Abstract

In this article, we estimate the level of risk diversification for a universe of US equity ETFs and observe the benefits of diversification for budgeting of active risk relative to a cap-weighted benchmark. We first introduce a risk model that only needs historical returns to break down relative risk into individual factor-related risk contributions, allowing for the construction of a measure of concentration directly inspired by the Equally weighted Risk Contribution (ERC) concept. We then use this concentration measure to highlight the impact of diversification on tracking error stability and find conclusive empirical evidence that US equity ETFs that have a diversified set of systematic active risk contributions have a more stable tracking error. These results suggest that investors seeking a stable tracking error for active risk budgeting purposes may benefit from selecting those ETFs that have a strong level of risk diversification.

Key takeaways:

• Investors only need historical returns to assess the level of risk diversification of a portfolio. The simple diversification metric that we propose relies on recent innovations in risk modelling that reconcile fundamental and statistical approaches.
• The diversification of factor-based active risk contributions is an effective way to manage active risk. It is associated with a more stable tracking error and in turn, facilitates budgeting of active risk.
• Investors in the US equity ETF market may benefit from these insights when selecting ETFs with strategies that are either actively managed or deviate from broad-based cap-weighted benchmarks.

Introduction

Nearly fifty years ago, Jack Bogle created the first index mutual fund, now known as the Vanguard 500 (Arnott and Sherrerd (2022)). Its purpose was to provide retail investors with exposure to the returns of the Standard & Poor’s 500 market-capitalisation weighted (CW) index. Specifically, Bogle created a passive investment product that was transparent and offered at a low cost for retail investors. Although some pension funds had already been able to invest in index strategies, ordinary retail investors did not have the practical means to do so (Malkiel (2022)). With the launch of the Vanguard 500 index mutual fund, the foundation was laid for the next step in the emergence of exchange-traded funds (ETFs) (Arnott and Sherrerd (2022)).

The next milestone was the creation of a vehicle that allowed a portfolio of stocks to be traded on stock exchanges as a single stock: the exchange-traded fund was born. In 1989, the world’s first ETF, known as the Cash Index Participation Unit (CIP)1, began trading on the Philadelphia Stock Exchange (PHLX). This was the first publicly available ‘portfolio in a share’ product in the US that could be traded on a stock exchange, making it available to both retail and institutional investors (see for example Ruggins (2017) for a detailed review on the history of CIPs). CIPs were designed in such a way as to provide more liquidity in the market and make trading much more efficient. The creation of CIPs was a seminal event that compelled the SEC to formally define an exchange-traded product and create legislation around it, setting the stage for the explosive growth of ETFs that later followed.

The first ETFs were designed as trading tools, an alternative to futures, that generated trading volume on stock exchanges for market participants that were unable or unwilling to trade on futures exchanges. Later, ETFs evolved to become suitable for long-term investors, and once structured as fund vehicles, were able to passively track CW indexes. However, this approach has since been acknowledged to have certain limitations. One such drawback of CW indexes is that a stock’s weight is directly tied to its market capitalisation. This can cause overvalued stocks to be given a disproportionately high weight and undervalued stocks to be given a lower weight in the index (Colby (2007)), in direct contradiction to the intuitive value-driven investment strategy of buying low and selling high. Consequently, any overvaluation in a stock’s price is magnified which can lead to a lag in performance compared to indexes with weightings based on other methods than valuation. Before 2005, there was no low-cost alternative weighting strategy (i.e., non-CW ETFs), that addressed the limitations of market capitalisation weighting; however, soon after, Rob Arnott, Jason Hsu and Philip Moore (2005) developed the Fundamental Index, a strategy that ignored stock price and market capitalisation, and instead weighted stocks using fundamental measures (Arnott and Sherrerd (2022)). This new strategy preserved a passive investment approach through combining an index-delivery structure with an alternative investment strategy. These straightforward, transparent, cost-effective investing solutions were later coined “smart beta” strategies, meaning valuation-indifferent strategies that follow a rules-based approach and often seek exposure to equity factors based on financial metrics such as value, quality, or momentum.

Today, there are two groups among the non-CW ETFs: those tracking a non-CW index (including sector ETFs and smart beta ETFs) and, more recently, those following a strategy devised by an active manager. Non-CW equity ETFs have in common their exposure to systematic equity risk factors other than the overall market factor (e.g., either fundamental risk factors that are deemed rewarded over the long term such as value, size and momentum, or industry risk factors). Actively managed ETFs presumably also include an additional layer of specific (non-systematic) risk linked to the manager’s skill. Their recent growth (both in number of funds and in AUM) is often attributed to several features that differentiate them from actively managed mutual funds, such as tax efficiency (secondary market trading and in-kind redemptions/creations ensure that tax liabilities are not mutualised between investors), intraday pricing and liquidity and generally lower fees.

Equity investors now have access to a large variety of ETFs following passively managed smart beta strategies as well as actively managed strategies. At the end of June 2022, although ETFs that follow CW equity benchmarks still represented 77% of the global equity ETF AUM, 18% of the equity ETF instruments globally available to investors were following a passive smart beta strategy and 14% were actively managed.

