Portfolio optimization by means of resampled efficient frontiers

• US 6,003,018 A
• Filed: 09/09/1998
• Issued: 12/14/1999
• Est. Priority Date: 03/27/1998
• Status: Expired due to Term

• Current Assignee: Michaud Partners LLP
• Original Assignee: Michaud Partners LLP
• Inventors: Michaud, Robert, Michaud, Richard O.
• Primary Examiner(s): Stamber, Eric W.
• Assistant Examiner(s): Campa, John
• Application Number:
  US09/149,912
• Time in Patent Office: 461 Days
• Field of Search: 705/1, 705/30, 705/35, 705/36, 705/38
• US Class Current: 705/36.00R
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or analysis

Abstract

A method for evaluating an existing or putative portfolio having a plurality of assets. A mean-variance efficient portfolio is computed for a plurality of simulations of input data statistically consistent with an expected return and expected standard deviation of return, and each such portfolio is associated, by means of an index, with a specified portfolio on the mean variance efficient frontier. A statistical mean of the index-associated mean-variance efficient portfolios is used for evaluating a portfolio for consistency with a specified risk objective.

Claims

1. A method for selecting a value of portfolio weight for each of a plurality of assets of an optimal portfolio, the value of portfolio weight chosen from values between zero and unity, 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. resampling 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;

d. computing a simulated mean-variance efficient portfolio for each of the plurality of simulations of input data;

e. 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;

f. 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;

g. selecting a portfolio weight for each asset from the resampled efficient frontier according to a specified risk objective; and

h. investing funds in accordance with the selected portfolio weights.

2. A method according to claim 1, wherein the step of indexing the set of portfolios includes associating a rank with each portfolio of the indexed set of portfolios located on the mean-variance efficient frontier.

3. A method according to claim 1, wherein the step of indexing the set of portfolios includes associating a lambda value for which φ

=σ

² -λ

μ

is minimized, where σ

² is the variance of each portfolio and μ

is the defined expected return of each portfolio of the set of portfolios located on the mean-variance efficient frontier.

4. A method for investing funds based on an evaluation of an existing portfolio having a plurality of assets, the existing portfolio having a total portfolio value, each asset having a value forming a fraction of the total portfolio value, 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 having a plurality of portfolios of assets 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. associating an index with each portfolio of assets of the mean-variance efficient frontier in such a manner as to create a set of indexed portfolios;

c. resampling 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;

d. computing a mean-variance efficient portfolio for each of the plurality of simulations of input data;

e. associating each simulated mean-variance efficient portfolio with a specified portfolio of the set of indexed portfolios for creating a set of identical-index-associated mean-variance efficient portfolios;

f. establishing a statistical mean for each set of identical-index-associated mean-variance efficient portfolios, the plurality of statistical means defining a resampled efficient frontier;

g. comparing the existing portfolio with a portfolio from the resampled efficient frontier characterized by a specified risk objective for determining a preferred portfolio; and

h. investing funds in accordance with the preferred portfolio.

5. A method for investing funds based on evaluation of an existing portfolio having a plurality of assets, the existing portfolio having a total portfolio value, each asset having a value forming a fraction of the total portfolio value, 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. associating an index with each portfolio of assets associated with the mean-variance efficient frontier in such a manner as to create a set of indexed portfolios;

c. resampling 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;

d. computing a simulated mean-variance efficient portfolio for each of the plurality of simulations of input data;

e. associating each simulated mean-variance efficient portfolio with a specified portfolio of the set of indexed portfolios for creating a set of identical-index-associated mean-variance efficient portfolios;

f. establishing a statistical mean for each set of identical-index-associated mean-variance efficient portfolios, the plurality of statistical means defining a resampled efficient frontier;

g. associating a norm having a value characterizing a similarity of each portfolio with respect to a corresponding portfolio on the resampled efficient frontier;

h. defining a index-associated resampled fuzzy region corresponding to portfolios having a norm value less than or equal to a value associated with a specified confidence level;

i. evaluating whether a current portfolio requires optimization based at least on a norm of the current portfolio in comparison with the index-associated resampled fuzzy region for creating an optimized portfolio; and

j. investing funds in accordance with the optimized portfolio.

6. 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 and for enabling investment of funds in the specified plurality of assets, the value of portfolio weight chosen from values between zero and unity, 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:

a. program code for causing a computer to perform the step of 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. a sequencer for indexing a set of portfolios located on the mean-variance efficient frontier;

c. a routine for causing the computer to resample 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;

d. program code for causing the computer to compute a mean-variance efficient portfolio for each of the plurality of simulations of input data;

e. program code for causing the computer to associate each simulated mean-variance efficient portfolio with a specified portfolio of the set of indexed portfolios for creating a set of identical-index-associated mean-variance efficient portfolios;

f. a module for causing the computer to establish a statistical mean for each set of identical-index-associated mean-variance efficient portfolios, the plurality of statistical means defining the resampled efficient frontier; and

g. program code for causing the computer to select a portfolio weight for each asset from the resampled efficient frontier according to a specified risk objective and for enabling an investor to invest funds in accordance with the selected portfolio weight of each asset.