JPH03103966A - Risk minimizing portfolio selection device utilizing mutual connection type network - Google Patents

Abstract

PURPOSE:To optionally select the optimum funds distribution ratio to respective issues so as to minimize a total risk from two conditions whose total return is maximum or fixed by forming a problem for minimizing the energy function of the mutual connection type network. CONSTITUTION:A user optionally selects either one of a 1st object condition for maximizing the total return and minimizing the total risk and a 2nd purpose condition for minimizing the total risk under the fixed state of the total return by an object changing means 16. Under the setting, a node value updating means 7 sequentially updates respective node values 14 in a network storing means 5 so that the value of the energy function is reduced and a decision output means 8 decides the minimum value of the energy function, so that the optimum funds distribution ratio 15 can be found out as respective node values 14 at the minimum of energy. Thus, the optimum funds distribution ratio 15 to respective issues can be found out under respective conditions.

Description

[Detailed Description of the Invention] [Summary] This invention relates to a risk-minimizing portfolio selection device that uses an interconnected network to allocate funds to bonds and stocks so as to reduce the risk factor when investing in bonds and stocks. Using interconnected networks, which are a promising method of computer architecture, we can achieve portfolio selection that seeks the minimum risk allocation, in which case,
The user can freely set whether to set the return to a predetermined value or to maximize the number of turns, reduce processing time, and make it possible to accurately determine the fund allocation ratio for each stock. A means for storing the structure of an interconnected network, the value of each node of the interconnected network corresponding to a fund allocation ratio to each of a plurality of stocks, and the links between the nodes. network storage means for storing weight values;
A purpose change means for selecting either the first purpose condition or the second purpose condition, and when the first purpose condition is selected by the purpose change means, the return and risk for each stock, and each stock In this case, when the value of the energy function found from each link weight value and each node value is minimal, the return for each stock and each node value is set. Each link weight value is set so that the total return determined is maximum, the total risk determined from each correlation coefficient and each node value is minimum, and the constraint conditions regarding each node value are most satisfied, and the weight values are stored in the network storage means. On the other hand, when the second objective condition is selected by the objective change means, each link weight value is calculated from the total return of each issue, the return and risk of each issue, and the correlation coefficient between each issue. Configure the settings, and in that case,
When the value of the energy function found from each link weight value and each node value is minimized, the total risk found from each correlation coefficient and each node value becomes minimum, and the constraint regarding each node value is most satisfied. A link weight value that sets each link weight value so that the total return determined from each stock return and each node value most closely approximates the input total return, and stores it in the network storage means. a setting means, a node value updating means for sequentially updating each node value on the network storage means based on the link weight value so that the value of the energy function decreases, and for each update operation,
Determining the value of the energy function found from each link weight value and each node value that define an interconnected network, and outputting each node value as the optimal fund allocation ratio for each issue when the value is minimal It is arranged to have an output means.

[Industrial application field]

The present invention relates to a risk-minimizing portfolio selection device that uses an interconnected network to allocate funds to bonds and stocks so as to reduce the risk factor when investing in bonds and stocks.

[Conventional technology]

As the securities market develops, various methods are required to determine the optimal combination of securities in order to reduce the risk of securities investment and make profits.

Here, when investing in securities such as bonds and stocks, the state in which funds are appropriately dispersed among each issue in order to avoid risks due to fluctuations in investment returns is generally called a boat folio. From a portfolio perspective, the problem of determining the optimal combination of securities mentioned above is an optimization problem called portfolio selection, which seeks to find the ratio of capital allocation to each stock that will maximize profits and minimize risk. Become.

As a conventional technique for performing the above-mentioned portfolio selection, there is a Markovic model that formulates a problem of optimizing a combination of securities using a model using quadratic programming (QP method).

The Markovits model is based on four definitions: two constraints on the fund allocation ratio, return and risk. Below, 11 and 12 of them will be specifically shown.

First, let us consider N stocks. The i-th stock is indicated by the variable i ranging from 1 to N.

Let the fund allocation ratio of each stock i be a variable Xi. At this time, for each i, there is a first constraint condition: 0≦Xi≦1 (1). Also, X++Xz+...+X, +...+XN=ΣX+=1
There is a second constraint condition (2). For example, when there is a fund of M yen, the funds are distributed as follows: MXX, yen, Mxx2 yen, - - ., MXX, yen, . . . -, MXXN yen.

Note that from now on, to simplify the notation, it may be indicated by .

Now, the average value of past investment returns for a certain stock i is called the return of that stock, and will be denoted by P1 from now on.

Further, the standard deviation of the past investment returns of the stock i is called the risk of the stock, and will be denoted by Si from now on.

Let Rij be the correlation coefficient of expected returns between stock i and stock j.

Here, the total return P is P=Σpt xt...(3)
far. This is the fund allocation ratio Xi for each of N stocks.
is the expected total profit when funds are allocated in the ratio of .

Furthermore, let the total risk R be . When R takes a minimum value, each X represents the allocation ratio with the minimum expected total risk based on the expected total profit P.

As described above, the Markovitz model is defined by formulating equations (1) to (4).

