determinants of national stock market risk premiums and how they evolve over time has no basis. Models with internationally perfect financial markets have severe limitations in explaining portfolio holdings and how portfolio holdings change over time.The home bias puzzle,which refers to the phenomenon that investors overweight the securities of their country in their portfolio,is inconsistent with models where investors have the same information across countries and where financial markets are assumed to be perfect.Recent research provides a wealth of 1
1 1. Introduction Over the last forty years, financial markets throughout the world have steadily become more open to foreign investors. Yet, most academic research on portfolio choice and asset pricing focuses only on local factors when investigating the determinants of portfolio choice and of expected returns on risky assets. For instance, a vast literature looks at the relation between the U.S. risk premium and the volatility of the U.S. stock market even though in global markets the U.S. risk premium ought to depend at least on the relation between U.S. stocks, a global market portfolio, and possibly exchange rates. In this paper, we examine the lessons from the theoretical and empirical finance literature on the extent to which global factors -- i.e., foreign stock markets and exchange rates -- affect asset demands and prices, and on when these factors can be ignored or have to be taken seriously. We start this paper by examining how portfolios would be chosen and asset prices determined in a world where financial markets are assumed to be internationally perfect. In such a world, an asset has the same price regardless of where it is traded and no finance is local. Markets where assets have the same price regardless of where they are traded are said to be integrated, while markets where the price of an asset depends on where it is traded are said to be segmented. In examining the empirical evidence on asset pricing models that assume financial markets to be internationally integrated, a case can be made for studying the cross-section of expected returns without regard for international influences, at least for large markets like the U.S. But, the case for ignoring international determinants of national stock market risk premiums and how they evolve over time has no basis. Models with internationally perfect financial markets have severe limitations in explaining portfolio holdings and how portfolio holdings change over time. The home bias puzzle, which refers to the phenomenon that investors overweight the securities of their country in their portfolio, is inconsistent with models where investors have the same information across countries and where financial markets are assumed to be perfect. Recent research provides a wealth of
empirical results on how foreign investors choose their asset holdings and on their performance. The picture that emerges from this literature is that there are systematic patterns in ownership of foreign stocks that are hard to reconcile with models assuming perfect financial markets.The only way to rationalize these patterns would be to argue that the gains from international diversification are too small to make holding foreign assets worthwhile.Though there is evidence suggesting that the gains from international diversification have become weaker over time,only investors with extremely strong priors against the hypothesis that assets are priced in internationally integrated markets are likely to conclude that international diversification is not worth it.The home bias decreases the relevance of international determinants of domestic stock prices. The 1990s showed that cross-country equity flows are highly volatile and raised important questions about whether and how flows affect stock prices.In 1998,net equity flows to Latin America amounted to $1.7 billion in contrast to $27.2 billion in 1993.Yet,at the same time,net capital flows to Latin America in 1998 were more than twice their amount in 1993.In other words,both the amounts of net equity flows and net equity flows in proportion to total capital flows are highly variable.Further,from 1994 to 1995,net equity flows to Latin America fell by roughly 40%while net equity flows to East Asia increased by a bit more than 40%. The growing importance of capital flows in the 1990s has led to concerns about contagion. Since national stock markets are correlated because of interdependence among countries,one would naturally expect a shock in one country to affect other countries.Some have called this transmission of shocks contagion,even though it has little to do with the traditional definition of contagion in epidemiology according to which a healthy individual is made sick by a disease transmitted in some way from a stricken individual.Contagion that makes a healthy country sick has been a source of concern in the 1990s,leading many to believe that such irrational or non- I See Edison and Warnock(2001),table 1. 2
