Methods and apparatus employing hierarchical conditional variance to minimize downside risk of a multi-asset class portfolio and improved graphical user interface

A computer-implemented method for interactively comparing performance of a plurality investment portfolios within windows of a graphical user interface on a computer screen and then selecting a preferred investment portfolio, the method comprising:

• electronically receiving by a programmed computer a plurality of investment portfolios;
• electronically generating a set of simulated returns for each investment portfolio;
• electronically receiving by the programmed computer an initial graphing style and graphing order for displaying each set of simulated returns;
• displaying a graphical representation of the simulated returns for each investment portfolio within a first window of a graphical user interface on a computer screen in the initial graphing style and graphing order such that each set of simulated returns is graphed on top of the previously graphed simulated returns;
• displaying in a second window of the graphical user interface on the computer screen a first user indicator that sets a modified graphing style or graphing order;
• monitoring the first user indication of the modified graphing style or graphing order;
• automatically redisplaying the graphical representation of the simulated returns for each investment portfolio within the graphical user interface on the computer screen in the graphing style and graphing order specified by the first user indication;
• displaying in a third window of the graphical user interface on the computer screen a second user indication that selects a preferred investment portfolio from the plurality of investment portfolios;
• monitoring the second user indicator selecting a preferred investment portfolio;
• automatically electronically outputting the preferred investment portfolio whenever the second user indication is activated to select a preferred investment portfolio.

A computer-implemented method for interactively engineering and selecting a preferred portfolio of investments within windows of a graphical user interface on a computer screen connected to a programmed computer, the method comprising:

• displaying within a first window of the graphical user interface on the computer screen a data set that defines a set of portfolio construction parameters needed to compute an investment portfolio that minimizes a conditional variance of a portfolio at a set of prescribed confidence levels, where the set of portfolio construction parameters include:
• a first user indicator in the first window of the graphical user interface of the computer screen a set of potential investment opportunities that are eligible to be included as part of the investment portfolio;
• a set of general portfolio construction requirements that all eligible portfolios are to satisfy;
• a data library for the set of investment opportunities containing data needed to model each potential investment opportunity mathematically on the programmed computer;
• a tolerance for the differences in conditional value-at-risk;
• using the programmed computer and the data library to generate a sequence of simulated returns for each potential investment opportunity;
• electronically receiving by a second user indication a set of two or more confidence levels at which a conditional value at risk is to be minimized;
• sequentially calculating using the programmed computer a set of investment portfolios that minimizes the conditional value-at-risk for the portfolio at each confidence limit prescribed by the second user indication such that the conditional value-at-risk for the portfolio is within a tolerance of its minimum possible value;
• displaying within a second window of a graphical user interface a distribution of returns for the portfolio of investment;
• interactively changing the second user indication to specify different sets of two or more confidence limits and redisplaying the distribution of returns until a preferred investment portfolio and return distribution is obtained;
• automatically electronically outputting the preferred investment portfolio whenever the second user indication is modified.

A computer implemented method of estimating risks of an optimized portfolio when assets with nonlinear and asymmetric return distributions are included in the optimized portfolio, the computer implemented method comprising:

• specifying assets that may be included in the optimized portfolio;
• employing a Monte-Carlo pricing engine to generate asset return scenarios for said assets;
• specifying at least two confidence levels for conditional value at risk (CVaR) estimation;
• specifying a CVaR tolerance;
• employing a Rockafeller-Uryasev methodology modified to utilize return scenarios lying in an elliptical uncertainty set to produce the optimized portfolio whose CVaR is within the CVaR tolerance of the minimum possible CVaR at each confidence level;
• and
• outputting the optimized portfolio and distributions of returns.

A computer implemented method of employing a hierarchical conditional value at risk (HCVaR) comprising:

• specifying at least two confidence levels for conditional value at risk (CVaR) estimation;
• constructing a first portfolio that minimizes CVaR at a first confidence level (CVaR1);
• storing the minimal CVaR for the first confidence level (CVaR1);
• constructing a second portfolio that minimizes CVaR at a second confidence level subject to a constraint that CVaR at the first confidence level is less than CVaR1 times a predetermined amount.