# US 8,751,357 B1 · Investment performance measurement

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- Number: US 8,751,357 B1
- Document ID: US8751357B1
- Status: Granted
- Kind: B1
- Application number: 13/398,244
- Filed: 2012-02-16
- Granted: 2014-06-10
- Earliest claimed: 2011-02-23
- Assignees: University Court of the University of St Andrews
- Applicants: Andreas G. F. Hoepner
- Inventors: Andreas G. F. Hoepner
- Web page: https://patentgrep.com/patent/US8751357B1

## CPC

- G06Q 40/06: Asset management; Financial planning or analysis
- G06Q 40/00: Finance; Insurance; Tax strategies; Processing of corporate or income taxes
- G06Q: INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR

## Abstract

Embodiments of the invention are directed to a system, method, or computer program product for evaluating risk adjusted performance of an investment portfolio. This invention may be applied to any asset which has a value. The invention evaluates risk adjusted performance of an investment portfolio by first determining at least one positive utility concept and at least one negative utility concept describing an asset. Then, the invention normalizes the at least one negative utility concept to an equivalent negative utility concept describing or deriving from a group of assets. Finally, the invention may relate at least one positive utility concept and at least one normalized negative utility concept to determine a performance measure. In this way, the invention normalized negative asset returns such that better investor utility ratings are not falsely provided.

## Claims

### Claim 1

A computer processor implemented method for measuring investment performance of asset A, wherein the computer processor is configured to execute stored computer-readable program code to:
determining at least one positive utility concept (PUC) describing the Asset A;
determining at least one negative utility concept (NUC) describing the Asset A;
normalizing the at least one negative utility concept (NUC) to an equivalent negative utility concept (GNUC) describing or deriving from a group of more than one Asset (N>1); and
relating a function of the at least one positive utility concept (PUC) and a function of the at least one normalized negative utility concept (NNUC) to determine a performance measure, wherein the step of relating involves division of the function of the at least one positive utility concept by the function of the at least one normalized negative utility concept or multiplication of the function of the at least one positive utility concept by an inverse function of the function of the at least one normalized negative utility concept or equivalent, so the performance measure is higher the lower the negative utility concept and lower the higher the negative utility concept for any non-zero positive utility concept value,
wherein the step of relating is done using the following relationship:
performance measure=fn1(PUC)−fn(fn2[mod(fn3(PUC))]fn4(NNUC))
where fn1 and fn3 are functions acting on the PUC; fn2 is a function acting on the modulus of (fn3(PUC)) and fn4 is a function acting on the NNUC, wherein fn is a function acting on fn2[mod(fn3(PUC))] and fn4(NNUC).

### Claim 2 (depends on 1)

A computer processor implemented method as claimed in claim 1 wherein fn2 is multiplication by 1 and the step of relating is done using the following relationship:
performance measure=fn1(PUC)−mod(fn3(PUC))·fn4(NNUC).

### Claim 3 (depends on 1)

A computer processor implemented method as claimed in claim 1 wherein the step of relating is done using the following relationship:
performance measure=fn1(PUC)−fn2[mod(fn3(PUC))][C1−C2/fn5(NNUC)]
where C1 and C2 are constants, and fn1-5 represent functions.

### Claim 4 (depends on 3)

A computer processor implemented method as claimed in claim 3 wherein the step of relating is done using the following relationship:
performance measure=fn1[PUC]+fn[mod(fn3(PUC))][1/fn5(NNUC)−1].

### Claim 5 (depends on 1)

A computer processor implemented method as claimed in claim 1 wherein the step of relating is done using the following relationship:
performance measure=fn1(PUC)+fn[mod(fn3PUC)][(fn(GNUC)−fn(NUC))/(fn(GNUC)+fn(NUC))].

### Claim 6

A computer processor implemented method for measuring investment performance of asset A, wherein the computer processor is configured to execute stored computer-readable program code to:
determining at least one positive utility concept (PUC) describing the Asset A;
determining at least one negative utility concept (NUC) describing the Asset A;
normalizing the at least one negative utility concept (NUC) to an equivalent negative utility concept (GNUC) describing or deriving from a group of more than one Asset (N>1); and
relating a function of the at least one positive utility concept (PUC) and a function of the at least one normalized negative utility concept (NNUC) to determine a performance measure, wherein the step of relating involves division of the function of the at least one positive utility concept by the function of the at least one normalized negative utility concept or multiplication of the function of the at least one positive utility concept by an inverse function of the function of the at least one normalized negative utility concept or equivalent, so the performance measure is higher the lower the negative utility concept and lower the higher the negative utility concept for any non-zero positive utility concept value,
wherein the step of relating is done using the following relationship:
performance measure=fn6PUC(fn7GNUC/fn8NUC)(fn9PUC/fn10mod PUC)
wherein fn6-10 are functions, and wherein the value of the performance measure is not equal to either 0 or 1.