Performing the portfolio selection described above under equations (1) to (4) above means: ■ If the total return is the same, the combination of funds that minimizes the total risk, ■ If the total risk is the same, the total return is The combination of funds that is the largest is 13 14 . In other words, the problem of portfolio selection, or the optimal portfolio, is to find the allocation ratio for allocating funds to bonds and stocks in a way that is expected to maximize profits and reduce risk. .

Here, the problem of optimal boat folio is as follows (aL
There are three possible types: (b) and (C).

(a) This is a problem of finding an allocation that increases return and reduces risk.

As the objective function, the fund allocation ratio X+ , X2 , ..., XI, which maximizes and minimizes the return P - ΣPI X1,
..., XN does not necessarily exist, so the degree to which the risk is to be reduced is determined relative to the magnitude of the return. That is, consider selecting appropriate positive constants a and b, defining an objective function F=-aP+bR, and minimizing F.

In other words, ``Under the constraints 0≦Xs≦1, ΣXt=1.0, Xi
Fund allocation ratio X1X2+ that minimizes XJ...
Find ・,X1,...,XN. The problem is J.

(b) This is a problem of finding the allocation that minimizes the risk while keeping the return constant. That is, under xt = p, the fund allocation ratio X+ , Xz , ..., X
Find i,...,XN. The problem is J.

(C) This is a problem of finding an allocation that maximizes return while keeping risk constant. That is, r constraint 0≦XI≦
1, ΣX+-1.0, distribution ratio X+ ,X2 ,...
・, Xi, ..., Find XN15 l6. The problem is J.

The optimal portfolio problems (a) and (b) above based on the Markovitz model have been solved by quadratic programming methods such as the QP method as a first conventional example. The QP method has an objective function of 2
The following equation is a nonlinear programming method when the constraint equation is linear.

Since risk is a quadratic equation, the QP method is used for the problem of minimizing risk.

FIG. 9 shows a block structure of a risk-minimizing portfolio determining device according to a first conventional example.

In this device, first, from the return/risk manual device 1, the number of stocks N, return Pi, risk Sl,
Input the return correlation coefficient Rib and the expected total return P. From now on, the mathematical expression for quadratic programming will be constructed using the mathematical expression model expression device 2.

Next, the quadratic programming calculation device 3 determines the optimal fund allocation ratio χI. A procedure is followed in which X2, . . . +"1+ . . .

On the other hand, as a second conventional example, although it is not a solution to the optimal boat folio problem that directly corresponds to the Markovitz model,
A promising method of computer architecture is to use interconnected networks to combine multiple stocks (e.g., 100
There is a system that selects an optimal combination of specific brands (for example, five brands) from among the brands (brands).

[Problem to be solved by the invention]

However, in the case of the first conventional example, the amount of calculation is approximately proportional to the cube of the number of stocks, so as the number of stocks increases, the processing time becomes enormous and the memory capacity used for calculation becomes enormous. There are problems. Another problem is that it may not be possible to solve the problem if the number of stocks increases.

On the other hand, in the case of the second conventional example, although the processing time is short, it is not possible to determine the fund allocation ratio to each stock in the portfolio, and it has the problem that it is not portfolio selection in the strict sense. are doing.

The present invention uses a promising interconnected network as a computer architecture to implement portfolio selection that seeks an allocation with minimal risk, in which case the user can take turns to maximize return. It is an object of the present invention to make it possible to freely set whether to set a predetermined value to a predetermined value, to shorten the processing time, and to accurately determine the fund allocation rate to each issue.

[Means to solve the problem]

FIG. 1 is a block diagram of the present invention.

The network memory 5 is a means for storing the structure of an interconnected network, and stores values 14 of each of a plurality of nodes corresponding to the fund allocation ratio to each of a plurality of stocks in investment in bonds and stocks. , link weight value 13 between each node
It is a means of memorizing. Furthermore, depending on the structure of the interconnected network, a threshold value may be stored for each node, which determines the magnitude of the total value manually input to each node from other nodes.

The purpose changing means 16 allows the user to select either the first objective condition or the second objective condition.

Next, the link weight value setting means 6 controls the purpose changing means 1.
In step 6, different operations are performed depending on whether the first objective condition is selected or the second objective condition is selected.

That is, when the first objective condition is selected, the link weight value setting means 6 sets the return 9 and risk 10 for each stock.
, and each link weight value 12 from the correlation coefficient 11 between each stock.
is set and stored in the network storage means 5. In this case, when the value of the energy function of the interconnected network determined from each link weight value 12 and each node value 13 is minimized, each stock return 9 and each node value 1
The total return calculated from 3 is maximum, and each correlation coefficient is 11
Each link weight value 12 is set so that the total risk determined from each node {i13 is minimized and the constraint conditions regarding each node value 13 are most satisfied. On the other hand, the second
If the objective condition is selected, link weight value setting means 6
sets each link weight value 13 from the total return 9 of each brand, the return 10 of each brand, the risk 1l, 19 20 and the correlation coefficient l2 between each brand, and stores it in the network storage means 5. In this case, when the value of the energy function of the interconnected network found from each link weight value 13 and each node value 14 is minimized, the total risk found from each correlation coefficient 12 and each node value 14 becomes minimum, Each link weight value 13 is set so that the constraint conditions regarding each node value 14 are most met, and the total return found from each stock return 10 and each node value 14 most closely approximates the input total return 10.
is set. Note that in the first or second objective condition described above, when each node has a threshold value as described above,
The above-described means may be a means for setting each link weight value as well as a threshold value to meet the same conditions as above. In this case, the energy function of the interconnected network is determined from each link weight value, each threshold value, and each node value.

