Method and system for jointly estimating cash flows, simulated returns, risk measures and present values for a plurality of assets

Abstract

Methods and apparatus for: (1) inputting economic variables expected to influence future asset values and asset-specific variables; (2) estimating financial statements, future asset values, and tentative asset NPVs using estimated economic variables and estimated asset-specific variables; (3) estimating different financial statements, future asset values and current asset NPVs assuming different estimates of the economic variables that affect asset values; and (4) processes to: (a) equate; or (2) reduce to acceptably small numbers the differences between: (i) the risk measures, terminal values, default premiums, and risk premiums used to determine current values, and (ii) risk measures, terminal values, default premiums, and risk premiums implied by the estimates of economic and firm-specific variables.

Claims

What is claimed is:

1. A data processing system for providing an indication of an output risk measure using jointly determined risk measures for a plurality of assets comprising:

(a) a computer processor including:

1) a first storage device for storing a computer program;

2) a second storage device for storing data corresponding to a plurality of variables, including:

(i) data corresponding to a set of economic variables including a risk premium, and

(ii) for each asset, data corresponding to a set of asset-specific variables including an input risk measure;

3) a central processing unit for processing data stored in said second storage device in accordance with said computer program stored in said first storage device;

4) an input device operable for entering said data for storage in said second storage device, and

5) an output device operable to provide an output of the results of said central processing unit;

(b) said computer processor operable under control of said computer program to carry out the following steps:

1) processing said data corresponding to said set of economic variables and said data corresponding to said set of asset-specific variables to determine initial cash flows for each of said plurality of assets;

2) generating alternate data corresponding to said plurality of economic and asset-specific variables;

3) processing said alternate data to determine corresponding alternate cash flows for each of said plurality of assets;

4) processing said data corresponding to said set of economic variables, said data corresponding to said set of asset-specific variables and said initial cash flows to determine an initial value for each of said plurality of assets and processing said alternate data and said alternate cash flows to determine an alternate value for each of said plurality of assets;

5) processing said initial values and said alternate values to determine a simulated asset return for each of said assets;

6) processing at least one of said initial values and at least one of said alternate values to determine a simulated index return;

7) jointly processing said simulated asset return and said simulated index return to determine said output risk measure for each of said assets; and

8) using a iterative converging process, comparing a value of said input risk measures and said output risk measures to determine whether said output risk measures are within a first predetermined acceptable range, and in response thereto either:

(i) if at least one said output risk measure is not within said first predetermined acceptable range, determine and substitute a new value for said input risk measure and use said new value for said input risk measure to process data according to steps (b) 4)-8), or

(ii) if said output risk measures are within said first predetermined acceptable range, then provide an indication of said output risk measure on said output device.

2. A data processing system as claimed in claim 1, wherein at least one of said plurality of assets has a known market value, and wherein said computer processor is operable under control of said computer program to carry our the following additional step:

9) determining a difference between said initial value and the known market value of at least one of said assets to determine whether said difference is within second predetermined acceptable range, and in response thereto either:

(i) if said difference is not within said second predetermined acceptable range, determine and substitute a new value for said risk premium and use said new value of said risk premium to process data according to steps (b) 4)-9), or

(ii) if said difference is within said second predetermined acceptable range, then the value of said output risk premium represents the risk premium determined by said data processing system; and

(d) means for creating a portfolio of assets in accordance with said risk premium determined by said data processing system.

3. A data processing system as claimed in claim 1 wherein at least two of said plurality of assets have a known market value, and wherein said economic variables further includes an inflation rate, and wherein said computer processor is operable under control of said computer program to carry out the following additional steps:

9) processing said data corresponding to said set of economic variables, including said inflation rate, and said data corresponding to said set of asset-specific variables to determine an initial value for each of said plurality of assets and processing said alternate data to determine an alternate value for each of said plurality of assets; and

10) determining a measure of a differences between the initial value and the respective known market value of at least two of said assets to determine whether said measure is within a third predetermined acceptable range, and in response thereto either:

(i) if said measure is not within said third predetermined acceptable range, determine and substitute a new value for said inflation rate and use said new value of said inflation rate to process data according to steps (b) 4)-10), or

(ii) if said measure is within said third predetermined acceptable range, then the value of said output inflation rate represents the inflation rate determined by said data processing system; and

(e) means for creating a portfolio of assets in accordance with said inflation rate determined by said data processing system.

4. A data processing system for providing an indication of an output risk measure using jointly determined risk measures for a plurality of assets comprising:

(a) a computer processor including:

1) a first storage device for storing a computer program;

2) a second storage device for storing data corresponding to a plurality of variables, including:

(i) data corresponding to a set of economic variables including a risk premium, and

(ii) for each asset, data corresponding to a set of asset-specific variables including an input risk measure;

3) a central processing unit for processing data stored in said second storage device in accordance with said computer program stored in said first storage device;

4) an input device operable for entering said data for storage in said second storage device, and

5) an output device operable to provide an output of the results of said central processing unit;

(b) said computer processor operable under control of said computer program to carry out the following steps:

1) processing said data corresponding to said set of economic variables and said data corresponding to said set of asset-specific variables to determine initial cash flows for each of said plurality of assets;

2) generating a plurality of sets of alternate data, each set of which corresponds to said plurality of economic and asset-specific variables;

3) processing said plurality of sets of alternate data to determine a corresponding plurality of sets of alternate cash flows for each of said plurality of assets;

4) processing said data corresponding to said set of economic variables, said data corresponding to said set of asset-specific variables and said initial cash flows to determine an initial value for each of said plurality of assets and processing said plurality of sets of alternate data and said plurality of sets of alternate cash flows to determine an alternate value for each of said plurality of assets;

5) processing said initial values and said plurality of sets of alternate values to determine a plurality of simulated asset returns for each of said assets;

6) processing at least one of said initial values and at least one of said plurality of sets of alternate values to determine a plurality of simulated index returns;

7) processing said plurality of simulated asset returns and said plurality of simulated index returns to determine said output risk measure for each of said assets; and

8) using an iterative converging process, comparing a value of said input risk measures and said output risk measures to determine whether said output risk measures are within a first predetermined acceptable range, and in response thereto either:

(i) if at least one said output risk measure is not within said first predetermined acceptable range, determine and substitute a new value for said input risk measure and use said new value for said input risk measure to process data according to steps (b) 4)-8), or

(ii) if said output risk measures are within said first predetermined acceptable range, then provide an indication of said output risk measure on said output device.

5. A data processing system as claimed in claim 4, wherein at least one of said plurality of assets has a known market value, and wherein said computer processor is operable under control of said computer program to carry our the following additional step:

9) determining a difference between said initial value and the known market value of at least one of said assets to determine whether said difference is within second predetermined acceptable range, and in response thereto either:

(i) if said difference is not within said second predetermined acceptable range, determine and substitute a new value for said risk premium and use said new value of said risk premium to process data according to steps (b) 4)-9), or

(ii) if said difference is within said second predetermined acceptable range, then the value of said output risk premium represents the risk premium determined by said data processing system; and

(d) means for creating a portfolio of assets in accordance with said risk premium determined by said data processing system.

6. A data processing system as claimed in claim 4 wherein at least two of said plurality of assets have a known market value, and wherein said economic variables further includes an inflation rate, and wherein said computer processor is operable under control of said computer program to carry out the following additional steps:

9) processing said data corresponding to said set of economic variables, including said inflation rate, and said data corresponding to said set of asset-specific variables to determine an initial value for each of said plurality of assets and processing said plurality of sets of alternate data to determine a plurality of alternate values for each of said plurality of assets; and

10) determining a measure of a differences between the initial value and the respective known market value of at least two of said assets to determine whether said measure is within a third predetermined acceptable range, and in response thereto either:

(i) if said measure is not within said third predetermined acceptable range, determine and substitute a new value for said inflation rate and use said new value of said inflation rate to process data according to steps (b) 4)-9), or

(ii) if said measure is within said third predetermined acceptable range, then the value of said output inflation rate represents the inflation rate determined by said data processing system; and

(e) means for creating a portfolio of assets in accordance with said inflation rate determined by said data processing system.

7. A data processing system as claimed in claim 4 wherein computer processor is operable under control of said computer program to carry out the following additional step:

9) determines an output risk measure for each of said assets by, for each asset, regressing said plurality of simulated asset returns against said plurality of simulated index returns.

8. A data processing system as claimed in claim 4 wherein said initial cash flows have been determined up to a predetermined and specific terminal date and wherein at least one of said plurality of assets has value beyond the said terminal date, said computer processor operable under control of said computer program to carry out the following additional steps:

9) processing said data corresponding to said set of economic variables and said data corresponding to said set of asset-specific variables to determine an initial value for each of said plurality of assets and processing said plurality of sets of said alternate data to determine a plurality of alternate values for each of said plurality of assets; and

10) determining the difference between two ratios wherein:

(i) said first ratio is a market value of said asset at said terminal date divided by a book value of said asset at said terminal date, and

(ii) said second ratio is said asset's market value at a date prior to said terminal date divided by said asset's book value at said date prior to said terminal date, to determine whether said difference is within a second predetermined acceptable range, and in response thereto either:

(i) if said difference is not within said second predetermined acceptable range, determine and substitute a now value for said market value at said terminal date and use said new value of said market value to process data according to steps (b) 4)-10), or

(ii) if said difference is within said second predetermined acceptable range, then the value of said output risk measures represent the risk measures determined by said data processing system.

9. A data processing system as claimed in claim 4 wherein at least one of said plurality of assets has debt and includes an asset-specific variable of an input default risk premium for said asset's debt, and wherein said computer processor is operable under control of said computer program to carry our the following additional steps: system further comprising:

9) determining a default risk premium corresponding to said asset with debt;

10) determining a difference between said input default risk premium and the default risk premium to determine whether said difference is within a second predetermined acceptable range, and in response thereto either:

(i) if said difference is not within said second predetermined acceptable range, determine and substitute a new value for said initial default risk premium and use said value of said default risk premium to process data according to steps (b) 4)-9), or

(ii) if said difference is within said predetermined acceptable range, then the value of said default risk premium represents the default risk premium determined by said data processing system;

(c) means for creating a portfolio of assets in accordance with said default risk premium determined by said data processing system.

10. A data processing system, as claimed in claim 5 wherein for a first set of at least one of said plurality of assets there is a first risk premium which corresponds to the risk premium determined in step 9) and for a second set of at least one other of said plurality of assets a second risk premium the value of which is input, and wherein said computer processor is operable under control of said computer program to carry our the following additional steps:

10) determining the risk measure of said second set of assets with respect to said first set of assets;

11) determining a ratio of said second risk premium and said first risk premium to determine whether the difference between said ratio and said risk measure determined in step 10) is within a third predetermined acceptable range, and in response thereto either:

(i) if said difference is not within said third predetermined acceptable range, determine and substitute a new value for said second risk premium and use said new value of said second risk premium to process data in accordance with steps (b) 4)-11), or

(ii) if said difference is within said third predetermined acceptable range, then the value of said second risk premium represents the risk premium determined by said data processing system;

(d) means for creating a portfolio of assets in accordance with said second risk premium determined by said data processing system.

