What is Tracking Error? - Definition, Formula & Example

Instructor: David Bartosiak

Dave draws off his years of experience as a Financial Advisor and Analyst to teach others all about finance and the investing world.

This lesson defines tracking error with regards to investment portfolios and funds. It also shows a detailed formula and step-by-step calculation of two examples of funds and indexes.

Tracking the Movement of a Benchmark

There are countless mutual funds and exchange-traded funds for which the goal is to track a index, which we call a benchmark index. Some funds do this better than others. To figure out which fund best tracks an underlying index, we can calculate the fund's tracking error.

Tracking error is the difference between a fund's performance and its underlying or benchmark index. There are two ways to find tracking error -- the simple, and the complex.

At its simplest: Tracking Error = Fund Performance - Benchmark Index Performance

Let's say that XYZ Fund is supposed to track the Big Stock Index. Last year, the Big Stock Index returned 10% while the XYZ Fund returned 9.7%. The difference between the two, 9.7% - 10% = -0.3%, is the tracking error.

Of course, this is a simplification of the overall calculation for tracking error. We can find a more accurate calculation by finding the standard deviation of the simple tracking error over time. Standard deviation is a measure of how spread out a data set is across a range (in this case, over different periods of time). The more complex and accurate equation for calculating tracking error is:

trackingerror

where F = fund return, I = index return, and N = number of periods.

Let's assume the following returns for XYZ Fund and the Big Stock Index:

  • Big Stock Index {10%, 5%, 7%, 2%, 8%}
  • XYZ Fund {9.7%, 4.6%, 7.2%, 2.2%, 7.8%}

How do we find the tracking error, given this knowledge?

  1. To begin, we calculate the simple tracking error of each period by subtracting the Big Stock Index's performance from XYZ Fund's performance. Doing so gives the following five values:{ -0.3%, -0.4%, 0.2%, 0.2%, -0.2% }
  2. Square each value: { 0.09%, 0.16%, 0.04%, 0.04%, 0.04% }
  3. Then, sum these five values to find: 0.37%.
  4. Divide the sum by N - 1, or (5 - 1): 0.0925%
  5. Lastly, take the square root of 0.0925% to find the tracking error: 0.304%.

That's it - we did it!

More Periods, More Accuracy

Typically, when an investor buys an index fund or an exchange-traded fund in order to emulate an index's performance, they want to have a very low tracking error. The lower the tracking error of a fund, the better it is at emulating the index. After all, that's the job of these funds -- investors buy them because they want to mirror the index.

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