Tracking error

Exchange-traded funds and Tracking Error

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Exchange-traded funds and Tracking Error

Micha FISHER

In this article, Micha FISHER (University of Mannheim, MSc. Management, 2021-2023) explains the concept of Tracking Error in the context of exchange traded funds (ETF).

This article will offer a short introduction to the concept of exchange-traded funds, will then describe several reasons for the existence of tracking errors and finish with a concise example on how tracking error can be calculated.

Exchange-traded funds

An exchange-traded fund is conceptionally very close to classical mutual funds, with the key difference being, that ETFs are traded on a stock exchange during the trading day. Most ETFs are so-called index funds and thus they try to replicate an existing index like the S&P 500 or the CAC 40. This sort of passive investing is aimed at following or tracking the underlying index as closely as possible. However, actively managed ETFs with the aim of outperforming the market do exist as well and typically come with higher management fees. There are several types of ETFs covering equity index funds, commodities or currencies with classical equity index funds being the most prominent.

The total volume of global ETF portfolios has increased substantially over the last two decades. At the beginning of the century total asset volume was in the low triple digit billions measured in USD. According to research by the Wall Street Journal total assets in ETF investments surpassed nine trillion USD in 2021.

The continuing attractiveness of exchange-traded index funds can be explained with the very low management fees, the clarity of the product objective, and the high liquidity of the investment vehicle. However, although especially the market leaders like BlackRock, the Vanguard Group or State Street offer products that come extremely close to mirroring their underlying index, exchange-traded funds do not perfectly track the evolution of the underlying index. This phenomenon is known as tracking error and will be discussed in detail below.

Theoretical measure of the Tracking Error

Simply speaking, the tracking error of an ETF is the difference in the returns of the underlying index (I for index) and the returns of the ETF itself (E for ETF). For a specific period, it is computed by taking the standard deviation of the differences between the two time-series.

Formula for tracking error

Theoretically, it is possible to fully replicate an index in a portfolio and thus reach a tracking error of zero. However, there are several reasons why this is not achievable in practice.

Origins of the Tracking Error

The most important and obvious reason is that the Net Asset Value (NAV) of index funds is necessarily lower than the NAV of its underlying index. An index itself has no liabilities, as it is strictly speaking an instrument of measurement. On the other hand, even a passively managed index fund comes with expenses to pay for infrastructure, personnel, and marketing. These liabilities decrease the Net Asset Value of the fund. In general, a higher tracking error could indicate that the fund is not working efficiently compared to products of competitors with the same underlying index.

Another origin of tracking error can be found in specific sector ETFs and more niche markets with not enough liquidity. When the trading volume of a stock is very low, buying / selling the stock would increase / decrease the price (price impact). In this case an ETF could buy more liquid stocks with the aim to mirror the value development of the illiquid stock, which in turn could lead to a higher tracking error.

Another source of tracking error that occurs more severely in dividend-focused ETFs is the so-called cash drag. High dividend payments that are not instantly reinvested drag down the fund performance in contrast to the underlying index.

Of course, transaction fees of the marketplaces can reduce the fund performance as well. This is especially true if large rebalancing efforts are necessary due to a change of the index composition.

Lastly, there are also ways to reduce the effects described above. Funds can engage in security lending to earn additional money. In this case, the fund lends individual assets within the portfolio to other investors (mostly short sellers) for an agreed period in return for lending fees and possible interest. It should be noted, that while this might reduce tracking error, it also exposes the fund to additional counterparty risk.

Tracking Error: An Example

The sheet posted below shows a simple example of how the tracking error can be computed. To not include hundreds of individual shares, the example transformed the top ten positions within the Nasdaq-100 index into an artificial “Nasdaq-10” index. Although the data for the 23rd of September is accurate, the future data is of course randomly simulated.

By using the individual weights of the index components and their corresponding weights, the index returns for the next three months can be computed.

Figure 1: Three-months simulation of “Nasdaq-10” index.
Three-months simulation of Nasdaq-10 index
Source: computation by the author.

At this point our made-up ETF is introduced with an initial investment of 100 million USD. This ETF fully replicates the Nasdaq-10 index by holding shares in the same proportion as the index. In this example only the management and marketing fees are incorporated. Security lending, index changes and transaction fees and dividends are omitted. Also, all the portfolio shares are highly liquid and allow for full replication. The fund works with small expenses for personnel of only ten thousand USD per month. Additionally, once per quarter, a marketing campaign costs additionally fifty thousand USD.

