Investment portfolio construction method and system

• US 7,050,998 B1
• Filed: 09/27/2000
• Issued: 05/23/2006
• Est. Priority Date: 09/27/1999
• Status: Expired due to Fees

• Current Assignee: Financiometrics Incorporated
• Original Assignee: Financiometrics Incorporated
• Inventors: Kale, Jivendra K., Best, Michael J.
• Primary Examiner(s): Colbert, Ella
• Application Number:
  US09/672,116
• Time in Patent Office: 2,064 Days
• Field of Search: 705 35- 37, 705/1, 702180-182, 707/10, 707/104.1, 709/203, 709/219
• US Class Current: 705/36.00R
• CPC Class Codes: G06Q 40/00 Finance; Insurance; Tax strategies; Processing of corporate or income taxes
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or analysis

Abstract

A method and a system for the optimal allocation of investment funds to construct an investment portfolio by using a two-segment, risk-averse utility function, where the first segment is a log-utility function indicative of the portfolio holder'"'"'s utility for positive rates of return and reflects the portfolio holder'"'"'s desire for maximizing portfolio growth, and the second segment is a power-utility function with a zero or negative power indicative of the degree to which the portfolio holder is averse to losses. An optimization algorithm determines the optimal investment weights for the assets in the investment portfolio to maximize the portfolio'"'"'s expected utility, which is based on the two-segment utility function. A computer software includes modules for carrying out the optimization to determine the optimal investment weights for the assets and to thereby construct the investment portfolio. The computer software is in the form of codes executed by a processor.

Claims

1. A computer-implemented method of allocating investment funds to a plurality of assets to construct an investment portfolio having a utility defined by at least a first function U₁ for positive rates of returns and a second function U₂ for negative rates of returns, the computer-implemented method comprising:

selecting a plurality of assets in the portfolio; and

allocating the investment funds to the said plurality of assets to maximize an expected utility of the investment portfolio;

wherein the at least first function U₁ is a log-utility function wherein said log-utility function is at least characterized by the following;

U₁=1+ln(1+r) for r≧

0

where U₁ presents the portfolio'"'"'s utility to the portfolio holder, r represents the portfolio'"'"'s return, and 1n is a symbol for natural logarithm, and wherein the at least second function U₂ is a power-utility function wherein said power-utility function is at least characterized by the following;

$U_2=\frac{1}{Y}<br><br>\left[{\left(I+r\right)}^y+Y-L\right]<br><br><br><br><br><br>f<br><br><br><br>o<br><br><br><br>r<br><br><br><br>r<<br><br>0$

where U₂ represents the portfolio'"'"'s utility to the portfolio holder, r represents the portfolio'"'"'s return, and γ

represents the loss-aversion of the portfolio holder and has a value of less than or equal to 0.

2. The method of claim 1 wherein allocating the investment finds to the plurality of assets in the investment portfolio to maximize the expected utility of the portfolio further comprises:

determining an optimal investment weight for each one of the plurality of assets in the investment portfolio.

3. The method of claim 2 wherein determining an optimal investment weight for each one of the plurality of assets in the investment portfolio further comprises:

computing the investment portfolio'"'"'s return for each one s of the plurality of economic events in accordance with the following;

$r_s=\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br><br><br>w_i<br><br>r_{\mathrm{is}}$

where r_s corresponds to the portfolio'"'"'s return in economic event s, w_i corresponds to a weight of asset i in the portfolio, r_is corresponds to a return for asset i in economic event s;

i corresponds to an asset number varying from 1 to N, and wherein N corresponds to the number of assets from which the portfolio is selected;

computing U_s the utility of the portfolio for the portfolio return r_s in economic event s;

wherein U_s is the function U₁ for r_s≧

0, and U_s is the function U₂ for r_s<

0;

multiplying the utility of the portfolio computed for each economic event with the probability of the occurrence of that economic event thereby generating a plurality of values p_sU_s wherein U_s corresponds to the portfolio holder'"'"'s utility in the economic event s;

p_s corresponds to a probability of occurrence of the economic event s,

summing the values to compute an expected utility as defined below;

$E<br><br>\left(U\right)=\underset{s=1}{\overset{S}{\sum <br><br>}}<br><br><br><br>p_s<br><br>U_s$

where S corresponds to the number of possible economic events and s varies from 1 to S; and

optimizing the investment weight w_i for each of the N assets from which the portfolio is selected to maximize the portfolio'"'"'s expected utility E(U).

4. A computer system for allocating investment funds to a plurality of assets to construct an investment portfolio having a utility defined by at least a first function U₁ for positive rates of returns and a second function U₂ for negative rates of returns, the computer system comprising:

a processor; and

a memory coupled to the processor, said memory storing a plurality of code modules for execution by the processor, the plurality of code modules comprising;

a code module for selecting a plurality of assets in the portfolio; and

code modules for allocating the investment funds to the said plurality of assets to maximize an expected utility of the investment portfolio;

wherein the at least first function U₁ is a log-utility function wherein said log-utility function is at least characterized by the following;

U₁=1+ln(1+r) for r≧

0

where U₁ presents the portfolio'"'"'s utility to the portfolio holder, r represents the portfolio'"'"'s return, and 1n is a symbol for natural logarithm, and wherein the at least second function U₂ is a power-utility function wherein said power-utility function is at least characterized by the following;

$U_2=\frac{1}{Y}<br><br>\left[{\left(I+r\right)}^y+Y-L\right]<br><br><br><br><br><br>f<br><br><br><br>o<br><br><br><br>r<br><br><br><br>r<<br><br>0.$

where U₂ represents the portfolio'"'"'s utility to the portfolio holder, r represents the portfolio'"'"'s return, and γ

represents the loss-aversion of the portfolio holder and has a value of less than or equal to 0.

5. The computer system of claim 4 wherein the code modules for allocating the investment funds to the plurality of assets in the investment portfolio to maximize the expected utility of the portfolio further comprise:

code modules for determining an optimal investment weight for each one of the plurality of assets in the investment portfolio.

6. The computer system of claim 5, wherein the code modules for determining an optimal investment weight for each one of the plurality of assets in the investment portfolio further comprise:

code module for computing the investment portfolio'"'"'s return for each one s of the plurality of economic events in accordance with the following;

$r_s=\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br><br><br>w_i<br><br>r_{\mathrm{is}}$

where r_s corresponds to the portfolio'"'"'s return in economic event s, w_i corresponds to a weight of asset i in the portfolio, r_is corresponds to a return for asset i in economic event s;

i corresponds to an asset number varying from 1 to N, and wherein N corresponds to the number of assets from which the portfolio is selected;

code module for computing U_s the utility of the portfolio for the portfolio return r_s in economic event s;

wherein U_s is the function U₁ for r≧

0, and U_s is the function U₂ for r_s<

0;

code module for multiplying the utility of the portfolio computed for each one of the plurality of economic events with the probability of the occurrence of that economic event thereby generating a plurality of values p_sU_s wherein U_s corresponds to the portfolio holder'"'"'s utility in the economic event s;

p_s corresponds to a probability of occurrence of the economic event s;

code module for summing the values to compute an expected utility as defined below;

$E<br><br>\left(U\right)=\underset{s=1}{\overset{S}{\sum <br><br>}}<br><br><br><br>p_s<br><br>U_s$

where S corresponds to the number of possible economic events and s varies from 1 to S; and

code module for optimizing the investment weight w_i for each of the N assets from which the portfolio is selected to maximize the portfolio'"'"'s expected utility E(U).