JP2005108263A - Method and device for evaluating/controlling/measuring portfolio - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To evaluate a portfolio according to estimated economic situation. <P>SOLUTION: An optimization processing part executes specification step (S33) for specifying a plurality of regimes from investment information, stored in a storage part by use of a plurality of pieces of observable data; calculation step (S34) for calculating the risk and return of the portfolio and a regime definition function/resume probability for each regime specified in the specification step; and optimization step (S35) for maximizing the return with a predetermined value or less of risk and minimizing the risk with a predetermined value or less of return, under the regime definition function or resume probability. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a portfolio evaluation / control / measurement method and system, and more particularly, portfolio evaluation / control for providing investors with services related to evaluation, control, and measurement in various investment problems. -It is related with the measuring method and its system.

  In recent years, services related to evaluation, control and measurement in various investment problems have been provided to investors. An investor investing in a plurality of assets simultaneously is called a portfolio, and a portfolio is constructed using such a service. As the portfolio selection theory, for example, the classic Markowitz theory and the Kelly universal portfolio theory (hereinafter referred to as KUP theory) are known. Both theories are those that optimally control the portfolio risk / return trade-off. That is, it is based on a “risk / return criterion” in which a portfolio with a large return is preferable if the risk is the same, and a portfolio with a small risk is preferable if the return is the same. The Markowitz theory only considers investment for one period, whereas the KUP theory is different in that it takes a medium- to long-term perspective and responds to a more realistic investment environment.

Assets that can be monitored for return on investment relative to invested capital. And here in the investment rate of return R _t,

Where S _t is the asset price of the current period, S _t−1 is the asset price of the previous period, and D _t is the gain excluding the gain obtained by the price movement of the asset price. For example, D _t corresponds to a dividend in stock investment. An investment refers to an investment made for all assets whose return on investment can be observed.

  FIG. 1 shows a conventional evaluation method for investment problems. First, the investor selects one or more assets and makes them a portfolio (S11). Next, all data relating to investor preferences for risk and return are entered as parameters. Further, investment information such as return on investment and financial data affecting the return on investment is collected and input for the selected asset. The investment information is obtained from, for example, an external data provider company or a newspaper (S12).

  The registered portfolio is optimized according to a predetermined standard (S13), and an optimum asset allocation ratio of the fund is determined (S14). Here, the fund means capital used by an investor or a group of investors for managing a portfolio and capital increased or decreased as a result of investment. Finally, a simulation for measuring return and risk is performed for the optimized portfolio (S15). When the evaluation result is fed back and further evaluation is performed, the process returns to step S12. When the feedback is not performed, the process ends.

  The predetermined criteria include the “risk / return criteria” described above. This criterion is, in the field of financial economics, what portfolio should be selected at each investment point to maximize the expected value of a general utility function derived from the portfolio value at the end of the investment period. , In the context of the expected utility maximization problem. It also discusses the question of what portfolio should be done at each point in the investment period, generally describing the state of the economy as a whole and assuming the return on asset dynamics. It has been.

  However, the portfolio based on the KUP theory is based on the assumption that the return of each investment period of assets to be included in the portfolio follows the same normal distribution independent from each other. It becomes constant at the point of time. This is an oversimplification of the rate of return on assets observed in the real market, does not fully describe its dynamics, and certain portfolios derived based on that assumption are not practical. There was a problem that it could not be used.

  On the other hand, in time series analysis, which is also a field of econometrics, the dynamics of macroeconomic indicators such as GDP (Gross Domestic Product) can be explained appropriately by using a time series model that explicitly incorporates two regimes. . For example, in the Hamilton model, the rate of return on assets is considered to have arisen from two normal distributions with different expected values and variances corresponding to two regimes of good economic conditions and bad economic conditions. In the real market, the asset return is observed as a mixed normal distribution in which two normal distributions are weighted with regime probabilities. However, the portfolio was not determined by explicitly using the risk / return criteria after specifying the regime based on the Hamilton model.

  The present invention has been made in view of such problems, and an object of the present invention is to provide a method and a system for evaluating, controlling, and measuring a portfolio in an estimated economic state.

