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An Analysis of a Source of Errors in Performance measurement
Jan 1, 1999
A portfolio's return is a measure commonly used to determine the success of its management. It is not uncommon that a portfolio's performance is compared to that of a benchmark, typically market indexes like the All Ordinaries and the SBC Bond Index. Most portfolios are actively managed and/or have contributions, withdrawals and income through performance measurement periods, and portfolio valuations are often less frequent (e.g. weekly or monthly); in these circumstances, money weighted return approximations are often used to calculate the portfolio managers return. If these money weighted returns are compared to the benchmark return, which by default is a time-weighted return if one uses the ratio of index values from the start to end of a period, then one is not comparing like with like since the portfolio return is not a time-weighted return. In this paper we consider the errors introduced in calculating portfolio returns using money weighted returns as an approximation to the time weighted return and produce a theoretical estimate of the distribution of errors. These errors depend on three variables, the timing of the cash flow through the performance measurement period, the size of the cash flow and the volatility of the portfolio value. Daily data over the last decade for the Australian and USA equity markets is used to empirically calculate these errors. The empirical results support the theoretical results. We conclude that the use of money-weighted returns can lead to the introduction of significant errors, even for small cash flows. We then provide a simple, practical method to check for the expected size of the errors. These errors have significant consequences when performing performance attribution since the errors can be the same order of magnitude as the asset allocation or stock selection components 'calculated' from the attribution analysis; thus the true attribution components may be buried in the noise resulting from these errors.
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