System and method for trading off upside and downside values of a portfolio

A system for determining an optimal portfolio from a plurality of portfolios using a non-variance-based method performed by computer, wherein in operation, a user directs the computer to compute the optimal portfolio, and wherein the system comprises:

• a first risk engine for computing a mark-to-future value for each of the plurality of portfolios,
• wherein the mark-to-future value for a portfolio is calculated from mark-to-future values for the instruments in the portfolio, and wherein the mark-to-future value for an instrument is a simulated expected value for the instrument under a future scenario at a time point;
• and
• a second risk engine adapted to perform steps comprising:
• for each of the plurality of portfolios, disaggregating the portfolio such that the portfolio is characterized by an upside value and a downside value,
• wherein the upside value is the expected value, over a plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized gains of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and a benchmark value where the mark-to-future value of the portfolio exceeds the benchmark value, and
• wherein the downside value is the expected value, over the plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized losses of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and the benchmark value where the benchmark value exceeds the mark-to-future value of the portfolio;
• determining at least one efficient portfolio from the plurality of portfolios,
• wherein each efficient portfolio is a portfolio in which the upside value therefor is maximized with the downside value therefor not exceeding a limit of one or more specified limits;
• obtaining a utility function provided as input, and selecting an optimal portfolio from the at least one efficient portfolio that maximizes the utility function;
• determining a price for portfolio insurance associated with the optimal portfolio by pricing a security having payoffs that match the unrealized losses of the optimal portfolio, wherein said step of determining the price for portfolio insurance comprises evaluating the formula,
• q
• ^
• i
• =
• 1
• r
• o
• ⁢
• M
• (
• i
• )
• T
• ⁢
• ρ
• where
• ⁢
• ⁢
• r
• o
• =
• r
• T
• ⁢
• ρ
• ,
• and wherein M(i) is replaced with the values of the unrealized losses of said optimal portfolio.

A system for determining an optimal portfolio from a plurality of portfolios using a non-variance-based method performed by computer, wherein in operation, a user directs the computer to compute the optimal portfolio, and wherein the system comprises:

• a first risk engine for computing a mark-to-future value for each of the plurality of portfolios,
• wherein the mark-to-future value for a portfolio is calculated from mark-to-future values for the instruments in the portfolio, and wherein the mark-to-future value for an instrument is a simulated expected value for the instrument under a future scenario at a time point;
• and
• a second risk engine adapted to perform steps comprising:
• for each of the plurality of portfolios, disaggregating the portfolio such that the portfolio is characterized by an upside value and a downside value,
• wherein the upside value is the expected value, over a plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized gains of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and a benchmark value where the mark-to-future value of the portfolio exceeds the benchmark value, and
• wherein the downside value is the expected value, over the plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized losses of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and the benchmark value where the benchmark value exceeds the mark-to-future value of the portfolio;
• determining at least one efficient portfolio from the plurality of portfolios,
• wherein each efficient portfolio is a portfolio in which the downside value therefor is minimized with the upside value therefor being at least a limit of one or more specified limits;
• obtaining a utility function provided as input, and selecting an optimal portfolio from the at least one efficient portfolio that maximizes the utility function;
• wherein the determining step comprises solving a linear program defined by:
• minimize(x,u,d) pTd
• such that
• pTu≧k (μ)
• u−d−(M−rqT)x=0 (π)
• −x≦−xL (ωL)
• x≦xU (ωU)
• u≧0
• d≧0
• where
• q is the current mark-to-market values of securities;
• M is the Mark-to-Future values (Mji=value of security i in scenario j);
• p is the subjective prior scenario probabilities;
• r is the benchmark growth rates;
• x is the position sizes;
• xL is the lower position limits;
• xU is the upper position limits;
• d is the portfolio unrealized loss or downside;
• u is the portfolio unrealized gain or upside.

A system for determining an optimal portfolio from a plurality of portfolios using a non-variance-based method performed by computer, wherein in operation, a user directs the computer to compute the optimal portfolio, and wherein the system comprises:

• a first risk engine for computing a mark-to-future value for each of the plurality of portfolios,
• wherein the mark-to-future value for a portfolio is calculated from mark-to-future values for the instruments in the portfolio, and
• wherein the mark-to-future value for an instrument is a simulated expected value for the instrument under a future scenario at a time point;
• and
• a second risk engine adapted to perform steps comprising:
• for each of the plurality of portfolios, disaggregating the portfolio such that the portfolio is characterized by an upside value and a downside value,
• wherein the upside value is the expected value, over a plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized gains of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and a benchmark value where the mark-to-future value of the portfolio exceeds the benchmark value, and
• wherein the downside value is the expected value, over the plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized losses of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and the benchmark value where the benchmark value exceeds the mark-to-future value of the portfolio;
• determining at least one efficient portfolio from the plurality of portfolios,
• wherein each efficient portfolio is a portfolio in which the downside value therefor is minimized with the upside value therefor being at least a limit of one or more specified limits;
• obtaining a utility function provided as input, and selecting an optimal portfolio from the at least one efficient portfolio that maximizes the utility function;
• determining a price for portfolio insurance associated with the optimal portfolio by pricing a security having payoffs that match the unrealized losses of the optimal portfolio, wherein said step of determining the price for portfolio insurance comprises evaluating the formula,
• q
• ^
• i
• =
• 1
• r
• o
• ⁢
• M
• (
• i
• )
• T
• ⁢
• ρ
• where
• ⁢
• ⁢
• r
• o
• =
• r
• T
• ⁢
• ρ
• ,
• and wherein M(i) is replaced with the values of the unrealized losses of said optimal portfolio.

