Time-varying tracking quality in partial index replication

Abstract

I test the tracking quality and time variance of selected partial index tracking approaches based on research on large dimensional factor models and time series clustering. To achieve this, I use both Monte Carlo simulations and empirical testing in the developed European markets.

I find significant and previously undiscovered time variance in the replication error of partial index replication, which increases particularly during greater benchmark volatility. The YoY increases can be as high as 128% as measured by mean absolute deviation. I discuss potential explanations and risk management practices to account for the time-varying effects.

My empirical testing with an extensive daily dataset shows, consistent with prior studies, that partial index replication has lower transaction costs and more flexibility over full replication with the trade-off of a higher replication error. Of the tested approaches, only the follow-the-leader approach by Jiang & Perez (2021) slightly outperforms random selection with a similar number of assets. The approach, with default methodology, achieves on average a 5% lower (better) ex-post tracking quality than simple random selection. However, the main driver of tracking quality remains the number of portfolio assets. Increasing the portfolio size from 20% to 50% of the constituents reduces ex-post tracing quality on average by 45%. I also suggest optimized selection strategies for the sampling approaches, which, combined with index weights, lower portfolio turnover on average by 84% with minimal impact on tracking quality. The strategies are tested along other alternative approaches to asset selection, portfolio weighting, and rebalancing frequency.

Comparing the approaches with real index ETF’s, I find that partial index replication can be a viable alternative particularly for large and highly correlated indexes with liquidity or other trading constraints. All the approaches can easily be adjusted to incorporate measures of liquidity or transaction costs, and they also have potential uses in synthetic replication and sustainable investing.