11. A data processing system as claimed in claim 1 wherein said initial cash flows have been determined up to a predetermined and specific terminal date and wherein at least one of said plurality of assets has value beyond the said terminal date, said computer processor operable under control of said computer program to carry out the following additional steps:

9) processing said data corresponding to said set of economic variables and said data corresponding to said set of asset-specific variables to determine an initial value for each of said plurality of assets and processing said plurality of sets of said alternate data to determine a plurality of alternate values for each of said plurality of assets; and

10) determining a difference between two ratios wherein:

(i) said first ratio is a market value of said asset at said terminal date divided by a book value of said asset at said terminal date, and

(ii) said second ratio is said asset's market value at a date prior to said terminal date divided by said asset's book value at said date prior to said terminal date, to determine whether said difference is within a second predetermined acceptable range, and in response thereto either:

(i) if said difference is not within said second predetermined acceptable range, determine and substitute a new value for said market value at said terminal date and use said new value of said market value to process data according to steps (b) 4)-10), or

(ii) if said difference is within said second predetermined acceptable range, then the value of said output risk measures represent the risk measures determined by said data processing system.

12. A data processing system for providing an indication of an output risk measure using jointly determined risk measures for a plurality of assets comprising:

(a) a computer processor including:

1) a first storage device for storing a computer program;

2) a second storage device for storing data corresponding to a plurality of variables, including:

(i) data corresponding to a set of economic variables including a risk premium, and

(ii) for each asset, data corresponding to a set of asset-specific variables including an input risk measure;

3) a central processing unit for processing data stored in said second storage device in accordance with said computer program stored in said first storage device;

4) an input device operable for entering said data for storage in said second storage device, and

5) an output device operable to provide an output of the results of said central processing unit;

(b) said computer processor operable under control of said computer program to carry out the following steps:

1) processing said data corresponding to said set of economic variables and said data corresponding to said set of asset-specific variables to determine initial cash flows for each of said plurality of assets;

2) generating alternate data corresponding to said plurality of economic and asset-specific variables;

3) processing said alternate data to determine corresponding alternate cash flows for each of said plurality of assets;

4) processing said data corresponding to said set of economic variables, said data corresponding to said set of asset-specific variables and said initial cash flows to determine an initial value for each of said plurality of assets and processing said alternate data and said alternate cash flows to determine an alternate value for each of said plurality of assets;

5) processing said initial values and said alternate values to determine a simulated asset return for each of said assets;

6) processing at least one of said initial values and at least one of said alternate values to determine a simulated index return;

7) jointly processing said simulated asset return and said simulated index return to determine said output risk measure for each of said assets; and

8) using an iterative converging process, comparing a value of said input risk measures and said output risk measures to determine whether said output risk measures are within a first predetermined acceptable range, and in response thereto either:

(i) if at least one said output risk measure is not within said first predetermined acceptable range, determine and substitute a new value for said input risk measure and use said new value for said input risk measure to process data according to steps (b) 1)-8), or

(ii) if said output risk measures are within said first predetermined acceptable range, then provide an indication of said output risk measure on said output device.

13. A data processing system as claimed in claim 12, wherein at least one of said plurality of assets has a known market value, and wherein said computer processor is operable under control of said computer program to carry our the following additional step:

9) determining a difference between said initial value and the known market value of at least one of said assets to determine whether said difference is within second predetermined acceptable range, and in response thereto either:

(i) if said difference is not within said second predetermined acceptable range, determine and substitute a new value for said risk premium and use said new value of said risk premium to process data according to steps (b) 1)-9), or

(ii) if said difference is within said second predetermined acceptable range, then the value of said output risk premium represents the risk premium determined by said data processing system; and

(d) means for creating a portfolio of assets in accordance with said risk premium determined by said data processing system.

14. A data processing system as claimed in claim 12 wherein at least two of said plurality of assets have a known market value, and wherein said economic variables further includes an inflation rate, and wherein said computer processor is operable under control of said computer program to carry out the following additional steps:

9) processing said data corresponding to said set of economic variables, including said inflation rate, and said data corresponding to said set of asset-specific variables to determine an initial value for each of said plurality of assets and processing said alternate data to determine an alternate value for each of said plurality of assets; and

10) determining a measure of a differences between the initial value and the respective known market value of at least two of said assets to determine whether said measure is within a third predetermined acceptable range, and in response thereto either:

(i) if said measure is not within said third predetermined acceptable range, determine and substitute a new value for said inflation rate and use said new value of said inflation rate to process data according to steps (b) 1)-10), or

(ii) if said measure is within said third predetermined acceptable range, then the value of said output inflation rate represents the inflation rate determined by said data processing system; and

(e) means for creating a portfolio of assets in accordance with said inflation rate determined by said data processing system.

15. A data processing system for providing an indication of an output risk measure using jointly determined risk measures for a plurality of assets comprising:

(a) a computer processor including:

1) a first storage device for storing a computer program;

2) a second storage device for storing data corresponding to a plurality of variables, including:

(i) data corresponding to a set of economic variables including a risk premium, and

(ii) for each asset, data corresponding to a set of asset-specific variables including an input risk measure;

3) a central processing unit for processing data stored in said second storage device in accordance with said computer program stored in said first storage device;

4) an input device operable for entering said data for storage in said second storage device, and

5) an output device operable to provide an output of the results of said central processing unit;

(b) said computer processor operable under control of said computer program to carry out the following steps:

1) processing said data corresponding to said set of economic variables and said data corresponding to said set of asset-specific variables to determine initial cash flows for each of said plurality of assets;

2) generating a plurality of sets of alternate data, each set of which corresponds to said plurality of economic and asset-specific variables;

3) processing said plurality of sets of alternate data to determine a corresponding plurality of sets of alternate cash flows for each of said plurality of assets;

4) processing said data corresponding to said set of economic variables, said data corresponding to said set of asset-specific variables and said initial cash flows to determine an initial value for each of said plurality of assets and processing said plurality of sets of alternate data and said plurality of sets of alternate cash flows to determine an alternate value for each of said plurality of assets;

5) processing said initial values and said plurality of sets of alternate values to determine a plurality of simulated asset returns for each of said assets;

6) processing at least one of said initial values and at least one of said plurality of sets of alternate values to determine a plurality of simulated index returns;

7) jointly processing said plurality of simulated asset returns and said plurality of simulated index returns to determine said output risk measure for each of said assets; and

8) using an iterative converging process, comparing a value of said input risk measures and said output risk measures to determine whether said output risk measures are within a first predetermined acceptable range, and in response thereto either:

(i) if at least one said output risk measure is not within said first predetermined acceptable range, determine and substitute a new value for said input risk measure and use said new value for said input risk measure to process data according to steps (b) 1)-8), or

(ii) if said output risk measures are within said first predetermined acceptable range, then provide an indication of said output risk measure on said output device.

16. A data processing system as claimed in claim 15, wherein at least one of said plurality of assets has a known market value, and wherein said computer processor is operable under control of said computer program to carry our the following additional step:

9) determining a difference between said initial value and the known market value of at least one of said assets to determine whether said difference is within second predetermined acceptable range, and in response thereto either:

(i) if said difference is not within said second predetermined acceptable range, determine and substitute a new value for said risk premium and use said new value of said risk premium to process data according to steps (b) 1)-9), or

(ii) if said difference is within said second predetermined acceptable range, then the value of said output risk premium represents the risk premium determined by said data processing system; and

(d) means for creating a portfolio of assets in accordance with said risk premium determined by said data processing system.

17. A data processing system as claimed in claim 15 wherein at least two of said plurality of assets have a known market value, and wherein said economic variables further includes an inflation rate, and wherein said computer processor is operable under control of said computer program to carry out the following additional steps:

9) processing said data corresponding to said set of economic variables, including said inflation rate, and said data corresponding to said set of asset-specific variables to determine an initial value for each of said plurality of assets and processing said plurality of sets of alternate data to determine a plurality of alternate values for each of said plurality of assets; and

10) determining a measure of a differences between the initial value and the respective known market value of at least two of said assets to determine whether said measure is within a third predetermined acceptable range, and in response thereto either:

(i) if said measure is not within said third predetermined acceptable range, determine and substitute a new value for said inflation rate and use said new value of said inflation rate to process data according to steps (b) 1)-9), or

(ii) if said measure is within said third predetermined acceptable range, then the value of said output inflation rate represents the inflation rate determined by said data processing system; and

(e) means for creating a portfolio of assets in accordance with said inflation rate determined by said data processing system.

18. A data processing system as claimed in claim 15 wherein computer processor is operable under control of said computer program to carry out the following additional step:

9) determines an output risk measure for each of said assets by, for each asset, regressing said plurality of simulated asset returns against said plurality of simulated index returns.

19. A data processing system as claimed in claim 15 wherein said initial cash flows have been determined up to a predetermined and specific terminal date and wherein at least one of said plurality of assets has value beyond the said terminal date, said computer processor operable under control of said computer program to carry out the following additional steps:

9) processing said data corresponding to said set of economic variables and said data corresponding to said set of asset-specific variables to determine an initial value for each of said plurality of assets and processing said plurality of sets of said alternate data to determine a plurality of alternate values for each of said plurality of assets; and

10) determining a difference between two ratios wherein:

(i) said first ratio is a market value of said asset at said terminal date divided by a book value of said asset at said terminal date, and

said second ratio is said asset's market value at a date prior to said terminal date divided by said asset's book value at said date prior to said terminal date, to determine whether said difference is within a second predetermined acceptable range, and in response thereto either:

(i) if said difference is not within said second predetermined acceptable range, determine and substitute a new value for said market value at said terminal date and use said new value of said market value to process data according to steps (b) 1)-10), or

(ii) if said difference is within said second predetermined acceptable range, then the value of said output risk measures represent the risk measures determined by said data processing system.

20. A data processing system as claimed in claim 15 wherein at least one of said plurality of assets has debt and includes an asset-specific variable of an input default risk premium for said asset's debt, and wherein said computer processor is operable under control of said computer program to carry our the following additional steps: system further comprising:

9) determining a default risk premium corresponding to said asset with debt;

10) determining a difference between said input default risk premium and the default risk premium to determine whether said difference is within a second predetermined acceptable range, and in response thereto either:

(i) if said difference is not within said second predetermined acceptable range, determine and substitute a new value for said initial default risk premium and use said value of said default risk premium to process data according to steps (b) 1)-9), or

(ii) if said difference is within said predetermined acceptable range, then the value of said default risk premium represents the default risk premium determined by said data processing system;

(c) means for creating a portfolio of assets in accordance with said default risk premium determined by said data processing system.

21. A data processing system, as claimed in claim 16 wherein for a first set of at least one of said plurality of assets there is a first risk premium which corresponds to the risk premium determined in step 9) and for a second set of at least one other of said plurality of assets a second risk premium the value of which is input, and wherein said computer processor is operable under control of said computer program to carry our the following additional steps:

10) determining the risk measure of said second set of assets with respect to said first set of assets;

11) determining a ratio of said second risk premium and said first risk premium to determine whether the difference between said ratio and said risk measure determined in step 10) is within a third predetermined acceptable range, and in response thereto either:

(i) if said difference is not within said third predetermined acceptable range, determine and substitute a new value for said second risk premium and use said new value of said second risk premium to process data in accordance with steps (b) 1)-11), or

(ii) if said difference is within said third predetermined acceptable range, then the value of said second risk premium represents the risk premium determined by said data processing system;

(d) means for creating said portfolio of assets in accordance with said second risk premium determined by said data processing system.

