Designing proxies for stock market indices is computationally hard

Abstract

In this paper, we study the problem of designing proxies(or portfolios) for various stock market indices based on historical data. We use four different methods for computing market indices, all of which are formulas used in actual stock market analysis. For each index, we consider three criteria for designing the proxy:the proxy must either track the market index, outperform the market index, or perform within a margin of error of the index while maintaining a low volatility, in all twelve cases(all combinations of four indices with three criteria) we show that the problem is NP-hard, and hence most likely intractable.