Figure 2: Computation of ETF return and tracking error.
Computation of ETF-return and Tracking Error
Source: computation by the author.

Calculating the net asset value (NAV) gives us the monthly returns of the fund which in turn allows us to calculate the three-month standard deviation of the tracking difference. Additionally, the Total Expense Ratio can be calculated as the percentage of expenses per year divided by the total asset value of the fund.

This example gives us a Total Expense Ratio of nearly 0.3 percent per annum which is within the competitive area of real passive funds. Vanguard is able to replicate the FTSE All-World index with 0.2 percent. However, the calculated tracking error is obviously smaller than most real tracking errors with only 0.0002, as only management fees were considered. Exemplary, Vanguards FTSE All-World ETF had an historical tracking error of 0.042 in 2021, due to the reasons mentioned in the section above.

Excel file for computing the tracking error of an ETF

You can also download below the Excel file for the computation of the tracking error of an ETF.

Download the Excel file to compute the tracking error of an ETF

Why should I be interested in this post?

ETFs in all forms are one of the major developments in the area of portfolio management over the last two decades. They are also a very interesting option for private investments.

Although they are conceptually very simple it is important to understand the finer metrics that vary between different service providers as even small differences can have a large impact over a longer investment period.

Related posts on the SimTrade blog

   ▶ Youssef LOURAOUI ETFs in a changing asset management industry

   ▶ Youssef LOURAOUI Passive Investing

   ▶ Youssef LOURAOUI Markowitz Modern Portfolio Theory

Useful resources

Academic articles

Roll R. (1992) A Mean/Variance Analysis of Tracking Error, The Journal of Portfolio Management, 18 (4) 13-22.

Business

ET Money What is Tracking Error in Index Funds and How it Impacts Investors?

About the author

The article was written in November 2022 by Micha FISHER (University of Mannheim, MSc. Management, 2021-2023).

My experience at the startup BSD Investing

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My experience at the startup BSD Investing

Rohit SALUNKE

In this article, Rohit SALUNKE (ESSEC Business School, Grande Ecole Program – Master in Management, 2018-2021) shares his experience working in a startup and the evolution of his role and responsibilities…

About BSD Investing

BSD Investing is an independent research firm operating in the asset management industry. It primarily provides research and analysis on active vs passive fund performances for equity and debt funds present across the global financial markets.

The funds are domiciled in Europe (i.e., these are European funds investing in domestic and international markets) and span across 62 universes (i.e., global markets and investment styles).

Logo BDS Investing

The goal of the research is to provide BSD Investing clients with insights into the active vs passive performances and help them optimize the portfolio to get better risk adjusted returns.

The evolution of my missions

I started working at this startup in July 2019 in a small office in Saint-Lazare area in Paris, France. At the beginning, it was just me and two others, the founder, and her colleague. We started from scratch, trying to figure out the best data source to use, figuring out the process flow, the product and much more. After selecting Morningstar as our primary data provider, I began writing codes in Python to fetch the data, create our own portfolios and develop performance key performance indicators (KPIs) for those portfolios. Since we did not have any employee skilled in IT, I was the one who took charge of creating the entire IT architecture from data handling to reporting.

After working for about eight months, we hired our head of IT, and he took over the handling of the IT system and made it much more efficient. That’s when I got the chance to devote my entire focus in developing quantitative models and simulations for the performances of our portfolios.

I started off with researching various technical indicators that gave insights into the market performances and how active funds fared in comparison to passive funds. A major portion of my time was devoted to simulating portfolio performances using various indicator signals. The signals were basically an indication to increase or decrease the active allocation to the portfolio.

Apart from this, I helped a lot with creating marketing materials, conducting market research, interviewing portfolio managers to understand the asset management industry and their needs.

In addition, I work very closely with the IT head to implement our models and key indicators onto the website.

Active and Passive funds

The asset management industry is broadly divided into two management styles: the active style and the passive style. Both styles follow a benchmark that could be an index (e.g., CAC 40), or a combination of indices, or a new portfolio that represent the entire universe of financial instruments in the category that the manager wants to invest in (e.g., Emerging countries large cap ESG funds).

Passive style

The goal of the passive fund manager is to create a portfolio that tracks closely the chosen benchmark. But, since a benchmark consists of a large number of stocks, investing in all of them is not very feasible or cost effective. Therefore, the passive manager creates a portfolio using a smaller number of instruments that aims to replicate the returns from the benchmark.