  In order to achieve such an object, the present invention provides a portfolio that is one or more selected assets that are input in advance from an input unit and stored in a storage unit. An optimization processing unit connected to the input unit and the storage unit is used to operate the portfolio using investor parameters related to the risk and return of the portfolio and investment information that affects the portfolio. In the portfolio evaluation / control / measurement method to be executed, the optimization processing unit has a plurality of regime definitions as a regime which is a column vector composed of a plurality of observable real values from the investment information stored in the storage unit. A function is generated, and a plurality of regime residence probabilities, which are real values obtained by calculating the regime definition function, are calculated and stored in the storage unit One calculation step, and the optimization processing unit uses any one of the investment information, the regime definition function generated in the first calculation step, and the regime retention probability stored in the storage unit, A second calculation step of calculating an expected value of the return on investment corresponding to the return of the portfolio and a variance of the return on investment corresponding to the risk of the portfolio; the regime definition function of the arbitrarily selected regime; and the regime residence probability Based on any of the above, using the investor parameters stored in the storage unit, the optimization processing unit, under the constraint that the risk is a real value specified by the investor parameters, A third calculation step of calculating a first portfolio with the maximum return, and the reggie of an arbitrarily selected regime Based on either the definition function or the regime residence probability, the optimization processing unit uses the investor parameter stored in the storage unit, and the optimization processing unit is configured to determine the return as a real value specified by the investor parameter. A fourth calculation step for calculating a second portfolio that minimizes the risk under the constraint condition, and the optimization processing unit includes the first portfolio and the fourth calculation calculated in the third calculation step. An optimization step of storing, in the storage unit, a portfolio for any selected regime among the second portfolios calculated in step as an optimization portfolio, and the optimization stored in the storage unit in the optimization step A measurement step of measuring a measurement portfolio and outputting a measurement result.

  As described above, according to the present invention, since the optimal asset allocation ratio of the fund is determined based on the risk-return criterion of the investment amount considering the regime, the portfolio asset is determined according to the estimated economic condition. Evaluation, control, and measurement can be performed.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The present invention evaluates, controls, and measures investments based on a risk / return criterion that considers a regime. Specifically, using information available in the market, (1) calculating the probability of staying in each regime for the regimes in all investment periods, and then calculating the return on assets under each regime. Perform calculations to specify the dynamics, and (2) determine the portfolio by risk / return criteria according to the quality of the specified regime.

  FIG. 2 shows the concept of portfolio selection theory according to the present invention. We think that asset prices such as stock prices are influenced by the invisible state of the market, that is, the regime. Regime is an economic condition that is distinguished by one or more and cannot be observed directly. For example, as shown in FIG. 2A, behind the market, there are two regimes, a boom regime G and a recession regime B, and the transition between each regime is expressed by a probability transition matrix P. Regimes are based on all information available in the market because they cannot be observed directly.

Next, as shown in FIG. 2B, the asset price generation structure is specified according to the regime. If the return on investment of an asset follows a normal distribution, return and risk parameters (μ ^(G) , σ ^(G) ) under boom and parameters (μ ^(B) , σ ^(B) ) under recession Are characterized by parameters with completely different values. As a result, high returns are observed with considerable frequency under favorable conditions, and the distribution is drawn on the right side of the figure. On the other hand, the return is generally low during the recession, and the distribution shifts to the left in the figure. Investors observe asset prices as a probabilistically weighted mixed distribution of the boom and recession distributions, as depicted by the solid line in the figure.

  Asset prices are generated by mixing different distributions for each regime. Therefore, in the portfolio selection theory according to the present invention, it is estimated by classifying into a boom and recession, so investors can construct a portfolio that explicitly controls return and risk according to the scenario according to the boom and recession. can do. Here, if the Markovitz theory is adopted as the risk / return criterion, the portfolio return is the expected return on investment,

It is represented by Portfolio risk is the return on investment (standard deviation),

It is represented by On the other hand, if the KUP theory is adopted as the risk / return criterion, the return of the portfolio is the average growth rate.

It is represented by Portfolio risk is volatility in growth rates.

