tracking error

What is tracking error?Tracking error in the context of mutual funds and hedge funds is the difference between return of an index fund and the index’s actual return. To understand this, one must be aware of an index fund and the Index.  A stock market index is a statistical measure of changes in the securities traded in a stock exchange. Example: Nifty, Sensex and Dow jones etc. An Index fund is a type of mutual fund in which a specific index is chosen and the money is invested in the securities comprised by target Index in the same proportions of the securities as they are in the target index.

The objective of an index fund manager is to achieve returns which are commensurate to that of the target Index (bench mark return). Since an index fund replicates the behavior of underlying index by investing in the shares of an index in the same weights, the return of index and index fund should be same. But there are instances where there exists a mismatch between the index fund return and return of the target index, which is expressed as tracking error. It is the the annualized standard deviation of the difference between the two returns.

Example:

Reliance index fund – Nifty index is an open ended mutual fund that invests in 50 stocks of Nifty in the same proportion as that of Nifty. If the annual average return of Nifty is 17% but the index fund has given only 16% then the difference 1% is considered as tracking error.

How to calculate the tracking error?

Step Process description
1 Collect the required data such as NAV of the index mutual fund and Total return (TR) index value of target index for each day of the total time period required. These can be obtained from the websites of mutual fund company and the stock exchange of underlying index.
2

Calculate the % change in NAV for each day over its previous day

=[NAV on today (t) – NAV as on day (t-1)]/ NAV on today (t)

3

Calculate the % change TR index for each day

=[TR index of day (t) – TR index of day (t-1)]/ TR index of day (t)

4 Calculate the difference between the percentage change in the NAV and the percentage change in the TR Index for each day (Step 3 result – step 2 result)
5 Calculate the standard deviation of the daily differences obtained in step 4
6

Calculate the annualized tracking error using the formula given below:

Annualized tracking error = Standard deviation obtained (Step 5) * √250

250 is the number of average working days of stock exchanges in India

Reasons for tracking error:

1. Rounding off of number of shares:

An index fund attempts to invest in the securities of the benchmarked Index in the same Proportion of the security as it has in the Index. But it is not possible to purchase the securities in proportion. So, the fund manager has to round off this proportion to minimum number of shares that can be purchased on the exchange. This leads to a slight difference in the weights of securities between the index and the fund eventually resulting in tracking error.

2. Expenses incurred by the fund:

Every mutual fund has to incur certain inevitable expenses such as transaction fee on sale or purchase of stocks, management fee etc. This is paid out of the corpus amount collected from the investors of the fund. So, the fund will invest less than what it has collected. This in turn will affects the returns as the fund will earn only on the amount which is invested. This difference will result in tracking error.

3. Setting aside a portion of corpus:

To meet the requirements of requests for redemption, receipt of dividend etc. the fund shall set aside certain portion of its corpus. Since the redemption requests have to be met within a few days, fund managers cannot invest the amount set aside in any other asset to earn something. This makes the fund manager to invest less than what is collected and results in tracking error.

4. Circuit filters leading in deviation in weightage of securities:

During the course of rebalancing the securities in the fund, the fund manager may not be able to buy or sell securities at the desired price or at the same time due to circuit filters imposed by the exchange. He might have to pay more to buy and receive less when he sells leading to distortion in the allocation of shares in same proportion as that of the benchmark index.

Why it matters?

Tracking error indicates how closely the fund is tracking the benchmark index. Low tracking errors indicates that the fund is closely replicating the benchmark index. Tracking error is an indicator of fund manager’s skills and the amount of degree of volatility in the market. So, it is very important to review the tracking error of your index funds and assess the reasons for it before making any further decisions.