Practical Portfolio Performance Measurement and Attribution, Second Edition

Appendix B

Multi-currency Attribution Methodology

The following methodology has been developed for use with multi-currency portfolios.

B.1 SCENARIO

Suppose we have a portfolio invested in n asset classes with some asset classes having currencies other than the base currency of the portfolio. Then, suppose that the performance of this portfolio is measured against a benchmark.

B.1.1 Portfolio returns

Let the weight of the portfolio in the ith asset class be w_i , where ∑ w_i = 1, and let the return of the portfolio assets in the ith asset class in local currency be r_Li and in the base currency of the portfolio be r_i . Now the total portfolio return in local currency is:

r_L = ∑w_ir_Li (or weighted average local return)

and in the base currency of the portfolio:

B.1.2 Benchmark returns

Let the weight of the benchmark in the ith asset class be W_i , where ∑ W_i = 1, and let the return of the benchmark for the ith asset class in local currency be b_Li, in the base currency of the portfolio be b_i and hedged into the base currency be b_Hi. Now the total benchmark return in local currency is:

and in the base currency of the portfolio:

B.1.3 Semi-notional returns

We define the semi-notional ...