It is represented by

  FIG. 3 is a configuration diagram illustrating a portfolio evaluation / control / measurement system according to an embodiment of the present invention. The evaluation / control / measurement system includes an arithmetic device 201, an input device 202, and an output device 203. The input device 202 and the output device 203 are connected to the interface unit 211 of the arithmetic device 201.

  The arithmetic unit 201 includes an input unit 212 for inputting data from the input unit 202 via the interface unit 211, an optimization processing unit 213 for evaluating the portfolio, and performing a simulation and receiving the result via the interface unit 211. And a measurement unit 214 that outputs to the output device 203. The computing device 201 includes a database 215 that stores data for evaluating a portfolio.

  With such a configuration, the input unit 212 inputs investor parameters, return on investment, financial data, macroeconomic indicators, and the like from the input device 202 via the interface unit 211 and stores them in the database 215. The optimization processing unit 213 performs investment evaluation and control based on a risk / return criterion in consideration of the regime. The measurement unit 214 performs simulation on the determined portfolio and outputs the measurement result to the output device 203 via the interface unit 211. The optimization processing unit 213 and the measurement unit 214 acquire data necessary for evaluation, control, and measurement from the database 215.

  FIG. 4 is a flowchart showing a portfolio evaluation / control / measurement method according to an embodiment of the present invention. First, the investor selects one or more assets and uses them as a portfolio (S31). Next, all data relating to the investor's preference for risk and return are input from the input device 202 as investor parameters. Further, for the selected asset, all information (hereinafter referred to as investment information) that affects the return on investment, financial data, macroeconomic indicators, and return on investment is collected and input from the input device 202 ( S32). The input unit 212 inputs these data via the interface unit 211 and stores them in the database 215.

  Next, the optimization processing unit 213 specifies a plurality of regimes deterministically or probabilistically using a plurality of observable data from the investment information stored in the database 215 (S33). For each regime, the expected value and variance of the return on investment of the assets, regime probabilities such as regime residence probability, regime transition probability, etc. are calculated (S34). Based on the regime governing the investment period, the trade-off between portfolio return and risk is controlled under regime conditions (S35).

  Thus, the measurement part 214 performs the simulation regarding a return or a risk under a regime condition about the portfolio constructed in this way (S36). The simulation may be performed for a portfolio held in the past or a portfolio held in the future. In addition, the information obtained by this simulation is fed back to refine the construction and restructuring of the portfolio. When the measured risk and return are fed back for further evaluation (S37), the process returns to step S34. When feedback is not performed (S37), the measurement unit 214 calculates expected time, bankruptcy probability, and the like, outputs an evaluation result (S38), and ends the process. The output of the evaluation result will be described later with reference to FIGS.

The method of expressing the regime is described in detail. Regime Y _ti refers to one or more invisible states of the market or the economy as good, bad, or very bad. The regime in the period t _i is represented by a column vector Y _ti . Regime _{Y ti} is, K pieces of realization _{{e 1, ..., e k} , ..., e K} take. However, _ek is a column vector in which only the kth element is 1 and the other elements are 0. Here, the investment period is set to [0, T], and N + 1 discrete time points 0 = t ₀ <t ₁ <... <T _i <... <T _N = T, the interval (t _i−1 , t _i ] is called period _{t i.} regime defined function _I ti (k) is

In expressed, indicating that the period t _i, stays regime k. Here, “<,>” represents an inner product.

Shows the expected return on investment and the variance of assets required for each regime. The number of assets incorporated into the portfolio is n, the investment rate of return on assets of period t _i,

And Here, “′” represents transposition. For the return on investment of the asset and all investment information that affects this, let Φ _τ be all the information obtained up to the period τ. The expected value and variance obtained based on the information Φ _τ (τ = t ₀ ... t _N )

It expresses. At this time, based on the information Φ _τ (τ = t ₀ ... T _N ), the expected return on investment and the variance calculated for each regime,

The use of the dispersion and the expected value of the ROI in the period t _i respectively,

It is expressed. In addition to the regime, μti and Σti can also be calculated as a function by specifying other factors that explain the return on investment, for example, the excess return of TOPIX, the company size, and the net asset ratio.

