ASSET ALLOCATION BASED ON EXPECTED UTILITY OF TIME AND WEALTH

• US 20100017342A1
• Filed: 07/01/2009
• Published: 01/21/2010
• Est. Priority Date: 07/01/2008
• Status: Active Grant

• Current Assignee: Penn State Research Foundation (Pennsylvania State University)
• Original Assignee: Penn State Research Foundation (Pennsylvania State University)
• Inventors: BOSCALJON, Brian
• Granted Patent: US 8,239,307 B2
• Time in Patent Office: Days
• US Class Current: 705/36.R
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or analysis

Abstract

A method and system for providing financial advice to individuals that includes outputting a target asset allocation for an individual and a critical wealth, a retirement wealth, a utility function, or a combination thereof. The target asset allocation includes a target securities allocation and is computed using a function analyzing a trade-off between retirement time and retirement consumption of the individual. The method includes computing a critical wealth of the individual, a retirement wealth of the individual, and a wealth utility function of the individual. A determination of whether the individual is in a wealth maximizing phase or a critical wealth phase is made. The determination is based on whether the individual has a current wealth equal to or greater than the calculated critical wealth threshold. Having determined the relevant wealth phase, a target asset allocation for the current assets of the individual is computed.

Claims

1. A method of providing financial advice to an individual, comprising:

computing a utility function, a critical wealth and a retirement wealth of an individual,

determining whether said individual is in a wealth maximizing phase or a critical wealth phase, said determining step comprising,

categorizing said individual in a wealth maximizing phase if said individual has a current wealth equal to or greater than said critical wealth, and

categorizing said individual in a critical wealth phase if said individual has a current wealth less than said critical wealth;

computing a target asset allocation for a current wealth of said individual; and

outputting said target asset allocation for said individual and at least one of said critical wealth, said retirement wealth, and said utility function, wherein said target asset allocation is computed using a function analyzing a trade-off between retirement time and retirement consumption of said individual, said target asset allocation comprising a target securities allocation.

2. The method according to claim 1, wherein computing said utility function comprising calculating:

$T<br><br><br><br>U<br><br>\left(W\right)=C<br><br>\left[T-\frac{\ln <br><br>\left(\mathrm{rTW}+S\right)-\ln <br><br>\left(\mathrm{rW}+S\right)}{\ln <br><br>\left(1+r\right)}\right]$

wherein;

TU(W)=time utility as a function of wealth,

C=target annual consumption during retirement,

T=remaining life span, i.e., life expectancy less the current age

r=estimated total annual return on investments,

TW=retirement wealth,

S=annual savings, and

W=current wealth.

3. The method according to claim 1, further comprising:

electronically monitoring an index of volatility of a stock index; and

advising said individual of a modified target securities allocation when said index crosses a pre-determined level, wherein said modified target securities allocation is

0% if said index exceeds said pre-determined level, and

said target securities allocation if said index is equal to or less than said pre-determined level for at least a pre-determined period of time.

4. The method according to claim 1, wherein said computing a target asset allocation step comprises:

assigning a wealth maximizing asset allocation as said target asset allocation if said individual is in a wealth maximizing phase, and

assigning to said target asset allocation a securities % as a target percentage of said current wealth invested in securities, if said individual is in a critical wealth phase, wherein

$\mathrm{Securities}<br><br><br><br>\%=\mathrm{Min}<br><br><br><br>\%+\left(\mathrm{Max}<br><br><br><br>\%-\mathrm{Min}<br><br><br><br>\%\right)<br><br>\frac{{\left(\mathrm{TW}-W\right)}^2}{{\left(\mathrm{TW}-C<br><br><br><br>W\right)}^2}$

wherein;

Min %=target percentage of assets in equities during retirement,

Max %=target percentage of assets in equities during wealth maximizing phase,

TW=retirement wealth,

W=current wealth, and

CW=critical wealth.

5. The method according to claim 1, wherein computing said critical wealth comprises computing CW*, wherein

$C$



W * = Cr ln 

( 1 + r ) - S r

wherein;

C=target annual consumption during retirement,

r=estimated total annual return on investments,

S=annual savings.

