A few days ago, we had discussed, what is the best way to invest in Nifty Next 50 Index? and among the 8 choices available to invest in the Nifty Next 50 Index – which by now most readers should recognise as a high-risk, potential high-reward, hard to beat index – we had singled out three. These are Reliance ETF Junior BeEs, ICICI Nifty Next 50 Index fund and the recently launched UTI Nifty Next 50 Index fund. In this post, I compare the tracking errors of Junior BeEs and the ICICI index fund.

This is in response to a comment on twitter (I forget now, who) that one should consider the tracking error before choosing an index fund. I am not a fan of the tracking error, I explain why and also provide an easier-to-understand alternative.

## What is tracking error?

We know that an index fund or ETF returns should be close to that of the underlying index. The tracking error is a measure of how closely the fund/ETF tracks the index. Higher the tracking error, poorer the tracking.

## What are the causes behind tracking error?

The following is sourced from the excellent introduction to tracking error by the NSE** As we shall see below the following sources of tracking error ignore one important aspect that affects ETF investors.**

1: All Index funds and ETFs hold about 5% cash or in short-term bonds to meet redemption requests (Even in ETFs it is possible to sell and buy directly with the AMC if units are large enough in number)

2: expenses which are inevitable to run a fund

3: If the individual stocks hit upper and lower circuits the fund will have trouble mimicking the index soon enough.

4: Corporate Actions by individual stocks may result in additional buying and selling resulting in higher expenses. Any delay in the realignment of fund portfolio weights with that of the index will cause tracking errors. One common example is a delay in the reinvestment of stock dividends.

5: Rounding off errors while determining weights.

Fund managers use futures contracts, stock lending and short-term bonds to offset the return loss from tracking errors, but a full offset is obviously not possible.

## What is the definition of tracking error?

1: Choose the total returns index for comparison with the fund or ETF.

2: Compute the daily returns of the total returns index and the fund/ ETF. For the fund obviously, the NAV is used. Unfortunately for the ETF too, the NAV is used by many. This, as I show below, can be quite misleading.

3: Compute the daily difference in return between the fund/ETF and the index. This will usually negative as the fund/ETF has expenses.

4: Calculate the standard deviation of the daily difference. This is a measure of how much each daily return deviates from the average. Higher the standard deviation, higher the deviation of the fund/ETF return from index return

5: Annualized the standard deviation by multiplying by the square root of the number of trading days in a year. We have about 15-16 trading holidays in addition to weekends. So I assume 250 trading days in a year. The square root stems from Einstein’s paper on Brownian motion (the random motion of dust in water). See this for a simple discussion

6: The final answer: (√250)x daily standard deviation = tracking error.

## ICICI Nifty Next 50 Index Fund vs Reliance ETF Junior BeEs

So let us now begin our comparison of these two funds. The UTI Nifty Next 50 Index fund, although promising is too young for any kind of analysis. However, since it has lower expenses than the ICICI fund, its tracking error should be reasonable if not lower.

First, let us state the tracking period as defined above. We will calculate the error from Jan 2013 when direct funds became available. According to Moneycontrol, the Junior BeEs ETF had its last dividend declared in July 2009. So that is a relief as we do not have to worry about them. Update: “according to Indiainfoline, the last dividend payout was on 11th March 2014″ as pointed out in a previous article. Thanks to @samdesai62 for pointing this out on twitter. So I have redone the calculation from 11-3-2014 but the conclusions are all the same.

Tracking error for ICICI Nifty Next 50 Index fund: 0.59%

Tracking error for Reliance ETF Junior BeEs: 0.28%

So does this mean that the Reliance ETF is a better choice? Not so fast! The above tracking error is calculated with the ETF NAV (and this is the standard practice from what I see).

The ETF NAV is of little use to me. I buy at the current price which is typically quite different from the NAV for most Indian ETFs. I sell at the current price. So my returns from the ETF are computed using the price and not the NAV. So it makes sense to use the price for the tracking error too!

Tracking error for Reliance ETF Junior BeEs (using price): 8.8%

Yeah, you read that right! The tracking error using NAV is only useful for the ETF fund manager! The investor needs to compute the tracking error with the price.

So does this now mean the Reliance ETF is a terrible choice? Again not so fast. First, let us admit that the tracking error (like volatility) is not something that you can immediately understand. So I think we need a simpler, better measure.

First, we ask, what is it that we want? If after 1Y, the index has given 10% returns, we want to know how much lower has the index fund or ETF given. The difference is the tracking error! So why not measure that directly instead of using standard deviation?!

1: So suppose we consider every possible 1Y,2Y,3Y,4Y and 5Y period possible between Jan 2013 and Sep 2018

2: Find the returns for the index fund or ETF and the total returns index for the above periods.

3: Find the difference in 1,2,3,4,5 year returns between fund/ETF and the index.

4: Look at the min, max, average, and median return difference we will get a fair idea of how much the index/ETF is underperforming wrt the index. This is a direct measure of the tracking error.

## Return difference for ICIC Nifty Next 50 Index Fund

The number in brackets in the top row represents the number of 5Y,4Y,3Y,2Y and 1Y data points considered for calculating the return difference.

**Note **in this picture the median and stdev labels are interchanged. Thanks to Bijananda Chabungbam for pointing it out.

First, notice the difference bet the max difference and min difference starting from right to left. That is from 1 to 5 years. Notice that they tend toward each other. This makes the average a lot more reliable for longer durations. The median is not far away from the average which is good. So due to the tracking error, the returns lost is about 1%.

## Return difference for Reliance ETF Junior BeEs using price data

The average return when you use price data is reasonable and only about 0.1 -0.2% higher than the index fund. However, notice that the difference between min and max is always quite high. This makes the average unreliable. So we use the median and this is about 0.1-0.2% higher than the index median.

Since we need to add demat and brokerage charges, it is reasonable to expect Reliance ETF Junior BeEs to return about 0.2% less than the Index fund.

This means about 1% less corpus if you use the ETF compared to the index fund over 5Y. About 2% over 10Y, 3.5% over 15Y and close to 5% over 20Y. Whether this difference is big enough or small enough is a matter of opinion and I would leave that to you.

All said and done, considering the fact that buying and selling units are easier with the AMC, the ICIC Nifty Next 50 fund (and quite likely UTI Nifty Next 50 fund) are better choices than Reliance ETF Junior BeEs.

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