Constant leverage synthetic assets

• US 20030225648A1
• Filed: 04/23/2003
• Published: 12/04/2003
• Est. Priority Date: 05/28/2002
• Status: Abandoned Application

• Current Assignee: Ronald Hylton
• Original Assignee: Ronald Hylton
• Inventors: Hylton, Ronald
• Application Number:
  US10/421,261
• Publication Number:
  US 20030225648A1
• Time in Patent Office: Days
• US Class Current: 705/35
• 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 of applying a substantially constant leverage to a value of a log-normal distributed asset includes providing an underlying log-normal distributed asset having an original volatility σ and an original yield q. The asset includes an associated value S denominated in a currency having an associated interest rate r. The method and system also include applying a leveraging factor L to produce a modified value, volatility and/or a modified yield.

Claims

1. A synthetic asset comprising a first underlying asset having a value S, wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L, where L is neither 0 nor 1 and L is substantially constant over a period of time.

4. The synthetic asset according to any of claims 1-3, wherein all underlying assets comprise a substantially log-normally distributed asset.

5. The synthetic asset according to claim 1, wherein the delta of the synthetic asset with regard to the underlying asset is substantially in accordance with the formula δ

=L*Z/S.

6. The synthetic asset according to claim 1, wherein the gamma of the synthetic asset with regard to the underlying asset is substantially in accordance with the formula γ

=L*(L−

1)*Z/S².

2. A synthetic asset comprising an underlying asset having a value S and a plurality of financial derivatives thereof, wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L, where L is neither 0 nor 1 and L is substantially constant over a period of time.

3. A synthetic asset comprising an underlying asset having a value S and a benchmark asset having a value of B, wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L/B^K, wherein neither L nor K is 0, the absolute value of either L or K differs from 1 and wherein L and K are substantially constant over a period of time.

7. A synthetic asset comprising at least one first underlying asset with value S and at least one financial derivative of the first underlying asset, wherein an instantaneous value of the synthetic asset is substantially in accordance with the formula Z=S^L, where L is substantially constant and is neither 0 nor 1.

9. The method according to claims 7 or 8, wherein the underlying asset comprises a substantially log-normally distributed asset.

8. A method of leveraging the value of an asset comprising:

providing an underlying asset having a value S;

selecting a substantially constant leveraging factor L; and

associating an instantaneous value Z to the asset substantially in accordance with the formula Z=S^L, where L is neither 0 nor 1.

10. A method of creating a synthetic asset based upon applying a substantially constant leverage to the value of an asset comprising:

providing an underlying asset having an associated value S; and

applying a substantially constant leveraging factor L to the underlying asset to create a synthetic asset, wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L, wherein L is different from 0 and 1.

11. The method according to claim 10, wherein the synthetic asset comprises the underlying asset and a plurality of financial derivatives thereof.

12. A method of creating a synthetic asset based upon applying substantially constant leverages to the values of a pair of assets comprising:

providing a first underlying asset, wherein the first asset includes an associated value S;

providing an underlying benchmark asset, wherein the benchmark asset includes an associated value B; and

applying a substantially constant leveraging factor L to the first asset and a substantially constant negative leveraging factor K to the benchmark asset to create a synthetic asset, wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L/B^K, wherein neither L nor K is 0 and wherein the absolute value of either L or K differs from 1.

13. The method according to claim 12, wherein one or both underlying assets comprise a substantially log-normally distributed asset.

14. The method according to claim 12, wherein the delta of the synthetic asset with regard to the first asset is substantially in accordance with the formula δ

=L* Z/S.

15. The method according to claim 12, wherein the gamma of the synthetic asset with regard to the first asset is substantially in accordance with the formula γ

=L* (L−

1)*Z/S².

16. The method according to claim 12, wherein the delta of the synthetic asset with regard to the benchmark asset is substantially in accordance with the formula δ

=−

K*Z/B.

