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Equity Valuation and Portfolio Management by Harry M. Markowitz, Frank J. Fabozzi

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DEFINITION OF TRACKING ERROR

The risk of a portfolio can be measured by the standard deviation of portfolio returns. This statistical measure provides a range around the average return of a portfolio within which the actual return over a period is likely to fall with some specific probability. The mean return and standard deviation (or volatility) of a portfolio can be calculated over a period of time.

The standard deviation or volatility of a portfolio or a market index is an absolute number. A portfolio manager or client can also ask what the variation of the return of a portfolio is relative to a specified benchmark. Such variation is called the portfolio's tracking error.

Specifically, tracking error measures the dispersion of a portfolio's returns relative to the returns of its benchmark. That is, tracking error is the standard deviation of the portfolio's active return where active return is defined as:

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A portfolio created to match the benchmark index (i.e., an index fund) that regularly has zero active returns (i.e., always matches its benchmark's actual return) would have a tracking error of zero. But a portfolio that is actively managed that takes positions substantially different from the benchmark would likely have large active returns, both positive and negative, and thus would have an annual tracking error of, say, 5% to 10%.

To find the tracking error of a portfolio, ...

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