Methodology and Process For Constructing Factor Indexes
Approaches to the construction of indexes are addressed wherein a portfolio of securities such as stocks, bonds, or the like and their associated investment weights or shares is generated. Indexes can be used as investment tools in various ways. For instance, indexes comprising a plurality of securities can often be bought and sold more cheaply than buying and selling the individual constituents of the index. This pricing differential allows investment with reduced transaction costs. Alternatively, in passive and enhanced indexing, investments are made with reference to an index. Performance statistics such as return and risk are reported with respect to the reference index. Factor indexes can serve as active manager benchmarks or the underlyers 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. Further, processes and methodology are described by which the index can have the best possible replication of the underlying factor returns as well as other desirable characteristics. 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 universe of possible investments;
defining a benchmark portfolio comprising a set of holdings in the universe;
selecting a first fully specified factor risk model defined for the universe of securities, said first factor risk model comprising a fully specified matrix of factor exposures, a matrix of factor covariances, and a matrix of specific risk variances;
selecting a target factor which is one of the factors defined by the first factor risk model;
constructing a target factor portfolio for the target factor whose holdings are fully determined by the universe, the benchmark portfolio, and the first factor risk model, and whose exposure to the target factor is substantially different than the exposure of the benchmark portfolio to the target factor;
selecting a second fully specified factor risk model defined for the universe of securities, said second factor risk model comprising a fully specified matrix of factor exposures, a matrix of factor covariances, and a matrix of specific risk variances;
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.
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 universe of securities 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.
8 . A computer system for constructing a factor index of portfolio weights comprising:
a programmed processor for selecting a universe of possible investments;
the programmed processor selecting a benchmark portfolio comprising a set of holdings in the universe;
the programmed processor selecting a first fully specified factor risk model defined for the universe of securities, said first factor risk model comprising a fully specified matrix of factor exposures, a matrix of factor covariances, and a matrix of specific risk variances;
the programmed processor selecting a target factor which is one of the factors defined by the first factor risk model;
the programmed processor constructing a target factor portfolio for the target factor whose holdings are fully determined by the universe, the benchmark portfolio, and the first factor risk model, and whose exposure to the target factor is substantially different than the exposure of the benchmark portfolio to the target factor;
the programmed processor selecting a second fully specified factor risk model defined for the universe of securities, said second factor risk model comprising a fully specified matrix of factor exposures, a matrix of factor covariances, and a matrix of specific risk variances;
the programmed processor 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
the programmed processor outputting the factor index weights as an electronic output.
9 . The computer system of claim 8 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.
10 . The computer system of claim 8 wherein the set of securities is selected by the programmed processor utilizing a second factor.
11 . The computer system of claim 10 wherein the second factor wherein the second factor indicates the country, region, currency, size, value or growth of each element in the universe.
12 . The computer system of claim 11 wherein the country factor comprises U.S. equities.
13 . The computer system of claim 8 further comprising:
the programmed processor limiting the exposure of the factor index to a second factor to insure factor neutrality to the second factor.