17. The method according to claim 12, wherein the gamma of the synthetic asset with regard to the benchmark asset is substantially in accordance with the formula γ

=K*(K+1)* Z/B².

18. The method according to claim 12, wherein the cross-gamma of the synthetic asset with regard to the first asset and the benchmark asset is substantially in accordance with the formula γ

=(−

L*K*Z)/(S*B).

19. A method of investing comprising:

providing an account having an amount of cash deposited therein by holder of the account;

allocating a portion of the cash for investing into at least one synthetic asset based on an underlying asset, wherein the underlying asset includes a value S; and

purchasing at least one synthetic asset with at least a portion of the allocated cash, wherein the synthetic asset includes an instantaneous value substantially in accordance with the formula Z=S^L, wherein L comprises a substantially constant leveraging factor which is neither 0 nor 1.

20. The method according to claim 19, further comprising selecting the value L.

21. The method according to claim 19, wherein the synthetic asset comprises a plurality of financial instruments

22. The method according to claim 21, wherein the plurality of financial instruments includes at least one of:

the underlying asset, one or more derivatives of the underlying asset and one or more cash equivalents.

23. The method according to claim 19, further comprising paying a commission proportional to the magnitude of the initial leverage L.

24. The method according to claim 19, further comprising paying an account fee.

25. The method according to claim 19, wherein the account is adjusted an amount corresponding to the cost or yield for the leverage over a time period.

26. The method according to claim 19, wherein the account is adjusted an amount corresponding to a dividend paid by the underlying asset.

27. The method according to claim 19, further comprising changing the leverage of the synthetic asset to a second leverage.

28. The method according to claim 27, wherein upon changing the leverage, the method further comprises paying a commission proportional to the magnitude of the change in leverage.

29. The method according to claim 28, wherein the commission comprises a higher amount for an immediate execution of the change in leverage.

30. The method according to claim 19, wherein leverage values are selected from a discrete set of predetermined values.

31. The method according to claim 27, wherein the second leverage value is selected from a discrete set of predetermined values.

32. The method according to claim 19, further comprising automatically adjusting the leverage value based upon a predetermined rule.

33. The method according to claim 32, wherein the predetermined rule comprises increasing the leverage in an upward moving market.

34. The method according to claim 32, wherein the predetermined rule comprises decreasing the leverage in a downward moving market.

35. The method according to claim 33, wherein the upward moving market comprises an upward moving market index.

36. The method according to claim 34, wherein the downward moving market comprises a downward moving market index.

37. The method according to claim 32, wherein the predetermined rule comprises a predetermined event.

38. The method according to claim 32, wherein the predetermined rule comprises liquidating a portion of the synthetic asset upon S substantially reaching a threshold.

39. The method according to claim 38, wherein liquidating comprises reducing the leverage L to 1 when L is greater than 1.

40. The method according to claim 38, wherein upon L being initially less than 0, liquidating comprises setting L to 0.

41. The method according to claim 38, wherein upon L being initially between 0 and 1, liquidating comprises setting L to 0 upon L being within a predetermined first range of values between approximately 0 and 1, and setting L to 1 upon L being within a predetermined second range of values between approximately 0 and 1.

42. The method according to claim 19, wherein the underlying asset is selected from the group consisting of:

stocks, equity indices, other log normally distributed indices, currency exchange rates, precious metals, commodities, bond prices and baskets of the preceding.

43. The method according to claim 19, wherein the cost or yield associated with the leverage is periodically adjusted.

44. The method according to claim 19, wherein the cost or yield associated with the leverage is periodically adjusted based upon a total demand in the underlying asset.

45. A synthetic asset comprising a first underlying asset having a value S and being leveraged by a substantially constant value L, wherein an instantaneous value of the synthetic asset is substantially in accordance with the formula Z=S^L, where L is neither 0 nor 1, and wherein the leverage is automatically increased in an upward moving market and automatically decreased in a downward moving market.

