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Appendix A

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

## A.1.1 Scenario

Suppose we have a portfolio invested in n asset classes or industrial sectors. Then, suppose that the performance of this portfolio is measured against a benchmark.

## A.1.2 Portfolio returns

Let the weight of the portfolio in the ith asset class be wi, where Σ wi = 1, and let the return of the portfolio assets in the ith asset class be ri . Now the total portfolio return is:

## A.1.3 Benchmark returns

Let the weight of the benchmark in the ith asset class be Wi , where Σ Wi = 1, and let the return of the benchmark for the ith asset class in the base currency of the portfolio be bi. Now the total benchmark return is:
(as it is in the base currency of the portfolio):

## A.1.4 Semi-notional returns

We define the semi-notional return of the ith asset class as wibi. Now the total semi-notional return is:

## A.1.5 Relative performance

We define the performance of the portfolio relative to the benchmark as:
and it is this relative ...

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