The node value updating means 7 updates each link weight {! from the link weight value setting stage 6 or the network storage stage 5. 13, each node value 14 on the network storage means 5 is sequentially updated so that the value of the energy function decreases. Note that when each node has a threshold value as described above, each threshold value also contributes to the update operation.

Then, the determination output means 8 outputs each link weight value 13 defining the interconnected network and each node value for each update operation. This means determines the value of the energy function obtained from the node value 14, and outputs each node value 14 when the value is minimal as the optimal fund allocation ratio 15 for each issue. Note that when each node has a threshold value as described above, each threshold value also contributes to the derivation of the energy function.

In the above configuration, an initial value setting means may be provided for randomly setting the initial value of each node value 1 on the network storage stage 5 within a range that conforms to the above-mentioned constraint conditions.

[For production]

In the present invention, each node of the interconnected network has a value of 1
4, the fund allocation ratios 21 22 for each of the plurality of issues are made to correspond to each other.

Then, the user can select either the first objective condition or the second objective condition using the objective change step 16.

When the first objective condition is selected, the link weight setting means 6 automatically determines that when the value of the energy function of the interconnected network is minimized, the total return is automatically maximized, the total risk is minimized, and Each link weight value 12 is set so as to satisfy the constraint conditions. On the other hand, when the second objective condition is selected, the link weight setting 1,000 stages 6 automatically becomes the minimum total risk when the value of the energy function of the interconnected network is minimum, and the constraint condition is satisfied. The filling,
In addition, each link weight value 13 is set so that the total return most closely approximates the manually generated total return 10.

Under such settings, the node value updating means 7 sequentially updates each node value 14 on the network storage means 5 so that the value of the energy function decreases, and the determination output means 8 detects the minimum value of the energy function. By determining the optimal fund allocation ratio I as each node value 14 when the energy is minimum
5 can be found.

Therefore, the present invention solves the problem of minimizing the energy function of an interconnected network by maximizing the total return.
The first objective condition is to minimize the total risk, or the second objective condition is to minimize the total risk with a constant total return.
Any of the objective conditions can be arbitrarily selected, and the optimal fund allocation ratio 15 to each issue can be determined under the conditions. In this case, the amount of processing calculation is approximately proportional to the square of the number of nodes corresponding to the number of brands, so compared to conventional quadratic programming etc. where the amount of calculation is approximately proportional to the cube of the number of brands. It is possible to realize processing that takes less time and requires less memory capacity during calculation.

〔Example〕

Embodiments of the present invention will be described below with reference to the drawings.

23 24 Ryoji Riichi Ryoichi First, before explaining specific embodiments of the present invention,
The principle of the present invention will be explained.

The present invention provides (
Solve both the problem of (a) finding the allocation of funds to each stock with the maximum return and the minimum risk, or (b) the problem of finding the allocation of funds to each stock with the minimum risk while keeping the return constant. This invention is particularly characterized in that either one can be freely selected.

Here, in the present invention, the above-mentioned optimal portfolio problem is solved using an interconnected network.

The interconnected network is a network having the following structure, for example, as shown in FIG.

■There are multiple nodes, and all nodes are connected to other nodes, including themselves, through directed links. The number of nodes is represented by N.

■Each node has one variable value as its value.

The value of node i is represented by Xi. Further, each node i has a fixed numerical value called a threshold value.

The threshold value of node i is expressed by θi.

■Each link between nodes has a numerical value as the link weight. The weight of the link from node j to node i is Wi
J (see Figure 6).

■The value of each node at the next point in time (updated value)
t + 1) is the current value of the node itself (before update {i) is determined using each value XJD) of the node on the opposite side of the link.

In particular, in the present invention, as shown in FIG. 7, a network using a value change rule of the following format is considered.

Here, f() is an appropriate function having one real number as an argument. Note that the format of this equation will be described later.

The structure of the interconnected network according to the present invention is shown below, assuming the interconnected network as described above.

■Prepare N nodes and associate each N brand with each node.

■The solution fund allocation ratio X1 (0≦XI≦l) of the issue is expressed by the value of the node.

■The constraints and objective functions (total return, total risk, etc.) are collectively expressed as one energy function Eo, and then distributed and expressed in the weights and thresholds of all links in the network. The weight of the link from node j to node i is W1
j, the threshold value of node i is expressed as θ,.

The operating rules of the interconnected network with the above structure are shown below.

(2) A value change rule for changing the value X1 of each node is defined so that the above energy Eo decreases.

(2) The energy expression EO is determined so that each constraint expression is satisfied and the objective function takes a minimum value when the energy expression EO becomes a minimum value.

? The operation of the interconnected network based on the above rules is shown below.

■Initially, each node is randomly assigned a value.

(2) Then, the value of each node changes one after another according to the value change rule.

