Tracking Error: Definition, Factors That Affect It, and Example

What Is a Tracking Error?

Tracking error is the divergence between the price behavior of a position or a portfolio and the price behavior of a benchmark. This is often in the context of a hedge fund, mutual fund, or exchange-traded fund (ETF) that did not work as effectively as intended, creating an unexpected profit or loss. Tracking error is reported as a standard deviation percentage difference, which reports the difference between the return an investor receives and that of the benchmark they were attempting to imitate.

Understanding a Tracking Error

Since portfolio risk is often measured against a benchmark, tracking error is a commonly used metric to gauge how well an investment is performing. Tracking error shows an investment's consistency versus a benchmark over a given period of time. Even portfolios that are perfectly indexed against a benchmark behave differently than the benchmark, even though this difference on a day-to-day, quarter-to-quarter, or year-to-year basis may be ever so slight. The measure of tracking error is used to quantify this difference.

Tracking error is the standard deviation of the difference between the returns of an investment and its benchmark. Given a sequence of returns for an investment or portfolio and its benchmark, tracking error is calculated as follows:

Tracking Error = Standard Deviation of (P - B)

• Where P is portfolio return and B is benchmark return.

From an investor's point of view, tracking error can be used to evaluate portfolio managers. If a manager is realizing low average returns and has a large tracking error, it is a sign that there is something significantly wrong with that investment and that the investor should most likely find a replacement.

It may also be used to forecast performance, particularly for quantitative portfolio managers who construct risk models that include the likely factors that influence price changes. The managers then construct a portfolio that uses the type of constituents of a benchmark (such as style, leverage, momentum, or market cap) to create a portfolio that will have a tracking error that closely adheres to the benchmark. 

Factors That Can Affect a Tracking Error

The net asset value (NAV) of an index fund is naturally inclined toward being lower than its benchmark because funds have fees, whereas an index does not. A high expense ratio for a fund can have a significantly negative impact on the fund's performance. However, it is possible for fund managers to overcome the negative impact of fund fees and outperform the underlying index by doing an above-average job of portfolio rebalancing, managing dividends or interest payments, or securities lending.

Beyond fund fees, a number of other factors can affect a fund's tracking error. One important factor is the extent to which a fund's holdings match the holdings of the underlying index or benchmark. Many funds are made up of just the fund manager's idea of a representative sample of the securities that make up the actual index. There are frequently also differences in weighting between a fund's assets and the assets of the index.

Illiquid or thinly-traded securities can also increase the chance of a tracking error, since this often leads to prices differing significantly from market price when the fund buys or sells such securities as a result of larger bid-ask spreads. Finally, the level of volatility for an index can also affect the tracking error.

Sector, international, and dividend ETFs tend to have higher absolute tracking errors; broad-based equity and bond ETFs tend to have lower ones. Management expense ratios (MER) are the most prominent cause of tracking error and there tends to be a direct correlation between the size of the MER and tracking error. But other factors can intercede and be more significant at times.

Premiums and Discounts to Net Asset Value

Premiums or discounts to NAV may occur when investors bid the market price of an ETF above or below the NAV of its basket of securities. Such divergences are usually rare. In the case of a premium, the authorized participant typically arbitrages it away by purchasing securities in the ETF basket, exchanging them for ETF units, and selling the units on the stock market to earn a profit (until the premium is gone). Premiums and discounts as high as 5% have been known to occur, particularly for thinly traded ETFs.

Optimization

When there are thinly traded stocks in the benchmark index, the ETF provider can't buy them without pushing their prices up substantially, so it uses a sample containing the more liquid stocks to proxy the index. This is called portfolio optimization.

Diversification Constraints

ETFs are registered with regulators as mutual funds and need to abide by the applicable regulations. Of note are two diversification requirements: 75% of its assets must be invested in cash, government securities, and securities of other investment companies, and no more than 5% of the total assets can be invested in any one security. This can create problems for ETFs tracking the performance of a sector where there are a lot of dominant companies. 

Cash Drag

Indexes don't have cash holdings, but ETFs do. Cash can accumulate at intervals due to dividend payments, overnight balances, and trading activity. The lag between receiving and reinvesting the cash can lead to a decline in performance known as drag. Dividend funds with high payout yields are most susceptible.

Index Changes

ETFs track indexes and when the indexes are updated, the ETFs have to follow suit. Updating the ETF portfolio incurs transaction costs. And it may not always be possible to do it the same way as the index. For example, a stock added to the ETF may be at a different price than what the index maker selected.