46. A method of creating a substantially log-normally distributed synthetic asset based upon applying substantially constant leverage to a value of a substantially log-normally distributed underlying asset comprising:

providing an underlying substantially log-normally distributed asset having an original volatility σ and

an original yield q, wherein the asset includes an associated value S and interest rate r;

applying a substantially constant leveraging factor L, which is neither 0 nor 1, to the asset to produce;

a modified volatility σ

_Z for the synthetic asset substantially in accordance with the formula σ

_Z=L σ

, and

a modified yield q_Z for the synthetic asset substantially in accordance with the formula q_Z=L q+(1−

L)r −

½

L(L−

1)σ

²,

wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L.

47. The method according to claim 46, wherein q_Z is maximized upon L being substantially equal to (½

−

(r−

q)/σ

²).

48. The method according to claim 46, wherein the contribution of volatility to q_Z is maximized upon L being substantially equal to about ½

.

49. A method of creating a substantially log-normally distributed synthetic asset based upon applying substantially constant leverages to values of a pair of substantially log-normally distributed assets, comprising:

providing a first underlying substantially log-normally distributed asset having an original volatility σ

_S and an original yield q_S, wherein the first asset includes an associated value S in a currency having an interest rate r;

providing an underlying substantially log-normally distributed benchmark asset having an original volatility σ

_B and an original yield q_B, wherein the benchmark asset includes an associated value B in the same currency;

providing a correlation factor ρ

between the first asset and the benchmark asset; and

applying a substantially constant leveraging factor L to the first asset and a substantially constant negative leveraging factor K to the benchmark asset to produce;

a modified volatility σ

_Z for the synthetic asset substantially in accordance with the formula

σ

_Z={(L²*σ

²_S)+(K²*σ

²_B)−

(2*L*K*ρ

*σ

_S*σ

_B)}^1/2, and

a modified yield q_Z for the synthetic asset substantially in accordance with the formula

q_Z=(L*q_S)−

(K*q_B)+((1+K−

L)*r)−

(½

*L*(L−

1)* σ

²_S)−

(½

*K*(K+1)* σ

²_B)+(L*K*ρ

*σ

_S*σ

_B)

wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L/B^K, wherein neither L nor K is 0 and the absolute value of either L or K differs from 1.

50. The method according to claim 49, wherein a correlation factor ρ

_Z between the synthetic asset and the benchmark asset is substantially in accordance with the formula ρ

_Z=(Lρ

σ

_S−

Kν

_B)/σ

_Z.

51. The method according to claim 49, wherein the yield q_Z is substantially maximized when L and K are substantially in accordance with the following respective formulas:

52. The method according to claim 49, wherein the yield q_Z is substantially maximized for a substantially fixed L upon K being substantially in accordance with the formula:

53. The method according to claim 49, wherein the yield q_Z is substantially maximized for a substantially fixed K upon L being substantially in accordance with the formula:

54. The method according to claim 49, wherein the yield q_Z is substantially maximized upon L being substantially in accordance with the formula:

55. The method according to any of claims 51-54, wherein the portion of the yield q_Z due to correlation and volatility is maximized upon applying the method with the values of r, q_S and q_b being substantially equal to zero.

56. The method according to claim 49, wherein the benchmark asset is selected from the group consisting of:

major indices and sector indices.

57. A system for leveraging the value of an asset comprising:

a computer system in communication with a computer network, wherein the computer system presents an underlying asset having a value S; and

input means for selecting a substantially constant leveraging factor L, wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L, wherein L is neither 0 nor 1.

58. The system according to claim 57, wherein the input means comprises at least one of:

a keyboard, a microphone, a mouse, a trackpad, a touchscreen, a bar-code reader, a data file and a database.

