Portfolio rebalancing by means of resampled efficient frontiers with forecast confidence level
First Claim
1. A computer-implemented method for selecting a value of a portfolio weight for each of a plurality of assets of an optimal portfolio, the value of portfolio weight chosen from specified values associated with each asset, between real numbers c1 and c2 that may vary by asset, each asset having a defined expected return and a defined standard deviation of return, each asset having a covariance with respect to each of every other asset of the plurality of assets, the method comprising:
- a. computing a mean-variance efficient frontier based at least on input data characterizing the defined expected return and the defined standard deviation of return of each of the plurality of assets;
b. indexing a set of portfolios located on the mean-variance efficient frontier thereby creating an indexed set of portfolios;
c. choosing a forecast certainty level for defining a resampling process of the input data consistent with an assumed forecast certainty of the input data;
d. resampling, in accordance with the process defined by the forecast certainty level, a plurality of simulations of input data statistically consistent with the defined expected return and the defined standard deviation of return of each of the plurality of assets;
e. computing a simulated mean-variance efficient portfolio for each of the plurality of simulations of input data;
f. associating each simulated mean-variance efficient portfolio with a specified portfolio of the indexed set of portfolios for creating a set of identical-index-associated mean-variance efficient portfolios;
g. establishing a statistical mean for each set of identical-index-associated mean-variance efficient portfolios, thereby generating a plurality of statistical means, the plurality of statistical means defining a resampled efficient frontier, wherein processes (a), (b), and (d)-(g) are digital computer processes;
h. selecting a portfolio weight for each asset from the resampled efficient frontier according to a specified utility objective; and
i. investing funds in accordance with the selected portfolio weights.
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Abstract
A computer-implemented method and computer program product for selecting a portfolio weight (subject to specified constraints) for each of a plurality of assets of an optimal portfolio. A mean-variance efficient frontier is calculated based on input data characterizing the defined expected return and the defined standard deviation of return of each of the plurality of assets. Multiple sets of optimization inputs are drawn from a distribution of simulated optimization inputs consistent with the defined expected return, the defined standard deviation of return of each of the plurality of assets and then a simulated mean-variance efficient frontier is computed for each set of optimization inputs. A meta-resampled efficient frontier is determined as a statistical mean of associated portfolios among the simulated mean-variance efficient frontiers, and a portfolio weight is selected for each asset from the meta-resampled efficient frontier according to a specified investment objective. The number of simulations and the number of simulation periods is determined on the basis of a specified level of forecast certainty.
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Citations
30 Claims
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1. A computer-implemented method for selecting a value of a portfolio weight for each of a plurality of assets of an optimal portfolio, the value of portfolio weight chosen from specified values associated with each asset, between real numbers c1 and c2 that may vary by asset, each asset having a defined expected return and a defined standard deviation of return, each asset having a covariance with respect to each of every other asset of the plurality of assets, the method comprising:
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a. computing a mean-variance efficient frontier based at least on input data characterizing the defined expected return and the defined standard deviation of return of each of the plurality of assets;
b. indexing a set of portfolios located on the mean-variance efficient frontier thereby creating an indexed set of portfolios;
c. choosing a forecast certainty level for defining a resampling process of the input data consistent with an assumed forecast certainty of the input data;
d. resampling, in accordance with the process defined by the forecast certainty level, a plurality of simulations of input data statistically consistent with the defined expected return and the defined standard deviation of return of each of the plurality of assets;
e. computing a simulated mean-variance efficient portfolio for each of the plurality of simulations of input data;
f. associating each simulated mean-variance efficient portfolio with a specified portfolio of the indexed set of portfolios for creating a set of identical-index-associated mean-variance efficient portfolios;
g. establishing a statistical mean for each set of identical-index-associated mean-variance efficient portfolios, thereby generating a plurality of statistical means, the plurality of statistical means defining a resampled efficient frontier, wherein processes (a), (b), and (d)-(g) are digital computer processes;
h. selecting a portfolio weight for each asset from the resampled efficient frontier according to a specified utility objective; and
i. investing funds in accordance with the selected portfolio weights. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A computer-implemented method for selecting a value of a portfolio weight for each of a plurality of assets of an optimal portfolio, the value of portfolio weight chosen from specified values associates with each asset, between real numbers c1 and c2 that may vary by asset, for the plurality of assets, having a defined expected return and a defined standard deviation of return, each asset having a covariance with respect to each of every other asset of the plurality of assets, the method comprising:
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a. computing a mean-variance efficient frontier, the frontier having at least one mean-variance efficient portfolio, based at least on input data characterizing the defined expected return and the defined standard deviation of return of each of the plurality of assets;
b. choosing a forecast certainty level from a collection of forecast certainty levels for defining a resampling process of the input data consistent with the assumed forecast certainty of the input data;
c. generating a plurality of optimization inputs drawn at least from a distribution of simulated optimization inputs consistent with the defined expected return, the defined standard deviation of return of each of the plurality of assets and the chosen forecast certainty level;
d. computing a simulated mean-variance efficient frontier, the frontier having at least one simulated mean-variance efficient portfolio, for each of the plurality of optimization inputs;
e. associating each mean-variance efficient portfolio with a specified set of simulated mean-variance efficient portfolios for creating a set of associated mean-variance efficient portfolios;
f. establishing a statistical mean for each set of associated mean-variance efficient portfolios, thereby generating a plurality of statistical means, the plurality of statistical means defining a meta-resampled efficient frontier;
g. selecting a portfolio weight for each asset from the meta-resampled efficient frontier according to a specified investment objective; and
h. investing funds in accordance with the specified portfolio weights. - View Dependent Claims (9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30)
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28. A computer program product for use on a computer system for selecting a value of portfolio weight for each of a specified plurality of assets of an optimal portfolio, the value of portfolio weight chosen from values between two specified real numbers, each asset having a defined expected return and a defined standard deviation of return, each asset having a covariance with respect to each of every other asset of the plurality of assets, the computer program product comprising a computer usable medium having computer readable program code thereon, the computer readable program code including:
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a. program code for computing a mean-variance efficient frontier based at least on input data characterizing the defined expected return and the defined standard deviation of return of each of the plurality of assets;
b. program code for aggregating a set of portfolios located on the mean variance efficient frontier;
c. a routine for generating a plurality of optimization inputs drawn from a distribution of simulated optimization inputs statistically consistent with the defined expected return and the defined standard deviation of return of each of the plurality of assets;
d. program code for computing a simulated mean-variance efficient frontier, the frontier comprising at least one simulated mean-variance efficient portfolio for each of the plurality of optimization inputs;
e. program code for associating each simulated mean-variance efficient portfolio with a specified portfolio of the set of aggregated portfolios for creating a set of associated mean-variance efficient portfolios;
f. a module for establishing a statistical mean for each set of associated mean-variance efficient portfolios, the plurality of statistical means defining a meta-resampled efficient frontier; and
g. program code for selecting a portfolio weight for each asset from the meta-resampled efficient frontier according to a specified risk objective.
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Specification