Methodology and process for constructing factor indexes
Construction of indexes are addressed wherein a portfolio of securities and their associated investment weights or shares is generated. Indexes comprising a plurality of securities can often be bought and sold more cheaply than buying and selling the individual constituents of the index resulting in reduced transaction costs. In passive and enhanced indexing, investments are made with reference to an index. Factor indexes can serve as active manager benchmarks for investable products such as exchange traded funds and mutual funds. Computer based systems, methods and software are addressed for constructing indexes that replicate the returns of a quantitative factor such as medium term momentum or value with the best possible replication of the underlying factor returns. The methodology provides an approach to determine the index even when all desirable characteristics of the index are not simultaneously achievable.
1. A computer based method of constructing a factor index of portfolio weights comprising:
selecting a set of possible investments;
defining a benchmark portfolio comprising a set of holdings in the set of possible investments;
selecting a first factor risk model defined for the set of possible investments, said first factor risk model comprising a matrix of factor exposures, a matrix of factor covariances, and a matrix of specific risk variances;
selecting scores of a target factor which is a linear combination of factors defined by the first risk model;
constructing utilizing a programmed computer a target factor portfolio for the target factor whose holdings are determined by the set of possible investments, the benchmark portfolio, the first factor risk model, and the target factor scores and whose exposure to the target factor scores is different than the exposure of the benchmark portfolio to the target factor scores;
selecting a second factor risk model defined for the set of possible investments, said second factor risk model comprising a matrix of factor exposures, a matrix of factor covariances, and a matrix of specific risk variances, said second factor risk model being different than the first factor risk model;
determining weights of each security for a factor index so that the tracking error between the factor index and the target factor portfolio as predicted by the second risk model is less than a prescribed amount; and
outputting the factor index weights as an electronic output by the programmed computer.
2. The computer based method of claim 1 wherein the target factor selected represents a linear combination of one or more of the following metrics: exchange rate sensitivity, growth, leverage, liquidity, market sensitivity, long term momentum, medium term momentum, short term momentum, size, value, volatility, one or more countries, one or more industries, one or more sectors, and one or more currencies.
3. The computer based method of claim 1 wherein the set of possible investments is selected based on a second factor.
4. The computer based method of claim 3 wherein the second factor indicates the country, region, currency, size, value or growth of each element in the universe.
5. The computer based method of claim 4 wherein the country factor comprises U.S. equities.
6. The computer based method of claim 1 further comprising:
limiting the exposure of the factor index to a second factor to insure factor neutrality to the second factor.
7. The computer based method of claim 6 wherein the second factor is a factor defined by the first risk model but is different than the target factor.