2 empirical results on how foreign investors choose their asset holdings and on their performance. The picture that emerges from this literature is that there are systematic patterns in ownership of foreign stocks that are hard to reconcile with models assuming perfect financial markets. The only way to rationalize these patterns would be to argue that the gains from international diversification are too small to make holding foreign assets worthwhile. Though there is evidence suggesting that the gains from international diversification have become weaker over time, only investors with extremely strong priors against the hypothesis that assets are priced in internationally integrated markets are likely to conclude that international diversification is not worth it. The home bias decreases the relevance of international determinants of domestic stock prices. The 1990s showed that cross-country equity flows are highly volatile and raised important questions about whether and how flows affect stock prices. In 1998, net equity flows to Latin America amounted to $1.7 billion in contrast to $27.2 billion in 1993. Yet, at the same time, net capital flows to Latin America in 1998 were more than twice their amount in 1993. In other words, both the amounts of net equity flows and net equity flows in proportion to total capital flows are highly variable. Further, from 1994 to 1995, net equity flows to Latin America fell by roughly 40% while net equity flows to East Asia increased by a bit more than 40%.1 The growing importance of capital flows in the 1990s has led to concerns about contagion. Since national stock markets are correlated because of interdependence among countries, one would naturally expect a shock in one country to affect other countries. Some have called this transmission of shocks contagion, even though it has little to do with the traditional definition of contagion in epidemiology according to which a healthy individual is made sick by a disease transmitted in some way from a stricken individual. Contagion that makes a healthy country sick has been a source of concern in the 1990s, leading many to believe that such irrational or non- 1 See Edison and Warnock (2001), table 1
fundamental contagion can destabilize economies.Neither the high volatility of equity flows nor contagion is consistent with models where investors act rationally,are similarly informed,and trade in financial perfect markets.Some models suggest that factors that have been advanced to explain the home bias can also help explain the volatility of equity flows and perhaps some forms of contagion.However,the volatility of equity flows and contagion increase the importance of international determinants of stock prices-at least for the countries affected by such phenomena. The paper proceeds as follows.Section 2 reviews the various international asset pricing models that assume internationally integrated financial markets,shows the conditions under which assets can be priced locally with these models,and surveys the empirical evidence on these models.Section 3 discusses the home bias.Section 4 addresses the issues of the volatility of equity flows and contagion.Section 5 concludes. 2.The Perfect Financial Markets Model How would individuals choose portfolios and how would asset prices be set in a world with perfect financial markets?In an international setting,the most important implication of perfect financial markets is that all investors face the same investment opportunity set because there are no barriers to international investment.However,in a world of perfect financial markets,the assumptions one makes about how goods prices in different currencies are related have important implications for how individuals choose portfolios and how asset prices are determined.If consumption opportunity sets are the same across countries,it does not matter where an investor is located.An investor can achieve the same expected lifetime utility given his wealth anywhere in the world.If consumption opportunity sets differ across countries and investors are not mobile, then an investor's expected lifetime utility depends on where she is located.In that case,an investor may hold a different portfolio depending on her country of residence.We consider successively the case where investors have the same consumption opportunity sets across countries and the case where they do not.We then present a general approach that encompasses 3
3 fundamental contagion can destabilize economies. Neither the high volatility of equity flows nor contagion is consistent with models where investors act rationally, are similarly informed, and trade in financial perfect markets. Some models suggest that factors that have been advanced to explain the home bias can also help explain the volatility of equity flows and perhaps some forms of contagion. However, the volatility of equity flows and contagion increase the importance of international determinants of stock prices – at least for the countries affected by such phenomena. The paper proceeds as follows. Section 2 reviews the various international asset pricing models that assume internationally integrated financial markets, shows the conditions under which assets can be priced locally with these models, and surveys the empirical evidence on these models. Section 3 discusses the home bias. Section 4 addresses the issues of the volatility of equity flows and contagion. Section 5 concludes. 