22. A data processing system as claimed in claim 12 wherein said initial cash flows have been determined up to a predetermined and specific terminal date and wherein at least one of said plurality of assets has value beyond the said terminal date, said computer processor operable under control of said computer program to carry out the following additional steps:

9) processing said data corresponding to said set of economic variables and said data corresponding to said set of asset-specific variables to determine an initial value for each of said plurality of assets and processing said plurality of sets of said alternate data to determine a plurality of alternate values for each of said plurality of assets; and

10) determining a difference between two ratios wherein:

(i) said first ratio is a market value of said asset at said terminal date divided by a book value of said asset at said terminal date, and

(ii) said second ratio is said asset's market value at a date prior to said terminal date divided by said asset's book value at said date prior to said terminal date, to determine whether said difference is within a second predetermined acceptable range, and in response thereto either:

(i) if said difference is not within said second predetermined acceptable range, determine and substitute a new value for said market value at said terminal date and use said new value of said market value to process data according to steps (b) 1)-10), or

(ii) if said difference is within said second predetermined acceptable range, then the value of said output risk measures represent the risk measures determined by said data processing system.

23. A data processing method for creating a portfolio of assets using jointly determining risk measures for a plurality of assets using the system of claim 1.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to computer implemented processes for estimating simulated returns, asset values and risk measures using estimated financial variables pertaining to an asset, such as economic variables and asset-specific characteristics.

2. Description of Related Art

There are numerous publications directed to financial risk analysis. Some of these papers will be referenced in the discussion below.

BIBLIOGRAPHY

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Black, Fischer, Emanuel Derman and William Toy, 1990, A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options, Financial Analysts Journal January-February, 33-40.

Black, Fischer, and Piotr Karasinski, 1991, Bond Option Pricing when Short Rates are Lognormal, Financial Analysts Journal July-August, 52-59.

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Cox, John C., Jonathan E. Ingersoll, Jr., 1985b, A Theory of the Term Structure of Interest Rates, Econometrica 53, 363-384.

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Fama, Eugene F. and Kenneth R. French, 1992, The Cross-Section of Expected Stock Returns, The Journal of Finance 47, 427-465.

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Financial analysts, investors, business persons, brokers, investment bankers, and others (hereinafter analysts) routinely estimate asset values. Such assets include, but are not limited to: equipment, real estate, debt instruments (e.g., bonds or notes), portions of companies, entire companies, and common stock or other classes of securities issued by companies or of other asset classes or derivatives of asset classes issued by investment firms.

Many known processes exist for estimating asset values. They can broadly be grouped as: (1) value-based processes, and (2) earnings or cash-flow based processes.

Value-based processes usually estimate values for an asset's separable parts. One value based process estimates the current market selling prices of an asset's separable parts. For example, if an owner receives a purchase-offer for an entire firm, one test of the reasonableness of the offer is whether a higher price can be obtained by selling the firm's separable parts. Another value-based process begins with original purchase prices for a firm's individual assets. Each asset's original cost is then adjusted for usage and estimated price changes since the acquisition date.

In contrast, earnings or cash-flow based valuation processes attempt to value an asset's projected future earnings or future cash-flows (the two are not equivalent, but estimated future earnings are often used to estimate future cash flows). Those processes usually apply the rule that a dollar today is worth more than a dollar in the future. Each asset's estimated earnings or cash flows are discounted at some rate (interest rate or discount rate) to determine the asset's current value, also referred to as present value or net present value (NPV). The cash flow/earnings valuation process consists of three separate and distinct parts: (1) estimate an asset's future earnings, cash flows, or earnings and cash flows; (2) estimate the discount rate (statistical methods and experience-based estimates are commonly used); and (3) discount the estimated future earnings or cash flows at the discount rate.

This invention deals with the earnings or cash-flow class of valuation processes, and therefore the balance of this background relates to such processes. It is highly preferable to discount estimated cash flows rather than to discount estimated earnings. The present invention may, however, be applied to either method.

There are many ways to estimate an asset's future earnings and future cash flows. Analysts typically estimate revenues and costs associated with an asset. An analyst may estimate that during the following year a firm's revenue will be $10,000,000 while its expenses will be $9,000,000. Those estimates, when combined, yield an estimated income of $1,000,000. A firm's projected investments and financing can be combined with income projections to estimate cash flows.

Estimated revenues, costs, and cash flows often depend on predicted economic conditions such as economy-wide or industry-specific growth rates, interest rates, specific price changes, and general inflation. There are countless ways to estimate economic variables and combine them with asset-specific assumptions to estimate an asset's earnings and cash flows. To an extent, the choice of an estimating process is a matter of personal preference, although some processes are more appropriate for particular asset classes. Further, the particular process is often less important than is an analyst's skill and effort. Although many processes are available to estimate an asset's earnings and cash flows, they may be misapplied by unskilled analysts.

As will be understood, an important feature of this invention is that it may be advantageously practiced with a wide range of earnings and cash-flow estimating processes. More specifically, this invention relates to an iterative process to estimate a discount rate for each of two or more assets. This invention relates to similar iterative processes to estimate other variables or coefficients that are useful in estimating an asset's risk or NPV. These include: (1) a risk premium for a class of assets based on the assumption that, in aggregate, that class of assets is correctly (efficiently) priced in the market; (2) an estimate of the implied long-run inflation rate used to value bonds or other assets; (3) a coefficient to estimate a firm's terminal value; (4) a risk premium or premiums for one or more asset classes based on the risk premium or premiums for one or more other asset classes; (5) a default premium for one or more specific debt issues; and (6) a general iterative process of additional variables.

Of the mentioned variables, most prior art has focused on estimating discount rates. Prior art relating to the additional five variables is either based on ad hoc rules, or on methods that are similar to prior art processes used to estimate discount rates. As will be evident, such prior art processes bear little relation to this invention regarding the additional five variables.

It is possible to estimate an asset's discount rate using qualitative judgment. For example, an analyst may wish to value a small firm at a time when 30-day U.S. Treasury bills pay a 6% annual interest rate. This rate is often referred to as the risk-free interest rate for two reasons. First, there is so little chance the U.S. Government will default that, for practical purposes, default risk is zero. Second, the interest-rate risk (a bond declines in value if interest rates rise) is very low because the bill matures in 30 days. The NPV of a Treasury bill is determined by discounting the principal payment back to the present, but the discount period is so short (30 days) that changes in the discount rate have little effect on a 30-day Treasury bill's value. Thus, for practical purposes, a 30-day Treasury bill is free of both default risk and interest-rate risk.

An analyst may use qualitative judgment to decide that when a risk-free investment pays a 6% return, an investment in the small firm should earn 14% because of numerous risks, including: (1) the firm's value may decline because of a recession; (2) the firm may be unable to compete with larger firms because it lacks technical expertise; or (3) the firm may be unable to obtain needed financing.

The judgment-based rate of 14% can be used to discount estimated future cash flows. Expected cash flows one year in the future would be divided by 1.14; expected cash flows two years in the future would be divided by 1.14.sup.2, while expected cash flows three years in the future would be divided by 1.14.sup.3.

In practice, many analysts do use judgment to estimate discount rates and many are highly successful investors and managers. Other analysts prefer a more objective process. The prior art development that has had by far the most significant influence on the field of finance was independently developed by William Sharpe and John Lintner in 1964 and 1965. That prior art developed a theoretical mathematical relation between an asset's risk and its return (on investment). The resulting risk-measure can be used to determine an asset's discount rate. The theoretical relation between an asset's risk and return is known in the prior art finance literature as the Sharpe-Lintner capital asset pricing model (CAPM):

(1) E(R.sub.i)=R.sub.f +.beta..sub.i .times.›E(RR.sub.m)-R.sub.f !

for i=1 . . . N, where n is an integer equal to the number of assets, and

where:

E(R.sub.i)=the expected value of the return from investing in asset i

R.sub.f =the return from investing in a risk-free asset (typically 30-day U.S. Treasury bills)

.beta..sub.i =the risk measure for firm i

E(R.sub.m)=the expected value of the return from investing in the market (typically the expected return to investing in some market index, such as the New York Stock Exchange ›NYSE! Index.TM., or the S&P 500 Index)

Because current methods are unable to estimate the expected value of the returns for investing either in an individual asset or in an index, in practice the CAPM is implemented using the following version of equation (1):

(2) R.sub.it =R.sub.ft +.beta..sub.i .times.(R.sub.mt -R.sub.ft)

where:

R.sub.it =the actual return from investing in asset i during a prior period t

R.sub.mt =the actual return from investing in the market portfolio during a prior period t

R.sub.ft =the actual risk-free rate during a prior period t

.beta..sub.i =the slope coefficient derived by regressing R.sub.it against R.sub.mt

a simplified version, sometimes referred to as the market model, is sometimes substituted for equation (2) because in practice there is little difference between the two:

(3) R.sub.it =.beta..sub.i .times.R.sub.mt

From its inception this simple linear model has been the basis for what is by far the most extensive body of academic research in the field of finance, which includes thousands of academic and applied or practical articles in the fields of finance, economics, and accounting. The CAPM is also widely used in the practice of business and finance. In both academic studies and in practice, the model is often used to estimate the risk of common stocks and possibly less often to estimate the value of common stocks. Typically the statistical method of linear regression is used to estimate an asset's risk as follows:

(1) Determine the monthly returns for a particular asset during some prior period. For example, determine the monthly returns for General Motors (GM) stock for each of the last 60 months.

(2) Determine the monthly returns for a stock index, such as the New York Stock Exchange Index (NYSE.TM.), during the same prior periods (each of the last 60 months).

(3) Using the statistical process of ordinary least squares regression, regress the returns for GM stock against the returns for the market index. The resulting regression yields a risk measure for General Motors stock. That risk measure, the slope of the regression line, is usually called beta (.beta.). The estimated .beta. can be used to estimate the discount rate for GM stock. That rate can then be used to discount estimated future cash flows; the result is GM's net present value (the estimated value of a share of GM's stock equals estimated NPV divided by the number of shares of stock outstanding).

Although the equation appears highly objective, and the previous three steps are straightforward, there is subjectivity in applying the model. First, the estimated .beta. depends on the time period chosen: a regression using the previous 30 months almost always produces a different .beta. than one using the previous 90 months. Second, it is possible to eliminate both asset and index returns for any periods with abnormal events. For example, an analyst might eliminate the return for a month when a firm's foreign subsidiary was expropriated; doing so yields a different .beta. than if that month's return is included in the regression. Third, the estimated .beta. depends on the measurement period; returns may be determined using annual returns, monthly returns, weekly returns, or daily returns. In practice, different return periods produce different .beta.s for the same firm. Fourth, the estimated .beta. depends upon the choice of an index.

There are also many theoretical statistical issues that support modifications to the above regression procedure. Such modifications are often subjective and complex but usually produce minor differences in the quality of the risk measure (one method may produce significantly different .beta.s than another, but there is little agreement that any one method is superior).