6. The method according to claim 1, wherein computing a retirement wealth comprises computing TW, wherein

TW=C/r_low

wherein:

C=target annual consumption during retirement, and

r_low=estimated total annual return on low risk investments.

7. The method according to claim 1, further comprising:

investing said current wealth according to said target asset allocation.

8. The method according to claim 1, further comprising:

computing a duration of said critical wealth phase, said critical wealth phase spanning a period starting when said current wealth equals or exceeds said critical wealth and ending when said current wealth equals or exceeds said retirement wealth,

said outputting step further comprising displaying said duration,

wherein computing said duration comprises computing t*;

$t^{*}=\frac{\ln <br><br>\left(\mathrm{rTW}+S\right)-\ln <br><br>\left(\mathrm{rW}+S\right)}{\ln <br><br>\left(1+r\right)}$

wherein;

r=estimated total annual return on investments,

TW=retirement wealth,

S=annual savings, and

W=current wealth.

9. The method according to claim 1,

(i) wherein computing said critical wealth comprises computing CW*, wherein

$C$



W * = Cr ln 

( 1 + r ) - S r

wherein;

C=target annual consumption during retirement,

r=estimated total annual return on investments,

S=annual savings; and

(ii) wherein computing a retirement wealth comprises computing TW, wherein

TW=C/r_low

wherein;

C=target annual consumption during retirement, and

r_low=estimated total annual return on low risk investments.

10. The method according to claim 9, further comprising:

electronically monitoring an index of volatility of a stock index; and

advising said individual of a modified target securities allocation when said index crosses a pre-determined level, wherein said modified target securities allocation is

0% if said index exceeds said pre-determined level, and

said target securities allocation if said index is equal to or less than said pre-determined level for at least 5 days.

11. The method according to claim 1,

(i) wherein said computing a target asset allocation step comprises:

assigning a wealth maximizing asset allocation as said target asset allocation if said individual is in a wealth maximizing phase, and

assigning to said target asset allocation a securities % as a target percentage of said current wealth invested in securities, if said individual is in a critical wealth phase, wherein

$\mathrm{Securities}<br><br><br><br>\%=\mathrm{Min}<br><br><br><br>\%+\left(\mathrm{Max}<br><br><br><br>\%-\mathrm{Min}<br><br><br><br>\%\right)<br><br>\frac{{\left(\mathrm{TW}-W\right)}^2}{{\left(\mathrm{TW}-C<br><br><br><br>W\right)}^2}$

wherein;

Min %=target percentage of assets in equities during retirement,

Max %=target percentage of assets in equities during wealth maximizing phase,

TW=retirement wealth,

W=current wealth, and

CW=critical wealth;

(ii) wherein computing said critical wealth comprises computing CW*, wherein

$C<br><br><br><br>W^{*}=\frac{\frac{\mathrm{Cr}}{\ln <br><br>\left(1+r\right)}-S}{r}$

wherein;

C=target annual consumption during retirement,

r=estimated total annual return on investments,

S=annual savings; and

(iii) wherein computing a retirement wealth comprises computing TW, wherein

TW=C/r_low

wherein;

C=target annual consumption during retirement, and

r_low=estimated total annual return on low risk investments.

12. The method according to claim 11, further comprising:

computing a duration of said critical wealth phase, said critical wealth phase spanning a period starting when said current wealth equals or exceeds said critical wealth and ending when said current wealth equals or exceeds said retirement wealth,

said outputting step further comprising displaying said duration,

wherein computing said duration comprises computing t*;

$t^{*}=\frac{\ln <br><br>\left(\mathrm{rTW}+S\right)-\ln <br><br>\left(\mathrm{rW}+S\right)}{\ln <br><br>\left(1+r\right)}$

wherein;

r=estimated total annual return on investments,

TW=retirement wealth,

S=annual savings, and

W=current wealth.

