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. 44 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