Capital-Gains Distributions

ETFs are more tax-efficient than mutual funds but have nevertheless been known to distribute capital gains that are taxable in the hands of unitholders. Although it may not be immediately apparent, these distributions create a different performance than the index on an after-tax basis. Indexes with a high level of turnover in companies (e.g., mergers, acquisitions, and spin-offs) are one source of capital-gains distributions. The higher the turnover rate, the higher the likelihood the ETF will be compelled to sell securities at a profit.

Securities Lending

Some ETF companies may offset tracking errors through security lending, which is the practice of lending out holdings in the ETF portfolio to hedge funds for short selling. The lending fees collected from this practice can be used to lower tracking error if so desired.

Currency Hedging

International ETFs with currency hedging may not follow a benchmark index due to the costs of currency hedging, which are not always embodied in the MER. Factors affecting hedging costs include market volatility and interest-rate differentials, which impact the pricing and performance of forward contracts. 

Futures Roll

Commodity ETFs, in many cases, track the price of a commodity through the futures markets, buying the contract closest to expiry. As the weeks pass and the contract nears expiration, the ETF provider will sell it (to avoid taking delivery) and buy the next month's contract. This operation, known as the "roll," is repeated every month. If contracts further from expiration have higher prices (contango), the roll into the next month will be at a higher price, which incurs a loss. Thus, even if the spot price of the commodity stays the same or rises slightly, the ETF could still show a decline. Vice versa, if futures further away from expiration have lower prices (backwardation), the ETF will have an upward bias. 

Maintaining Constant Leverage

Leveraged and inverse ETFs use swaps, forwards, and futures to replicate on a daily basis two or three times the direct or inverse return of a benchmark index. This requires rebalancing the basket of derivatives daily to ensure they deliver the specified multiple of the index's change each day.

Ex-Post Tracking Error vs. Ex-Ante Tracking Error

Ex-post tracking error, also known as realized tracking error, is a backward-looking measure. It provides a factual account of how closely the portfolio has tracked its benchmark over a specific period in the past. Ex-post tracking error is useful for performance evaluation, as it shows the actual deviation that occurred between the portfolio and its benchmark.

Ex-ante tracking error, on the other hand, is a forward-looking estimate that attempts to predict how much a portfolio might deviate from its benchmark in the future. This measure is typically calculated using risk models, factor analysis, and statistical techniques that consider the current portfolio composition. Ex-ante tracking error is most useful in risk management and portfolio construction.

Aside from the usefulness mentioned above, the key difference between these two types of tracking errors lie in their calculation methods. Ex-post uses actual historical returns, while ex-ante uses predictive models and current portfolio characteristics. For this reason, it may be easier to get ex-post data as that is based on actuals; in order to determine an ex-ante tracking error, you have to come up with the future data yourself.

Tools to Monitor Tracking Errors

A variety of tools and software solutions are available for analyzing tracking error depending on your size and need.

At the most basic level for retail investors or recreational investors, spreadsheet applications like Microsoft Excel or Google Sheets can be used to calculate tracking error. You'd have to manually input portfolio and benchmark returns, but you can leverage spreadsheet formulas to compute both ex-post tracking error and basic ex-ante estimates.

More advanced options for sophisticated investors or day traders include specialized financial software packages such as Morningstar Direct or through a Bloomberg Terminal. These platforms offer automated data feeds, pre-built analytics tools, and customizable reporting where you can set up your portfolio and the tracking errors are calculated for you.

For institutional investors and large asset managers, there are more sophisticated risk management and portfolio analytics systems like BlackRock's Aladdin, MSCI Barra, or Axioma. These platforms provide advanced modeling capabilities. These types of platforms often integrate with trading systems and can provide real-time analytics.

Example of a Tracking Error

Assume that there is a large-cap mutual fund benchmarked to the S&P 500 index. Next, assume that the mutual fund and the index realized the following returns over a given five-year period:

• Mutual Fund: 11%, 3%, 12%, 14% and 8%.
• S&P 500 index: 12%, 5%, 13%, 9% and 7%.

Given this data, the series of differences is then (11% - 12%), (3% - 5%), (12% - 13%), (14% - 9%) and (8% - 7%). These differences equal -1%, -2%, -1%, 5%, and 1%. The standard deviation of this series of differences, the tracking error, is 2.50%.

The Bottom Line

Tracking error is a measure of how closely a portfolio follows its benchmark index, typically calculated as the standard deviation of the difference between the portfolio and index returns over time. It's crucial for evaluating the performance of index funds and ETFs, with lower tracking errors indicating better replication of the benchmark.