When the boat rocks: trading during an index rebalancing — Quant Simplified
Unlike previous articles in the Quant Simplified series, which largely dived into the mathematics and theories of Quantitative Finance, this article focuses on a practical aspect of the equity market and attempts to analyze index rebalancing with quantitative methods.
The motivations for this article are
- To introduce the concept of an equity index to beginners
- To evaluate if an index rebalancing arbitrage exists
- To explain some observations using ex-post (after-the-facts) analysis
This article is inspired by a project done in one of the courses under Singapore Management University’s Masters in Quantitative Finance program.
Equity Indices — The Multi-Trillion Dollar Fruit Baskets
An index acts as an indicator of the overall performance of the investable universe it represents. Most notably, broad-based equity indices such as the S&P 500, FTSE 100, and the STOXX Europe 600 serve as a measure of market growth in the US, United Kingdom, and Continental Europe, respectively. While indices are not limited to equities as an asset class (there are also indices based on commodities and credit), our analysis focuses on broad-based equity indices only.
Apart from serving as an indicator of equity market growth, equity indices also play a crucial role as benchmarks for index funds. There are two primary types of index funds: a passive fund that aims to closely replicate the index and an actively managed fund where the fund manager endeavors to beat the benchmark. According to an article from VettaFi, the combined Asset Under Management (AUM) of the top 10 equity index ETFs total up to USD 2.3 trillion (VettaFi, 2023). This substantial AUM pertains only to passive ETFs, with more existing in the active fund sphere. Consequently, any alterations made to the benchmark index could result in significant movements of capital, potentially creating tradable opportunities.
Due to its crucial role in the world of investing, index providers must ensure that index construction is clear, concise, and replicable. To create an index, one must first define its objective — what exposure investors would achieve by replicating the index — and its methodology. The methodology should address the following:
- Eligibility — determining the universe of stocks considered in the index based on its objective.
- Construction — establishing a systematic process that dictates which stocks within the eligible universe enter or exit the index to fulfill its objective.
- Calculation — employing a methodical approach to derive the index’s value, accounting for corporate actions and adjustments.
- Maintenance — implementing a standard operational procedure to safeguard the index’s integrity, ensuring it consistently meets its objective over time.
Rebalancing — A Reshuffle of Hands
To maintain the index, index providers need to incorporate within the methodology a process to assess whether the current set of stocks in the basket still aligns with the index objectives. If not, adjustments to the constituents are necessary. This process is known as index rebalancing.
Index rebalancing occurs at predetermined intervals, often annually, semi-annually, or quarterly. Rebalancing frequencies higher than quarterly are rare due to the increased costs associated with frequent changes, making index maintenance expensive. During rebalancing, significant amounts of money can be expected to shift as passive fund managers sell off stocks excluded from the index and purchase newly included stocks to mirror the index composition. The act of rebalancing generates buying and selling pressures on newly included and excluded stocks, respectively.
Since rebalancing is essentially a compulsory action for passive fund managers to ensure accurate tracking of the index, it can create ‘arbitrage’ opportunities. Stocks anticipated to enter the index may experience price appreciation during the buying process, causing upward price momentum. Conversely, stocks expected to exit the index may undergo depreciation when the selling occurs.
Capturing the elusive — A study on FTSE UK Index Universe
In our attempt to evaluate the feasibility of capturing arbitrage opportunities during rebalancing, we analyzed the FTSE UK Index universe, i.e. the FTSE 100 Index and the FTSE 250 Index.
Our selection of these indices is guided by specific criteria:
- Simple and objective index methodology — We focused solely on indices with a fixed number of constituents and straightforward quantitative inclusion criteria. Indices incorporating subjective factors like ESG considerations were excluded due to their subjective nature.
- Transparency — Preference was given to indices where data regarding the index and its constituents are publicly accessible, and obtainable at relatively low costs, ensuring transparency in the analysis process.
- ETF AUM — e chosen indices needed to have a sufficiently substantial AUM in ETFs to guarantee sufficient liquidity and active trading.
