# Tracking Error

A measure of the difference between the return fluctuations of an investment portfolio and the return fluctuations of a chosen benchmark

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## What is Tracking Error?

Tracking error is a measure of financial performance that determines the difference between the return fluctuations of an investment portfolio and the return fluctuations of a chosen benchmark. The return fluctuations are primarily measured by standard deviations.

Generally, a benchmark is a diversified market index that represents part of the total market. The most common benchmarks for equity portfolios are the S&P 500 and the Dow Jones Industrial Average (DJIA) for portfolios with large-cap stocks, and the Russell 2000 for small-cap portfolios.

### Importance of Tracking Error

Tracking error is one of the most important measures used to assess the performance of a portfolio, as well as the ability of a portfolio manager to generate excessive returns and beat the market or the benchmark. Due to the abovementioned reasons, it is used as an input to calculate the information ratio.

Tracking error is frequently categorized by the way it is calculated. A realized (also known as “ex post”) tracking error is calculated using historical returns. A tracking error whose calculations are based on some forecasting model is called an “ex ante” tracking error.

Low errors indicate that the performance of the portfolio is close to the performance of the benchmark. Low errors are common with index funds and ETFs that replicate the composition of major stock market indices.

High errors reveal that the portfolio’s performance is significantly different from the performance of the benchmark. The high errors can indicate that the portfolio substantially beat the benchmark, or signal that the portfolio significantly underperforms the benchmark.

### Formula for Tracking

Tracking efficiency is calculated using the following formula:

Where:

• Var – the variance
• r– the return of a portfolio
• rb – the return of a benchmark

### Example of Tracking Error

Five years ago, Sam invested \$100,000 in Fund A. The fund primarily invests in large-cap US equities. During the five-year period, the fund showed positive returns. Also, the economy also grew during the period and equity markets rose.

In order to assess how successful his investment was, Sam decides to compare the returns of Fund A against the returns of a benchmark. In such a case, the most appropriate benchmark is the S&P 500 because it tracks the performance of the biggest large-cap companies.

The comparison of the fund against the benchmark can be measured using the tracking error.

The following data is available for the yearly returns for both Fund A and the S&P 500:

We can plug this data into the formula to calculate the tracking error:

In the scenario above, the small tracking error indicates that Fund A does not significantly outperform the benchmark. Therefore, Sam may consider withdrawing his money from the fund and putting it into other, more promising investment opportunities. Alternatively, he may be satisfied with the fact that his portfolio is keeping pace with the gains of the overall market.

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