During the first twenty years after the CAPM's introduction most academic researchers and some practitioners believed that the previously described three-step process (statistical regression on prior returns) was a highly successful application of a theory (the CAPM). Many studies suggested that .beta. estimated by that process was valuable for estimating correct values for assets and for predicting asset prices under varying economic conditions. Many practitioners questioned the process but offered no better alternative and no convincing evidence that the process was incorrect. The research, however, is based on relatively complex mathematics.

Beginning in the mid-1980s academic researchers also began to question the validity of risk measures generated by the statistical process. By 1991 Eugene Fama and Kenneth French, two prominent finance professors, questioned whether the CAPM, as implemented through statistical regression on prior returns, had any value. An article they published in 1992 found that prior-period estimated .beta. had almost no ability to explain actual returns for investments in common stock. Because the risk measure is estimated by a process (statistical regression using prior returns) based on a theory (the CAPM), it has been unclear whether there are problems with the statistical process, with the theory, or with both.

As problems with the CAPM implementation became apparent, researchers spent more time testing an earlier extension to the CAPM. That extension, introduced by Stephen Ross in 1976, is called the arbitrage pricing theory (APT) in the prior art. The APT allows more than one factor to influence an asset's return. As seen in equation (1), under the CAPM, the expected return to the market, R.sub.mt, determines an asset's expected return. The term R.sub.ft is also a factor, but since researchers use R.sub.mt -R.sub.ft, under current art the CAPM is called a one-factor model (Using this claimed invention, however, it would better be termed a single-index model, since this claimed process allows many economic factors to influence an asset's returns).

Although the APT allows an unlimited number of factors to influence an asset's return, in both research and in practice, the APT is usually limited to four or five factors, such as: oil prices, inflation rates, measures of commercial and industrial activity, and one or more interest rates. If the model, as applied, included two factors it would appear as follows:

(4) R.sub.it =R.sub.ft +.beta..sub.1i .times.(i R.sub.m1t -R.sub.ft)+.beta..sub.2i .times.(R.sub.m2t -R.sub.ft)

where:

.beta..sub.1i =risk measure with respect to factor 1 for firm i

.beta..sub.2i =risk measure with respect to factor 2 for firm i

R.sub.m1t =the average market return from investing in factor 1 during period t

R.sub.m2t =the average market return from investing in factor 2 during period t

As with the CAPM, the APT is a theory of how asset prices should be determined; it says nothing about how the theory should be implemented. It differs from the CAPM only in that when implemented using prior returns, it allows multiple factors to influence an asset's return, which is its potential advantage (a potential advantage because sometimes additional factors reduce explanatory power).

Like the CAPM, the APT is typically implemented by applying statistical regression to returns for prior periods. Although the processes are conceptually similar, in practice the APT implementation is considerably more subjective and complex for one primary reason: it is necessary to identify not simply a factor that influences an asset's return, but also the return to investing in that factor (e.g., R.sub.m1t might be the average return to investing in assets influenced primarily by industrial production). Most researchers and practitioners would probably agree that methods used to implement the APT have not produced significantly better predictions than methods used to implement the CAPM. Some analysts do, however, use the APT.

Conceptually the CAPM and the APT seem like reasonable theories. Their premise is simply that investments in more-risky assets should provide higher returns than investments in less-risky assets (the relation should be linear because if it were not linear it would be possible to construct portfolios with zero risk that outperformed zero-risk Treasury bills). Given that the premise seems completely reasonable and obvious, it is very surprising that CAPM or APT results are so unsatisfactory.

Many researchers are now studying the issue. Two primary areas of their focus are: (1) methodological problems in applying statistical methods to prior returns, and; (2) the likelihood that asset risk changes from previous periods, when risk was estimated using regression, to later periods, when the model's ability to predict asset returns is tested.

Statistical methodology issues probably received most attention from finance researchers during the past two decades. As mentioned, that research probably led to only minor improvements in the quality of risk measures estimated using either the CAPM or the APT. Recently finance researchers are spending relatively more time on how risk measures change over time.

One method of avoiding changes in the risk measure is to estimate risk over the same period during which the model is tested (concurrent periods; sometimes referred to as leapfrogging). That is, the risk measure (CAPM) or measures (APT) are estimated using regression on alternate months (assume even months); those risk measures are then used to test the ability of the model to predict returns during the odd months for that particular asset. As with prior implementations of the CAPM and APT, the results indicate a weak relation between predicted and actual returns.

Another method uses statistical analysis on previous operating, financing, and accounting information. The coefficients determined through that process are used to estimate an asset's current risk given its current operating, financing, and accounting information. That estimated risk measure is sometimes averaged with a statistically estimated .beta. based on historical returns. Because of the numerous variables that can be used, and because the process usually involves complex statistical methods, the process is subjective, difficult to implement, and difficult to interpret. The results have not been particularly successful.

In addition to these applied methods of estimating an asset's NPV, there are theoretical methods based on calculus that currently are applied to what are best described as hypothetical assets (because they are far more simple than real assets). Grossman and Stiglitz, among others, use a methodology, usually called the equilibrium approach, although sometimes called state contingent or rational expectation methodology. As an example of a hypothetical asset used by this class of methods, an asset might earn a return of 15 percent when economic conditions are favorable and 4 percent when they are unfavorable. Although it is entirely possible to construct an actual financial asset that would pay its owner such returns, in practice these assets do not exist. These models currently appear to be used only in theoretical articles because they cannot be applied to the types of assets that exist in practice given the existing level of development of the closed form calculus methodology. A September, 1992, article by Longstaff and Schwartz attempts to value extremely simple, yet real, bonds using closed form methods, but is limited to using two input variables, as opposed to this claimed invention, which can utilize an almost unlimited number of input variables using a non closed form method. Pearson and Sun (1994) used closed-form methods to test what is known as the Cox-Ingersoll-Ross model (1985) on actual Treasury bonds. Pearson and Sun reject the model as being unable to explain Treasury prices.

The advantage of equilibrium models is that they do not rely on prior asset or index returns. Economic and asset-specific parameters are specified in such a way that there exists a mathematical solution for the value of the assets. As mentioned, these methods have not been used to value actual assets found in the current market and do not involve risk-return type asset pricing models.

Although there is voluminous academic and applied literature in the prior art, there is limited prior patent art. IBM Technical Disclosure Bulletin (April 1971; literature and foreign patent section; U.S. Class 364, Subclass 408) describes a program to determine the rate of return and the cost of government subsidy for real estate investments. The process also provides an iterative procedure for finding the rent that must be charged to obtain a given rate of return. The iterative process in the IBM bulletin appears to be simply a way to determine what is known as the internal rate of return. It is a process well-known in the prior art since the 1950s. It bears almost no relation to this claimed invention.

U.S. Pat. No. 3,270,170 to Lambert (Aug. 30, 1966) describes an apparatus for evaluating the capital appreciation potential of investments and for predicting future prices of common stock. Lambert discloses (in 1962 before the CAPM's development) a linear model of the relation between stock prices and variables such as: earnings, dividends, asset values, and trading volume. The process apparently uses linear regression of prior stock prices against prior values of the previously-mentioned variables. The resulting regression coefficients are multiplied by predicted values for each of the mentioned variables. The result is a predicted price for common stock. The process does not adjust for risk, does not consider the effect of the mentioned variables on risk, and involves no numerical processes other than simple linear regression and multiplication.

Lambert's process is very different from the present invention because the present invention: (1) does not use coefficients for the types of variables specified in Lambert's invention, (2) does not directly use regression on past values of any variables although regression on prior values may be used indirectly to estimate inputs to this claimed invention; (3) to the extent that the present invention uses predicted values for the types of variables specified in Lambert's invention (e.g., earnings and dividends), it uses them in a discounting process, not in a process whereby they are multiplied by coefficients from regressions on prior values to determine current asset values; and (4) some of the variables used as input to Lambert's process (e.g., prior stock prices and trading volume) need not be used in the present invention application because the models are so dissimilar.

U.S. Pat. No. 4,989,141 to Lyons et al. (Jan. 29, 1991) describes a database process that classifies, stores, and retrieves data that can be used for financial analysis and reporting. Although Lyons et al. could potentially be used as input to the present invention, Lyons et al. does not estimate asset risk or NPV.

U.S. Pat. No. 4,953,085 to Atkins (Aug. 28, 1990) describes a process that selects investments to maximize returns subject to: (1) existing tax laws; (2) investor risk-preferences; and (3) forecasts of economic and financial variables. In particular, the Atkins invention seeks to optimize the allocation of an individual's funds between investments and mortgage payments. The Atkins invention estimates neither asset risk nor asset NPV.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a method and apparatus to estimate an asset's risk and NPV that, instead of using prior-period returns to estimate risk: (1) estimates an asset's operating, financing and accounting characteristics, (2) estimates general and sector economic relations, and (3) estimates certain current economic conditions, such as interest rates, and to create a portfolio based on the estimated asset risk and NPV.

It is another object of the present invention to provide a method and apparatus for creating a portfolio by: (1) estimating an initial set of cash flows for each asset in a set of two or more assets using known or conventional methods; (2) generate additional estimated cash flows based upon different estimates for one or more economic variables; (3) adjust the original set of cash flows and each additional set of cash flows for expected inflation; (4) determine an initial input risk measure for each asset based on a risk-return type asset pricing model; (5) determine an initial discount rate for each asset using the initial input risk measure for each asset and using different economic variables that relate to each set of cash flows (for example, the risk-free rate and the market risk premium which are typically different for each set of cash flows); (6) discount the inflation-adjusted cash flows at the discount rate to determine a present value for each set of cash flows; (7) use the present values to determine simulated returns for each asset; (8) use the simulated returns for each asset to determine at least one simulated market index return; (9) regress simulated asset returns against simulated market returns or else use division to determine an output risk measure for each asset; (10) use the resulting output risk measure for each asset to estimate a new input risk measure and; (11) repeats steps 1 through 10 (or 4 through 10 in some implementations) in an iterative process until, for each asset, the output risk measure approximates to within desired accuracy the input risk measure used to determine the most recently iterated discount rate.

It is a further object of this invention to provide a method and apparatus to combine the previous iterative process with an iterative process that adjusts the estimated risk premium for a group or class of assets until the estimated total value of those assets approximates their total market value.

It is a further object of this invention to provide a method and apparatus to combine one or more of the previous iterative processes with an iterative process that adjusts the long-run inflation rate until the estimated value of individual assets is close to the actual market prices for those individual assets.

It is a further object of this invention to provide a method and apparatus to estimate the risk premium for one or more assets groups based on the risk premium for a different group of assets.

It is a further object of this invention to provide a method and apparatus to estimate the default premium for debt.

It is a further object of this invention to provide a method and apparatus to estimate the terminal value of an asset.

These and other objects of the invention are accomplished by providing a data processing system that jointly estimates: future cash flows under varying economic conditions; simulated returns; risk; and value for a set of two or more assets. The process of the present invention differs from the prior art, inter alia, in that it may be successfully carried out based upon as few as the following three inputs: (1) estimated economic variables, such as projected interest rates, inflation rates, economy-wide growth rates, and segment growth rates, with an option to include: (a) correlations between economic variables, and (b) specifications as to how those economic variables fluctuate over time; (2) estimated operating, financing, and accounting variables for two or more assets; and (3) a risk-return type asset pricing model or models (such as the CAPM, the APT, or non-linear versions of the CAPM or APT).

