CVaR-LASSO Enhanced Index Replication (CLEIR): outperforming by minimizing downside risk

Index-funds are one of the most popular investment vehicles among investors, with total assets indexed to the S&P500 exceeding $8.7 trillion at-the-end of 2016. Recently, enhanced-index-funds, which seek to outperform an index while maintaining a similar risk-profile, have grown in popularity. We propose an enhanced-index-tracking method that uses the linear absolute shrinkage selection operator (LASSO) method to minimize the Conditional Value-at-Risk (CVaR) of the tracking error. This minimizes the large downside tracking-error while keeping the upside. Using historical and simulated data, our CLEIR method outperformed the benchmark with a tracking error of 1%. The effect is more pronounced when the number of the constituents is large. Using 50–80 large stocks in the S&P 500 index, our method closely tracked the benchmark with an alpha 2:55%.