What is a Tracking Error?

Tracking error is the difference between a portfolio's returns and the benchmark or index it was meant to mimic or beat. Tracking error is sometimes called active risk.

There are two ways to measure tracking error. The first is to subtract the benchmark's cumulative returns from the portfolio's returns, as follows:

Returnp - Returni = Tracking Error

p = portfolio
i = index or benchmark

However, the second way is more common, which is to calculate the standard deviation of the difference in the the portfolio and benchmark returns over time. The formula is as follows:


How Does a Tracking Error Work?

Let's assume you invest in the XYZ Company mutual fund, which exists to replicate the Russell 2000 index, both in composition and in returns. If the XYZ Company mutual fund returns 5.5% in a year but the Russell 2000 (the benchmark) returns 5.0%, then using the first formula above, we would say that the XYZ Company mutual fund had a 0.5% tracking error.

As time goes by, there will be more periods during which we can compare returns. This is where the second formula becomes more useful. The consistency (or inconsistency) of the 'spreads' between the portfolio's returns and the benchmark's returns is what allows analysts to try to predict the portfolio's future performance. If, for example, we knew that the portfolio's annual returns were 0.4% higher than the benchmark 67% of the time during the last five years, we would know that this would probably be the case going forward (assuming the portfolio manager made no major changes). The predictive value of these calculations gets even better when there are more data points and when the analyst accounts for how the portfolio's securities move relative to one another (this is called co-variance).

Several factors generally determine a portfolio's tracking error:
1. The degree to which the portfolio and the benchmark have securities in common
2. Differences in market capitalization, timing, investment style, and other fundamental characteristics of the portfolio and the benchmark
3. Differences in the weighting of assets between the portfolio and the benchmark
4. The management fees, custodial fees, brokerage costs and other expenses affecting the portfolio that don't affect the benchmark
5. The volatility of the benchmark
6. The portfolio's beta

Further, portfolio managers must accommodate inflows and outflows of cash from investors, which forces them to rebalance their portfolios from time to time. This too involves direct and indirect costs.

Why Does a Tracking Error Matter?

Low tracking error means a portfolio is closely following its benchmark. High tracking errors indicates the opposite. Thus, tracking error gives investors a sense of how 'tight' the portfolio in question is around its benchmark or how volatile the portfolio is relative to its benchmark. It is important to note that some benchmarked portfolios are allowed more tracking error than others -- this is why investors should understand whether their benchmarked portfolios are intended to either replicate a benchmark, invest in ways that mirror the spirit of the benchmark, or merely attempt to statistically recreate the behaviors of the benchmark.

Although some investors may be happy that the portfolio in our example outperformed the benchmark, the tracking error actually suggests that the fund manager took on greater risk. This is not always what the fund's investors want, and this is why tracking error is in some ways a measure of excess risk.

Although the benchmark represents a feasible alternative to the portfolio in question, calculating tracking error does not mean the wise investor must limit comparison to just the benchmark; he or she will also evaluate the tracking errors of other portfolios with the same objective.

Ultimately, tracking error is an indicator of a manager's skill and a reflection of how actively or passively a portfolio is managed. Actively managed portfolios seek to provide above-benchmark returns, and they generally require added risk and expertise to do so. In these cases, the investor seeks to maximize tracking error. On the other hand, passively managed portfolios seek to replicate index returns, and so a large tracking error is generally considered undesirable for these investors. This is why tracking error can be used to set acceptable performance ranges for portfolio managers.