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300 RISK BUDGETING manager is generating excess returns from market timing when claiming his or her skill


is stock selection, then there is clear deception going on. The client may not believe in market timing, or if it was desired could probably implement a market timing strategy more cost-effectively using a combination of cash and futures contracts than by hiring an active equity manager. The other reason for managers to be true to their style is that a particular portfolio manager is most likely but one component of a broader strategy implemented by the client. The performance of the client's overall portfolio is highly dependent on each investment mandate adhering to its guidelines. Deviating from one's assigned mandate would have the same impact on performance as a concert pianist switching to the drums in a Mozart piano sonata! COMPUTING RETURNS Portfolio and asset returns are a cornerstone of return attribution. In this section we define one-period asset returns that are used in the calculation of domestic and international portfolio returns. Let R%(t) represent the local return on the ?zth asset as measured in percent format: Kit-i) where P(t) = Time t local price of the security or asset djt - b,t) = Dividend (per share) paid out at time t for period t-h through t 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 U.K. 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). Suppose that P*(t) represents the price, in euros, of one share of Siemens stock (traded in Germany). Xt(t) is the exchange rate expressed as the rth currency per unit of currency ;'. For example, with USD as the reporting currency, the exchange rate where X (t) = 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 nxh asset expressed in reporting currency is