Penalized enhanced portfolio replication with asymmetric deviation measures

Passive investment strategies, such as those implemented by Exchange Traded Funds (ETFs), have gained increasing popularity among investors. In this context, smart beta products promise to deliver improved performance or lower risk through the implementation of systematic investing strategies, and they are also typically more cost-effective than traditional active management. The majority of research on index replication focuses on minimizing tracking error relative to a benchmark index, implementing constraints to improve performance, or restricting the number of assets included in portfolios. Our focus is on enhancing the benchmark through a limited number of deviations from the benchmark. We propose a range of innovative investment strategies aimed at minimizing asymmetric deviation measures related to expectiles and quantiles, while also controlling for the deviation of portfolio weights from the benchmark composition through penalization. This approach, as compared to traditional minimum tracking error volatility strategies, places a greater emphasis on the overall risk of the portfolio, rather than just the risk relative to the benchmark. The use of penalization also helps to mitigate estimation risk and minimize turnover, as compared to strategies without penalization. Through empirical analysis using simulated and real-world data, we critically examine the benefits and drawbacks of the proposed strategies in comparison to state-of-the-art tracking models.