Abstract: In existing performance attribution, composite investments are resolved into simple assets, and the performance attribution provides results only for the resolved, net investment in the simple assets. As a result, the individual investment in the composite investment in isolation is lost, and it is impossible to determine if the investment in the composite investment in isolation helped or hurt performance. Approaches are described to determine attribution in a manner in which the attribution hierarchy is altered so that, after reporting on the performance of the full portfolio, a further level of attribution reports on a set of sub-portfolios. The first sub-portfolio represents the original investments in simple assets only while the other sub-portfolios represent investments in each composite investment. This composite-first performance attribution determines the individual contribution to performance of each composite investment, resulting in more detailed, practical, and intuitive results.

Abstract: The traditional Markowitz mean-variance-optimization (MVO) framework that uses the standard deviation of the possible portfolio returns as a measure of risk does not accurately measure the risk of multi-asset class portfolios whose return distributions are non-Gaussian and asymmetric. A scenario-based conditional value-at-risk (CVaR) approach for minimizing the downside risk of a multi-asset class portfolio is addressed that uses Monte-Carlo simulations to generate the asset return scenarios. These return scenarios are incorporated into a modified Rockafellar-Uryasev based convex programming formulation to generate an optimized hedge. One example addresses hedging in an equity portfolio with options. Testing shows that a hierarchical CVaR approach generates portfolios with better predicted worst case loss, downside risk, standard deviation, and skew.

Abstract: Techniques for using factor risk models to more accurately estimate the risk or active risk of an investment portfolio are disclosed. Inherent “modeling error” in factor risk models is identified and compensated for. One or more factors are added to compensate for factors that are unspecified or unattributed in the original factor risk model and which lead to modeling error. The approach can be used with a variety of different factor risk models, and for a variety of securities. Knowledge of the risk associated with modeling error can be utilized when estimating risk or active risk using factor risk models or when constructing optimal portfolios by mean-variance optimization or other portfolio construction strategies using factor risk models.

Abstract: On the basis of simulated backtests, many portfolios including so-called smart beta and other factor products often boast impressive track records. However, given the additional trading that occurs, can such advertised performance truly be realized once transaction costs are taken into account? One might expect these products to make a concerted effort to manage liquidity. However, explicit efforts to manage liquidity in existing smart beta and factor ETF and index products have been relatively modest. A new set of rules are provided that are independent of the notional value of the portfolio that can be used to better manage the liquidity of investment portfolio.

Abstract: In existing performance attribution, composite investments are resolved into simple assets, and the performance attribution provides results only for the resolved, net investment in the simple assets. As a result, the individual investment in the composite investment in isolation is lost, and it is impossible to determine if the investment in the composite investment in isolation helped or hurt performance. Approaches are described to determine attribution in a manner in which the attribution hierarchy is altered so that, after reporting on the performance of the full portfolio, a further level of attribution reports on a set of sub-portfolios. The first sub-portfolio represents the original investments in simple assets only while the other sub-portfolios represent investments in each composite investment. This composite-first performance attribution determines the individual contribution to performance of each composite investment, resulting in more detailed, practical, and intuitive results.

Abstract: Factor-based performance attribution results are often used to identify portfolio exposures or bets that either perform well or underperform. By identifying particular exposures or bets that appear to be opportune to be increased or reduced, the overall performance of the portfolio can potentially be improved. However, the factors present in standard factor risk models are often too broad to identify exposures or bets which can be easily altered. Changing exposures based on the original risk model factors can involve trading too many stocks, or can involve trading stocks that a portfolio manager may not want to trade. The present invention allows portfolio managers to split the original risk model factors into more granular factors that cover smaller sub-sets of the assets in the portfolio. The over- and under-performing exposures of split factors are often easier to alter in practice and can be used to improve the performance of the portfolio.

Abstract: Tools for analyzing the risk of a portfolio of financial investments such as equities, bonds, and the like, are addressed. More particularly, computer based systems, processes and software are addressed for calculating factor risk models and for predicting the risk and tracking error of portfolios. A particular approach that can be utilized to revise the factor-factor covariance estimates of a factor risk model is provided. This approach is applied to factor risk model predictions, portfolio construction using the factor risk model, and performance attribution using the factor risk model.

Abstract: Performance attribution results of investment portfolios are often misleading due to correlation between the factor and specific contributions. This correlation is not correctly accounted for in standard factor-based attribution thus leading to potentially erroneous results. The present invention produces an adjusted factor-based performance attribution methodology that moves a portion of the specific return that is correlated with the factor contributions into the factor portion. This methodology adjusts the contribution to a subset of factors and to the specific contributions such that the resulting factor and specific contributions have small correlation.

