## 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 fundmutual fund or exchange-traded fund (ETF) that did not work as effectively as intended, creating an unexpected profit or loss instead.

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 he was attempting to imitate.

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## BREAKING DOWN '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. Tracking error is used to quantify this difference.

## Calculation of Tracking Error

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).

For example, assume that there is a large-cap mutual fund that is benchmarked to the Standard and Poor's (S&P) 500 index. Next, assume that the mutual fund and the index realized the follow 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 2.79%.

## Interpretation of Tracking Error

If you make the assumption that the sequence of return differences is normally distributed, you can interpret tracking error in a very meaningful way. In the above example, given this assumption, it can be expected that the mutual fund will return within 2.79%, plus or minus, of its benchmark approximately every two years out of three.

From an investor 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. Evaluating the past tracking error of a portfolio manager may provide insight into the level of benchmark risk control the manager may demonstrate in the future.

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. The tracking error can be viewed as an indicator of how actively a fund is managed and its corresponding risk level.

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. Commonly, there are 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, due to larger bid-ask spreads. Finally, the level of volatility for an index can also affect the tracking error.

## Other Factors That Can Affect an ETF Tracking Error

Sectorinternational 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

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: no more than 25% of assets are permitted in any one security and securities with more than a 5% share are restricted to 50% of the fund. 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 variance. 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 transactions 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., mergersacquisitions 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 are 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. The tracking error is minuscule for the daily change in indexes, but some investors may not understand how leveraged and inverse ETFs work and will be under the impression that they are supposed to return twice or three times the direct or inverse index change for periods longer than a day. However, these ETFs won't accomplish this most of the time because daily rebalancing of the derivatives changes the amount of principal compounded each period.

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