Then, as the value of the node changes, the energy function E according to the value change rule. is decreasing.

■Energy function E. will someday reach a minimum value.

Energy function E. is determined so that when it becomes a minimum, each constraint formula of the optimal portfolio problem is satisfied and the objective function takes a minimum value, so the value X of each node at that time is the optimal fund for stock i. Indicates the allocation ratio.

This makes it possible to calculate an optimal portfolio using an interconnected network.

The most important thing in order to make the above operation possible is to combine the objective function and constraints in the boat folio into one energy function E, as described in (2) above. It is to express it as. In this case, it is necessary to express the energy so that when Eo becomes a minimum, the objective function becomes a minimum and each constraint expression is satisfied, as in the above-mentioned (2).

Therefore, here we first start with the energy expressions El and E of the constraints.
2 and E5, the energy representations E3 and E4 of the objective function are defined, and then they are combined into one energy representation Eo.

First, energy expression E2 representing the constraint “0≦Xi≦1”
Define about. E1 must be expressed in such a way that each i tends to satisfy 0≦X1≦1 when it becomes small to a certain extent. For example, the following expression:

There is one.

E2 = (IXX1)2...16)
Next, the objective function, that is, the energy expression of the total risk E3
Define.

In order to ensure that when the energy expression E3 representing the objective function becomes minimum, the expected total risk also becomes minimum,
E3 uses the exact formula representing total risk. Therefore, from equation (4) above, when E3 takes the minimum value, each Xi
represents the fund allocation ratio to stock i when the risk is minimum.

Similarly, when the energy expression representing the objective function becomes minimum, the energy expression E4 expressing the total return is determined so that the expected total return is as large as possible. For example, the ghee expression E2 is defined from the above equation (3). When E2 becomes local minimum, the constraint ΣXi =
This is an expression that satisfies 1.0. For example, the following formula takes the maximum value, so when it is guaranteed that there are no other maximum values, each individual Xi is the amount of money invested in stock i when the expected total return is maximum. Allocation ratio 2
9 30 Show.

The following describes the expression E5. E5 is expressed as being at a maximum. For example, one of the expressions is:

E5-(P-ΣPIXl)2 ...(9) Above, using the energy expression of the objective function and constraints shown in equations (5)-(8), the above-mentioned boat folio interval N (
a) is expressed as follows.

"Energy function Eo = aE+ +bE2 +cEz+dE4 (after appropriately determining coefficients a, b, c, and d)
Minimize. ” Of course, in these energy expressions, other expressions that satisfy the constraints and objective function conditions can also be considered.

Here, the energy function of the interconnected network defined by the above-mentioned items 1 to 2 is generally expressed as follows. On the other hand, the energy function E 6 −a E H + b found from (5) to (8) in the aforementioned boat folio problem (a)
E 2 + C E 3 +d E a is also the node value X
It is expressed in the form of a quadratic equation.

Therefore, by correlating the above equations 00) and (I+) as identities, we can calculate the link weight value WtJ between each node and the threshold value θi of each node when the boatfolio problem (a) is applied to a mutually connected network. , can be determined as follows.

The above equation (1l) is transformed as follows.

Eo = aE+ +bE2+ CE3 + dE4 When X is viewed as a variable, it can be expressed in the form of a quadratic equation of X.
1 2Xi +2X+2) 3l 32 +d(-ΣP+ Xi) dΣPi X1 Here, δIj=1 (when j=j), 10(i≠
j), and since Σ1=N, +Σ (2a-2b-dPi)Xi+aN+b The transformation result of the above equation (11) can be expressed as the energy function of the mutually coupled network of the above 0(I) equation. By associating with the general form, the link weight WiJ and threshold value θ1 are determined as follows. That is, the weight of the link from node j to i is wfj-4aδ+i 2b 2cSt sJRt
J...02) dΣPi Xi +aN+b. Also, the threshold value of node i is θr-2a 2b dPt...Q3)
becomes.

On the other hand, considering the above-mentioned portfolio problem, this problem can be solved using the energy expression of the objective function and constraints shown in equations (5) to (7) and (9) above.
It is expressed as follows.

``Minimize the energy function Eo -a E+ + b E2 +33 34 cE3+dE5 (after appropriately determining coefficients a, b, c, and d). ” Of course, in these energy expressions, other expressions that satisfy the constraints and objective function conditions can also be considered.

Here, the energy function in the above portfolio problem (6) found from equations (5) to (7) and (9) is Eo = aE+ +bEz +cE. +dE51a
Σ(N-X+)2+x+2) I? Since it is expressed in the form of a quadratic equation for the node {1i The link weight value W between each node when problem (b) is applied to a mutually connected network. J and the threshold value θ■ of each node can be determined as follows.

The above-mentioned formula 041 is modified as follows.

