Index Funds—Construction and Performance Measurement

An index fund is an investment vehicle which mimics a stock-market index and thus exhibits market risk only. Fund managers can passively invest in index funds and concentrate on actively managing the remainder of their funds. This paper looks in detail at the use of statistical selection methods in the construction of these funds. The measurement of the ability of these funds to track the underlying index is examined. Emphasis is placed on the relevance of the horizon of the investor to the choice of measure of tracking error. Four different methods of index-fund construction are described and applied to Japanese stock-market data. The tracking abilities of the constructed funds, both in and out of sample, are compared and contrasted.     

Market neutral portfolios

In this paper we consider the problem of constructing a market neutral portfolio. This is a portfolio of financial assets that (ideally) exhibits performance independent from that of an underlying market as represented by a benchmark index. We formulate this problem as a mixed-integer nonlinear program, minimising the absolute value of the correlation between portfolio return and index return. Our model is a flexible one that incorporates decisions as to both long and short positions in assets. Computational results, obtained using the software package Minotaur, are given for constructing market neutral portfolios for eleven different problem instances derived from universes defined by S&P international equity indices. We also compare our approach against an alternative approach based on minimising the absolute value of regression slope (the zero-beta approach).