59. A system for creating a synthetic asset based upon applying substantially constant leverages to the values of a pair of assets comprising:

a computer system in communication with a computer network, the computer system for presenting a first underlying asset, wherein the first asset includes an associated value S, and for presenting an underlying benchmark asset, wherein the benchmark asset includes an associated value B; and

input means for selecting a substantially constant leveraging factor L for the first asset and a substantially constant negative leveraging factor K for the benchmark asset, and wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L/B^K, wherein neither L nor K is 0 and the absolute value of either L or K differs from 1.

60. The system according to claim 59, wherein the input means comprises at least one of:

a keyboard, a microphone, a mouse, a trackpad, a touchscreen, a bar-code reader, a data file and a database.

61. A system for investing in an asset comprising:

a computer system in communication with a computer network, the computer system for presenting and/or interacting with an account having an amount of cash deposited therein by holder of the account; and

input means for allocating a portion of the cash for investment into at least one synthetic asset based on an underlying asset and/or for selecting a substantially constant leverage value L which is neither 0 nor 1, wherein the underlying asset includes a value S, the synthetic asset is purchased with at least a portion of the allocated cash, and the synthetic asset includes an instantaneous value substantially in accordance with the formula Z=S^L.

62. The system according to claim 61, wherein the input means comprises at least one of:

a keyboard, a microphone, a mouse, a trackpad, a touchscreen, a bar-code reader, a data file and a database.

63. A system for investing in an asset comprising:

a computer system in communication with a computer network, the computer system for presenting and/or interacting with an account having an amount of cash deposited therein by holder of the account; and

input means for allocating a portion of the cash for investment into at least one synthetic asset based on an underlying asset and a benchmark asset, and/or for selecting substantially constant leverage factors, wherein the underlying asset includes a value S, the synthetic asset is purchased with at least a portion of the allocated cash, and the synthetic asset includes an instantaneous value substantially in accordance with the formula Z=S^L/B^K, wherein L is a substantially constant leverage factor, B is a value associated with the benchmark asset, and wherein K is a substantially constant negative leveraging factor, wherein neither L nor K is 0 and the absolute value of either L or K differs from 1.

64. A synthetic asset comprising a financial derivative of an underlying asset having a value S, wherein the synthetic asset includes a value at time t substantially in accordance with the formula Z=(S/S_BREAK-EVEN(t))^L, wherein L is a leverage value different from 0 and 1.

65. The synthetic asset according to claim 64, wherein S_BREAK-EVEN(t)=S₀e⁻

(y/L)(t−

T₀⁾.

66. A multi-period compound synthetic asset comprising an underlying asset and/or a financial derivative thereof, the underlying asset having a value S and being leveraged by a substantially constant value L during each period, wherein the return of the synthetic asset during each period is substantially in accordance with the difference between a second Z value of the synthetic asset at the end of the period and a first Z value at the beginning of the period divided by the first Z value, wherein Z is substantially in accordance with the formula Z=S^L, wherein the total return of the synthetic asset is the compounded return of the distinct periods, and where L is potentially neither 0 nor 1 in at least one period.

67. The multi-period synthetic asset according to claim 66, wherein L differs from period to period.

68. The multi-period synthetic asset according to claim 66, wherein the underlying asset S is selected in each period in accord with a predetermined rule and L is potentially different from 1 in at least one period.

69. The multi-period compound synthetic asset according to claim 66, wherein L is selected in each period in accord with a predetermined rule.

70. The multi-period synthetic asset according to claim 66, wherein the synthetic asset is used as an underlier in another financial derivative.

71. A multi-period synthetic asset comprising a pair of underlying assets, wherein the return of the synthetic asset during each period is substantially in accordance with the difference between a second value Z of the synthetic asset at the end of the period and a first value Z at the beginning of the period divided by the first value Z, wherein Z is substantially in accordance with the formula Z=S^L/B^K, wherein the total return of the synthetic asset is the compounded return of the distinct periods, wherein L is substantially constant during each period and may be different from 1 in one or more periods, and K is substantially constant during each period and may be different from 0 in one or more periods and wherein either or both of L and K may change in at least one period.