It is reasonable for investors looking to allocate capital away from a CW ETF to a given non-CW ETF to assess the relative (incremental) risk they can expect from the latter. Note that for the remainder of the article and for ease of reading, we will interchangeably designate this relative risk as “active risk”. More generally, the decision to invest in a non-CW ETF is always going to be implicitly compared to the optically safer choice of investing in a CW ETF because the latter is fully understood by investors and has acquired a you-get-what-you-pay-for status. The risk resulting from the purchase of a non-CW ETF is not only financial (the investment policy followed by the fund may indeed lead to relative underperformance compared to a CW ETF) but also somewhat reputational (for an institutional investor) or psychological (for a retail investor) because “deviating from the crowd” increases the chances of being singled out, for better or for worse. The metric traditionally provided by active managers or promoters of non-CW indices to inform an investor’s assessment of active risk is the Tracking Error (TE), which can be estimated from the past returns of an ETF. Investors therefore translate their combined levels of risk appetite and trust with respect to a non-CW investment strategy into a TE risk budget they are willing to tolerate. Unfortunately, an empirically estimated TE is by design an ex-post (backward-looking) risk metric that may not always be a good estimator of future TE, especially if the investment strategy followed by the non-CW ETF generates large variations of TE. Therefore, investors need to carefully analyse the make-up of the observed TE after having identified its various components to ultimately assess whether they are comfortable relying on a backward-looking risk measurement for active risk budgeting purposes. Our intention in this article is to propose an ex-post risk analysis methodology that will help investors make such an assessment for non-CW ETFs.

It is well established that rigorous risk analysis ought to identify and separate systematic risk from non-systematic (specific) risk, because the former is more persistent, can be somewhat quantified, and cannot be fully diversified away. This approach is equally valid for investors trying to analyse active (relative) risk. For the equity asset class, the standard practice within academia and in the industry is to use a common set of factors to describe the systematic risk of equity portfolios (see for example Amenc and Goltz (2016) for an overview). Provided these systematic factors explain most of the risk prevailing in the equity portfolios we wish to analyse, it may then be possible for a risk model to break down relative risk (and therefore TE) into individual factor-related risk contributions. The concept of risk contribution is commonly used among institutional investors to budget risk in accordance with the constraints of their mandate (see Qian (2006) for an intuitive interpretation of risk contributions as expected contributions to potential portfolio losses), and our study here aims at helping investors with their active risk budgeting process when reviewing a non-CW ETF: the more ex-post evidence one has about the stability of an ETF’s TE, the easier it is to determine whether an appropriate amount of capital was allocated to this ETF as part of a risk budgeting review.

The question of how investors should use the relative risk contributions (obtained via the factor risk model) may be first addressed with a bit of intuition. A key insight of portfolio theory is indeed that diversifying the sources of uncertain returns leads (all else being equal) to lower portfolio risk, and more specifically, to smaller variations in portfolio returns. Going slightly “meta” and applying this insight to volatility itself tells us that diversifying the sources of (i.e., the contributions to) volatility should lead to smaller variations in portfolio volatility, all else equal. In other words, a diversified set of active risk contributions should be associated with smaller variations in TE. Maillard, Roncalli and Teïleteche (2010) have shown that diversifying risk contributions is an interesting portfolio construction heuristic (proved to be optimal under specific assumptions) that somewhat addresses the shortcomings of two other portfolios commonly used by practitioners: the naïve equal-dollar (1/N) portfolio and the minimum variance (MV) portfolio. Despite its out-of-sample robustness, the risk of the 1/N portfolio is often concentrated in the most volatile assets, while the MV portfolio is often concentrated (both in dollar and risk contributions) in the assets with the lowest ex-ante volatility, leading to out of sample instability. The Equal Risk Contribution (ERC) portfolio can be seen as a risk-aware 1/N portfolio, aiming for a balanced risk budget. It is shown to produce improved out-of-sample results compared to the two other portfolios, especially when the portfolio constituents are not strongly correlated. More specifically, the ERC portfolio is overall less volatile than the 1/N portfolio and less concentrated than the MV portfolio, therefore carrying smaller tail risk (VaR, drawdown). Roncalli and Weisang (2012) transpose the diversification problem to a factor-based framework (with fewer sources of risk that tend to be less correlated) and confirm that the factor-ERC portfolio has attractive properties in terms of tail risk (smaller kurtosis, smaller drawdowns) compared to the 1/N portfolio and even the asset-ERC portfolio. These properties are particularly useful for our (active/relative) risk budgeting exercise: a smaller tail risk is associated with limited variations in volatility and therefore, in line with our earlier intuition, the ERC portfolio appears to be a good reference point when evaluating the stability of a portfolio’s risk.

To conclude, we now transpose the above insights to the universe of non-CW ETFs and apply the (factor) ERC concept to active risk: we expect non-CW ETFs whose TE is diversified in terms of (factor) active risk contributions to carry lower active tail risk and therefore have experienced a more stable TE. Conversely, non-CW ETFs whose TE is concentrated (in terms of factor active risk contributions) are expected to have had a more volatile TE, making the active risk budgeting exercise more challenging for investors.

The objective of the article is to empirically test this insight for the US equity ETF market by proposing an ex-post methodology to assess active risk diversification based on the proximity with an ERC portfolio of active risks. Note that our analysis does not seek to uncover an ex-ante metric that would have attractive out-of-sample predictive power on the stability of future TE, but rather aims to verify that risk diversification and stable TE have historically gone hand in hand, thus providing evidence that one way of stabilising TE (for active risk budgeting purposes) is to maintain a good level of diversification of active risk contributions. A key feature of our methodology is that it does not require any knowledge of an ETF’s holdings. The rest of the article is organised as follows. In the first section, we present our ETF dataset. In the second section, we briefly introduce the equity risk model we intend to use to assess factor risk contributions. In the third section, we introduce a measure of concentration in terms of factor active risk contributions directly inspired from the ERC concept and provide some intuitive interpretation of it. In the final section, we empirically observe the benefits of diversification for active risk budgeting in the US equity ETF universe.

Authors

Benjamin Herzog
Chief Executive Officer,
Scientific Portfolio

Shahyar Safaee
Deputy CEO and Business Development Director,
Scientific Portfolio

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