Constant leverage synthetic assets
First Claim
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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=SL, where L is neither 0 nor 1 and L is substantially constant over a period of time.
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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.
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Citations
103 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=SL, where L is neither 0 nor 1 and L is substantially constant over a period of time.
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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=SL, where L is neither 0 nor 1 and L is substantially constant over a period of time.
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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=SL/BK, 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=SL, where L is substantially constant and is neither 0 nor 1.
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8. A method of leveraging the value of an asset comprising:
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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=SL, where L is neither 0 nor 1.
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10. A method of creating a synthetic asset based upon applying a substantially constant leverage to the value of an asset comprising:
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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=SL, wherein L is different from 0 and 1. - View Dependent Claims (11)
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12. A method of creating a synthetic asset based upon applying substantially constant leverages to the values of a pair of assets comprising:
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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=SL/BK, wherein neither L nor K is 0 and wherein the absolute value of either L or K differs from 1. - View Dependent Claims (13, 14, 15, 16, 17, 18)
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19. A method of investing comprising:
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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=SL, wherein L comprises a substantially constant leveraging factor which is neither 0 nor 1. - View Dependent Claims (20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44)
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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=SL, 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.
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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:
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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
, anda modified yield qZ for the synthetic asset substantially in accordance with the formula qZ=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=SL. - View Dependent Claims (47, 48)
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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:
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providing a first underlying substantially log-normally distributed asset having an original volatility σ
S and an original yield qS, 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 qB, 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 formulaσ
Z={(L2*σ
2S)+(K2*σ
2B)−
(2*L*K*ρ
*σ
S*σ
B)}1/2, anda modified yield qZ for the synthetic asset substantially in accordance with the formula qZ=(L*qS)−
(K*qB)+((1+K−
L)*r)−
(½
*L*(L−
1)* σ
2S)−
(½
*K*(K+1)* σ
2B)+(L*K*ρ
*σ
S*σ
B)wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=SL/BK, wherein neither L nor K is 0 and the absolute value of either L or K differs from 1. - View Dependent Claims (50, 51, 52, 53, 54, 55, 56)
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57. A system for leveraging the value of an asset comprising:
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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=SL, wherein L is neither 0 nor 1. - View Dependent Claims (58)
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59. A system for creating a synthetic asset based upon applying substantially constant leverages to the values of a pair of assets comprising:
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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=SL/BK, wherein neither L nor K is 0 and the absolute value of either L or K differs from 1. - View Dependent Claims (60)
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61. A system for investing in an asset comprising:
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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=SL. - View Dependent Claims (62)
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63. A system for investing in an asset comprising:
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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=SL/BK, 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.
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- 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/SBREAK-EVEN(t))L, wherein L is a leverage value different from 0 and 1.
- 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=SL, 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.
- 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=SL/BK, 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.
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73. A method of managing an investment account comprising:
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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*SL, 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. - View Dependent Claims (74, 75, 76)
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77. A method of managing an investment account comprising:
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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*SL/BK, 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. - View Dependent Claims (78, 79, 80)
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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:
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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=SL.
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82. A computer application program operational on a computer system for performing a method of leveraging the value of an asset, the method comprising:
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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=SL.
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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:
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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=SL/BK, wherein neither L nor K is 0 and wherein the absolute value of either L or K differs from 1.
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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:
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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=SL/BK, wherein neither L nor K is 0 and wherein the absolute value of either L or K differs from 1.
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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:
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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=SL where L is a substantially constant leverage factor which is neither 0 nor 1.
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86. A computer application program operational on a computer system for performing a method of investing in an asset, the method comprising:
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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=SL, wherein L is a substantially constant leverage value which is neither 0 nor 1.
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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:
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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
, anda modified yield qZ for the synthetic asset substantially in accordance with the formula qZ=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=SL, wherein L is neither 0 nor 1.
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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:
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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
, anda modified yield qZ for the synthetic asset substantially in accordance with the formula qZ=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=SL.
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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:
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providing a first underlying substantially log-normally distributed asset having an original volatility σ
S and an original yield qS, 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 qB, 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 formulaσ
Z={(L2*σ
2S)+(K2*σ
2B)−
(2*L*K*ρ
*σ
S*σ
B)}1/2, anda modified yield qZ for the synthetic asset substantially in accordance with the formula qZ=(L*qS)−
(K*qB)+((1+K−
L)*r)−
(½
*L*(L−
1)* σ
2S)−
(½
*K*(K+1)* σ
2B)+(L*K*ρ
*σ
S*σ
B)wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=SL/BK, wherein neither L nor K is 0 and wherein the absolute value of either L or K differs from 1.
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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:
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providing a first underlying substantially log-normally distributed asset having an original volatility σ
S and an original yield qS, 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 qB, 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 formulaσ
Z={(L2*σ
2S)+(K2*σ
2B)−
(2*L*K*ρ
*σ
S*σ
B)}1/2, anda modified yield qZ for the synthetic asset substantially in accordance with the formula qZ=(L*qS)−
(K*qB)+((1+K−
L)*r)−
(½
*L*(L−
1)* σ
2S)−
(½
*K*(K+1)*σ
2B)+(L*K*ρ
*σ
S*σ
B)wherein an instantaneous value Z of the synthetic asset is substantially in accordance with the formula Z=SL/BK, wherein neither L nor K is 0 and wherein the absolute value of either L or K differs from 1.
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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:
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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*SL, 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. - View Dependent Claims (92)
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93. A computer application program operational on a computer for performing a method of managing an investment account, the method comprising:
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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*SL, 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. - View Dependent Claims (94)
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95. A system for managing an investment account comprising:
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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*SL, 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.
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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:
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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*SL/BK, 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. - View Dependent Claims (97)
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98. A computer application program operational on a computer system for performing a method of managing an investment account, the method comprising:
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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*SL/BK 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. - View Dependent Claims (99)
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100. A system for performing a method of managing an investment account comprising:
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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*SL/BK, 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. - View Dependent Claims (101)
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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=SL, where L is neither 0 nor 1 and L is substantially constant over a period of time.
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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=SL, where L is neither 0 nor 1 and L is substantially constant over a period of time.
Specification