72. The multi-period synthetic asset according to claim 71, wherein the synthetic asset is used as an underlier in another financial derivative.

73. A method of managing an investment account comprising:

allocating an amount of cash in an investment account for purchasing one or more position in one or more underlying assets and/or derivatives thereof;

purchasing at least one such position for the account with the allocated cash; and

targeting a value Z of each position of the account substantially in accordance with the formula Z=A*S^L, wherein each value of S is substantially equal to the value of the corresponding underlying asset, L is a substantially constant leverage factor for the corresponding position, and wherein A is the number of units of the corresponding position.

74. The method according to claim 73, wherein targeting comprises:

determining a first delta value corresponding to a targeted value Z for a position in the account;

determining a second delta value of the holdings for the position; and

comparing the second delta value with the first delta value.

75. The method according to claim 74, wherein upon the second delta value being outside a predetermined range of the first delta value, the method further comprises purchasing positions in the corresponding underlying asset and/or derivatives thereof to produce a third delta value of the position, wherein the third delta value is within the predetermined range.

76. The method according to claim 73, wherein the leverage changes according to a predetermined rule.

77. A method of managing an investment account comprising:

allocating an amount of cash in an investment account for purchasing one or more positions in one or more underlying target or benchmark assets and/or derivatives thereof;

purchasing at least one such position for the account with the allocated cash; and

targeting a value Z of each position of the account substantially in accordance with the formula Z=A*S^L/B^K, wherein S is substantially equal to the value of a corresponding target asset, L is a substantially constant leverage factor for the corresponding target asset, A is the number of units of the corresponding position, B is the value of a corresponding benchmark asset and wherein K is a substantially constant negative leverage factor for the benchmark asset.

78. The method according to claim 77, wherein at least one of the leverages change according to a predetermined rule.

79. The method according to claim 77, wherein targeting comprises:

determining a first delta value corresponding to a targeted value Z for a position in the account;

determining a second delta value of the holdings for the position; and

comparing the second delta value with the first delta value.

80. The method according to claim 79, wherein upon the second delta value being outside a predetermined range of the first delta value, the method further comprises purchasing positions in the corresponding underlying target or benchmark asset and/or derivatives thereof to produce a third delta value of the position, wherein the third delta value is within the predetermined range.

81. A computer readable medium including computer instructions provided thereon for enabling a computer system to perform a method of leveraging the value of an asset, the method comprising:

providing an underlying asset having a value S;

selecting a substantially constant leveraging factor L which is neither 0 nor 1; and

associating an instantaneous value Z to the leveraged asset substantially in accordance with the formula Z=S^L.

82. A computer application program operational on a computer system for performing a method of leveraging the value of an asset, the method comprising:

providing an underlying asset having a value S;

selecting a substantially constant leveraging factor L which is neither 0 nor 1; and

associating an instantaneous value Z to the leveraged asset substantially in accordance with the formula Z=S^L.

83. A computer readable medium having computer instructions provided thereon for enabling a computer system to perform a method of creating a synthetic asset based upon applying substantially constant leverages to the values of a pair of assets, the method comprising:

providing a first underlying asset, wherein the first asset includes an associated value S;

providing an underlying benchmark asset, wherein the benchmark asset includes an associated value B;

applying a substantially constant leveraging factor L to the first asset; and

applying a substantially constant negative leveraging factor K to the benchmark asset, wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L/B^K, wherein neither L nor K is 0 and wherein the absolute value of either L or K differs from 1.

84. A computer application program operational on a computer system for performing a method of creating a synthetic asset based upon applying substantially constant leverages to the values of a pair of assets, the method comprising:

providing a first underlying asset, wherein the first asset includes an associated value S;

providing an underlying benchmark asset, wherein the benchmark asset includes an associated value B; and

applying a substantially constant leveraging factor L to the first asset;

applying a substantially constant negative leveraging factor K to the benchmark asset, wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L/B^K, wherein neither L nor K is 0 and wherein the absolute value of either L or K differs from 1.