A system for evaluating a portfolio using a non-variance-based method performed by computer, wherein in operation, a user directs the computer to compute performance measures for the portfolio, wherein the system comprises:

• a first risk engine for computing a mark-to-future value for the portfolio,
• wherein the mark-to-future value for a portfolio is calculated from mark-to-future values for the instruments in the portfolio, and wherein the mark-to-future value for an instrument is a simulated expected value for the instrument under a future scenario at a time point;
• and
• a second risk engine adapted to perform steps comprising:
• disaggregating the portfolio such that the portfolio is characterized by an upside value and a downside value,
• wherein the upside value is the expected value, over a plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized gains of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and a benchmark value where the mark-to-future value of the portfolio exceeds the benchmark value, and
• wherein the downside value is the expected value, over the plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized losses of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and the benchmark value where the benchmark value exceeds the mark-to-future value of the portfolio;
• and
• computing one or more performance measures for the portfolio, each performance measure calculated as a function of at least one of the upside and downside values for the portfolio;
• wherein the one or more performance measures comprises at least one measure selected from the following group:
• downside value;
• upside value;
• upside value−downside value;
• upside value/downside value;
• and
• upside value−λ(downside value), where λ is a constant indicative of a level of risk aversion.

A non-variance-based method of determining an optimal portfolio from a plurality of portfolios, wherein the steps of the method are performed by computer, a user directing the computer to compute the optimal portfolio, the method comprising the steps of:

• a) computing a mark-to-future value for each of the plurality of portfolios,
• wherein the mark-to-future value for a portfolio is calculated from mark-to-future values for the instruments in the portfolio, and wherein the mark-to-future value for an instrument is a simulated expected value for the instrument under a future scenario at a time point;
• b) for each of the plurality of portfolios, disaggregating the portfolio such that the portfolio is characterized by an upside value and a downside value,
• wherein the upside value is the expected value, over a plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized gains of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and a benchmark value where the mark-to-future value of the portfolio exceeds the benchmark value, and
• wherein the downside value is the expected value, over the plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized losses of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and the benchmark value where the benchmark value exceeds the mark-to-future value of the portfolio;
• c) determining at least one efficient portfolio from the plurality of portfolios,
• wherein each efficient portfolio is a portfolio in which the upside value therefor is maximized with the downside value therefor not exceeding a limit of one or more specified limits;
• d) obtaining a utility function provided as input, and selecting an optimal portfolio from the at least one efficient portfolio that maximizes the utility function.

A non-variance-based method of determining an optimal portfolio from a plurality of portfolios, wherein the steps of the method are performed by computer, a user directing the computer to compute the optimal portfolio, the method comprising the steps of:

• a) computing a mark-to-future value for each of the plurality of portfolios,
• wherein the mark-to-future value for a portfolio is calculated from mark-to-future values for the instruments in the portfolio, and wherein the mark-to-future value for an instrument is a simulated expected value for the instrument under a future scenario at a time point;
• b) for each of the plurality of portfolios, disaggregating the portfolio such that the portfolio is characterized by an upside value and a downside value,
• wherein the upside value is the expected value, over a plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized gains of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and a benchmark value where the mark-to-future value of the portfolio exceeds the benchmark value, and
• wherein the downside value is the expected value, over the plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized losses of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and the benchmark value where the benchmark value exceeds the mark-to-future value of the portfolio;
• c) determining at least one efficient portfolio from the plurality of portfolios,
• wherein each efficient portfolio is a portfolio in which the downside value therefor is minimized with the upside value therefor being at least a limit of one or more specified limits;
• d) obtaining a utility function provided as input, and selecting an optimal portfolio from the at least one efficient portfolio that maximizes the utility function.

A non-variance-based method of evaluating a portfolio, wherein the steps of the method are performed by computer, a user directing the computer to compute performance measures for the portfolio, the method comprising the steps of:

• a) computing a mark-to-future value for the portfolio,
• wherein the mark-to-future value for a portfolio is calculated from mark-to-future values for the instruments in the portfolio, and wherein the mark-to-future value for an instrument is a simulated expected value for the instrument under a future scenario at a time point;
• b) disaggregating the portfolio such that the portfolio is characterized by an upside value and a downside value,
• wherein the upside value is the expected value, over a plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized gains of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and a benchmark value where the mark-to-future value of the portfolio exceeds the benchmark value, and
• wherein the downside value is the expected value, over the plurality of future scenarios, each with an associated probability of future occurrence, of the unrealized losses of the portfolio calculated as the absolute differences between the mark-to-future value of the portfolio and the benchmark value where the benchmark value exceeds the mark-to-future value of the portfolio;
• and
• c) computing one or more performance measures for the portfolio, each performance measure calculated as a function of at least one of the upside and downside values for the portfolio.