A significant advantage of the present invention is that it fully utilizes current information that affects asset risk. In particular, the CAPM is traditionally considered a one factor model but this invention can use many factors in the CAPM without the complexity required by the APT. In addition, because the invention uses forecasted cash flows, it can be used for virtually any asset, including stocks, bonds, real estate, newly formed companies, bankrupt companies, derivative assets (assets derived from other assets), and potential assets, such as assets to be issued in the future. In contrast, with prior art processes the CAPM and APT are rarely used to value assets other than common stocks.

The process begins by estimating an initial set of financial statements and cash flows for each asset (only cash flows if the asset is a bond or similar asset) for some number of periods using estimated operating, financing, accounting and economic variables an analyst has input into the process. Estimated cash flows may be also be adjusted for expected price changes, such as inflation.

The second step is to estimate additional sets of cash flows based upon the initial sets of cash flows. The additional sets of cash flows are determined by using a different estimate for at least one of the economic variables. By way of example, five additional sets of cash flows for each asset may be determined by using five additional sets of estimates for the economic variables. Thus, in this example, there will be a total of six sets of cash flows for each asset (the initial estimate and five additional estimates), where each set of cash flows for an asset may show, for example, estimated quarterly cash flows for the following ten years.

As should be evident, there are several different ways to carry out the second step of the invention. According to one embodiment of the invention, the initial estimates for economic variables, which were used to generate the initial set of cash flows, are revised 5 times as of the date the initial forecast is made (instantaneous changes to the initial and subsequent forecasts) or five times as of some later date, such as 30 days later so as to correspond with the period of the risk-free 30-day Treasury bill. By way of example, suppose that the process is being run as of Feb. 1, 1993, and that an analyst's best estimate is that industrial production will grow by 3% annually (thus, expected industrial growth is one economic variable in this example. It is expected to influence the cash flows of some of the assets, which may be, by way of example, firms producing industrial goods.). The initial growth rate economic variable estimate of 3% may be used to generate an initial set of cash flows for each asset. Next, five revised growth rates, such as, for example, 2.8%, 3.3%, etc., which may be pseudo-randomly generated by a computer using estimated distributions for each economic variable, may be used to generate five additional different sets of cash flows for each asset. Thus, the original growth estimate and the five revised growth estimates are used to generate six sets of estimated cash flows for each of the assets.

The third through sixth steps of the process of the present invention determine a NPV for each of the sets of cash flows for each asset. In the third step cash flows are adjusted for expected inflation. Inflation-adjusted cash flows an investor would receive from each asset (e.g., dividends and terminal value or principal and interest payments) are then discounted by each asset's discount rate. Since, at least initially, the discount rate is unknown, the fourth step is to determine an initial estimate of each asset's risk measure (.beta.). The fifth step is to determine each asset's discount rate based upon the initial estimate of that asset's risk measure .beta., the risk-free rate and the market risk premium. In the sixth step, an NPV is determined for each asset for each of the six sets of estimated cash flows by discounting the inflation-adjusted cash flows from step three by the discount rates from stop five (typically different discount rates for the initial set of cash flows and for each of the five additional sets of cash flows for each of the assets in the portfolio). In subsequent iterations of the process, a new set of discount rates for each of the assets is determined based upon a new and updated risk measure, .beta., determined in subsequent steps in this process. The third through sixth steps and the following steps of the process are repeated until the risk measure .beta. used in this step to determine the discount rate approximates to desired accuracy the risk measure .beta. determined subsequently in the process.

In the seventh step of the process of the present invention, the NPVs determined from the sixth step are used to determine simulated period-returns for each asset. According to one embodiment of the invention, the first simulated return for each asset is determined by dividing its second NPV by its first NPV and subtracting 1 in order to express the ratio as a return; the second simulated return is determined by dividing its third NPV by its first NPV and subtracting 1 in order to express the ratio as a return, etc. This process is repeated such that, in accordance with the foregoing example, five simulated period-returns are determined for each asset.

In the eighth step of the present invention, the simulated period-returns from the seventh step are used to determine simulated index returns, also sometimes referred to as market returns. For example, the first index return may be determined by dividing the sum of the second NPVs for all assets by the sum of the first NPVs for all assets and subtracting 1 in order to express the ratio as a return. Similarly, the second index return may be determined by dividing the sum of the third NPVs for all assets by the sum of the first NPVs for all assets and subtracting 1 in order to express the resulting ratio as a return. If a version of the APT is used, returns would be determined for a plurality of indexes.

In the ninth step, simulated returns for each asset are regressed against the simulated index returns to estimate a risk measure, commonly referred to as .beta. (or .beta.s with the APT), for each asset. As an alternative to regression, an easier but less theoretically preferred method uses only two simulated returns for each asset and two simulated index returns to determine risk. This is equivalent to using simple division to find the slope of a line through two points. A still easier and less preferred method uses only one return for each asset and one index return. This is equivalent to using division to find the slope of a line that passes through one point and the origin. An indirect alternative is to use the pricing relationships implicit in the efficient frontier, the securities market line or the capital market line.

The tenth step is to revise the risk measure .beta. (the input .beta.) most recently used in step four using the risk measure determined in step nine (the output .beta.). The process repeats steps five through ten (or one through ten in some cases) until there is a very small difference between the input .beta. in step four and the output .beta. from step nine. At this point the system can be considered to be in equilibrium, and the .beta. output in step nine represents the estimated .beta. determined according to the process of the present invention. Assuming that the estimated inflation rates and the estimated returns to the market are correct, the process has determined a value for each asset and the riskiness .beta. for each asset. Accordingly, one may create a portfolio using the value and risk of each asset.

In accordance with alternative embodiments of the invention, the subsequent steps may also:

(1) adjust the market risk premium used to determine the discount rate in step five (which is different than asset risk) until the estimated total market values for one or more assets approximately equals the sum of their actual market values. To estimate the variability of the risk premium, however, it may be necessary to run the process over a 24-36 month initialization period, in a time march. For example, U.S. Treasury securities are among the largest and most active markets in the world. An analyst may believe that, in total, Treasury securities are fairly priced but that some Treasury securities are mis-priced relative to others. This feature of the invention claimed in this application allows an analyst to search for mis-priced securities. A limited test of this invention indicates it is able to help detect underpriced and overpriced assets;

(2) adjust the long-term inflation rate until the sum-of-squares, sum-of-absolute values or other measure of the differences between the estimated value of each asset and the actual market price of each asset is minimized. To estimate the variability of the long-run inflation rate, however, it may be necessary to run the process over a 24-36 month initialization period, in a time march. This feature of the claimed invention permits an analyst to search for undervalued assets without specifying a long-term inflation rate;

(3) equate the risk premium for one or more asset classes, such as U.S. stocks or U.K. Treasury securities (or risk factors in the APT) with the risk premium implied by: the relation between that asset class and the risk premium from an asset class believed to be efficiently priced, such as U.S. Treasury securities. For example, R.sub.i in equation 1 of the background description of this application can be an individual asset or a group of assets. Similarly, R.sub.m, can be all assets or a particular group of assets. Simple linear relations can be used to determine the risk premium for one group of assets assuming the risk premium for a different group of assets is correct. For example, an analyst may assume the risk measure for U.S. Treasury securities determined using this invention is correct. By regressing returns for an index of simulated corporate stock returns against the index of simulated U.S. Treasury security returns, it is possible to estimate a corporate stock risk premium. This may be a particular advantage since current methods of comparing the price of corporate stocks with the price of U.S. Treasury securities probably rely more on judgement and on statistics than on formal risk-return analysis;

(4) equate the default risk premium for corporate debt with the default risk premium as implied by the likelihood of default under various economic outcomes;

(5) equate the value of a company's terminal market value to a value implied by its ratio of market value to book value at some earlier date or as implied by various accounting ratios under various economic conditions;

(6) Estimate different .beta.s for each additional set of economic conditions (because risk measures are different under different economic conditions, this may sometimes be desirable). Thus, a different discount rate for each set of economic conditions would be used to determine discounted cash flows under each set of different economic conditions.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is described in reference to the accompanying drawings in which:

FIG. 1A is a block diagram of the hardware which is used in accordance with the invention;

FIG. 1 is a schematic drawing of the overall iterative process, including how various models and variables are combined to estimate the value of two or more assets;

FIG. 2 is a schematic drawing in greater detail of how the iterative process is used to estimate the value of bonds;

FIG. 3 is a schematic drawing of how different estimates for economic variables are used to estimate projected cash flows for each asset, how those cash flows are used to determine NPVs for each asset and for an index, how NPVs are used to determine simulated returns, how simulated returns are used to determine output risk measures, and how the iterative process is used to re-estimate NPVs and asset values;

FIG. 4 is a schematic drawing illustrating how information is input into the claimed invention to determine discounted cash flows for bonds;

FIG. 5 is a schematic drawing that begins at the finish of FIG. 4 and that illustrates the iterative process for bonds;

FIG. 6 is a schematic drawing of the initial iteration of the iterative process as applied to four actual Treasury bonds for August, 1991;

FIG. 7 is a schematic drawing of the iterative process from FIG. 6 where the iterative process has been repeated until the process is in equilibrium (i.e., for each asset, the input beta is approximately equal to the output beta);

FIG. 8 is a schematic drawing of the iterative process from FIG. 7 where the risk premium has been adjusted until the sum of the estimated values of the four bonds is approximately equal to the sum of the market prices of the four bonds;

FIG. 9 is a schematic drawing of a portion of the iterative process applied to two or more companies. It is similar to portions of FIG. 4, a schematic drawing that applies to bonds;

FIG. 10 is a schematic drawing of another portion of the iterative process applied to two or more companies; it is similar to portions of FIG. 4 and to all of FIG. 5, which are schematic drawings that apply to bonds;

FIG. 11 is a schematic drawing of how variables are combined to determine a firm's net income; it is an expansion of portions of FIG. 10;

FIG. 12 is a schematic drawing of how variables are combined to determine a firm's balance sheet; it is an expansion of portions of FIG. 10;

FIG. 13 is a schematic drawing of how variables are combined to determine a firm's statement of cash flows; it is an expansion of portions of FIG. 10; and

FIG. 14 is a schematic drawing of how information from FIGS. 11-13 is used to estimate cash flows for an investor and the net present value of those cash flows; it is an expansion of portions of FIG. 10.