85. A computer readable medium having computer instructions provided thereon for enabling a computer system to perform a method of investing in an asset, the method comprising:

providing an account having an amount of cash deposited therein by holder of the account;

allocating a portion of the cash for investing into at least one synthetic asset based on an underlying asset, wherein the underlying asset includes a value S; and

purchasing the synthetic asset with at least a portion of the allocated cash, wherein the synthetic asset includes an instantaneous value substantially in accordance with the formula Z=S^L where L is a substantially constant leverage factor which is neither 0 nor 1.

86. A computer application program operational on a computer system for performing a method of investing in an asset, the method comprising:

providing an account having an amount of cash deposited therein by holder of the account;

allocating a portion of the cash for investing into at least one synthetic asset based on an underlying asset, wherein the underlying asset includes a value S; and

purchasing the synthetic asset with at least a portion of the allocated cash, wherein the synthetic asset includes an instantaneous value substantially in accordance with the formula Z=S^L, wherein L is a substantially constant leverage value which is neither 0 nor 1.

87. A computer readable medium having computer instructions provided thereon for enabling a computer system to perform a method of creating a substantially log-normally distributed synthetic asset based upon applying substantially constant leverage to a value of a substantially log-normally distributed asset, the method comprising:

providing an underlying substantially log-normally distributed asset having an original volatility σ and

an original yield q, wherein the asset includes an associated value S and interest rate r; and

applying a substantially constant leveraging factor L to the asset to produce;

a modified volatility σ

_Z for the synthetic asset substantially in accordance with the formula σ

_Z=L σ

, and

a modified yield q_Z for the synthetic asset substantially in accordance with the formula q_Z=L q+(1−

L)r −

½

L (L−

1) σ

²,

wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L, wherein L is neither 0 nor 1.

88. A computer application program operational on a computer system for performing a method of creating a substantially log-normally distributed synthetic asset based upon applying substantially constant leverage to a value of a substantially log-normally distributed asset, the method comprising:

providing an underlying substantially log-normally distributed asset having an original volatility σ and

an original yield q, wherein the asset includes an associated value S and interest rate r; and

applying a substantially constant leveraging factor L to the asset which is neither 0 nor 1 to produce;

a modified volatility σ

_Z for the synthetic asset substantially in accordance with the formula σ

_Z=L σ

, and

a modified yield q_Z for the synthetic asset substantially in accordance with the formula q_Z=L q+(1−

L) r−

½

L (L−

1) σ

²,

wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L.

89. A computer readable medium having computer instructions provided thereon for enabling a computer system to perform a method of creating a substantially log-normally distributed synthetic asset based upon applying substantially constant leverages to values of a pair of substantially log-normally distributed assets, the method comprising:

providing a first underlying substantially log-normally distributed asset having an original volatility σ

_S and an original yield q_S, wherein the first asset includes an associated value S in a currency having an interest rate r;

providing an underlying substantially log-normally distributed benchmark asset having an original volatility σ

_B and an original yield q_B, wherein the benchmark asset includes an associated value B in the same currency; and

providing a correlation factor ρ

between the first asset and the benchmark asset;

applying a substantially constant leveraging factor L to the first asset and a substantially constant negative leveraging factor K to the benchmark asset to produce;

a modified volatility σ

_Z for the synthetic asset substantially in accordance with the formula

σ

_Z={(L²*σ

²_S)+(K²*σ

²_B)−

(2*L*K*ρ

*σ

_S*σ

_B)}^1/2, and

a modified yield q_Z for the synthetic asset substantially in accordance with the formula

q_Z=(L*q_S)−

(K*q_B)+((1+K−

L)*r)−

(½

*L*(L−

1)* σ

²_S)−

(½

*K*(K+1)* σ

²_B)+(L*K*ρ

*σ

_S*σ

_B)

wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L/B^K, wherein neither L nor K is 0 and wherein the absolute value of either L or K differs from 1.

