N. Meade | Searcharxiv

arXiv2025

Asset pre-selection for a cardinality constrained index tracking portfolio with optional enhancement

Index trackers are important passive investments offering the return and risk of the market encapsulated by the index, the largest US index tracker was valued at $900 billion in early 2026. Using a two-stage approach of asset selection followed by estimation on S&P 500 data, we explore the role of cardinality constraints in determining the effectiveness of the tracker's reproduction of market return and risk. We compare eight pre-selection procedures: forward selection or backward elimination; implemented using ordinary least squares or least absolute deviation regression; with or without a regression constant. We show experimentally that out-of-sample tracking errors decrease according to the inverse of the square root of cardinality and out-of-sample tracking error, transaction volume and return-risk ratios all improve as the cardinality constraint is relaxed. By contrast for enhanced returns, cardinalities of the order 10 to 20 are most effective.

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arXiv2019

Quantitative portfolio selection: using density forecasting to find consistent portfolios

In the knowledge that the ex-post performance of Markowitz efficient portfolios is inferior to that implied ex-ante, we make two contributions to the portfolio selection literature. Firstly, we propose a methodology to identify the region of risk-expected return space where ex-post performance matches ex-ante estimates. Secondly, we extend ex-post efficient set mathematics to overcome the biases in the estimation of the ex-ante efficient frontier. A density forecasting approach is used to measure the accuracy of ex-ante estimates using the Berkowitz statistic, we develop this statistic to increase its sensitivity to changes in the data generating process. The area of risk-expected return space where the density forecasts are accurate, where ex-post performance matches ex-ante estimates, is termed the consistency region. Under the 'laboratory' conditions of a simulated multivariate normal data set, we compute the consistency region and the estimated ex-post frontier. Over different sample sizes used for estimation, the behaviour of the consistency region is shown to be both intuitively reasonable and to enclose the estimated ex-post frontier. Using actual data from the constituents of the US Dow Jones 30 index, we show that the size of the consistency region is time dependent and, in volatile conditions, may disappear. Using our development of the Berkowitz statistic, we demonstrate the superior performance of an investment strategy based on consistent rather than efficient portfolios.

q-fin.PM↗