TABLE OF ABBRIVATIONS

In the drawings the following abbreviations are used:

Abs=Absolute

Abs diff=Absolute difference

Bal=Balance

Bid-ask mid=Midpoint of the bid (offering) price and the ask (selling) price

Co=Company

Co betas=Company betas

Cum=Cumulative

Cum infl=Cumulative inflation

Cur=Current

Diff=Difference

Disc=Discount

Dtd=Determined

Econ=Economic

Econ vars=Economic variables

Est=Estimated or Estimate

Est infl=Estimated inflation

Ests=Estimates

Infl=inflation

Intl=Initial

Mat=Maturity

Mid=Midpoint

Mkt=Market

Mo=Month

NPV=Net present value

NPVs=Net present values

Oper=Operating

Oper sgmt=Operating segment

Param=Parameters

Rel=Relative

RF=free rate

RF/infl=Risk-free rate adjusted for inflation

Rprem=Risk premium

Sgmt=Segment or Segments

Vars=Variables

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The data processing system for carrying out the invention comprises means for entering estimates of economic variables that are expected to affect inflation-adjusted future cash flown of one or more assets, means for entering estimates of operating, finance, and accounting variables for two or more assets, a processing unit for computing estimated financial statements, estimated cash flows, and inflation-adjusted cash flows for two or more assets (only cash flows or inflation adjusted cash flows if the assets are bonds) using the initial estimates of economic variables and asset-specific variables, and a processing unit for computing the NPV of each of said two or more assets, given a discount rate for each asset as implied by a preferred asset pricing model. In an iterative or recursive numerical process, an initial estimate of the discount rate is selected.

Said data processing unit also contains means for selecting different estimates of said economic variables. Said different estimates may be selected randomly or non-randomly and may be based on estimated behavior of said economic variables. The data processing unit means for computing estimated future financial statements, cash flows, and NPVs are then applied to each of the different estimates of economic variables to produce one or more additional said NPVs for each said asset. Said NPVs, which include all cash flows to or from owners of said assets, are used to estimate simulated returns for one or more periods for each said asset. Said data processing unit also contains means for computing an index or indexes of returns for each economic variable or set of economic variables comprising at least one asset affected by said economic variable or set of economic variables.

Said data processing unit contains means for computing a risk measure or measures for each asset using a preferred risk-return type asset pricing model and said simulated asset and index returns. The data processing unit also contains means for reducing to an acceptably small number the difference between the discount rate initially used to discount estimated cash flows and the discount rate implied by the estimated risk measure or measures for each asset. Said data processing unit can also contain means to reduce to acceptably small numbers the differences between several other variables, including: (1) the estimated risk premium or premiums for a group of one or more assets and the risk premium implied by assuming the total market value of the group of assets is correct; (2) the estimated risk premiums for a group of assets and the risk premium implied by assuming the risk premium for a different group of assets is correct; (3) the estimated long-term inflation rate that minimizes the sum-of-squares, sum-of-absolute values, or other measure of the differences between estimates of the value of individual assets and the actual market prices of those assets; (4) the estimated default-risk premium used to determine an asset's value and the risk premium implied by one or more variables determined in the iterative process; and (5) the estimated ratio of market value to book value used to determine an asset's terminal value and the ratio implied by the iterative process.

With the foregoing overview in mind, the process and system of the present invention will now be described in greater detail and in conjunction with FIGS. 1-14.

The invention is preferably implemented using a digital processor such as a programmable digital computer system 1 shown in FIG. 1A. The computer system 1 comprises a central processing unit (CPU) 2, (which may be replaced by a plurality of CPUs, preferably configured for parallel processing), a read only memory (ROM) 3, and a random access memory (RAM) 4, an I/O port 5, an input device 6, an output device such as a display 7, data storage device 8 and a modem 9. The CPU 2 includes an arithmetic and logic unit (ALU), registers, a program counter, instruction registers and the like as is well known to those skilled in the art. Conventional data and address busses interconnect the CPU with the ROM 3 and RAM 4 and I/O port 5. Input device 6, such as a keyboard 6a, is connected to the I/O port 5 for providing electrical input data signals to the CPU 2 representative of input parameters as explained further below. It is understood that the input device may additionally or alternately comprise a voice actuated input device 6b generating electrical signals corresponding to a user's voice for both command sequences and data input, or may alternately or additionally comprise a mouse 6c used in conjunction with display 7 to select appropriate input data. Other devices may of course be used to provide part of all of the data input such as data from a data storage device 8 (hard drive or floppy, tape, magnetic and/or optical disk, flash memory, etc.) used alone or in conjunction with the keyboard 6a and/or display 7 and mouse 6c. Some input data may be obtained directly from a live price feed from, for example, the New York Stock Exchange via a direct phone line, a satellite link, or other communications methods.

The I/O port provides queries to the user typically through an output device in the form of a display 7 such as a video monitor, liquid crystal display or the like. A voice synthesizer could additionally or alternately be used as an output device. A printer may also be used as an output device especially when a hard copy of the output data is desired. Further, output data may be stored on the data storage medium 8 and/or sent via a modem 9 (or similar network interface such as Ethernet, Fiber Distributed Data Interface (FDDI), Integrated Services Digital Network (ISDN) known to those of skill in the art) to remote locations. Typically, the modem may be used to place buy and sell orders so as to create a portfolio in accordance with the risk measures as taught herein. Of course, buy and sell orders may also be placed over the telephone by calling a stock broker.

In carrying out an embodiment of the invention, a computer program is stored in ROM 3 and/or RAM 4 and is executed in accordance with certain mathematical and non-mathematical algorithms. The program is designed to halt at various times after prompting the user for input of certain data. After the user provides the requested data, generally followed by a command signal resulting from depressing, for example, the "enter" key on the keyboard 6, the computer continues to execute program instructions utilizing the data input by the user. The programmed computer is interactive with the user and transforms certain input data signals, generated, for example, by keystrokes on the keyboard 6, into different electrical signals during execution of the program, and finally providing output electrical signals corresponding to the output risk measure as determined in the computer. These output risk measures are provided on the output device such as display 7. From these output risk measures, a portfolio is created by buying and/or selling assets. Stocks, bonds or other assets having a higher market price than the present value may be sold and those with a lower market price than the determined price may be purchased. Similarly, a portfolio with unacceptable risk, as measured by the risk measures determined by the process described herein, may be adjusted to an appropriate risk level by purchasing additional stocks, bonds or other assets that are not presently part of the portfolio or by selling some of those that are part of the portfolio. In addition, incentive compensation payments may be made to managers or employees of a company or to sellers of a company or asset based on the determined present value.

In carrying out the program, computer system 1 sets up and utilizes certain data files which may physically reside in the RAM 4 and/or the data storage device 8.

The steps set forth below in relation to the flow charts of FIGS. 1-5 and 9-10 may be implemented into a computer program loaded into the RAM 4 of computer system 1. Computer system 1 may comprise a programmable digital computer such as any of the many types of personal computers readily available on the market. It is contemplated that the application program used in carrying out the invention would require a computer having at least 8 megabytes of RAM storage capacity, and would most optimally operate in a window-type environment. As a non-limiting example, the computer may be an IBM PS/2 model 77 computer containing a 486 family central processor with a hard disk drive storage capacity of about 30 megabytes. The exemplary data shown in FIGS. 6-8 were obtained using QuatroPro, a commercially available spreadsheet program.

Referring first to FIG. 1, there is illustrated an overview of the process of the present invention. In Step 10, one or more asset-specific variables, such as a bond's coupon rate and principal, or a company's current sales, are entered into the computer system 1 via input device 6. According to a preferred embodiment of the invention, the particular asset-specific variables are determined by reference to one of several predetermined asset models 20. Thus the asset models 20, which may be comprised of look-up tables for the data elements or other data structures (meaning herein physical relationships among the stored data elements) stored in RAM 4 and/or data storage device 8. These data structures together with associated program instructions, specify and/or prompt the user to input information required in Step 10. The computer instructions interactively prompt the user for asset specific data and receive electronic signals indicative thereof followed by at least one command signal, e.g., generated from, for example, the "enter" key on the keyboard. Economic information, such as the risk-free rate and the current rate of inflation, is entered in the same interactive manner in Step 30. According to a preferred embodiment of the invention, the particular economic information input in Step 30 is specified with reference to one of several predetermined economic models 40 which may be comprised of look-up tables or similar physical data structures. In Step 50, several sets of cash flows are determined for a specified number of periods, such as each of the next twenty quarters, for each asset under various economic conditions. The cash flows determined in Step 50 are preferably determined with reference to one of several predetermined asset cash flow models 60. The asset cash flow models 60 may specify how cash flows are to be determined, such as quarterly or semi-annually, as well as how to determine the last cash flow (terminal value) if the asset has value beyond the last period for which cash flows are determined.

With respect to choosing inflation rates, there are many possibilities. Currently, the preferred method is to use a 4-6 month average of the CPI as the inflation rate for one month. One then divides 1.0+the 30-day Treasury yield by 1.0 plus the one-month inflation rate to determine the risk-free rate. Next one determines the cumulative inflation rate as of one year from the valuation date by dividing 1.0 plus the 1-year Treasury yield by 1.0 plus the computed risk-free rate. One then assumes that the inflation rate changes uniformly, on a daily basis, from the 30-day rate to the one-year rate. Thus, for example, the one-year cumulative inflation rate might be 5.6% but the rate as of one year might be 5.9%, which is the level needed to increase the cumulative inflation rate from its level as of one month to its cumulative level of 5.6% as of one year. That is done through an iterative or convergent process. One can next use an anchor year that the user can specify, such as two or three years. One can then increase the inflation rate uniformly on a daily basis from its level as of one year (5.9% in this example) to the long-term inflation rate as of the anchor year. Thus, if the anchor year is 3, and the long-term inflation rate is 8.0%, the inflation rate increase increases uniformly, on a daily basis from 5.9% to 8.0%. As is obvious to one skilled in the art, users of said process may prefer other methods of estimating inflation rates.

In Step 70 net present values (NPVs) for each of the assets are determined, preferably by reference to one of several predetermined discounting models in Step 80. The discounting models in Step 80 specify if and how cash flows are to be adjusted for inflation, the risk-return type asset pricing model to be used for discounting, and how the discount rate is determined from the risk-return type asset pricing model and from economic variables including an initial estimate of the risk measure for each asset. In Step 90 simulated returns for each of the assets are determined using net present values from Step 70. The simulated returns are preferably determined according to one of several predetermined simulated return models 100. In Step 110 a risk measure .beta. is determined for each asset using the simulated returns from Step 90 in accordance with one of several predetermined risk-return models 120.

Step 130 tests whether the difference between each asset's input risk measure used to discount projected cash flows in Step 70 and that asset's output risk measure determined in Step 110 is within a predetermined acceptable range. If, in Step 130, the difference between the input risk measure and the output risk measure is greater than a predetermined amount for any asset, a new, adjusted input risk measure .beta. is determined in Step 140 for each such asset and the process returns back to Step 70 (or to Step 50 in some implementations where cash flows depend on the risk measure). However, unlike the iterative process for asset risk measures and for the risk premium, this difference cannot be reduced to an arbitrarily small amount, only to a minimum value that depends upon various input parameters and market prices for individual assets. Typically, but not in all cases, selecting a new .beta. that is between the input .beta. and the output .beta. will assure that the process will converge, as desired. If the difference between the input and output risk measures is less than a predetermined limit for each asset, Step 130 passes control to Step 150. Step 150, which is an optional, yet preferred step to the basic process, tests whether the difference between the sum of one or more estimated asset values in Step 70, and the sum of the actual market prices of those assets, is within a predetermined limit. If, in Step 150, the difference is greater than the predetermined limit, the process continues to Step 160 where a new market risk premium (E(R.sub.m)-R.sub.f) is determined. For example, if the total actual market value of the assets is greater than the total market value determined by the process, then the estimated risk premium should be increased. After the risk premiums are adjusted in Step 160, the process returns back to Step 70. When the difference between the total actual market value of the assets and the total values determined by the process are within a predetermined limit, the process continues from Step 150 to Step 162.