E o = a E + 10b E 2 + C E
3 +d E 5=aΣ((I Xl)2+Xt 2
)t? d (P1ΣP.X1)2 1aΣ(1 2X+ +2Xi”) 10b[:1-2
ΣX. +(ΣX■)2〕+CΣΣS+ SJ Rij
Xt (when i≠j), and since ,I1=N, Eo=aN-2aΣXI+2aΣΣXIXJ δIJI
J +b-2bΣX t +bΣΣXtX■1j 35 36 +CΣΣSi S,I RIJ Xt XJ+d
P2 -2dP ΣPI X amount + dΣΣPi PJXIXJ iJ -2aΣΣX4 χj δ1 +bΣΣX,X,1J
1j+C
ΣΣSi SJ Rij XI XJ1' 10dΣΣPiPJ XI
d P 2-(1/2)ΣΣ (-4aδIJ
2biJ 2 C Si Si Rlj 2dP+ PJ )Xi XJ 10Σ( 2a 2b 2dPPI)Xt+aN+
b+dP2 By associating the transformation result of the above equation 041 with the general form of the energy function of the mutually coupled network of the 0ω equation described above, the link weight WiJ and the threshold value θ5 are determined as follows. That is, the weight of the link from node j to i is W. J--4aδij 2b 2cSt s, RiJ
2dPt PJ...05)? Become. Also,
The threshold value of node i is θi − 2a 2b 2dPPt...Q
becomes ω.

Next, the energy function E determined by the OI formula, 02) formula and 03) formula, or 00) formula, 05) formula and 06) formula
Below, we will explain the specific operation of the value change rule described above, ``J, which changes the value Xi of each node so that E decreases.

First, at each node X■, Xi (t+1)=Xt (t)+dXi...
07), the value of Xi (t) is changed.

Here, Xi(t) indicates the XIO value before update, and Xi(t)
t+1) indicates the updated XiO value.

Further, dXi is the amount of change (difference) in Xt for each update operation. At this time, a value change rule within the node is determined so that the energy function E decreases.

Now, assuming that the time change (differential/difference) of E is dE, and the time change (differential/difference) of Xi is dX+, and we differentiate both sides of the above equation 37 38 00), we get d E - (1/2) (ΣΣ CXIj(d
)XiIj +Wt, +Xt (cl x, ) ])+Σθi(d
xl)+XI (dXj ))) +Σθ+(dX,
)WiJ=WJl, then +ΣθI (dX1). That is, in general, (ΣWiJxJ -θi) (dXl)≧0.'' If we set dE≦0, E will decrease.

At this time, there is the following equivalence relation <1>.

(ΣW I J X j-θt) (dXt) ≧0<
1> ((ΣWijXJ−θI)≧0 and dX1≧O
j? or [(ΣWIJXj-θl)≦O j and dX■≦0] Therefore, if the value change rule of the node is changed so that the following holds true, the energy E decreases.

As a specific example of the value change rule based on the above formula 08), 0
9) Something like this can be considered.

By substituting the above equation 09) into the above equation 0'r), the specific operation of the value change rule can be expressed by an update equation such as [A is a positive constant]...Ql.

Above, formula 00), formula 02) and formula 03), or 00)
The expression of the energy function defined by equations 051 and 06), and Q. Based on the value change rule specified by the I formula, by executing the operations of the interconnected network described in ■ to ■, a portfolio with maximum return and minimum risk, or a portfolio with fixed return and minimum risk can be created. You can ask for it.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Specific embodiments of the present invention based on the above-mentioned principle and structure will be described below. FIG. 2 is a block diagram of a specific embodiment of the present invention.

The interconnected network 21 is configured as a computer memory or dedicated hardware, and has an array of values of each node X (i) and an array of link weight values between each node w(i, jL Threshold value array θ(i) for each node
The structure of an interconnected network consisting of is memorized.

The link weight/threshold setting device 19 is a purpose change switch 2
5, if the specification is made to seek a boat folio with the maximum return and minimum risk, the return and risk of each stock manually entered from the return/risk input device 17, the correlation coefficient between each stock, and The link weight value between each node and the threshold value of each node are set from each parameter for setting the energy function manually inputted from the parameter input device 18, and set in the interconnected network 21. On the other hand, if the objective change switch 25 specifies that a portfolio with fixed return and minimum risk is desired, the total return of each issue, the return and risk of each issue, input manually from the return/risk input device 17, The link weight value between each node and the threshold value of each node are set from the correlation coefficient between each brand and each parameter for setting the energy function manually entered from the parameter input device 18, and the interconnection type network 21 is set. Set.

The value change rule setting device 20 is a mutually coupled network 2
Based on each link weight value and each threshold value stored in 1, each node value on the same network is sequentially updated so that the value of the energy function decreases. Note that here is an array Xold (i) that stores the old values of the nodes,
1≦i≦N is stored.

The energy minimization determination device 23 performs the following for each update operation:
Defining the interconnected network 21 41 42 Determine the value of the energy function found from each link weight value, each threshold value, and each node value, and if the value becomes minimum, notify the distribution ratio output device 24 to that effect. However, if the value does not become minimum, the value change rule setting device 20 is instructed to perform the next update operation.

The distribution ratio output device 24 is an energy minimization determination device 23.
When receiving a notification that the energy function has become minimum, the interconnected network 21 outputs each node value at that time as the optimal fund allocation ratio to each issue.

On the other hand, the initial value setting device 22 sets the initial value of each node value on the interconnected network 21.

The operation of the specific embodiment of the above configuration will be explained based on the operation flowcharts of FIGS. 3 to 5.