A good metric to measure the performance of a passive fund is tracking error. It is the divergence between the fund returns and those of the benchmark. A low tracking error means that the fund is tracking the benchmark closely and thus is performing well. Since, a passive fund (also known as ETF or index fund) manager does not aim to outperform the benchmark, but just to simply replicate its returns. Therefore, passive funds charge low fees.

Active style

An active manager on the other hand aims to beat the funds benchmark through stock picking, sector rotation and/or other methods. He or she thus takes a larger risk than a passive fund manager and needs a lot more research, expertise, and management. Therefore, an active fund generally charges more fees than a passive fund. For example, among the France large cap funds, an average passive fund charges around 0.25% of fees, whereas an active manager’s fee may range from 1-2%, in some cases more than 4%.

Active managers are alpha seeking. Alpha is the excess return that an active manager generates compared to its benchmark. There are multiple ways to calculate alpha. One such way is using the CAPM model. We predict the expected return of the portfolio using the CAPM model. Subtracting this return from the active managers portfolio gives the alpha. A passive funds alpha is supposed to be zero.

Fund of funds managers create a portfolio of active and/or passive funds to meet their return and risk objectives.

Best style?

In the asset management industry, there is an ongoing debate about which management style is better and are the extra fees charged by the active managers really worth it?

In the US, for example, the active funds have performed very poorly as compared to the ETFs. Whereas, in Europe the performance was mixed and in Japan, the active funds performed better. However, these are the results over the entire period of 10 years. There have been many periods when the active funds outperformed.

Taking the recent example, after the Covid-19 pandemic, the markets went haywire. Since then, in most of the universes active funds have outperformed the passive funds. Therefore, higher returns can be achieved by understanding the markets and allocating the portfolio to the right management style at the right time.

My key learnings

Working in a startup is always challenging and the job comes with heavy responsibilities.

And although working in a startup sounds very interesting, most of the work during the very beginning is quite tedious when it comes to data handling. I spent a few months just understanding the data, checking for errors from the source, figuring out ways to deal with data errors and so on.

Once, I started working on the quantitative models and the simulations, I felt that my work has just begun. During this time, I learnt a big lesson regarding building quantitative models. I build very sophisticated models including machine learning models such as neural networks, gradient boosted trees and so on. However, despite the good results, I had to use simpler logistic models because selling overly sophisticated models would become very difficult.

People in the asset management industry need to know what the real meaning of the data is. And giving recommendations using a black box model does not make it very easy to understand the functioning of the model.

Working on the various indicators, trying to understand their correlations with active and passive fund performances gave me good insights about them. For instance, one good variable that works the best for me is dispersion. This is the standard deviation of returns among funds or stocks. During periods of high dispersion, I observed that active funds generally outperformed the passive funds. I saw a similar result during periods of high volatility. An explanation to this is that a high dispersion could signify a period of high inefficiency in the market, which the active managers could take advantage of. When markets are highly efficient, it makes sense to invest in ETFs, and reduce your costs. Whereas, during periods of high inefficiency, a good active manager could be worth the higher fees that he/she charges. As described above, since March 2019, the active managers have generally outperformed the passive funds across many universes. And this period is also marked with high dispersion and volatility.

In addition, we found that bear periods were more conducive to active outperformance, while bull periods were not. This can be understood since the volatility and dispersion is generally high during bear periods. However, periods after March 2019 were an anomaly to this, since although the markets are in a bull run, there is high dispersion and volatility, and the active funds are outperforming the ETFs.

Knowledge and skills required

For this job I had to have strong data skills, coding skills as well as sound knowledge about finance.
In addition, since I had little to no guidance in my role, I had to come up with my own tasks, define the product and its objects and then learn the essential skills to build it.

Therefore, there was a lot of market research, visits to stackoverflow, reading research papers, cold mailing portfolio managers and so on. Thus, project management and communication skills are essential.

Hard Skills

  • Python
  • SQL
  • HTML
  • MorningstarDirect
  • Capital Markets
  • Portfolio Management, Optimization …
  • Risk Management
  • Market Research

Soft Skills

  • Communication
  • Project Management
  • Leadership
  • Entrepreneurial Thinking
  • Ability to handle pressure
  • Dedication to your project and display of ownership

Related posts on the SimTrade blog

   ▶ All posts about Professional experiences

   ▶ Youssef LOURAOUI Passive Investing

   ▶ Youssef LOURAOUI Active Investing

Useful resources

BSD Investing

Morningstar

About the author

The article was written in December 2021 by Rohit SALUNKE (ESSEC Business School, Grande Ecole Program – Master in Management, 2018-2021).