# Tracking Error

Typically, tracking error explains the difference between the price behaviour of an index or benchmark and the position of an investment portfolio. To benefit from the same in terms of investment portfolio management, individuals need to become familiar with the concept and functioning of tracking error.

## What is a Tracking Error?

Tracking error can be described as the relative risk of an investment portfolio when compared to its benchmark. It helps to measure the performance of a particular investment. It also aids to compare the performance of said investment against a concerned benchmark over a specific period. As a result, it serves as an indicator that helps to understand how well a fund is managed and what risks accompany it.

In simpler words, tracking error can be defined as the difference between an investment portfolio’s returns and the index it mimics or tries to beat. Often tracking error comes handy in gauging the performance of portfolio managers and is known as active risk and is mostly used for hedge funds, ETFs or mutual funds.

## How to Calculate a Tracking Error?

Typically, there are two distinct ways of computing tracking error.

In the first method,

The cumulative returns of the benchmark are deducted from the investment portfolio’s returns –

Tracking Error = Return(P) – Return(i)

Here,

P = portfolio

i = index or benchmark

In the second method,

The portfolio returns are deducted from the benchmark first. Subsequently, the standard deviation of the outcome is calculated using this tracking error formula –

Tracking Error = Standard Deviation of (P – B)

Here,

P = Portfolio returns

B = Benchmark returns

## Example of Tracking Error Calculation

Suppose, a large-cap mutual fund is benchmarked to S&P 500 index; its index and mutual fund realised the following returns over 5 years –

For S&P 500 Index –

12%, 5%, 13%, 9% and 7%

For Mutual Fund –

11%, 3%, 12%, 14% and 8%

From the available data, the series of difference stood at –

(11% – 12%) = -1%

(3% – 5%) = -2%

(12% – 13%) = -1%

(14% – 9%) = 5%

(8% – 7%) = 1%

With the help of the tracking error formula–

TE = Standard Deviation of (P – B)

= 2.79%

Any fund which shows a low tracking error signifies that its portfolio is following its benchmark quite closely. Contrarily, a high tracking error signifies that a fund is not following the set benchmark.

Notably, in index funds, the tracking error is never zero because of – expenses ratio, funds’ cash flow, and portfolio realignment due to changes in index composition.

## What is a Good Tracking Error?

The type of investment portfolio decides whether a tracking error is good or bad. Typically, a smaller number indicates tightly bound portfolio earnings against benchmark returns. For instance, index fund managers opt for passive management and try to keep the differential returns significantly low to keep the tracking error low. Regardless, the decision of whether a certain degree of tracking error is good or bad depends entirely on the objectives of investment.

## Factors Influencing Tracking Error

Several factors tend to influence the tracking error. For example, the table below highlights the factors that affect the ETF’s tracking error.

 Factor Impact Discounts & Premium to NAV Bidding the market price of ETFs above or below their NAV results in discounts or premiums, which further leads to divergence. Cash drag Cash holdings are a factor with ETF as there is a significant time lag between receiving and reinvesting cash. This leads to variance in tracking error. Optimisation ETF providers cannot purchase thinly traded stock on benchmark without raising their prices upwards. This is why; they use samples that comprise more liquid stocks that can serve as a proxy to index. Currency hedging Owing to the cost of currency hedging, foreign ETFs with implementing the same usually do not follow any benchmark index. Factors like interest rates and volatility affect the price of hedging and in turn, influence the tracking error. Capital gain distribution Though ETFs are tax-efficient, they distribute taxable capital gains. Such distributions tend to impact performance differently than the index. Changes in index ETFs must keep up with the changes in the index. Generally, during the update, an ETF portfolio is likely to incur a transactional cost. Security lending ETF companies may counterbalance tracking errors with the help of securities lending. It is essentially a practice of lending holdings in ETF-based portfolios so that one could hedge funds for short selling. Expense ratio A high expense ratio influences the performance of ETF funds negatively. Illiquidity and volatility Illiquid securities often accompany a bid-ask spread which leads to errors in tracking. Similarly, the volatility of the benchmark also influences the tracking error.

## Significance of Tracking Error

These pointers indicate the importance of tracking error –

• Tracking error helps to measure and compare the performance of a portfolio with its concerned benchmark or index.
• Enables to gauge the consistency of excessive returns.
• It helps to convert the difference between an investment portfolio and concerned benchmark into a one-digit number for better comparison and understanding.
• It helps portfolio managers to ascertain how close a portfolio is to the benchmark.
• Tracking error serves as a neutral point and allows portfolio managers to make an informed decision.
• It helps investors to ascertain the significance of differences between the returns of benchmark and portfolio.
• Further helps to determine how active and proficient a portfolio manager’s investment strategy is.

Though there are numerous benefits of tracking error, it has its shares of limitations too.

## Limitations of Tracking Error

Tracking error is extensively used to measure and compare both underperformance and outperformance of a fund against its benchmark. Typically, investors prefer a high tracking error in the event that there is a certain degree of outperformance. Alternatively, a low tracking error is preferred during consistent underperformance. Regardless, tracking error does not help distinguish between the two right away.

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