Being the sixth biggest country by GDP, the United Kingdom makes a good target for the index rebalancing study. With a developed equity market, the FTSE 100 ETFs have collectively about 30 yards (20 bn EUR) in AUM, while FTSE 250 (mid-cap) ETFs have approx 3 yards (JustETF.com, 2023).
The data required can also be obtained easily. All data are accessed via Refinitiv Datastream Python API through the WRDS subscription.
Our Hypothesis
In this study, our hypothesis posits the presence of statistically significant non-zero returns on the target indices during rebalancing. As rebalancing may result in a shuffling between the FTSE 100 and FTSE 250 indexes, an exclusion from the FTSE 100 index may mean an inclusion into the FTSE 250 index. Consequently, selling pressure to reduce exposure in FTSE 100 funds is countered by buying pressure to increase exposure in FTSE 250 funds. To explore this phenomenon, we conduct a two-tailed test, assuming a null hypothesis of a zero average return, without specifying the direction of the alternative hypothesis.
This study analyzes a total of 42 rebalancing periods spanning a decade from 2013 to Q2 2023, encompassing 488 unique instances. Additionally, to ensure that observed returns are attributed solely to rebalancing activities rather than other events (such as dividends, trading suspensions, or delistings), we implement the following exclusions.
- Stocks that were impacted by delisting or extraordinary events (e.g. trading suspensions)
- Stocks that have corporate actions around the rebalancing period
- Stocks that the team has not been able to get reliable price data on (delisted stocks or stocks that have ambiguous/ multi-venue listing)
- Due to the rarity of the event, we do not consider stocks that enter FTSE 100 out of nowhere (only 2 occurrences in the entire history)
The FTSE 100 and FTSE 250 historic additions and deletions are based on published files that can be found on the LSEG website.
Specific to the FTSE UK index series (FTSE Russell, 2023), the inclusion or exclusion of stocks is determined by their free-float market capitalization at the rank date. This date is defined as the Tuesday falling within the week of the 1st Friday of the rebalancing month, approximately T-14 trading days. The FTSE UK series follows a quarterly rebalancing schedule, occurring in March, June, September, and December. The actual rebalancing occurs immediately after the third Friday of the rebalancing month, coinciding with the expiry of the index futures. This date is referred to as the ‘rebal date’.
Our analysis revolves around a set of Ex-ante (pre-event) and Ex-post (post-event) dates. We aim to determine the optimal timing for entering a position to yield significant non-zero returns.
Our results — the expected and unexpected
We categorized the rebalancing into 4 distinct cases
- Dropping out from FTSE 100 into FTSE 250 (FTSE100_FTSE250)
- Entering FTSE 100 from FTSE 250 (FTSE250_FTSE100)
- Dropping out from FTSE 250 into small caps (drop_FTSE250)
- Entering FTSE 250 (new_FTSE 250)
Our statistical analysis revealed statistically significant non-zero returns in each case, albeit occurring at different timings. The signs of the average returns mostly align with expectations. Typically, average returns tend to be positive in response to perceived good news and negative in reaction to perceived bad news. However, there’s an exception observed in the case of new entrants into FTSE 250. This deviation from the expected trend might be explained by investor risk aversion.
Dropping out from FTSE 100 into FTSE 250
In this scenario, we observed statistically significant negative average returns from 20 trading days before the rebal date to after rebalancing. This outcome aligns with our expectations, considering that stocks dropping from a large-cap to a mid-cap index might be perceived as unfavorable news. One possible explanation for the observed negative returns is linked to risk-averse investor behavior. When a stock is potentially facing exclusion from the index due to its market cap before the rank date, investors are prone to initiating sell-offs, anticipating the impending negative news.
Entering FTSE 100 fromFTSE 250
In contrast to the previous case, we observed positive average returns after the rebalancing in this scenario. However, these positive returns were evident only when compared to prices from 1 day before the rebal date. One potential explanation could be linked to risk-averse investor behavior, where investors might display less sensitivity or hesitancy in reacting to perceived good news. They might be inclined to act cautiously, preferring certainty rather than taking chances on an increase in stock prices prematurely.
