  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 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.