Next, based on the information Φ _τ (τ = t ₀ ... T _N ), the probability that the regime of the period τ stays at k, that is, the probability of Y _ti = e _k is _defined as the regime residence probability ξ _{ti | τ} .

Represented by Here, the information [Phi _tau, represents all information available at the time tau. The regime residence probability is also a value obtained by specifically calculating the regime definition function I _ti (k) in the period t _i . Regime defined function _I ti (k) is calculated based on information _{Φ τ (τ = t 0 ...} t N), discrete values _{{e 1, ..., e k} , ..., e K} as, or real-valued It can also be calculated as a regime residence probability ξ _{ti | τ} .

Period _t regime transition probability _{P ti} from the _i-1 of the regime to the regime of the period _{t i} is,

It is represented by Here, l rows regime transition probabilities _{P ti,} k columns of elements _p kl (ti) represents the probability of transition from regime k periods _{t i-1} to the regime l periods _{t i.} Regime transition probabilities may be calculated as synchronicity, depending on the nature of the return on investment, and information that affects this, such as logarithmic growth rate of industrial production index, interest rate period structure, short-term interest rate, number of corporate bankruptcies log change rate, stock dividend yield, wage income logarithmic change rate and represents the information set [Phi _tau, sometimes calculated to have a time variable.

  The control in step S35 in FIG. 4 will be described. According to the portfolio selection theory according to the present invention, funds are allocated to assets constituting the portfolio. The portfolio is restructured by reviewing the allocation to each asset that has already been made, incorporating new assets if necessary, and increasing / decreasing funds if necessary, and updating the allocation to each asset.

It shall be made the investment for all of the period t _i. At this time, based on the regime Y _ti (t _i = t ₀ ... T _N ) that controls the investment period T, the portfolio return is maximized while controlling the portfolio risk to a certain value or less. At the same time, the portfolio risk is minimized while controlling the portfolio return below a certain value. For example, investment funds V ₀ in the beginning, and as a result, it becomes V _T in the year-end. If the KUP theory is adopted as the risk / return criterion, the variability of the growth rate of the portfolio value, that is, the logarithmic variance Var [logV _T ] of the portfolio value at the end of the period is taken as a risk and controlled to a certain value or less. At the same time, the growth rate of the portfolio value, that is, the expected value of the logarithm of the portfolio value at the end of the period, E [logV _T ] is used as a return to maximize the value.

The constraints on portfolio weight imposed in practice are the upper limit of investment amount, the lower limit, the explicit inclusion restriction given to certain assets such as the constraint of prohibition of short sale. In addition, in consideration of various constraint conditions, the turnover rate and the transaction cost may be taken into consideration. The turnover rate is the ratio expressed by the absolute value of the asset replacement amount with respect to the market value of the portfolio when the portfolio is reconstructed. The transaction cost can be suppressed by setting the rotation rate to a certain value or less.

For example, when a stock follows the geometric Brownian motion, the portfolio folio selection problem at each time point t _i (t _i = t ₀ ... T _N ) can be expressed in the form of an expected value and a variance considering the regime.

Here, as described above, the regime definition function I _t (k) may be a discrete value e _k (k = 1,..., K) or a regime that is an estimated value depending on the specific method. It can also be a retention probability.

  The simulation in step S36 in FIG. 4 will be described. The simulation may be performed for a portfolio held in the past or a portfolio held in the future. The former is based on historical asset prices and data that affect them, or based on an appropriate model related to asset prices that is built based on historical asset prices and data that affects them. A simulation is performed based on the asset price generated by the control / measurement system and the data affecting it. In this way, when the past asset price structure is realized in the future, the return and risk of the portfolio held are evaluated.

  The latter is based on forecast scenarios and models for asset prices and data affecting them. Estimate future scenarios and models, or evaluate future returns and risks of portfolios held, taking into account both this prediction and historical asset prices and the structure of factors affecting them.