2. The Perfect Financial Markets Model How would individuals choose portfolios and how would asset prices be set in a world with perfect financial markets? In an international setting, the most important implication of perfect financial markets is that all investors face the same investment opportunity set because there are no barriers to international investment. However, in a world of perfect financial markets, the assumptions one makes about how goods prices in different currencies are related have important implications for how individuals choose portfolios and how asset prices are determined. If consumption opportunity sets are the same across countries, it does not matter where an investor is located. An investor can achieve the same expected lifetime utility given his wealth anywhere in the world. If consumption opportunity sets differ across countries and investors are not mobile, then an investor’s expected lifetime utility depends on where she is located. In that case, an investor may hold a different portfolio depending on her country of residence. We consider successively the case where investors have the same consumption opportunity sets across countries and the case where they do not. We then present a general approach that encompasses
the special cases we discuss in the first two parts of this section.We conclude the section with a discussion of the empirical evidence on the predictions of the perfect markets model for security returns. 2.A.Identical Consumption Opportunity Sets Across Countries Consider a world where goods and financial markets are perfect,so that we have no transportation costs,no tariffs,no taxes,no transaction costs,and no restrictions to short sales. Grauer,Litzenberger,and Stehle (1976)modeled such a world using a state-preference framework.We assume further that there is only one consumption good.?In such a world,every investor has the same consumption and investment opportunity sets regardless of where she resides.Further,the law of one price holds for the consumption good,so that if e(t)is the price of foreign currency at date t,P(t)is the price of the good in the domestic country,and p*(t)is the price in the foreign currency,it must be that P(t)=e(t)P*(t).In such a world,an investor can use the consumption good as the numeraire,so that all prices and returns are expressed in units of the consumption good. We now consider a one-period economy in which real returns are multivariate normal and there is one asset that has a risk-free return in real terms,earning r.Investors care only about the distribution of their real terminal wealth.The properties of the multivariate normal distribution (see Fama,1976,Chapters 4 and 8)imply that: E(g)-r=&+B[E(a)-r], (1) 2 The consumption good can be a basket of goods where the spending proportions on each good are constant. 4
4 the special cases we discuss in the first two parts of this section. We conclude the section with a discussion of the empirical evidence on the predictions of the perfect markets model for security returns. 2. A. Identical Consumption Opportunity Sets Across Countries Consider a world where goods and financial markets are perfect, so that we have no transportation costs, no tariffs, no taxes, no transaction costs, and no restrictions to short sales. Grauer, Litzenberger, and Stehle (1976) modeled such a world using a state-preference framework. We assume further that there is only one consumption good.2 In such a world, every investor has the same consumption and investment opportunity sets regardless of where she resides. Further, the law of one price holds for the consumption good, so that if e(t) is the price of foreign currency at date t, P(t) is the price of the good in the domestic country, and P*(t) is the price in the foreign currency, it must be that P(t) = e(t)P*(t). In such a world, an investor can use the consumption good as the numéraire, so that all prices and returns are expressed in units of the consumption good. We now consider a one-period economy in which real returns are multivariate normal and there is one asset that has a risk-free return in real terms, earning r. Investors care only about the distribution of their real terminal wealth. The properties of the multivariate normal distribution (see Fama, 1976, Chapters 4 and 8) imply that: [ ] d E(r ) r E(r ) r i i id −= + − α β , (1) 2 The consumption good can be a basket of goods where the spending proportions on each good are constant
where E(.)denotes an expectation,ri is the real return on asset i,ra is the real return on the domestic market portfolio,Ba is the domestic beta of asset i defined as Cov(r a)where Var(ra) Cov(.,)denotes a covariance and Var(.)denotes a variance,and o is a constant.If domestic investors can only hold domestic assets and if foreign investors cannot hold domestic assets,then we know that o must be equal to zero for all assets because then the capital asset pricing model (CAPM)must hold in the domestic country.However,in a world where domestic investors have access to foreign assets,the CAPM must hold in real terms using the world market portfolio. Consequently: E(c)-r=B"[E(w)-r], (2) where rw is the real return on the world market portfolio,B is the world beta of asset i defined as CovWe call qution (2)the"world CAPMto conrast it with the traditional Var(r) implementation of the CAPM that uses the domestic market portfolio,which we call the domestic CAPM. We now build on Stulz(1995)to analyze the mistake in using the domestic CAPM when the world CAPM is appropriate.Equations(1)and(2)imply that oi must satisfy: &=[B-Ba][E(w)-r] (3) Equation(3)shows that systematic mistakes are possible when one uses the domestic CAPM and when domestic investors have access to world markets.At the same time,though,equation (3)puts a bound on the economic importance of these mistakes.Since the domestic market 5