FIG. 3 is an operational flowchart of the main procedure.

First, S1 is a structural adjustment process for the interconnected network 21, which is executed by the link weight/threshold setting device 19 based on the human power conditions of the purpose change switch/control switch 25 shown in FIG. In other words, an array w (i, j
) and a procedure for setting values in the array θ(i) indicating the threshold value is executed. The above W(++j) and θ(i) are determined by the above-mentioned “
The subscripts i. ．． The meaning of j is also the same.

The operation here corresponds to the item "■" explained in the "Explanation of Principle" above.

The specific operation of S1 above is shown in FIG.

First, the link weight/threshold setting device 19 in FIG. 2 takes in the input state of the purpose change switch 25 (311 in FIG. 4).
). The purpose change switch 25 allows the user to
As described above, either a specification is made to obtain a boat folio with maximum return and minimum risk, or a specification is made to obtain a boat folio with fixed return and minimum risk.

Next, from the return/risk input device 17, the number of stocks N, the return Pi of stock i, the correlation coefficient RiJ between the expected returns of stocks i and j, and the risk S of stock i are input (312 in FIG. 4). .

If the value of the purpose change switch 25 indicates the maximum return specification, the process goes to 314 in FIG.
Fig. 4 813).

If maximum return is specified, link weight/
The threshold value setting device l9 inputs each energy function E1 to E1 shown by the above-mentioned equations (5) to (8) from the parameter input device 18.
Input each coefficient a, b, c, and d to reflect E4 in the energy function Eo as in equation (11) above (
Figure 4 314). These coefficients are determined empirically.

Then, the link weight/threshold value setting device 19 performs the step S12 described above.
and S1 After that input operation, the link weight value W
(IJ) and threshold value θ(i).

That is, for 1≦I +J≦N, w(i, j)−4aδ+i2b 2CSl s, RIJ θ(i)−2a−2b−dP, is calculated (FIG. 4, 315). Each link weight value w (i, j) and each threshold value θ(i) (
1≦i, j≦N) is set (stored) in the interconnected network 21, and the process of FIG. 31 is completed.

If fixed return is specified, link weight/
The threshold value setting device operator 9 manually inputs the total return P expected by the user from the parameter input device 18 in addition to the above-mentioned manual operation at Sl2 in FIG. 4 (FIG. 4, 316). Also,
Each of the energy functions E. -Each coefficient a, b for reflecting E3 and E5 in the energy function Eo as in the above-mentioned formula 04)
, c and d manually (Fig. 4, 317). These coefficients are also determined empirically as in the case described above.

Then, the link weight/threshold value setting device 19 performs the step S12 described above.
, S16 and S17, the link weight value w(i,j) and the threshold value θ(i) are calculated based on equations 05) and 06) explained in the section of "Principle Explanation" above. That is, for 1≦i +j≦N, w (i, j) -4 aδiJ-2b2cSt S3 Rij 2dP
+Piθ(i)=−2a−2b−2dPP+ 45 46 is calculated (FIG. 4, 318). Each link weight value w(IJ) and each threshold value θ(i) (l≦
I +J≦N) is set (stored) in the mutually coupled network 21, and the process of FIG. 3 Sl ends.

Next, 32 in FIG. 3 is a process for initializing the interconnected network 21, and the initial value setting device 22 in FIG.
executed by In other words, an array X indicating node values
A procedure for setting an initial value in (i) is executed. The above X (i) corresponds to the node value Xi explained in the above-mentioned "Principle Explanation" section.

The operation here is based on the section ``■
” corresponds to

The specific operation of S2 above is shown in FIG. That is, the initial value setting device 22 sets the node value array X(i) corresponding to each brand from 1 to N in the node array X in the interconnected network 21, 1≦I, as shown in FIG. 5 321.
For +J≦N, the range of X(i) is 0.0 to 1.0
Then, the sum of all node values X(i), 1≦I +J≦N is 1, and the average of each node value X (i) is equal, that is, 1
．． The initial value is set using a random number so that it becomes 0/H. Note that, empirically, it is better that the variance of random numbers is not too large. Array X of each node value set by this (
i), I≦1+j≦N is set (stored) in the interconnected network 21, and the process of FIG. 32 is completed.

Next, in Fig. 333, the past energy record E o
l Set the dO value to the initial value of 0.0.

The loop from FIG. 384 to S8 corresponds to the operations in the sections "■, ■" explained in the "Explanation of Principle" above.

First, the energy minimization determination device 23 in FIG. 2 starts up the mutually coupled network 21 and calculates the energy E based on the above-mentioned formula 00 (FIG. 3 34). That is, the array X of each node value on the interconnected network 21
(+), each link weight value W(IIJ) and each threshold value θ(i
), (both 1≦i+J≦N), the energy E is found as 47 48.

Next, FIG. 35 shows an operation end determination process, which is executed by the energy minimization determination device 23 of FIG. 2.

That is, it is determined whether the difference between the current energy E calculated as described above and the past energies E0 and 4 is equal to or less than a certain threshold value B. Note that the threshold value B is set in advance by the second
Assume that the input is from the paramec human-powered device 18 shown in the figure.