90. A computer application program operational on a computer for performing a method of creating a substantially log-normally distributed synthetic asset based upon applying substantially constant leverages to values of a pair of substantially log-normally distributed assets, the method comprising:

providing a first underlying substantially log-normally distributed asset having an original volatility σ

_S and an original yield q_S, wherein the first asset includes an associated value S in a currency having an interest rate r;

providing an underlying substantially log-normally distributed benchmark asset having an original volatility σ

_B and an original yield q_B, wherein the benchmark asset includes an associated value B in the same currency;

providing a correlation factor p between the first asset and the benchmark asset; and

applying a substantially constant leveraging factor L to the first asset and a substantially constant negative leveraging factor K to the benchmark asset to produce;

a modified volatility σ

_Z for the synthetic asset substantially in accordance with the formula

σ

_Z={(L²*σ

²_S)+(K²*σ

²_B)−

(2*L*K*ρ

*σ

_S*σ

_B)}^1/2, and

a modified yield q_Z for the synthetic asset substantially in accordance with the formula

q_Z=(L*q_S)−

(K*q_B)+((1+K−

L)*r)−

(½

*L*(L−

1)* σ

²_S)−

(½

*K*(K+1)*σ

²_B)+(L*K*ρ

*σ

_S*σ

_B)

wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L/B^K, wherein neither L nor K is 0 and wherein the absolute value of either L or K differs from 1.

91. A computer readable medium having computer instructions provided thereon for enabling a computer system to perform a method of managing an investment account, the method comprising:

allocating an amount of cash in an investment account for purchasing one or more positions in one or more underlying assets and/or derivatives thereof;

purchasing at least one such position for the account with the allocated cash; and

targeting a value Z of each position substantially in accordance with the formula Z=A*S^L, wherein S is substantially equal to the value of the corresponding underlying asset, L is a substantially constant leverage value of the corresponding position and wherein A is a number of units of the corresponding position.

92. The computer readable medium according to claim 91, wherein targeting comprises:

determining a first delta value corresponding to the targeted value Z for a position in the account,

determining a second current delta value of the holdings for the position, and

comparing the second delta value with the first delta value, and wherein

upon the second delta value being outside a predetermined range of the first delta value, the method further comprises purchasing positions in the underlying asset and/or derivatives thereof to produce a third delta value of the position, wherein the third delta value is within the predetermined range.

93. A computer application program operational on a computer for performing a method of managing an investment account, the method comprising:

allocating an amount of cash in an investment account for purchasing one or more positions in one or more underlying assets and/or derivatives thereof,

purchasing at least one such position for the account with the allocated cash; and

targeting a value Z of each position of the account substantially in accordance with the formula Z=A*S^L, wherein S is substantially equal to the value of the corresponding underlying asset and L is a substantially constant leverage value of the corresponding position and A is a number of synthetic units of the corresponding position.

94. The computer application program according to claim 93, wherein targeting comprises:

determining a first delta value corresponding to the targeted value Z for a position in the account,

determining a second current delta value of the holdings for the position, and

comparing the second delta value with the first delta value, and wherein

upon the second delta value being outside a predetermined range of the first delta value, the method further comprises purchasing positions in the underlying asset and/or derivatives thereof to produce a third delta value of the position, wherein the third delta value is within the predetermined range.

95. A system for managing an investment account comprising:

a computer system in communication with a computer network for presenting and/or interacting with an investment account; and

input means for allocating an amount of cash of the investment account for purchasing a position in one or more underlying assets or derivatives thereof and/or for selecting a leveraging value and for purchasing at least one position for the account in at least one asset with the allocated cash, wherein a value Z of each position of the account is targeted substantially in accordance with the formula Z=A*S^L, wherein each value of S is substantially equal to the value of the corresponding underlying asset and L is a substantially constant leverage value for the corresponding position and A is a number of units of the corresponding position.