5 where E(.) denotes an expectation, ri is the real return on asset i, rd is the real return on the domestic market portfolio, d βi is the domestic beta of asset i defined as i d d Cov(r ,r ) Var(r ) where Cov(.,.) denotes a covariance and Var(.) denotes a variance, and αi is a constant. If domestic investors can only hold domestic assets and if foreign investors cannot hold domestic assets, then we know that αi must be equal to zero for all assets because then the capital asset pricing model (CAPM) must hold in the domestic country. However, in a world where domestic investors have access to foreign assets, the CAPM must hold in real terms using the world market portfolio. Consequently: [ ] w E(r ) r E(r ) r i iw −= − β , (2) where rw is the real return on the world market portfolio, w βi is the world beta of asset i defined as i w w Cov(r , r ) Var(r ) . We call equation (2) the “world CAPM” to contrast it with the traditional implementation of the CAPM that uses the domestic market portfolio, which we call the domestic CAPM. We now build on Stulz (1995) to analyze the mistake in using the domestic CAPM when the world CAPM is appropriate. Equations (1) and (2) imply that αi must satisfy: [ ] w wd α β ββ i i di w =− − E(r ) r . (3) Equation (3) shows that systematic mistakes are possible when one uses the domestic CAPM and when domestic investors have access to world markets. At the same time, though, equation (3) puts a bound on the economic importance of these mistakes. Since the domestic market
portfolio has a beta of one,the weighted average of the alphas in equation(3)must be equal to zero.To understand the nature of the mistakes,we have to understand how the world beta of asset i,B,differs from the product of the world beta of the domestic market,B,and of the domestic beta of asset i,Bd.Using the multivariate normal distribution,we can write the return of asset i as: 5-r=&+B[-r]+e. (4) Similarly,the return of the domestic market portfolio can be written as: ra -r=B rw -r e. (5) Substituting equation(5)into equation(4),we have: 5-r=&+[B[w-r]+ea+e. (6) The world market beta of asset i is therefore: B=阳+ Cov(ed, (7) Var(r) Substituting(7)into(3),we get the result of Stehle(1977)that the pricing mistake from using the domestic CAPM when the global CAPM is appropriate is: 6
6 portfolio has a beta of one, the weighted average of the alphas in equation (3) must be equal to zero. To understand the nature of the mistakes, we have to understand how the world beta of asset i, w βi , differs from the product of the world beta of the domestic market, w βd , and of the domestic beta of asset i, d βi . Using the multivariate normal distribution, we can write the return of asset i as: [ ] d d i i id i r r rr −= + − + α β ε . (4) Similarly, the return of the domestic market portfolio can be written as: [ ] w w d dw d r r rr −= − + β ε . (5) Substituting equation (5) into equation (4), we have: [ ] dw w d i i i dw d i r r rr −= + − + + α β β ε ε . (6) The world market beta of asset i is therefore: d w dw i w i id w Cov( , r ) Var(r ) ε β ββ = + . (7) Substituting (7) into (3), we get the result of Stehle (1977) that the pricing mistake from using the domestic CAPM when the global CAPM is appropriate is:
=Cov(e)[E()-r]. (8) Var(r) Equation(8)shows that the domestic CAPM understates the return of assets whose market model residual is positively correlated with the world market portfolio.However,the domestic CAPM correctly prices those assets whose market model residual is uncorrelated with the world market portfolio.If high domestic beta stocks have risk diversifiable internationally but not domestically,using the domestic CAPM inappropriately would lead one to conclude that the security market line is too flat.One would expect multinational corporations to have returns correlated with foreign markets in such a way that the domestic market portfolio return does not capture all their systematic risk. Our analysis so far shows that,even when the assumptions required for the CAPM to hold are made,the domestic CAPM does not hold in global markets.One inevitably makes pricing mistakes using the domestic CAPM as long as Cov()is not zero for every security.There exists an upper bound on the absolute value of the pricing mistakes.Let Rbe the R-square of a regression of the return of asset i on asset j.With this notation,the bound can be written as: 风≤-R-心E)-1 (9) Consider an asset that has a variance that is four times the variance of the world market portfolio.If the variance of security i is four times the variance of the world market,the R-square of a regression of the security on the domestic market portfolio is 0.3,the R-square of a regression of the world market on the domestic market is 0.2,and the world market risk premium is 6%,the bound is 9%.Consider now an asset with the same volatility but in the U.S.,where a 7