Abstract: Construction of factor risk models that better predict the future volatility of returns of a portfolio of securities such as stocks, bonds, or the like is addressed. More specifically, improved factor-factor covariance estimation is made even when the covariances change rapidly over time. Methods and techniques for achieving better accuracy, responsiveness, and stability of factor risk models are addressed.

Abstract: The quantitative construction of investment portfolios of securities such as stocks, bonds, or the like using optimization is addressed. More specifically, during optimization, constraints on non-target factor exposures are automatically converted to constraints on the exposure of the projections of the non-target factors that are orthogonal to a specified target factor. The target factor may be the implied alpha of a reference portfolio, such as a traditional minimum risk portfolio. Such constraints may be utilized to produce portfolios with superior performance to those produced with traditional factor exposure constraints.

Abstract: Construction of factor risk models that better predict the future volatility of returns of a portfolio of securities such as stocks, bonds, or the like is addressed. More specifically, improved factor-factor covariance estimation is made even when the covariances change rapidly over time. Methods and techniques for achieving better accuracy, responsiveness, and stability of factor risk models are addressed.

Abstract: The quantitative construction of investment portfolios of securities such as stocks, bonds, or the like using optimization is addressed. More specifically, during optimization constraints on non-target factor exposures are automatically converted to constraints on the exposure of the projections of the non-target factors that are orthogonal to a specified target factor. Such constraints may be utilized to produce portfolios with superior performance to those produced with traditional factor exposure constraints.

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.

Abstract: Construction of factor risk models that more advantageously predict the future volatility of returns of a portfolio of securities such as stocks, bonds, or the like is addressed. More specifically, factor risk models with more than one estimate of specific risk or, alternatively an original specific risk estimate together with a set of specific risk differences derived from more than one estimate of specific risk.

Abstract: Construction of factor risk models that better predict the future volatility of returns of a portfolio of securities such as stocks, bonds, or the like is addressed. More specifically, improved factor-factor covariance estimation is made even when the covariances change rapidly over time. Methods and techniques for achieving better accuracy, responsiveness, and stability of factor risk models are addressed.

Abstract: Until recently, risk models have been built using low frequency data, such as weekly or monthly data. This approach has resulted in a necessary compromise between model stability for which one needs a long history of data, and model responsiveness, for which, the shorter the history, the better. Stability plus responsiveness can be achieved if one uses daily data, which allows for a large number of observations to be used in model estimation without using long out-of-date data. Daily data have other problems, however, as the differing closing times of markets worldwide may induce spurious relationships across model factors. In particular, correlations between markets may appear lower than they truly are due to a market lag effect. To address such issues, a stable, daily data-based factor risk model is described which takes account of the differing market closing times and corrects the model factor correlations and specific returns accordingly.

Abstract: 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.

Abstract: Until recently, risk models have been built using low frequency data, such as weekly or monthly data. This approach has resulted in a necessary compromise between model stability for which one needs a long history of data, and model responsiveness, for which, the shorter the history, the better. Stability plus responsiveness can be achieved if one uses daily data, which allows for a large number of observations to be used in model estimation without using long out-of-date data. Daily data have other problems, however, as the differing closing times of markets worldwide may induce spurious relationships across model factors. In particular, correlations between markets may appear lower than they truly are due to a market lag To address such issues, a stable, daily data-based factor risk model is described which takes account of the differing market closing times and corrects the model factor correlations and specific returns accordingly.

Abstract: Techniques for using factor risk models to more accurately estimate the risk or active risk of an investment portfolio are disclosed. Inherent “modeling error” in factor risk models is identified and compensated for. One or more factors are added to compensate for factors that are unspecified or unattributed in the original factor risk model and which lead to modeling error. The approach can be used with a variety of different factor risk models, and for a variety of securities. Knowledge of the risk associated with modeling error can be utilized when estimating risk or active risk using factor risk models or when constructing optimal portfolios by mean-variance optimization or other portfolio construction strategies using factor risk models.

Abstract: Techniques for more accurately estimating the risk, or active risk, of an investment portfolio when using factor risk models are disclosed. This improved accuracy is achieved by identifying and compensating for the inherent “modeling error” present when risk is represented using a factor risk model. The approach adds one or more factors that depend on the investment portfolio and that explicitly compensate for factors that are unspecified or unattributed in the original factor risk model. These unspecified factors of the original factor risk model lead to modeling error in the original factor risk model. The approach can be used with a variety of different factor risk models, such as, fundamental, statistical and macro risk models, for example, and for a variety of securities, such as equities, international equities, composites, exchange traded funds (ETFs), or the like, currencies, and fixed-income, for example.