### Claim 7

A computer processor implemented method for measuring investment performance of asset A, wherein the computer processor is configured to execute stored computer-readable program code to:
determining at least one positive utility concept (PUC) describing the Asset A;
determining at least one negative utility concept (NUC) describing the Asset A;
normalizing the at least one negative utility concept (NUC) to an equivalent negative utility concept (GNUC) describing or deriving from a group of more than one Asset (N>1); and
relating a function of the at least one positive utility concept (PUC) and a function of the at least one normalized negative utility concept (NNUC) to determine a performance measure, wherein the step of relating involves division of the function of the at least one positive utility concept by the function of the at least one normalized negative utility concept or multiplication of the function of the at least one positive utility concept by an inverse function of the function of the at least one normalized negative utility concept or equivalent, so the performance measure is higher the lower the negative utility concept and lower the higher the negative utility concept for any non-zero positive utility concept value,
wherein the step of relating is done using the following relationship:
performance measure=fn11[PUC(fn12GNUC/fn12NUC)((C3+1)fnPUC/fn mod PUC)−C4],
and wherein the value of the performance measure is not equal to either 0 or 1.

### Claim 8 (depends on 1)

A computer processor implemented method as claimed in claim 1 wherein the positive utility concept describes or is a function of the Asset A's return.

### Claim 9 (depends on 1)

A computer processor implemented method as claimed in claim 1 wherein the positive utility concept describes or is a function of Asset A's excess return over a risk free rate.

### Claim 10 (depends on 1)

A computer processor implemented method as claimed in claim 1 wherein the positive utility concept describes or is a function of Asset A's excess return over a risk free rate and the negative utility concept describes or is a function of Asset A's return deviation.

### Claim 11 (depends on 10)

A computer processor implemented method as claimed in claim 10 wherein the return deviation of the group of more than one Asset (N>1) is measured over the longest available sample period.

### Claim 12 (depends on 1)

A computer processor implemented method as claimed in claim 1 wherein the positive utility concept describes or is a function of Asset A's excess return over a risk free rate and the negative utility concept describes or is a function of Asset A's excess return standard deviation.

### Claim 13 (depends on 12)

A computer processor implemented method as claimed in claim 12 wherein the excess return standard deviation of the group of more than one Asset (N>1) is measured over the longest available sample period.

### Claim 14

An apparatus comprising:
a memory for storing at least one positive utility concept (PUC) describing Asset A and at least one negative utility concept (NUC) describing Asset A; and
a computer processor communicably coupled to the memory and configured to use the at least one positive utility concept (PUC) and at least one negative utility concept to:
normalize the at least one negative utility concept (NUC) to an equivalent negative utility concept (GNUC) describing or deriving from a group of more than one Asset (N>1); and
relate, using the computer processor, a function of the at least one positive utility concept (PUC) and a function of the at least one normalized negative utility concept (NNUC) to determine a performance measure, wherein the step of relating involves division of the function of the at least one positive utility concept by the function of the at least one normalized negative utility concept or multiplication of the function of the at least one positive utility concept by an inverse function of the function of the at least one normalized negative utility concept or equivalent, so the performance measure is higher the lower the at least one negative utility concept and lower the higher the at least one negative utility concept for any non-zero positive utility concept value,
wherein the relating is done using the following relationship:
performance measure=fn1(PUC)−fn(fn2[mod(fn3(PUC))]fn4(NNUC))
where fn1 and fn3 are functions acting on the PUC; fn2 is a function acting on the modulus of (fn3(PUC)) and fn4 is a function acting on the NNUC, wherein fn is a function acting on fn2[mod(fn3(PUC))] and fn4(NNUC).