13. A system for providing financial advice to an individual, comprising:

at least one processor for executing processor-executable instructions for causing the system to compute a target asset allocation for an individual and at least one of a critical wealth of said individual, a retirement wealth of said individual, and a utility function;

a module on said at least one processor configured to execute instruction for computing at least one of a critical wealth of said individual, a retirement wealth of said individual, and a utility function of wealth of said individual;

a module on said at least one processor configured to execute instruction for determining whether said individual is in a wealth maximizing phase or a critical wealth phase, said determining step comprising,

categorizing said individual in a wealth maximizing phase if said individual has a current wealth equal to or greater than said critical wealth, and

categorizing said individual in a critical wealth phase if said individual has a current wealth less than said critical wealth;

a module on said at least one processor configured to execute instruction for computing a target asset allocation for a current wealth of said individual; and

a display device for outputting said target asset allocation for said individual and at least one of said critical wealth, said retirement wealth, and a plot of at least a portion of said utility function, wherein said target asset allocation is computed using a function analyzing a trade-off between retirement time and retirement consumption of said individual.

14. The system according to claim 13, wherein computing said utility function comprising calculating:

$T<br><br><br><br>U<br><br>\left(W\right)=C<br><br>\left[T-\frac{\ln <br><br>\left(\mathrm{rTW}+S\right)-\ln <br><br>\left(\mathrm{rW}+S\right)}{\ln <br><br>\left(1+r\right)}\right]$

wherein;

TU(W)=time utility as a function of wealth,

C=target annual consumption during retirement,

T=remaining life span, i.e., life expectancy less the current age

r=estimated total annual return on investments,

TW=retirement wealth,

S=annual savings, and

W=current wealth.

15. The system according to claim 13, wherein said module for computing a target asset allocation is configured for assigning a wealth maximizing asset allocation as said target asset allocation if said individual is in a wealth maximizing phase, and

assigning to said target asset allocation a securities % as a target percentage of said current wealth invested in securities, of said individual is in a critical wealth phase, wherein

$\mathrm{Securities}$



% = Min 



% + ( Max 



% - Min 



% ) 

( TW - W ) 2 ( TW - C 



W ) 2

wherein;

Min %=target percentage of assets in equities during retirement,

Max %=target percentage of assets in equities during wealth maximizing phase,

TW=retirement wealth,

W=current wealth, and

CW=critical wealth.

16. The system according to claim 13, wherein said module for computing said critical wealth is configured for computing CW*, wherein

$C$



W * = Cr ln 

( 1 + r ) - S r

wherein;

C=target annual consumption during retirement,

r=estimated total annual return on investments,

S=annual savings.

17. The system according to claim 13, wherein said module for computing said retirement wealth is configured for computing TW, wherein

TW=C/r_low

wherein:

C=target annual consumption during retirement, and

r_low=estimated total annual return on low risk investments.

18. The system according to claim 13, further comprising:

a module on said at least one processor configured to execute instruction for computing a duration of said critical wealth phase, said critical wealth phase spanning a period starting when said current wealth equals or exceeds said critical wealth and ending when said current wealth equals or exceeds said retirement wealth,

said display device for displaying said duration,

wherein computing said duration comprises computing t*;

$t^{*}=\frac{\ln <br><br>\left(\mathrm{rTW}+S\right)-\ln <br><br>\left(\mathrm{rW}+S\right)}{\ln <br><br>\left(1+r\right)}$

wherein;

r=estimated total annual return on investments,

TW=retirement wealth,

S=annual savings, and

W=current wealth.

19. The system according to claim 13,

(i) wherein said module for computing said critical wealth is configured for computing CW*, wherein

$C$



W * = Cr ln 

( 1 + r ) - S r

wherein;

C=target annual consumption during retirement,

r=estimated total annual return on investments,

S=annual savings; and

(ii) wherein said module for computing said retirement wealth is configured for computing TW, wherein

TW=C/r_low

wherein;

C=target annual consumption during retirement, and

r_low=estimated total annual return on low risk investments.

20. The system according to claim 19, further comprising:

a module on said at least one processor configured to execute instruction for computing a duration of said critical wealth phase, said critical wealth phase spanning a period starting when said current wealth equals or exceeds said critical wealth and ending when said current wealth equals or exceeds said retirement wealth,

said display device for displaying said duration,

wherein computing said duration comprises computing t*;

$t^{*}=\frac{\ln <br><br>\left(\mathrm{rTW}+S\right)-\ln <br><br>\left(\mathrm{rW}+S\right)}{\ln <br><br>\left(1+r\right)}$

wherein;

r=estimated total annual return on investments,

TW=retirement wealth,

S=annual savings, and

W=current wealth.