Loading patent…
AssigneeIbbotson Associates, Inc.
InventorBarry Feldman
Estimating the term…
Historical data on the returns of a set of risky assets are resampled in each of a plurality of simulations to create sets of resampled risky asset return data. Simulated efficient investment portfolios of assets are assembled on a sheaf of efficient frontiers, one for each simulation. A set of intervals of a statistical input parameter (such as standard deviation) is defined. Each simulated efficient investment portfolios is assigned to an interval. A summary statistical procedure operates on all of the simulated investment portfolios associated with each interval, thereby deriving a resampled efficient investment portfolio. The resampled efficient investment portfolios reside on a resampled efficient frontier and are presented to an investor as a guide to making investments or are used as an input for other automated procedures.
A method for determining portfolios on a resampled efficient frontier for a set of risky assets, each risky asset having a return characterized by statistical input parameters, comprising:
A method for generating portfolios for possible investment from a plurality of risky assets, comprising the steps of:
A method for creating a plurality of investment portfolios on an efficient frontier, the portfolios varying from each other in risk and return, the method comprising the steps of:
A machine-readable medium having stored thereon data representing sequences of instructions, the sequences of instructions which, when executed by a processor, cause the processor to perform the steps of:
A computer system comprising:
A data signal embodied in a propagation medium, the data signal including a plurality of instructions, which when executed by a processor, cause the processor to perform the steps of:
A system for creating a plurality of investment portfolios for presentation to an investor or investment advisor or for use an input to another computational process such as automated account management procedure or a multiperiod optimization procedure, comprising:
Dependencies are inferred from the claim text.
Drawings are temporarily unavailable. Open the PDF at USPTO
No related US applications are recorded in the indexed filing history.
Backward citations are indexed for grants only.
Finance; Insurance; Tax strategies; Processing of corporate or income taxes: asset management; Financial planning or analysis
Information and communication technology [ict] specially adapted for administrative, commercial, financial, managerial
Term end not estimated
The present invention pertains to the selection of investments, and more particularly to the optimal allocation of investment among a set of risky assets subject to measurement error in the statistical properties of the expected returns of those assets.
One formulation of the task of an investment manager is to seek a maximum return for a given level of risk. This is done by investing a sum of money among a number of risky assets. H. Markowitz, Portfolio Selection; Efficient Diversification of Investments (Wiley, 1959) developed a solution for this problem wherein risk is measured in terms of the variance of a risky asset's returns and wherein only a single time period is considered. The return of an asset over a time period is the percentage change in its price plus the value, in percentage terms relative to its initial price, of any dividends or other distributions. Markowitz showed how to construct an optimal portfolio for a specified level of risk given only the expected returns and variances of the returns on each risky asset and the correlations between pairs of risky asset returns. These are the statistical parameters of the mean-variance optimization problem. The set of all mean-variance optimal portfolios describes an efficient frontier.
FIG. 1 illustrates a mean-variance chart and an efficient frontier. The horizontal axis of the chart represents the standard deviation of the return of a risky asset or portfolio of risky assets. The vertical axis of the chart represents the expected return of a risky asset or portfolio of risky assets. A portfolio's location on the chart is determined by its expected return and standard deviation. Investors will prefer portfolios with higher expected returns, given the same expected standard deviation in that return. Thus, portfolio A is preferred to portfolio B, directly below it. Similarly, investors will prefer portfolios with less risk given the same expected return. Thus, portfolio A will be preferred to portfolio C, directly to its right. The mean-variance efficient frontier 100 represents the set of portfolios having the property that no portfolio has a higher expected return with the same, or lower, expected standard deviation. Equivalently, portfolios on the efficient frontier 100 have the property that no other portfolio has the same or higher return at a lower level of expected standard deviation. Portfolio D is an example of a portfolio on the mean variance or efficient frontier 100.
Further aspects of the invention and their advantages can be ascertained from the detailed description set forth below, when taken in conjunction with the drawings, in which like characters illustrate like parts and in which:
FIG. 1 is a graph illustrating a mean-variance efficient frontier, as is known in the art;
FIG. 2 is a graph illustrating a resampled efficient frontier;
FIG. 3 illustrates a method 10 for determining portfolios on a resampled efficient frontier for a set of risky assets whose returns are characterized by statistical input parameters.
At step 11 a set of risky assets is provided, wherein each risky asset is characterized by a vector of statistical input parameters, such as an expected return, a standard deviation, and a correlation of the assets' returns to the returns of each other risky asset in the set. The statistical input parameters may be based upon historically observed returns, or may be generated by other means. Such other means may include professional judgment, asset pricing models, risk forecasting models, and other methods known to those familiar with the art.
At step 12 a portfolio performance measure is selected. Typical portfolio performance measures include a standard deviation of a portfolio and its expected return. In a preferred embodiment of this invention standard deviation is used as a portfolio performance measure when identifying portfolios on a resampled mean-variance efficient frontier. A portfolio expected return may be used instead, but it will then usually be advisable to discard portfolios with standard deviations higher than the standard deviation of the maximum return risky asset. Other portfolio performance measures may also be selected. For example, when a measure of risk other than standard deviation is used, it may also be selected as a performance measure. Examples of alternative risk measures include semi-standard deviation, interquartile range, the gini coefficient, and custom measures based on skew or kurtosis. It is not necessary that the portfolio performance measure selected is utilized directly in the optimization process.