In Step 162, the value of each of the bonds is compared to its respective market price (it is possible to use assets other than bonds in this step, but because of their known cash flows, bonds or other fixed income instruments are probably preferable to other assets). If the value of any particular bond, or a subset of all the bonds, significantly differs from the market value, this is an indication that the long term inflation estimates used by the process were likely inaccurate. Thus, in Step 162 if a measure of the difference between the value of each of the bonds and their market value (such as the sum of squares of individual differences) is greater than a predetermined amount, the process continues to Step 164 where the long term inflation rates used by the process are adjusted and the process loops back to Step 70. If in Step 162 the measure of the difference between the value of each of the bonds and their market value is less than a predetermined amount, the process continues at Step 170 where the risk measure determined by the process may be printed or otherwise displayed to the user, with other useful information including asset prices, estimated inflation, estimated risk premiums, estimated standard deviations for each bond (which may be useful for evaluating options) and, if desired, over and under valued assets. In Step 172, the portfolio may be created (using the modem or telephone to buy/sell assets) based on the various outputs of Step 170. Thus, bonds in a portfolio determined to be over priced might be sold and those not in the portfolio that were determined to be underpriced might be purchased. Similarly, if the risk measure of a portfolio was deemed to be unacceptably high, such as a portfolio having a .beta. of 2.0 when a .beta. of 1.5 was the desired risk level, certain bonds in the portfolio with .beta.s above 1.5 might be sold and certain bonds not in the portfolio with .beta.s below 1.5 might be purchased. Thus, the portfolio can be modified or created based on some target risk measure. Because the relationship is linear, .beta.s are additive. Thus, if one buys $10,000 of a bond with a .beta. of 1.0 and $10,000 of a bond with a .beta. of 2.0, the portfolio .beta. is 1.5.

As will now be described with reference to FIG. 2, the process of the present invention may be implemented to determine the risk measure and value for a plurality of bonds which essentially define the market used in the analysis. Preferably, many bonds will be included with a relatively wide range of maturities and coupon rates in order to provide a broad and meaningful sample. In addition, such diversity will ensure that the effect of one mis-priced bond is minor and will not significantly distort the overall results of the process.

Referring now to FIG. 2, an embodiment of the process of the present invention is illustrated which estimates the risk measure and value of a plurality of bonds. Beginning with Step 180, information relating to the particular characteristics of the bonds which may be useful to estimate a bond's projected cash flows is entered into the computer system 1. Such information may include, for example, the maturity date of the bond, the coupon rate, the interest payment dates and the call provisions. In the relatively simple case of a U.S. Treasury bond, for example, in Step 180, a user will input: (1) the coupon rate (used to determine semi-annual interest payments, and which may be zero for a zero-coupon bond), (2) the maturity date (used to determine how long the bonds will pay interest), and (3) the principal amount (which may be zero for an interest-only bond). In the case of a callable bond, call provisions may also be specified in Step 180 by entering the first call date, subsequent call dates and call prices.

In Step 190 estimates are entered into computer system 1 for an initial set of economic variables relating to the bonds input in Step 180. For example, the risk-free rate may be entered as 3.0% annually, with an expected standard deviation over a 30-day period of 0.4%. In an alternative embodiment of the invention, standard econometric methods may be used to define a relatively complex model of how the risk-free rate or inflation or any other economic variable is expected to fluctuate over time. For example, the risk-free rate may be expected to fluctuate or vary somewhat randomly over time, but more significant changes over time may be dependent on another variable, such as inflation. Such a model may be defined as the distribution of each economic variable, or alternatively, in combination with a relationship between one or more of the economic variables used in the process. With respect to some variables, such as the risk premium and the long-term inflation rate, which can be determined by said iterative process, it may be necessary to estimate variability by running said entire iterative process over a 24-36 month initialization period, in a time march.

In Step 200, n additional sets of estimates are generated for each of the economic variables input in Step 190. Thus, after Step 200 is completed, n+1 sets of estimates for the economic variables will have been generated. These additional sets of estimates may be determined in relation to the initial economic estimates input in Step 190. For example, if the risk-free rate entered in Step 190 is 3.0% annually, Step 200 might pseudo-randomly generate different rates of 3.3%, 3.5%, etc. based on the distribution of the risk-free rate entered in Step 190 and also based on the correlations entered in Step 190. Additional economic estimates may be generated: (1) as of the current date, such that different estimates could be expected immediately; (2) as of 30 days from the current date, such that different estimates could be expected to coincide with the 30-day T-bill rate, which is often considered the risk-free rate, or (3) as of some later date.

In Step 210 an initial set of cash flows is generated, beginning with the first bond, usually for the life of the bond. Those projected cash flows are then adjusted for the inflation as input in Step 190 (which, as discussed, may include a short-term inflation rate, a long-term inflation rate, and an anchor year, which defines the transition time between the sort-term and long-term inflation rates). The process then continues to Step 220, where an additional set of inflation-adjusted cash flows for the first bond using the first additional set of economic variables is generated in Step 200. In Step 230, the process continues looping back to Step 220 until n additional sets of inflation-adjusted cash flows for the first bond have been generated relating to the n additional sets of economic variable estimates input in Step 200. Thus, when the process continues for the first time from Step 230 to Step 240, n+1 inflation-adjusted cash flows will have been determined relating to the first bond. A similar process of generating an initial and n additional sets of inflation-adjusted cash flows for each of the remaining bonds is performed by control looping from Step 240 to Step 210 after n+1 cash flows have been generated for the first bond. Thus, the second time the process continues to Step 240, n+1 inflation-adjusted cash flows will have been generated for the second bond. When n+1 inflation-adjusted cash flows have been generated for each of the bonds, the process continues from Step 240 to Step 250.

In Step 250, the initial economic variables input in Step 190 are combined with a risk return type asset pricing model and an initial estimate of each bond's risk measure (.beta.) to determine a discount rate for each bond. For example, the initial risk-free rate may be added to the product of the initial estimate of the market risk premium of Step 190 and the initial estimate of the bond's risk measure .beta.. For each bond, each of the n+1 sets of inflation-adjusted cash flows are discounted at that bond's discount rate to produce n+1 NPVs for each of the i bonds.

In Step 260 NPVs determined from Step 250 are used to determine a set of simulated returns for each of the bonds. For example, the first simulated return for the first bond may be determined by dividing the NPV from the first generated set of inflation-adjusted cash flows by the NPV from the initial set of inflation-adjusted cash flows and subtracting 1 to express the ratio as a return. The second simulated return for the first bond may be determined by dividing the NPV from the second generated set of inflation-adjusted cash flows by the NPV from the initial set of inflation-adjusted cash flown and subtracting 1 to express the ratio as a return. It should be evident that there are other suitable techniques for determining simulated returns from the NPVA. For example, as an alternative technique, the second simulated return for the first bond may be determined by dividing the NPV from the second generated set of inflation-adjusted cash flows by the NPV from the first generated set of inflation-adjusted cash flows and subtracting 1 to express the ratio as a return. In practice the results of these two different techniques have been nearly identical.

In Step 270 simulated index returns are determined using the simulated bond returns determined in Step 260. There are well-known methods of constructing a value-weighted index, including summing the NPVs of individual bonds for the first generated set of inflation-adjusted cash flows, summing the NPVs of individual bonds for the initial set of inflation-adjusted cash flows, and then dividing the first sum by the second sum and subtracting 1 to express the ratio as a return.

In Step 280 the simulated returns for each bond and the simulated index returns are used to determine a risk measure (.beta.) for each bond. In a preferred embodiment of the invention, the original Sharpe-Lintner asset pricing model will be used together with the statistical technique of linear regression in order to determine the risk measure associated with each bond. According to another embodiment, the Sharpe-Lintner model may be implemented using only two simulated returns for each bond, or only one simulated return for each bond based upon the assumption that the origin is a second point, i.e., a 0.0% excess return for an asset and 0.0% excess return for the index (0.0% in excess of Rf). In either of these simplified methods simple division can replace linear regression as a technique to determine a bond's risk measure.

Step 290 compares the input risk measure used in Step 250 with the output risk measure determined in Step 280 with a pre-determined limit. If the difference between the input and output risk measure exceeds the predetermined limit, in Step 300 a new risk measure is determined such that in the next iteration of Steps 250 through 280 it is likely that the difference between this new input risk measure, and the next output risk measure determined in Step 280, will be reduced. For example, if a bond's input risk measure is 0.8 and its output risk measure is 0.9, Step 300 might choose a new input risk measure of 0.85. Choosing a new input risk measure closer to the output risk measure will generally cause the input and output risk measures to converge more rapidly, but in some cases if the new input beta is too close to the output beta the two numbers may diverge. Further, in some situations it may be necessary to choose a new input risk measure outside of the range 0.8 to 0.9. According to a preferred embodiment of the invention, Step 290 will include a technique to determine whether the input and output betas are converging or diverging. As should be evident, the process may provide the user with the option of choosing a process that is likely to converge rapidly but that may diverge, or a process that is likely to converge slowly but that is unlikely to diverge. Once the difference between input and output risk measures is below the pre-determined limit for each bond, Step 290 passes control to Step 310.

Steps 310 and 322 represent optional, yet preferred steps in the process of the present invention. In Step 310, the sum of estimated values for one or more bonds is compared with the sum of the market prices of those bonds. If the difference between the sum of the estimated bond values and the sum of the market prices exceeds the predetermined limit, in step 310 a new market risk premium is determined such that in the next iteration of steps 250 through 300 it is likely that the difference between the new sum of the estimated bond values and their market prices, as determined in step 310, is likely to be reduced. If the difference is less than a predetermined limit, the process continues to Step 322. In Step 322 the value of each bond, as determined by the process, is compared to the market value of each bond. If the sum-of-absolute value or other measure of the difference between the determined value and the market value of each bond is not at its minimum value within a predetermined amount, this is an indication that the long term inflation rate estimate used by the process was different than the long term inflation rate implied by the market and the process continues to Step 324 to adjust the long term inflation rate. After the long term inflation rate is adjusted in Step 324, the process loops back to Step 250 to determine anew the risk measure .beta. and value of each of the bonds, and to 320 which adjusts the market risk premium so that it is likely that the previous difference will be reduced after the next iteration of Steps 250 through 300. When the difference is less than the pre-determined limit, Step 322 passes control to Step 330, where the portfolio is implemented (purchases or sales) in accordance with the risk means determined. After completion of the process in Step 330, a risk measure and value for each of the bonds has been determined by the process of the invention and a portfolio created accordingly. It should be noted that while steps 310 and 322 are preferred steps in building the present invention, they are best implemented as optional steps, since some users may prefer other alternatives.

