Method and apparatus for the topographical mapping of investment risk, safety and efficiency

• US 7,415,433 B2
• Filed: 08/04/2003
• Issued: 08/19/2008
• Est. Priority Date: 08/04/2003
• Status: Expired due to Fees

• Current Assignee: Elisa Financiere
• Original Assignee: Elisa Financiere
• Inventors: Huneault, Paul
• Primary Examiner(s): Kramer; James
• Assistant Examiner(s): BORLINGHAUS, JASON M
• Application Number:
  US10/633,301
• Publication Number:
  US 20050033678A1
• Time in Patent Office: 1,842 Days
• Field of Search: 705/36
• US Class Current: 705/36.00R
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or analysis
• CPC Class Codes: G06Q 40/08 Insurance

Abstract

A method and a system for evaluating at least one of a risk, safety and efficiency property of a portfolio belonging to a class of one of a probability density and a probability distribution, for a given time frame are provided. The method comprises: obtaining portfolio pricing data over said given time frame; obtaining at least one benchmark X_b; with respect to investment returns, fitting one of a stochastic investment class over said given time frame in relation to said benchmark X_b by obtaining a location parameter a, a scale parameter b and other corresponding shape parameters; and an empirical investment class over said given time frame in relation to said benchmark X_b; determining a mean return value X_m and a standard deviation σ_x using said class; graphically illustrating said portfolio in relation to said benchmark X_b using said return value X_m and said standard deviation σ_x on an investment chart; determining for said portfolio by using properties of said class a solution to (X_m−X_b)=[(E_S−X_b)·α]+[(E_P−X_b)·γ]=I′_S+I′_P; graphically illustrating at least one said component of said expression (X_m−X_b), in the form of a topographical map on said investment chart using said benchmark X_b.

Claims

1. A method for evaluating at least one of a risk, safety and efficiency property of a portfolio belonging to a class of one of a probability density and a probability distribution, for a given time frame, comprising:

obtaining portfolio pricing data over said given time frame;

obtaining at least one benchmark X_b having benchmark profit, benchmark loss and benchmark return values;

with respect to investment returns, fitting one of

a stochastic investment class over said given time frame in relation to said benchmark X_b by obtaining a location parameter a, a scale parameter b and other corresponding shape parameters; and

an empirical investment class over said given time frame in relation to said benchmark X_b;

determining a mean return value X_m and a standard deviation σ

_x using said class;

graphically illustrating said portfolio in relation to said benchmark X_b using said return value X_m and said standard deviation σ

_x on an investment chart;

determining for said portfolio by using properties of said class a solution to (X_m−

X_b)=[(E_S−

X_b)·

α

]+[(E_P−

X_b)·

γ

]=I′

_S+I′

_P with I′

_S=[(E_S−

X_b)·

α

] and I′

_P=[(E_P−

X_b)·

γ

], wherein (E_S−

X_b) is a component of (X_m−

X_b) and I′

_S representing an Expected Shortfall, (E_P−

X_b) is a component of (X_m−

X_b) and I′

_P representing an Expected Profit, γ

is a component of (X_m−

X_b) and I′

_P representing a probability of profit, α

is a component of (X_m−

X_b) and I′

_S representing a probability of loss, I′

_S is a component of (X_m−

X_b) representing an insurance against an Expected Shortfall and I′

_P is a component of (X_m−

X_b) representing an insurance against an Expected Profit;

graphically illustrating at least one said component of said expression (X_m−

X_b), in the form of a topographical map on said investment chart using said benchmark X_b;

whereby said portfolio can be evaluated in terms of at least one of risk, safety and efficiency.

2. A method as claimed in claim 1, further comprising:

determining at least one of E₁ efficiency as the ratio of the probability of profit γ

to the probability of loss α

, E2 efficiency as the negative value of the ratio of Expected Profit (E_P−

X_b) to Expected Shortfall (E_S−

X_b), E3 efficiency as the negative value of the ratio of the insurance against an Expected Profit I′

_P to the insurance against an Expected Shortfall I′

_S and E4 efficiency as the ratio of the risk premium (X_m−

X_b) to the probability of loss α

;

graphically illustrating at least one of said efficiencies, in the form of a topographical map on said investment chart using said benchmark X_b.