7 [ ] d i w i w w Cov( , r ) E(r ) r Var(r ) ε α = − . (8) Equation (8) shows that the domestic CAPM understates the return of assets whose market model residual is positively correlated with the world market portfolio. However, the domestic CAPM correctly prices those assets whose market model residual is uncorrelated with the world market portfolio. If high domestic beta stocks have risk diversifiable internationally but not domestically, using the domestic CAPM inappropriately would lead one to conclude that the security market line is too flat. One would expect multinational corporations to have returns correlated with foreign markets in such a way that the domestic market portfolio return does not capture all their systematic risk. Our analysis so far shows that, even when the assumptions required for the CAPM to hold are made, the domestic CAPM does not hold in global markets. One inevitably makes pricing mistakes using the domestic CAPM as long as d Cov( ,r ) i w ε is not zero for every security. There exists an upper bound on the absolute value of the pricing mistakes. Let 2 Rij be the R-square of a regression of the return of asset i on asset j. With this notation, the bound can be written as: [ ] 2 2 ( ) (1 )(1 ) ( ) ( ) i i id wd w w Var r R R Er r Var r α ≤− − − . (9) Consider an asset that has a variance that is four times the variance of the world market portfolio. If the variance of security i is four times the variance of the world market, the R-square of a regression of the security on the domestic market portfolio is 0.3, the R-square of a regression of the world market on the domestic market is 0.2, and the world market risk premium is 6%, the bound is 9%. Consider now an asset with the same volatility but in the U.S., where a
regression of the world market portfolio on the domestic market portfolio would have an R- square of at least 0.8.In this case,the bound would be 4.49%.If we are willing to make assumptions about the correlation between the domestic market model residual of an asset and the return of the world market portfolio that is not explained by the domestic market portfolio,we can compute the limits of the pricing mistakes.Consider,for example,a correlation of 0.2.In this case,the asset in a country whose market portfolio is poorly explained by the world market portfolio has a pricing mistake no greater than 1.8%,while the U.S.asset has a pricing mistake of 0.88% It follows from this analysis that using a domestic CAPM is more of a problem in countries whose market has a lower beta relative to the world market portfolio.Since the U.S.is a country where the R-square of a regression of the world market portfolio on the domestic market portfolio is high,the mistakes made by using the domestic market portfolio for U.S.risky assets are smaller than for risky assets of other countries where the R-square of similar regressions is much smaller.Further,the mistakes are likely to be less important for larger firms simply because the domestic market portfolio explains more of the return of these firms. We now turn to the issue of the determinants of the market risk premium.We keep the same assumptions,but now we have an investor who chooses her portfolio to maximize her expected utility of terminal real wealth,E[U(W)],with U(W)strictly increasing and concave in W. Consider first an investor who can only hold U.S.assets,so that the investor holds the U.S. market portfolio.Using a first-order Taylor-series expansion,the first-order conditions of the investor's portfolio choice problem imply that: E(ra)-r=TRVar(ra), (10) 8
8 regression of the world market portfolio on the domestic market portfolio would have an Rsquare of at least 0.8. In this case, the bound would be 4.49%. If we are willing to make assumptions about the correlation between the domestic market model residual of an asset and the return of the world market portfolio that is not explained by the domestic market portfolio, we can compute the limits of the pricing mistakes. Consider, for example, a correlation of 0.2. In this case, the asset in a country whose market portfolio is poorly explained by the world market portfolio has a pricing mistake no greater than 1.8%, while the U.S. asset has a pricing mistake of 0.88%. It follows from this analysis that using a domestic CAPM is more of a problem in countries whose market has a lower beta relative to the world market portfolio. Since the U.S. is a country where the R-square of a regression of the world market portfolio on the domestic market portfolio is high, the mistakes made by using the domestic market portfolio for U.S. risky assets are smaller than for risky assets of other countries where the R-square of similar regressions is much smaller. Further, the mistakes are likely to be less important for larger firms simply because the domestic market portfolio explains more of the return of these firms. We now turn to the issue of the determinants of the market risk premium. We keep the same assumptions, but now we have an investor who chooses her portfolio to maximize her expected utility of terminal real wealth, E[U(W)], with U(W) strictly increasing and concave in W. Consider first an investor who can only hold U.S. assets, so that the investor holds the U.S. market portfolio. Using a first-order Taylor-series expansion, the first-order conditions of the investor’s portfolio choice problem imply that: R E(r ) r T Var(r ) d d − = , (10)