96. A computer readable medium having computer instructions provided thereon for enabling a computer to perform a method of managing an investment account, the method comprising:

allocating an amount of cash in an investment account for purchasing one or more position in one or more underlying target or benchmark assets and/or derivatives thereof,

purchasing at least one such position for the account with the allocated cash; and

targeting a value Z of each position of the account substantially in accordance with the formula Z=A*S^L/B^K, wherein S is substantially equal to the value of the corresponding target asset, L is a substantially constant leverage value of the corresponding target asset, A is a number of units of the corresponding position and wherein B is the value of a corresponding benchmark asset and K is a substantially constant negative leveraging factor for the corresponding benchmark asset.

97. The computer readable medium according to claim 96, wherein targeting comprises:

determining a first delta value corresponding to a targeted value Z for a position in the account;

determining a second delta value of the holdings for the position, and

comparing the second delta value with the first delta value, wherein upon the second delta value being outside a predetermined range of the first delta value, the method further comprises purchasing positions in the corresponding target or benchmark assets and/or derivatives thereof to produce a third delta value of the position, and wherein the third delta value is within the predetermined range.

98. A computer application program operational on a computer system for performing a method of managing an investment account, the method comprising:

allocating an amount of cash in an investment account for purchasing one or more positions in one or more underlying target or benchmark assets;

purchasing at least one such position for the account with the allocated cash; and

targeting a value Z of each position of the account substantially in accordance with the formula Z=A*S^L/B^K wherein each value of S is substantially equal to the value of the corresponding target asset, L is a substantially constant leverage value associated with the corresponding target asset, A is a number of units of the corresponding position and wherein B is

the value of a corresponding underlying benchmark asset and K is a substantially constant negative leveraging factor for the corresponding benchmark asset.

99. The computer application program according to claim 98, wherein targeting comprises:

determining a first delta value corresponding to a targeted value Z for the position;

determining a second delta value of the holdings for the position, and

comparing the second delta value with the first delta value, wherein upon the second delta value being outside a predetermined range of the first delta value, the method further comprises purchasing positions in the corresponding target or benchmark asset and/or derivatives thereof to produce a third delta value of the position, and wherein the third delta value is within the predetermined range.

100. A system for performing a method of managing an investment account comprising:

a computer system in communication with a computer network for presenting and/or interacting with an investment account for purchasing one or more positions in one or more underlying target or benchmark assets or derivatives thereof; and

input means for allocating an amount of cash for purchasing such a position and/or for selecting leverage factors and for purchasing at least one such position for the account with the allocated cash, wherein a value Z of each position of the account is targeted substantially in accordance with the formula Z=A*S^L/B^K, wherein S is substantially equal to the value of a corresponding target asset, L is a substantially constant leverage value of the corresponding target asset, A is a number of units of the corresponding position, B is the value of the corresponding underlying benchmark asset, and

K is a substantially constant negative leverage value associated with the corresponding benchmark asset.

101. The system according to claim 100, wherein targeting comprises:

determining a first delta value corresponding to a targeted value Z for the position and determining a second delta value of the holdings in the position,

comparing the second delta value with the first delta value, wherein upon the second delta value being outside a predetermined range of the first delta value, and

purchasing positions in the corresponding underlying target or benchmark asset and/or derivatives thereof to produce a third delta value of the position, and wherein the third delta value is within the predetermined range.

102. A method of delta-hedging a synthetic asset substantially in accordance with the formula δ

=L*(Z/S), wherein the synthetic asset comprises a first underlying asset having a value S, wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L, where L is neither 0 nor 1 and L is substantially constant over a period of time.

103. A method of delta-hedging a synthetic asset substantially in accordance with the formula δ

=L*(Z/S), wherein the synthetic asset comprises at least one underlying asset having a value S and at least one financial derivatives thereof, wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=S^L, where L is neither 0 nor 1 and L is substantially constant over a period of time.