Referring to FIG. 3, the general flow of information according to the process of the present invention is illustrated. Block 340 represents an initial set of estimates for economic variables that are input into computer system 1 by a user of the process. As can be seen, there are 0 through n (hereinafter 0-n) different sets of estimates of economic variables. As should be evident, Blocks 340, 350, 360, and 362 would likely be implemented as a three dimensional matrix with one dimension corresponding to the number of periods for the estimates, a second dimension corresponding to the number of different economic variables and the third dimension corresponding to the number of sets n of different estimates of the economic variables. For example, Block 340 may contain information such as an estimated inflation rate over the next year of 2.1%, and an estimated 30-day U.S. Treasury bill rate of 3.0%. In Block 350 an additional set of economic variables is stored which may have been generated possibly randomly within a specified range by using, for example, a set of distributions and correlations input by a user. Block 350 may contain a different estimate for the inflation rate of 2.3%, and an estimate for the 30-day U.S. Treasury bill rate of 3.3%. Similarly, Block 362 contains information relating to the last and nth additional set of economic variables that will be used by the process.

Block 370 represents the set of projected cash flows for the first asset. As can be seen, for each of the i assets, one set of cash flows is determined for each set of economic variables. In the illustrated case, for the first asset, ASSET 1, there are 0-n projected cash flows. Thus, given n+1 sets of economic variables, there will be generated n+1 sets of cash flows for each asset. As should be evident, Blocks 370, 400 and 430 may be readily implemented as a three dimensional matrix with one dimension corresponding to the number of periods for which cash flows are estimated, a second dimension corresponding to the number of sets n of different estimates of the economic variables and a third dimension corresponding to the number i of different assets. Some of the cells of the matrix may, of course, not be used in the process because of the differing maturities of the bonds. As illustrated, the economic variable estimates from Block 340 (SET 0) are used to determine the initial set of projected cash flows (SET 0) for each asset. As shown with respect to Block 370, 0-n projected cash flows are determined for ASSET 1 which correspond, respectively, to the 0-n estimates of the economic variables. For example, if asset 1 is a bond, the initial annual inflation rate of 2.1% in Block 340 would be used to compute set 0 of the inflation-adjusted cash flows which would be stored as SET 0 in Block 370. As can be seen, each set of cash flows for each asset represents essentially a stream or list of estimates, whereby one estimate is provided for each set of economic estimates. Likewise, estimates for another set of economic variables from SET 1 is used to determine the second set of projected cash flows (SET 1) for each of the assets. The second set of projected cash flows for ASSET 1 would also be stored in Block 370. For example, if ASSET 1 were a bond, an estimated inflation rate of 2.3% from Block 350, would be used to inflation adjust the principal value and interest payments in SET 1 of ASSET 1 in order to generate SET 1 of inflation-adjusted cash flows stored in Block 370. Similarly, the nth estimated economic variable information from Block 362 is used to determine cash flows for the nth set of cash flows for each of the assets.

In Block 380 cash flows from Block 370, corresponding to ASSET 1, are discounted at the discount rate implied by: (a) economic variables under each set of economic conditions, (b) the selected risk-return type asset pricing model, and (c) the input risk measure for that asset. For example, one economic variable used in the Sharpe-Lintner asset pricing model is the risk free rate (30-day Treasury bill rate). Thus, the 30-day rate of 3.0% from Block 340, and SET 0 of the projected cash flows corresponding to ASSET 1 from Block 370, are used to determine NPV 0 for ASSET 1 in Block 380. The 30-day rate of 3.3% from Block 350 and SET 1 of the projected cash flows corresponding to ASSET 1 from Block 370 are used to determine NPV 1 in Block 380.

As should be evident, Blocks 380, 410 and 440 (including possibly Block 460 as well) may be implemented as a two-dimensional matrix with one dimension corresponding to the number of assets and the second dimension corresponding to the number of different estimates of economic variables. Thus, the three dimensional matrix formed from Blocks 370, 400 and 430 is transformed into a two dimensional matrix in Blocks 380, 410 and 440 whereby the dimension corresponding to the number of periods for which inflation-adjusted cash flows are estimated has essentially been "collapsed" to a single value in order to give the not present value for an asset given a particular set of estimates of economic variables.

The 0-n NPVs from Block 380 are used to determine 1-n simulated returns which are stored in Block 390. As illustrated in Block 390, RETURN 1 for ASSET 1 is determined by dividing NPV 1 from Block 380 by NPV 0 from Step 380 and subtracting 1. The last return, RETURN n, is determined by dividing NPV n in Block 380 by NPV 0 in Block 380 and subtracting 1. The other returns corresponding to ASSET 1 are determined in a similar manner and stored in Block 390. According to an alternative embodiment of the invention, the returns may be determined differently, such that RETURN n in Block 390 could be determined by dividing NPV n in Block 380 by NPV n-1, in Block 380 and subtracting 1. Similar to Blocks 380, 410 and 440, Blocks 390, 420 and 450 may be implemented as a two-dimensional matrix with one dimension corresponding to the number of assets and the second dimension corresponding to the number of additional estimates of economic variables (total sets of economic estimates minus one).

The type of information stored in Blocks 400 through 420 is similar to that stored in Blocks 370 through 390. Blocks 400 through 420, however, contain information relating to the second asset, ASSET 2. Similarly, the type of information stored in Blocks 430 through 450 is similar to that stored in Blocks 370 through 390, but Blocks 430 through 450 relate to information for the last asset, ASSET i.

In Block 460 there is stored an index NPV 0 which is determined by adding the NPV 0 for each of the assets 1 through i in Blocks 380, and 410 through 440. Similarly, in Block 460 there is stored an index NPV for each set of NPV's used in the process. For example, in Block 460 there is stored index NPV 1 which is determined by adding the NPV 1 of each of the assets 1 through i; in Block 460 there is also stored index NPV n which is determined by adding NPV n for each of the assets 1 through i.

In Block 470 there are stored index returns determined using the index NPVs stored in Block 460. For example, index return 1 is determined by dividing NPV 1 from Block 460 by NPV 0 of Block 460 and subtracting 1. Index return n, which is also stored in Block 470, is determined by dividing index NPV n of Block 460 by index NPV 0 of Block 460 and subtracting 1 or, alternatively, by dividing index NPV n by index NPV n-1 and subtracting 1.

In Block 480 there is stored a risk measure for ASSET 1 that is determined by regressing the n simulated asset returns of Block 390 against the n simulated index returns of Block 470. Similarly, in Block 490 there is stored the risk measure for ASSET 2 which is similarly determined by regressing the index returns of Block 420 against the n index returns of Block 470, and in Block 500 there is stored the risk measure for ASSET i which is determined by regressing the returns from Block 450, corresponding to ASSET i, against the index returns of Block 470.

As should be evident, Blocks 480, 490 and 500 may be implemented as a one dimensional matrix, or a list of a length i corresponding to the number of assets used in the process. Each element of the list corresponds to the risk measure .beta., i.e., the output risk measure, which has been determined by the process for each of the i assets.

The output risk measures .beta. for ASSET 1 through ASSET i which are determined as part of the process of the present invention are stored respectively in Blocks 480 through 500 and are used to determine new input risk measures .beta. which will be used to determine new NPVs for each of the assets which will then be stored back in Blocks 380, 410, and 440, and a new set of index NPVs to be stored in Block 460. That is, the output risk measure .beta. stored in Block 480 is used to determine a new input risk measure .beta. for use to determine a new set of NPVs for ASSET 1 which will be stored in Block 380. Typically, the output risk measure .beta. stored in Block 480 will be combined with the previous risk measure .beta. (used to determine the previous set of NPVs of Block 380), so that the process may determine a revised NPV 0, and NPV 1 through NPV n for ASSET 1. Similarly, the output risk measure .beta. for ASSET 2 in Block 490 is used, in combination with the previous risk measure .beta. for ASSET 2, to determine a revised NPV 0, and NPV 1 through NPV n for ASSET 2 which will be stored in Block 410; the output risk measure .beta. from Block 500 is used, in combination with the previous risk measure .beta. for ASSET i, to determine a revised NPV 0, and NPV 1 through NPV n for ASSET i which will be stored in Block 440.

Each time the process loops back, the information stored in Blocks 380 through 500 is revised and updated using the i new risk measures determined based on the previous i input risk measures used in Blocks 380 through 440 and the i output risk measures determined in Blocks 480 through 500. The process continues determining revised values for information stored in various memory blocks until: (1) the output risk measure from Block 480 approximates the input risk measure most recently used in Block 380 to determine NPV 0, NPV 1, and NPV n for asset 1; (2) the output risk measure from Block 490 approximates the input risk measure most recently used in Block 410 to determine NPV 0, NPV 1, and NPV n for asset 2; and (3) the output risk measure from Block 500 approximates the input risk measure most recently used in Block 440 to determine NPV 0, NPV 1, and NPV n for asset i.

Referring now to FIG. 4, the process of the present invention is described with respect to an implementation for bonds in greater detail than in FIG. 2, based on the flow of information described in FIG. 3. In Step 510 a starting date for the process is input as well as a set of parameters which dictate how selected sets of economic variables are to be used by the process. In FIGS. 1-5 and in subsequent FIGS. 6-8, revised sets of economic variables are assumed to have been determined at a point in time (both the initial set of cash flows, and the five revised sets of cash flows, were all valued as of Aug. 31, 1991). In contrast, the revised cash flows would have been valued as of a later date. For example, assume that the initial set of cash flows is determined as of a particular date, such as May 15, 1993. Additional revised sets of cash flows are determined as of Jun. 15, 1993, or one month later, so as to correspond with the 30-day period of risk-free Treasury bills.

As an alternative, Step 510 permits an analyst to determine revised sets of cash flows periodically or intermittently. For example the first revised set of economic variables, and associated set of cash flows and simulated returns, may be made as of one month (or one quarter) later, and a second revised set of economic variables and associated set of cash flows and simulated returns an additional month (or quarter) later. Typically, periods will be uniform, such as weekly, monthly, or quarterly. Analysts may differ on which method is superior, so the preferred embodiment of this claimed invention allows a choice of methods.

In the case of periodic simulated returns, Step 520 permits an analyst to use the same number of projected cash flows (such as twenty quarters) for each set of projected cash flows or fewer projected cash flows for the revised sets of cash flows. For example, if the asset is a company, and projected cash flows are revised quarterly, the first set of cash flows can be made for twenty quarters, while the second set of cash flows can be made for nineteen quarters, in which case both sets of cash flows end on the same date. Alternatively, the second set of projected cash flows can also be made for twenty quarters, in which case the second set of cash flows will extend one calendar quarter later than the first set of projected cash flows. As in the case of Step 510, the preferred embodiment allows an analyst to choose the method in Step 520 because analysts may express a preference for one method or the other. However, the preferred embodiment is probably point-in-time.

In Step 530 an analyst selects a risk-return type asset pricing model. Preferably this Step will allow a user to select one of a plurality of predetermined asset pricing models, such as the original Sharpe-Lintner asset pricing model, Ross' APT model, or a non-linear version of either of those models. Although such models may be implemented using a variety of conventional techniques, the selection in Step 530 will essentially involve selection of one of several sets of rules corresponding to the available asset pricing models. The selection may be made by selecting one of several models as prompted by computer system 1.

In Step 540 the user specifies (via entering data into computer system 1) the total number of sets of estimated economic variables to be used in the process of the invention. The minimum number of sets is two so that there may be at least one return determined for each asset. Preferably, however, a considerably larger number of sets of economic variables will be selected, which will likely provide better results from the process.

In Step 550 the user specifies the number and type of economic variables to be used. By way of example, in the case of bonds the proces