Methodology and process for constructing factor indexes

Abstract

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 that replicate returns associated with a target factor while simultaneously reducing implementation costs flowing from a large number of names and unintended bets on other factors comprising:
 selecting a set comprising a plurality of possible investments;   defining a benchmark portfolio of weights comprising a subset of the set comprising a plurality of possible investments and a weight for each member of the subset;   selecting a first factor risk model defined for the set comprising a plurality of possible investments, said first factor risk model defining a first matrix of factor exposures which gives a numerical exposure value for every possible investment for a set of factors;   selecting a target factor for one of the factors defined by the first factor risk model;   constructing a target factor portfolio of weights for the target factor for the set comprising a plurality of possible investments, the benchmark portfolio of weights, and the first factor risk model, and whose weighted average exposure to the target factor is different than the weighted average exposure of the benchmark portfolio to the target factor;   selecting a second factor risk model defined for the set comprising a plurality of possible investments, said second factor risk model defining a second matrix of factor exposures, wherein at least one factor exposure in the second matrix of factor exposures of the second factor risk model is different than all the factor exposures of the first matrix of factor exposures of the first factor risk model;   performing a first optimization by determining weights of each of the plurality of possible investments for a factor index so that a tracking error between the factor index and the target factor portfolio of weights as predicted by the second factor risk model is less than or equal to 5% and a one-way turnover is less than 7.5%; and   outputting the factor index weights as an electronic output displayed on a display.   
     
     
         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 set of possible investments. 
     
     
         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 that replicate returns associated with a target factor while simultaneously reducing implementation costs flowing from a large number of names and unintended bets on other factors comprising:
 a programmed processor for selecting a set comprising a plurality of possible investments;   the programmed processor selecting a benchmark portfolio comprising a subset of holdings from the set comprising a plurality of possible investments;   the programmed processor selecting a first factor risk model defined for the set comprising a plurality of possible investments, said first factor risk model defining a first matrix of factor exposures;   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 set comprising a plurality of possible investments, the benchmark portfolio, and the first factor risk model, and whose exposure to the target factor is different than the exposure of the benchmark portfolio to the target factor;   the programmed processor selecting a second factor risk model defined for the set comprising a plurality of possible investments, said second factor risk model defining a second matrix of factor exposures, wherein at least one factor exposure in the second matrix of factor exposures of the second factor risk model is different than all the factor exposures of the first matrix of factor exposures of the first factor risk model;   the programmed processor performing a first optimization by determining weights of each of the plurality of possible investments for a factor index so that a tracking error between the factor index and the target factor portfolio as predicted by the second factor risk model is less than or equal to 5% and a one-way turnover is less than 7.5%;   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 set of possible investments. 
     
     
         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. 
 
     
     
         14 . A computer system for constructing a factor index of portfolio weights that replicate returns associated with a target factor while simultaneously reducing implementation costs flowing from a large number of names and unintended bets on other factors comprising:
 a first and a second factor risk selecting programmed processor for selecting a set comprising a plurality of possible investments;   the first and a second factor risk selecting programmed processor selecting a benchmark portfolio comprising a subset of holdings from the set comprising a plurality of possible investments;   the first and a second factor risk selecting programmed processor selecting a first factor risk model defined for the set comprising a plurality of possible investments, said first factor risk model comprising a first matrix of factor exposures, a first matrix of factor covariances, and a first matrix of specific risk variances;   the first and a second factor risk selecting programmed processor selecting a target factor which is one of the factors defined by the first factor risk model;   the first and a second factor risk selecting programmed processor constructing a target factor portfolio for the target factor whose holdings are fully determined by the set comprising a plurality of possible investments, the benchmark portfolio, and the first factor risk model, and whose exposure to the target factor is different than the exposure of the benchmark portfolio to the target factor;   the first and a second factor risk selecting programmed processor selecting a second factor risk model defined for the set comprising a plurality of possible investments, said second factor risk model comprising a second matrix of factor exposures, a second matrix of factor covariances, and a second matrix of specific risk variances wherein at least one factor exposure in the second matrix of factor exposures of the second factor risk model is different than all the factor exposures of the first matrix of factor exposures of the first factor risk model;   the first and a second factor risk selecting programmed processor performing a first optimization by determining weights of each of the plurality of possible investments for a factor index so that a tracking error between the factor index and the target factor portfolio as predicted by the second factor risk model is less than or equal to 5% and a one-way turnover is less than 7.5%; and   the first and a second factor risk selecting programmed processor outputting the factor index weights as an electronic output.   
     
     
         15 . The computer based method of  claim 1  wherein the target factor comprises momentum. 
     
     
         16 . The computer based method of  claim 15  wherein the target factor further comprises size. 
     
     
         17 . The computer based method of  claim 16  further comprising:
 generating a restricted list of hard to trade assets; and 
 removing any assets on the restricted list of hard to trade assets from the set comprising a plurality of investments. 
 
     
     
         18 . The computer based method of  claim 15  wherein the target portfolio is a 35% cap-weighted long-short momentum target portfolio. 
     
     
         19 . The computer based method of  claim 1  further comprising:
 sequentially performing a second optimization to reduce turnover by minimizing turnover subject to the maximum allowable tracking error of 5% by relaxing the one-way turnover. 
 
     
     
         20 . The computer based method of  claim 19  further comprising:
 sequentially performing a third optimization in which exposure of the target factor to a second factor is less than 25%.