00-100) = -11.31% 100 + 7.94 Clearly, the do liar-weighted return calculation takes into account the timing of the decisions to sell or buy as reflected by the -25.50 percent return. COMPUTING RETURNS_____________________________ Let B^ (?) represent the local return on the nth asset as measured in percent: ^ Pi(?) + <(?-^,?)-^(?-l) (17B6) pi(t-i) P^ (?) = Time ? local price of security or asset djt - b,t) = Dividend (per share) paid out at time ? for period ? - h through ? In a global framework we need to incorporate exchange rates into the return calculations. We define exchange rates as the reporting currency over the local currency (reporting/local). The local currency is sometimes referred to as the risk currency. For example, USD/GBP would be the exchange rate where the reporting currency is the U.S. dollar and the risk currency is the British pound. A USD-based investor with holdings in U.K. equities would use the USD/GBP rate to convert the value of the stock to U.S. dollars. Suppose a portfolio with U.S. dollars as its reporting currency has holdings in German, Australian, and Japanese equities. The local and/or risk currencies are EUR, AUD, and JPY, respectively. The total return of each equity position consists of the local return on equity and the return on the currency expressed in reporting/local. We assume that a generic portfolio contains N assets (n = 1, . . . , N). Let Pn (?) represent the price, in euros, of one share of Siemens stock. Xt{t) is the exchange rate expressed as the zth currency per unit of currency /. For example, with USD as the reporting currency, the exchange rate where X (?) = USD/EUR (i is USD and / is EUR) is used to convert Siemens equity (expressed in euros) to U.S. dollars. In general, the exchange rate is expressed in reporting over local currency. It follows from these definitions that the price of the wth asset expressed in reporting currency is ?(?) = Pi (?)X,y(?) (17B.7) We use (17B.7) as a basis for defining total return, local return, and exchange rate return. The total return of an asset or portfolio is simply the return that incorporates both the local return and exchange rate return. Depending on how returns are defined-continuous or discrete (percent)-we get different equations for how