### Claim 15

A computer program product comprising a non-transitory computer-readable medium, the non-transitory computer-readable medium comprising computer-executable program instructions stored therein, the computer-executable program instructions being configured for:
determining at least one positive utility concept (PUC) describing Asset A;
determining at least one negative utility concept (NUC) describing Asset A, wherein the negative utility concept is a function of a third or higher moment of the return distribution of Asset A, a non-linear function of the difference between the return of Asset A and the return of a market benchmark, a function describing a proportional relation between the return distribution of Asset A and the return distribution at least one related asset such as the market benchmark or a combination of the return distribution of Asset A and at least one other risk characteristics of Asset A; and
relating, using a computer processor, a function of the at least one positive utility concept (PUC) to a function of the at least one negative utility concept (NUC) to determine a performance measure, wherein the step of relating involves division of the function of the at least one positive utility concept by the function of the at least one negative utility concept or multiplication of the function of the at least one positive utility concept by an inverse function of the function of the at least one negative utility concept or equivalent, so the performance measure is higher the lower the risk and lower the higher the risk for any non-zero positive utility concept value,
wherein the relating is done using the following relationship:
performance measure=fn1(PUC)−fn(fn2[mod(fn3(PUC))]fn4(NNUC))
where fn1 and fn3 are functions acting on the PUC; fn2 is a function acting on the modulus of (fn3(PUC)) and fn4 is a function acting on the NNUC, wherein fn is a function acting on fn2[mod(fn3(PUC))] and fn4(NNUC).

### Claim 16 (depends on 15)

A computer program product as claimed in claim 15 wherein fn is multiplication of fn2[mod(fn3(PUC))] and fn4(NNUC).

### Claim 17 (depends on 15)

A computer program product as claimed in claim 15 wherein fn1 and fn3 are the same function.

### Claim 18 (depends on 1)

A computer processor implemented method as claimed in claim 1, wherein fn is multiplication of fn2[mod(fn3(PUC))] and fn4(NNUC).

### Claim 19 (depends on 1)

A computer processor implemented method as claimed in claim 1, wherein fn1 and fn3 are the same function.

### Claim 20 (depends on 6)

A computer processor implemented method as claimed in claim 6 wherein the positive utility concept describes or is a function of the Asset A's return.

### Claim 21 (depends on 6)

A computer processor implemented method as claimed in claim 6 wherein the positive utility concept describes or is a function of Asset A's excess return over a risk free rate.

### Claim 22 (depends on 6)

A computer processor implemented method as claimed in claim 6 wherein the positive utility concept describes or is a function of Asset A's excess return over a risk free rate and the negative utility concept describes or is a function of Asset A's return deviation.

### Claim 23 (depends on 22)

A computer processor implemented method as claimed in claim 22 wherein the return deviation of the group of more than one Asset (N>1) is measured over the longest available sample period.

### Claim 24 (depends on 6)

A computer processor implemented method as claimed in claim 6 wherein the positive utility concept describes or is a function of Asset A's excess return over a risk free rate and the negative utility concept describes or is a function of Asset A's excess return standard deviation.

### Claim 25 (depends on 24)

A computer processor implemented method as claimed in claim 24 wherein the excess return standard deviation of the group of more than one Asset (N>1) is measured over the longest available sample period.

### Claim 26 (depends on 7)

A computer processor implemented method as claimed in claim 7 wherein the positive utility concept describes or is a function of the Asset A's return.

### Claim 27 (depends on 7)

A computer processor implemented method as claimed in claim 7 wherein the positive utility concept describes or is a function of Asset A's excess return over a risk free rate.

### Claim 28 (depends on 7)

A computer processor implemented method as claimed in claim 7 wherein the positive utility concept describes or is a function of Asset A's excess return over a risk free rate and the negative utility concept describes or is a function of Asset A's return deviation.

### Claim 29 (depends on 28)

A computer processor implemented method as claimed in claim 28 wherein the return deviation of the group of more than one Asset (N>1) is measured over the longest available sample period.

### Claim 30 (depends on 7)

A computer processor implemented method as claimed in claim 7 wherein the positive utility concept describes or is a function of Asset A's excess return over a risk free rate and the negative utility concept describes or is a function of Asset A's excess return standard deviation.

### Claim 31 (depends on 30)

A computer processor implemented method as claimed in claim 30 wherein the excess return standard deviation of the group of more than one Asset (N>1) is measured over the longest available sample period.

### Claim 32 (depends on 14)

An apparatus as claimed in claim 14 wherein fn is multiplication of fn2[mod(fn3(PUC))] and fn4(NNUC).

### Claim 33 (depends on 14)

An apparatus as claimed in claim 14 wherein fn1 and fn3 are the same function.

