Formulation of Optimized Investment Indeces
Investment performance indices and methods of their formulation are described. The indices are determined by selecting a representative subset of assets (e.g., exchange-traded index funds) from a relatively larger number of possibilities in a given asset class. A performance index for the asset class is created by determining optimized weightings in each asset in the subset. The weightings can be optimized according to any number of optimization algorithms, including MVO, CVaR, and G-CAPM and tailored to a given investor risk profile. One or more “investor-centered” indices may be generated in this manner, for the asset class.
1 . A method, comprising:
(a) selecting a subset of assets from an asset class by
(i) identifying a plurality of assets that represent a behavior of the asset class as a whole, and including said plurality of assets in the subset of assets, wherein said plurality of assets is fewer than the number of assets in the asset class; and
(ii) applying one or more business rules to the plurality of assets to remove one or more assets having unreliable historical data from the subset of assets;
(b) determining an optimal investment weighting corresponding to each asset in said subset of assets; and
(c) generating an investment performance index for the asset class based on the optimal investment weighting of each asset in the subset of assets.
2 . The method of claim 1 , wherein said asset class comprises exchange-traded funds (ETFs).
3 . The method of claim 2 , further comprising (d) generating a plurality of investment performance indexes for the asset class based on a plurality of investment risk levels.
4 . The method of claim 3 , wherein each of the plurality of investment performance indexes comprises an optimal investment weighting corresponding to each asset in said subset of assets based on the corresponding investment risk level.
5 . The method of claim 1 , wherein said optimal investment weightings are determined for a predetermined risk level.
6 . The method of claim 5 , wherein said risk level is quantified based on the second moment or a higher moment of the distribution of returns of said investment performance index.
7 . The method of claim 1 , wherein said investment weightings correspond to a portfolio of said subset of assets on a minimum-variance frontier or a constrained risk-return frontier obtained from optimization using CVaR or G-CAPM.
8 . The method of claim 1 , wherein said subset of assets is selected according to a selection methodology comprising utilizing the covariance or correlation between performance parameters of assets in said asset class.
9 . The method of claim 8 , wherein said covariance or correlation between performance parameters is utilized in one or more statistical analyses selected from the group consisting of principal component analysis, factor analysis, and cluster analysis.
10 . The method of claim 8 , wherein said performance parameters comprise historical prices or returns of said assets in said asset class.
11 . The method of claim 8 , wherein said asset class comprises one or more index funds and said performance parameters comprise historical prices or returns of indices associated with said one or more index funds.
12 . The method of claim 8 , wherein said selection methodology further comprises evaluating one or more financial parameters to winnow said asset class.
13 . The method of claim 8 , wherein said financial factors are selected from the group consisting of market capitalization, liquidity, expense ratio, and combinations thereof.
14 . The method of claim 1 , wherein said investment weightings correspond to a portfolio of said subset of assets on a minimum-variance frontier or a constrained risk-return optimization of said subset of assets.
15 . The method of claim 14 , wherein said constrained minimum-variance frontier or constrained risk-return optimization excludes short positions in any of said subset of assets.
16 . A method for establishing a performance benchmark for an asset class, the method comprising formulating an investment performance index for said asset class according to claim 1 over a time period or over a succession of multiple time periods.
17 . The method of claim 16 , wherein said time period is about three months.
18 . The method of claim 16 , further comprising gauging the performance of an individual investment portfolio, a target maturity fund, or a family of funds over said time period, based on said performance benchmark.
19 . A method of formulating an optimized investment portfolio for an asset class, the method comprising formulating an investment performance index for said asset class according to claim 1 and investing in said subset of assets, according to said optimal investment weightings, determined for a given risk level, for each asset in said subset of assets.
20 . One or more tangible computer readable media storing executable instructions that, when executed, cause a data processing system to perform a method comprising steps of:
(a) selecting a subset of assets from an asset class by
(i) identifying a plurality of assets that represent a behavior of the asset class as a whole, and including said plurality of assets in the subset of assets, wherein said plurality of assets is fewer than the number of assets in the asset class; and
(ii) applying one or more business rules to the plurality of assets to remove one or more assets having unreliable historical data from the subset of assets;
(b) determining an optimal investment weighting corresponding to each asset in said subset of assets; and
(c) generating an investment performance index for the asset class based on the optimal investment weighting of each asset in the subset of assets.
21 . The computer readable media of claim 20 , wherein said asset class comprises securities.
22 . The computer readable media of claim 20 , said method further comprising (d) storing a plurality of calculated investment performance indexes for the asset class based on a plurality of investment risk levels.
23 . The computer readable media of claim 22 , wherein each of the plurality of investment performance indexes comprises an optimal investment weighting corresponding to each asset in said subset of assets based on the corresponding investment risk level.
24 . The computer readable media of claim 20 , wherein said optimal investment weightings are determined for a predetermined risk level.
25 . The computer readable media of claim 24 , wherein said risk level comprises a standard deviation about an expected return of said investment performance index.
26 . The computer readable media of claim 25 , wherein said investment weightings correspond to a portfolio of said subset of assets on a minimum-variance frontier or a constrained risk-return optimization obtained from mean-variance optimization of said subset of assets, and said risk level is associated with a divergence from a tangent portfolio on said minimum-variance frontier.
27 . The computer readable media of claim 26 , wherein said risk level is a coefficient of risk aversion and said optimal investment weightings are determined based on maximization of a utility function utilizing said coefficient of risk aversion.
28 . The computer readable media of claim 20 , wherein said subset of assets is selected according to a selection methodology comprising utilizing the covariance or correlation between performance parameters of assets in said asset class.
29 . The computer readable media of claim 28 , wherein said covariance or correlation between performance parameters is utilized in one or more statistical analyses selected from the group consisting of principal component analysis, factor analysis, and cluster analysis.
30 . The computer readable media of claim 28 , wherein said performance parameters comprise historical prices or returns of said assets in said asset class.
31 . The computer readable media of claim 28 , wherein said asset class comprises one or more index funds and said performance parameters comprise historical prices or returns of indices associated with said one or more index funds.
32 . The computer readable media of claim 28 , wherein said selection methodology further comprises evaluating one or more financial parameters to winnow said asset class.
33 . The computer readable media of claim 28 , wherein said financial factors are selected from the group consisting of market capitalization, liquidity, expense ratio, and combinations thereof.
34 . The computer readable media of claim 20 , wherein said investment weightings correspond to a portfolio of said subset of assets on a minimum-variance frontier or a constrained minimum-variance frontier of said subset of assets.
35 . The computer readable media of claim 20 , wherein said constrained minimum-variance frontier excludes short positions in any of said subset of assets.
36 . The computer readable media of claim 21 , wherein said securities consist of exchange traded funds (ETFs).
37 . One or more tangible computer readable media storing executable instructions that, when executed, cause a data processing system to perform a method comprising steps of:
(a) selecting a subset of exchange traded funds (ETFs) from available ETFs by
(i) identifying a plurality of ETFs that represent a behavior of available ETFs, and including said plurality of ETFs in the subset of ETFs, wherein said plurality of ETFs is fewer than the number of available ETFs; and
(ii) applying one or more business rules to the plurality of ETFs to remove one or more ETFs having unreliable historical data from the subset of ETFs;
(b) determining an optimal investment weighting corresponding to each ETF in said subset of ETFs;
(c) generating an initial ETF investment performance index based on the optimal investment weighting of each ETF in the subset of ETFs; and
(d) generating a plurality of additional ETF investment performance indexes based on a plurality of corresponding investment risk levels, wherein each said risk level comprises a standard deviation about an expected return of said initial investment performance index.