3. A method as claimed in claim 1, further comprising:

determining and graphically illustrating complementary orthogonal trajectories to the topographical map.

4. A method as claimed in claim 2, further comprising:

determining and graphically illustrating complementary orthogonal trajectories to the topographical map.

5. A method as claimed in claim 1, further comprising:

determining and graphically illustrating the rescaling of said given time frame for self affine probability densities or distributions.

6. A method as claimed in anyone of claims 1 to 5, wherein said graphically illustrating further comprises delimiting at least one set as first preference made up of an investment zone and a complementary exclusion zone for said evaluation based on at least one of an investors perception of desirability or tolerance to risk, safety and efficiency.

7. A system for evaluating at least one of a risk, safety and efficiency property of a portfolio belonging to a class of one of a probability density and a probability distribution, for a given time frame, comprising:

a portfolio pricing database over said given time frame;

a benchmark identifier for obtaining at least one benchmark X_b having benchmark profit, benchmark loss and benchmark return values;

with respect to investment returns, a class fitter for fitting one of

a stochastic investment class over said given time frame in relation to said benchmark X_b by obtaining a location parameter a, a scale parameter b and other corresponding shape parameters; and

an empirical investment class over said given time frame in relation to said benchmark X_b;

a parameter calculator for determining a mean return value X_m and a standard deviation σ

_x using said class;

an illustrator for graphically illustrating said portfolio in relation to said benchmark X_b using said return value X_m and said standard deviation σ

_x on an investment chart;

a component determiner for determining for said portfolio by using properties of said class a solution to (X_m−

X_b)=[(E_S−

X_b)·

α

]+[(E_P−

X_b)·

γ

]=I′

_S+I′

_P with I′

_S=[(E_S−

X_b)·

α

] and I′

_P=[(E_P−

X_b)·

γ

], wherein (E_S−

X_b) is a component of (X_m−

X_b) and I′

_S representing an Expected Shortfall, (E_P−

X_b) is a component of (X_m−

X_b) and I′

_P representing an Expected Profit, γ

is a component of (X_m−

X_b) and I′

_P representing a probability of profit, α

is a component of (X_m−

X_b) and I′

_S representing a probability of loss, I′

_S is a component of (X_m−

X_b) representing an insurance against an Expected Shortfall and I′

_P is a component of (X_m−

X_b) representing an insurance against an Expected Profit;

said illustrator for graphically illustrating at least one said component of said expression (X_m−

X_b), in the form of a topographical map on said investment chart using said benchmark X_b;

whereby said portfolio can be evaluated in terms of at least one of risk, safety and efficiency.

8. A system as claimed in claim 7, further comprising:

a component efficiency determiner for determining at least one of E₁ efficiency as the ratio of the probability of profit γ

to the probability of loss α

, E2 efficiency as the negative value of the ratio of Expected Profit (E_P−

X_b) to Expected Shortfall (E_S−

X_b), E3 efficiency as the negative value of the ratio of the insurance against an Expected Profit I′

_P to the insurance against an Expected Shortfall I′

_S and E4 efficiency as the ratio of the risk premium (X_m−

X_b) to the probability of loss α

;

said illustrator graphically illustrating at least one of said efficiencies, in the form of a topographical map on said investment chart using said benchmark X_b.

9. A system as claimed in claim 7, further comprising:

an orthogonal trajectory determiner for determining complementary orthogonal trajectories to the topographical map, and said illustrator graphically illustrating the same.

10. A system as claimed in claim 8, further comprising:

an orthogonal trajectory determiner for determining complementary orthogonal trajectories to the topographical map, and said illustrator graphically illustrating the same.

11. A system as claimed in claim 7, further comprising:

a time rescaler for determining the rescaling of said given time frame for self affine probability densities or distributions, and said illustrator graphically illustrating the same.

12. A system as claimed in anyone of claims 7 to 11, further comprising a set delimiter for delimiting at least one set as first preference made up of an investment zone and a complementary exclusion zone for said evaluation based on at least one of an investor'"'"'s perception of desirability or tolerance to risk, safety and efficiency.