Benchmark-Relative Optimisation

Bernd Scherer


Tracking error measures the dispersion (volatility) of active returns (portfolio return minus benchmark return) around the mean active return. It is designed as a measure of relative investment risk and was introduced into the academic arena in the early 1980s (see Sharpe 1981). Since then it has become the single most important risk measure in communications between asset manager, client and consultant.

Benchmark-relative investment management has often been rationalised from either a risk perspective (a benchmark anchors the portfolio in risk–return space and thus gives sponsors confidence in what their money is invested in and what risk this investment carries) or a return perspective (claiming that it is easier to forecast relative returns than total returns). However, the return argument looks spurious; to say that forecasting relative distances is possible whereas forecasting absolute distances is not ignores the fact that the two are closely related: a total distance is the same as the benchmark distance times a relative distance. A more plausible argument that is made is that the estimation error is smaller for relative than for

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