Designing proxies for Stock Market Indices is Computationally Hard

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Stephen R. Tate, Professor and Department Head (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/

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 formulae 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 eleven of the twelve cases (all combinations of four indices with three criteria except the problem of sacrificing return for less volatility using the price-relative index) we show that the problem is NP-hard, and hence most likely intractable.

Additional Information

Publication
Quantitative Finance, Volume 1, Number 3, May 2001, pp. 361-371.
Language: English
Date: 2001
Keywords
Stock market, Prediction, Non-deterministic polynomial-time hard, Proxies, Mathematical models, Complexity theory