### Claim 34

An apparatus comprising:
a memory for storing at least one positive utility concept (PUC) describing Asset A and at least one negative utility concept (NUC) describing Asset A; and
a computer processor communicably coupled to the memory and configured to use the at least one positive utility concept (PUC) and at least one negative utility concept to:
normalize the at least one negative utility concept (NUC) to an equivalent negative utility concept (GNUC) describing or deriving from a group of more than one Asset (N>1); and
relate, using the computer processor, a function of the at least one positive utility concept (PUC) and a function of the at least one normalized negative utility concept (NNUC) to determine a performance measure, wherein the step of relating involves division of the function of the at least one positive utility concept by the function of the at least one normalized negative utility concept or multiplication of the function of the at least one positive utility concept by an inverse function of the function of the at least one normalized negative utility concept or equivalent, so the performance measure is higher the lower the at least one negative utility concept and lower the higher the at least one negative utility concept for any non-zero positive utility concept value,
wherein the step of relating is done using the following relationship:
performance measure=fn6PUC(fn7GNUC/fn8NUC)(fn9PUC/fn10mod PUC)
wherein fn6-10 are functions, and wherein the value of the performance measure is not equal to either 0 or 1.

### Claim 35

A computer program product comprising a non-transitory computer-readable medium, the non-transitory computer-readable medium comprising computer-executable program instructions stored therein, the computer-executable program instructions being configured for:
determining at least one positive utility concept (PUC) describing Asset A;
determining at least one negative utility concept (NUC) describing Asset A, wherein the negative utility concept is a function of a third or higher moment of the return distribution of Asset A, a non-linear function of the difference between the return of Asset A and the return of a market benchmark, a function describing a proportional relation between the return distribution of Asset A and the return distribution at least one related asset such as the market benchmark or a combination of the return distribution of Asset A and at least one other risk characteristics of Asset A; and
relating, using a computer processor, a function of the at least one positive utility concept (PUC) to a function of the at least one negative utility concept (NUC) to determine a performance measure, wherein the step of relating involves division of the function of the at least one positive utility concept by the function of the at least one negative utility concept or multiplication of the function of the at least one positive utility concept by an inverse function of the function of the at least one negative utility concept or equivalent, so the performance measure is higher the lower the risk and lower the higher the risk for any non-zero positive utility concept value,
wherein the step of relating is done using the following relationship:
performance measure=fn6PUC(fn7GNUC/fn8NUC)(fn9PUC/fn10mod PUC)
wherein fn6-10 are functions, and wherein the value of the performance measure is not equal to either 0 or 1.

### Claim 36

An apparatus comprising:
a memory for storing at least one positive utility concept (PUC) describing Asset A and at least one negative utility concept (NUC) describing Asset A; and
a computer processor communicably coupled to the memory and configured to use the at least one positive utility concept (PUC) and at least one negative utility concept to:
normalize the at least one negative utility concept (NUC) to an equivalent negative utility concept (GNUC) describing or deriving from a group of more than one Asset (N>1); and
relate, using the computer processor, a function of the at least one positive utility concept (PUC) and a function of the at least one normalized negative utility concept (NNUC) to determine a performance measure, wherein the step of relating involves division of the function of the at least one positive utility concept by the function of the at least one normalized negative utility concept or multiplication of the function of the at least one positive utility concept by an inverse function of the function of the at least one normalized negative utility concept or equivalent, so the performance measure is higher the lower the at least one negative utility concept and lower the higher the at least one negative utility concept for any non-zero positive utility concept value,
wherein the step of relating is done using the following relationship:
performance measure=fn11[PUC(fn12GNUC/fn12NUC)((C3+1)fnPUC/fn mod PUC)−C4],
and wherein the value of the performance measure is not equal to either 0 or 1.

### Claim 37

A computer program product comprising a non-transitory computer-readable medium, the non-transitory computer-readable medium comprising computer-executable program instructions stored therein, the computer-executable program instructions being configured for:
determining at least one positive utility concept (PUC) describing Asset A;
determining at least one negative utility concept (NUC) describing Asset A, wherein the negative utility concept is a function of a third or higher moment of the return distribution of Asset A, a non-linear function of the difference between the return of Asset A and the return of a market benchmark, a function describing a proportional relation between the return distribution of Asset A and the return distribution at least one related asset such as the market benchmark or a combination of the return distribution of Asset A and at least one other risk characteristics of Asset A; and
relating, using a computer processor, a function of the at least one positive utility concept (PUC) to a function of the at least one negative utility concept (NUC) to determine a performance measure, wherein the step of relating involves division of the function of the at least one positive utility concept by the function of the at least one negative utility concept or multiplication of the function of the at least one positive utility concept by an inverse function of the function of the at least one negative utility concept or equivalent, so the performance measure is higher the lower the risk and lower the higher the risk for any non-zero positive utility concept value,
wherein the step of relating is done using the following relationship:
performance measure=fn11[PUC(fn12GNUC/fn12NUC)((C3+1)fnPUC/fn mod PUC)−C4],
and wherein the value of the performance measure is not equal to either 0 or 1.