  FIG. 5 is a diagram showing a first example of a portfolio evaluation result. An example in which the measurement unit 214 outputs the measured evaluation result and the like to the output device 203 via the interface unit 211 is shown. Regarding the output of the evaluation results, the vertical axis indicates asset value and the horizontal axis indicates time, and shows the value movement of the portfolio value 501 and the constituent stock 502. At a glance, you can understand the value of the portfolio at each point in the investment period. The value 501 of the portfolio is marked and displayed, for example, at the time of rebalancing or when it has increased by 10% or more. The slider 503 is a cursor for displaying detailed information at that time on the mini window.

  In this way, the value of the portfolio at each point in the investment period can be visually grasped in the estimated economic state.

  FIG. 6 is a diagram showing a second example of portfolio evaluation results. The vertical axis represents the growth rate of the portfolio value, the horizontal axis represents the variability, and a profile is displayed for each regime. In addition, various measurement results such as a simulation period are displayed simultaneously. In this way, it is possible to visually grasp the profile of the fund held, and for example, it can be compared with an index such as Nikkei 225.

FIG. 7 is a diagram showing a third example of portfolio evaluation results. The initial investment V _0, when the investment in end to V _T, the probability of the probability and initial investment for the initial investment over a fold in 1 / b times or less, respectively,

It becomes. Similarly, the expected time to increase the initial investment amount by a times or more and the expected time to reduce the initial investment amount to 1 / b times or less are respectively:

It becomes. FIG. 7 shows the expected time t ₁ until the initial investment amount becomes 1.5 times or more, with the vertical axis representing the investment amount and the horizontal axis representing the time.

  Finding the normal mix that determines the optimal allocation of funds among assets around the world is a very important issue for institutional investors. Also, determining the optimal fund allocation ratio among hedge funds and mutual funds is a very important issue for pension fund sponsors. According to the present embodiment, it is possible to determine an optimal allocation rate of funds in such an investment problem.

It is the flowchart which showed the evaluation method in the conventional investment problem. It is a figure for demonstrating the concept of the portfolio selection theory concerning this invention. It is the block diagram which showed the evaluation / control / measurement system of the portfolio concerning one Embodiment of this invention. It is the flowchart which showed the evaluation / control / measurement method of the portfolio concerning one Embodiment of this invention. It is the figure which showed the 1st example of the evaluation result of a portfolio. It is the figure which showed the 2nd example of the evaluation result of the portfolio. It is the figure which showed the 3rd example of the evaluation result of the portfolio.

Explanation of symbols

201 arithmetic unit 202 input device 203 output device 211 interface unit 212 input unit 213 optimization processing unit 214 measurement unit 215 database

Claims (1)

Using a portfolio that is one or more selected assets, input from the input unit in advance and stored in the storage unit, investor parameters relating to the risk and return of the portfolio, and investment information that affects the portfolio In the portfolio evaluation / control / measurement method executed by the optimization processing unit connected to the input unit and the storage unit in order to operate the portfolio,
The optimization processing unit generates, from the investment information stored in the storage unit, a plurality of regime definition functions as a regime that is a column vector composed of a plurality of observable real values, and calculates the regime definition function Calculating a plurality of regime residence probabilities, which are real values, and storing them in the storage unit;
The optimization processing unit corresponds to a return of the portfolio using any one of the investment information, the regime definition function generated in the first calculation step, and the regime retention probability stored in the storage unit. A second calculation step of calculating an expected return on investment and a return on investment corresponding to the risk of the portfolio;
Based on either the regime definition function of the arbitrarily selected regime or the regime residence probability, the optimization processing unit uses the investor parameter stored in the storage unit to allocate the risk to the investment. A third calculation step of calculating a first portfolio that maximizes the return under a constraint that is a real value specified by a house parameter;
Based on either the regime definition function of the arbitrarily selected regime or the regime residence probability, the optimization processing unit uses the investor parameter stored in the storage unit to return the return to the investment A fourth calculation step of calculating a second portfolio that minimizes the risk under a constraint that is a real value specified by a house parameter;
The optimization processing unit sets, as an optimized portfolio, a portfolio for any selected regime out of the first portfolio calculated in the third calculation step and the second portfolio calculated in the fourth calculation step. An optimization step of storing in the storage unit;
A portfolio evaluation / control / measurement method comprising: performing a measurement step of measuring the optimized portfolio stored in the storage unit in the optimization step and outputting a measurement result.

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