As a result of the above judgment, E and E. 1 is less than the threshold value B, it is determined that the energy E has reached the minimum value, and the distribution ratio output device 24 in FIG. 2 is notified of this fact.

As a result, the allocation ratio output device 24 outputs the array X (i) of each node value from the interconnected network 21 to the brand i
Output as the optimal fund allocation ratio and finish the operation (
Figure 3 39).

The above processing operations of 35 and S9 are explained in the above-mentioned "principle explanation".
Corresponds to the operation described in section "■".

On the other hand, the results of the determination in FIG. 35 are E and E. If the difference from ld is equal to or greater than threshold B, the energy minimization determination device 23 in FIG. 2 sets the current energy value E in the past energy record Eold (36 in FIG. 3), and then determines the value change. The rule setting device 20 is instructed to update the node value array X (i).

As a result, the value change rule setting device 20 operates from S7 to S7 in FIG.
The node value update operation of S8 is executed.

That is, the value change rule setting device 20 first converts the contents of the array X of node values on the interconnected network 21 into the old array X of node values. ld (Figure 3, 37). Note that the storage area for this old array is provided inside the value change rule setting device 20.

Specifically, X0+d(i) -X(i), 1≦i
, j≦N is executed.

Next, the value change rule setting device 20 uses the parameter input device W1.
After inputting coefficient A from B, for all node value arrays X(i), 1≦i+J≦N, the above-mentioned formula 07),
09) The following update operation is performed based on the equation and the QΦ equation. That is, 49 50 update calculations are performed. As a result, the updated array X(i) of each node value, 1≦1+J≦N, is set (stored) in the interconnected network 21, and the process of FIG. 38 is completed.

After the above update operation, the process returns to FIG. 3 again and the above-described operation is repeated.

The specific embodiments described above make it possible to optimally determine the fund allocation ratio for each issue.

In this case, the processing time of this embodiment is compared to the conventional quadratic programming method (
Figure 6 shows the estimation results compared with the processing time of the QP method. The amount of processing calculation in this embodiment is approximately proportional to the square of the number of nodes corresponding to the number of brands, while the amount of processing calculation of quadratic programming (QP method) is approximately proportional to the third power of the number of brands. Therefore, as is clear from FIG. 6, as the number of brands increases, this embodiment can realize processing that takes less processing time and requires less memory capacity during calculation. In addition, the number of stocks in actual securities investment etc. is thought to be about 1,000 to 2,000 stocks.

The embodiment shown in FIG. 2 can be implemented either in the form of software executed on a general-purpose computer or in the form of dedicated hardware. In particular, if it is realized as a dedicated hardware chip, it will be possible to realize a high-speed and highly reliable system.

〔Effect of the invention〕

According to the present invention, as a problem of minimizing the energy function of an interconnected network, the optimal capital allocation ratio to each stock that minimizes the total risk is determined by the problem of minimizing the energy function of an interconnected network. It becomes possible to arbitrarily select and obtain from among the following conditions. That is, the optimal portfolio under two types of conditions can be calculated with one type of device.

In this case, the amount of processing calculation is approximately proportional to the square of the number of nodes corresponding to the number of brands, so compared to conventional quadratic programming etc. where the amount of calculation is approximately proportional to the cube of the number of brands. It becomes possible to realize processing that takes less time and requires less memory capacity during calculation.

In particular, in the interconnected network according to the present invention51 52, when the value of each node is updated sequentially so that the value of the energy function decreases, the value of each node becomes discrete as shown in the above-mentioned QO equation etc. Since it is possible to update so that it changes not as a value but as a continuous value, by making each node value correspond to the fund allocation ratio for each issue, it becomes possible to obtain an accurate fund allocation ratio.

[Brief explanation of drawings]

FIG. 1 is a block diagram of the present invention, FIG. 2 is a block diagram of a specific embodiment of the present invention, FIG. 3 is an operational flowchart of the main procedure, and FIG.
Figure 5 is an operational flowchart of the procedure for setting link weights and thresholds; Figure 5 is a flowchart of the procedure for setting initial values of nodes; Figure 6 is a diagram showing an example of an interconnected network; The functional diagrams of the nodes are shown in Fig. 8 and Fig. 9. 5... 6... 7... 8... 9... 10... 11... 12... 13... 14... 15... 16... Main implementation Comparison of processing time between the example and the conventional example The block structure of the first conventional example is shown: network storage means, link weight value setting means, node value updating means, judgment output means, total return, return by each brand, by each brand Risk, correlation coefficient between each stock, link weight value between each node, value of each node, optimal fund allocation ratio, purpose change means.