Dropping out from FTSE 250 into small caps
Similar to the first case, we observed sharp negative returns on stocks from 20 trading days before the rebal date. The transition from mid-cap (FTSE 250) to small-cap is particularly negatively perceived, given that small-cap companies are often seen as less established and inherently riskier assets.
Due to this perception, risk-averse investors tend to act decisively and at an earlier stage, offloading stocks expected to exit the FTSE 250 universe. Moreover, the AUM of FTSE small-cap funds is notably lower compared to FTSE 250 funds. Unlike FTSE 100 dropouts, where both buying and selling pressures exist, dropouts from the FTSE 250 face substantial selling pressures with limited demand for buying.
An intriguing observation is that despite the initial sharp decline, there are some, albeit less significant, positive returns when trading 1 day before the rebal date up until 20 days post-rebalancing. This could be attributed to an exaggerated reaction to the news of the dropout, causing these stocks to potentially be undervalued. Consequently, some investors might seize the opportunity to buy, resulting in marginal buying pressure, although not as substantial as the sell-off.
New entrants into FTSE 250
Arguably the most counterintuitive among the cases, new entrants into the FTSE 250 exhibited, on average, negative returns when traded from 1 day before the rebal date until 10 days post-rebalancing, despite the ostensibly positive news.
We theorize that even though the inclusion into the FTSE 250 index from the small-cap category might be perceived as favorable news, speculators were likely capitalizing on these smaller-cap stocks to realize their profits. Risk-averse investors typically exhibit a cautious response to positive news, leading to a delayed onset of buying activity compared to the sell-off. Consequently, this led to an initial decrease in value, followed by a return to initial levels much later.
Arbitrage — gotta catch ’em all?
The feasibility of the opportunities is largely dependent on the cost of and ability to capture the arbitrage. One key assumption is that traders can freely buy and short-sell stocks and that the costs incurred are negligible compared to the returns. However, these assumptions do not always hold.
In some instances, short-selling may not be feasible. Short-selling a stock requires locating a willing lender for the stock. While this might be feasible for large-cap stocks, it might prove challenging for small-cap ones. Even when possible, the cost of short-borrowing tends to be inversely correlated with stock availability. The scarcer the stock for short-borrowing, the higher the associated borrowing cost. Consequently, this limitation might impede the feasibility of capitalizing on certain opportunities, especially those reliant on short sales.
All in all, the substantial influence of equity indices on investments and the vast capital invested in index funds can generate trading prospects through changes in index constituents, notably during index rebalancing.
While the price momentum due to index rebalancing is largely in line with expectations, the timing is pretty much impacted by investors’ risk aversion. Our study on the FTSE UK Series emphasizes the critical role of behavioral finance in investment dynamics.
Moreover, even when trading prospects arise, it’s essential to consider the ability and cost of seizing these opportunities to determine their feasibility. Varied indices offer distinct opportunities, making the search for such prospects an exhilarating and dynamically evolving pursuit.
Disclaimer: This article is purely didactical and should not be construed as investment advice. The content of this study is academic in nature and has been written by the author as a graduate student enrolled in Singapore Management University’s Masters in Quantitative Finance program. The views expressed in this article do not represent those of the author’s employing company. All analyses are based on publicly available information.
For a tutorial on Refinitiv Datastream API, go to: https://github.com/Finsinyur/QF603_QAFM_Project/blob/main/notebooks/00_WRDS_tutorial_refinitiv_quant_analytics.ipynb
References
[1] FTSE 100 ETFs, JustETF.com
[2] FTSE 100 Historic Additions and Deletions, FTSE Russell
[3] FTSE 250 ETFs, JustETF.com
[4] FTSE 250 Historic Additions and Deletions, FTSE Russell
[5] Guide to Calculation Methods for the FTSE UK Index Series, FTSE Russell