Claims (1)

[Scope of Claims] 1) Means for storing the structure of an interconnected network, wherein the values (14
), network storage means (5) for storing link weight values (13) between the nodes, and purpose changing means (16) for selecting either the first purpose condition or the second purpose condition. , when the first objective condition is selected by the objective changing means, the return for each issue (10)
and the risk (11), and the correlation coefficient (12) between each stock.
) to set each link weight value (13), and in that case, each link weight value (13) and each node value (
14) When the value of the energy function obtained from The total risk determined from each node value (14) is minimal, and each node value (14)
The respective link weight values (13) are set and stored in the network storage means (5) in such a way as to best suit the constraints on the purpose change means (16).
), when the second objective condition is selected, the total return for each issue (9), the return for each issue (9),
10), risk (11), and the correlation coefficient (12) between the respective stocks, and in that case, each link weight value (13) and each node value are set. When the value of the energy function found from (14) is minimal, the total risk found from each of the correlation coefficients (12) and each node value (14) becomes minimal, and the constraints regarding each node value (14) are The returns for each stock (10) and the node values (14) that best match the conditions;
The total return calculated from is the input total return (
10), each link weight value (1
3) and save it to the network storage means (5)
a link weight value setting means (6) for storing each node value (14) on the network storage means (5), based on the link weight value (13), so that the value of the energy function decreases; a node value updating means (7) that sequentially updates the node values so that the link weight values (13) and the node values (13) that define the interconnected network are updated for each update operation;
Judgment output means (4) that judges the value of the energy function obtained from the equation and outputs each node value (14) when the value is minimal as the optimal fund allocation ratio (15) to each brand.
8) A risk-minimizing portfolio selection device using an interconnected network. 2) Means for storing the structure of an interconnected network, the values of each of a plurality of nodes of the interconnected network corresponding to the fund allocation ratios to each of a plurality of stocks, and the links between the nodes. network storage means for storing a weight value and a threshold provided for each node for determining the magnitude of the total value inputted to each node from other nodes; and a first objective condition or a second objective condition. objective changing means for selecting one of the above; The link weight value and each threshold value are set, and in that case, when the value of the energy function found from each link weight value, each threshold value, and each node value is minimized, the return for each stock and the above Each of the link weight values and Each of the threshold values is set and stored in the network storage means, and when the second objective condition is selected by the purpose changing means, the total return of each brand and the return of each brand are determined. The link weight value and each threshold value are set from the correlation coefficient between each brand, the risk, and the correlation coefficient between each brand, and in that case, the value of the energy function determined from each link weight value, each threshold value, and each node value. is minimized, the total risk determined from each of the correlation coefficients and each node value is minimized, and the constraint conditions regarding each node value are most met, and the return for each stock and each node value is link weight value/threshold value setting means for setting each of the link weight values and each of the threshold values so that the total return obtained from the above most closely approximates the inputted total return, and storing them in the network storage means; node value updating means for sequentially updating each of the node values on the network storage means based on each of the link weight values and each of the threshold values, such that the value of the energy function decreases; and for each update operation, Determine the value of the energy function obtained from each of the link weight values, each of the threshold values, and each of the node values that define the interconnected network, and determine the optimal value of each node for each brand when the value is minimal. 1. A risk-minimizing portfolio selection device using an interconnected network, characterized in that it has a determination output means for outputting a fund allocation ratio. 3) Let the number of the plurality of stocks be N, and i and j are each 1≦i
As a variable that changes as ≦N and 1≦j≦N, let the value of each node be X_i, and the link weight value between each node be W_i_
j, the threshold value for each node is θ_i, the total return of each brand is P, the return of each brand is P_i, the risk of each brand is S_i, the correlation coefficient between each brand is R
＿i＿j、The total risk of each of the above stocks is ▲There are mathematical formulas, chemical formulas, tables, etc.▼、The total return calculated from the return for each stock and the above node values is ▲The above energy function is When ▲There are mathematical formulas, chemical formulas, tables, etc.▼, the link weight value/threshold value setting means sets the first objective condition by the purpose changing means, with a, b, c, and d being predetermined constants. When is selected, the energy function E is equivalently as follows: ▲There are mathematical formulas, chemical formulas, tables, etc.▼ +▲There are mathematical formulas, chemical formulas, tables, etc.▼ +▲There are mathematical formulas, chemical formulas, tables, etc.▼ +▲ There are mathematical formulas, chemical formulas, tables, etc. ▼ Set each link weight value W_i_j and each threshold value θ_i so that w_i_j=-4aδ_i_j-2b-2cS_iS_
jR_i_jHowever, δ_i_j=[1(i=j),0(
i≠j)] θ_i=-2a-2b-dP_i, and when the second objective condition is selected by the objective changing means, the energy function E equivalently becomes ▲mathematical formula, chemical formula, table etc. ▼ Each link weight value W_i_j and each threshold value θ_i are set as w_i_j=-4aδ_i_j-2b-2cS_iS_
jR_i_j−2dP_iP_jHowever, δ_i_j=[
1(i=j), 0(i≠j)]θ_i=-2a-2b-
3. The risk-minimizing portfolio selection device using an interconnected network according to claim 2, wherein 2dPP_i is set as 2dPP_i. 4) The node value updating means stores each of the node values before update as X_i(t) and each of the node values after update as X_i(t).
+1) and A is a predetermined positive constant, X_i(t+
1)=X_i(t)+A(Σw_i_jX_i(t)+
4. The risk-minimizing portfolio selection device using an interconnected network according to claim 3, wherein each node value is sequentially updated so as to satisfy θ_i). 5) The mutual coupling according to claim 1 or 2, further comprising an initial value setting means for randomly setting the initial value of each node value on the network storage means within a range that complies with the constraint condition. A risk-minimizing portfolio selection device using a type network.