JPH0635918A - Port folio optimizing method - Google Patents

Abstract

PURPOSE:To accurately decide the providing ratio of funds for a port folio by designating a port folio constituting brand and estimating distribution convarience between these port folio constituting brands based on the price trend of a stock price model and the stock market. CONSTITUTION:N pieces of brands constituting the port folio are designated in processing 1. The distribution convarience of a stock price profit rate between the individual bills constituting the port folio is estimated in processing 2. In processing 3, distribution deltap of the port folio estimated in the processing 2 is calculated by the formula (defining the convarience of brands (i) and (j) as deltaij, defining the distribution of the brand (i) as deltaii and defining the distribution convarience adding both of them as deltaij.) Then, the distribution is minimized by using the non-linear optimizing method and an investiment ratio ci to individual bills is decided.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to optimization for determining a fund input ratio to a portfolio of financial assets, and more particularly to improvement of prediction accuracy of portfolio diversification by a statistical method.

[0002]

2. Description of the Related Art As an optimization method for determining the incorporation ratio of each stock in a portfolio composed of multiple stocks,
Junko Maru, Megumi Suto, Midori Komine "Modern Securities Market Analysis" p
59-p63 As described in Toyo Keizai Inc., a method is known that determines the portfolio variance from the variance-covariance of the stock price-earnings ratio among individual securities and determines the incorporation ratio so as to minimize the variance. There is. Here, the price-earnings ratio between individual securities is a sample variance covariance based on past stock price data.

[0003]

The above-mentioned prior art has a problem in that the estimation of the variance covariance of the stock price profit ratio between individual securities is directly obtained from the sample variance covariance. That is, the portfolio is constructed for asset management in the future, but only the past data is used and no consideration is given to the future price structure.

[0004]

[Means for Solving the Problems] In order to solve the above problems, the following means are newly provided.

A means for constructing a stock price model having not only the spatial correlation structure of the price fluctuation process of a large number of stocks but also the time series correlation structure is provided. In addition, based on the original term that is not explained from the correlation of other issues among the price fluctuation terms of each issue determined from the above model, the past price-earnings ratio data is corrected to data that considers the time structure, and the variance between issues is adjusted. Means were provided to estimate the covariance based on this modified data.

[0006]

In the portfolio optimizing method of the present invention, the portfolio constituent issues are designated, and the variance covariance between the constituent issues is estimated based on the stock price model and the price trend of the stock market. At this time, the structure is estimated from the stock price of the stock based on the stock price model composed of the observation equation and the state equation described by the stock price return of the portfolio constituents and the common variable factor variable, and the common fluctuation determined from the model. From the original variable factor term that cannot be explained only by the factor variable, the past price-earnings ratio data is modified in consideration of the time structure, and the variance-covariance among stocks is estimated based on this modified data. Then, by minimizing the portfolio variance calculated based on the estimated variance covariance, the investment ratio of each issue in the portfolio composition can be determined.

[0007]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the portfolio optimizing method of the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram of a portfolio optimization method according to the present invention, and FIG. 2 is a detailed diagram of a variance / covariance estimation unit of the stock price profit ratio among individual securities constituting the portfolio.

In process 1, N brands constituting the portfolio are designated. In the process 2, the variance covariance of the price-earnings ratio among the individual securities of the portfolio composition (the covariance σij of the i issue and the j issue, the variance σii of the i issue, both are described as the variance covariance σij) is estimated. In process 3, based on the variance covariance between the individual securities that make up the portfolio estimated in process 2, the portfolio variance σp is obtained by (Equation 10), and the nonlinear optimization method is used to minimize this variance. Then, the investment ratio ci for the individual securities is determined.

Next, the variance / covariance estimator of the price / earnings ratio among the individual securities constituting the portfolio in FIG. 1-Process 3 will be described with reference to FIG.

The process 5 obtains the price-earnings ratio during the analysis period (t = 1, ..., T T is the portfolio setting date) of the issues (N issues) that make up the portfolio. this is,
First, the stock price Pit (stock i, time t) of each stock from period 0 to T is read from the stock price database 13, and the stock price profit ratio, which is the continuous yield of stock prices, is calculated by the following formula.

[0012]

[Equation 1]

Judgment 6 judges whether the current stock market is in a stock price rising phase, a stock price falling phase, or in any other state.
When the stock price is in the rising period, the processes 7, 8 and 9 are performed, in the stock price falling period, the sample price-earnings ratio git corrected by the processes 7, 8 and 10 and in the other times is calculated, and the process 12 is performed.
Variance covariance between stocks in the portfolio composition
Find ij.

In process 7, the stock structure is obtained by the state space model. Regarding this, Japanese Patent Application No. 03-26356
Detailed in 2. That is, the stock structure is calculated according to the following model. Stock return rate xit (i =
1 ,. ． ． , T), there are q common factors fjt (j = 1, ..., q) as common variation factors. This is a model in which xit fluctuates due to fluctuation factors of the common factor. This model consists of the following two equations.

1. Observation equation: A model expressing the relationship between xit and fjt

[0016]

[Equation 2]

Here, εit is a unique variation factor of each brand.

2. State equation: A model expressing the time structure of the common factor fjt

[0019]

[Equation 3]

Here, ηit is white noise.

Here, it is assumed that the stock price follows the above equation, and the constant coefficient ai is calculated based on the stock price profit ratio obtained in the process 5.
The stock structure is calculated by finding j and bjk.

In process 8, the unique fluctuation factor Eit in consideration of the unique fluctuation factor εit and the time structure of the model is calculated from the actual stock price profit ratio and the model calculated in the process 7.

The unique fluctuation factor εit is obtained by subtracting the part explained from the common fluctuation factors of the model from the actual price-earnings ratio as in the following formula.

[0024]

[Equation 4]

Unique variation factor Eit considering the time structure
Is calculated as follows. First, the model

Le

Based on [Equation 3], the common variation factor Fjt from time 1 period (t-1) to time t is obtained from the following equation.

[0027]

[Equation 5]

Next, the unique variation factor E considering the time structure
It is calculated from the actual price-earnings ratio as shown in the following expression and the common fluctuation factor of the model using the common fluctuation factor Fjt predicted from the model.

[0029]

[Equation 6]

In process 9, corrected stock price earnings ratio data dt is calculated by the following equation using the unique variable factor εit found in process 8 and the unique variable factor Eit considering the time structure.

[0031]

[Equation 7]

Further, when the stock price is in the declining period, the stock price profit ratio data git corrected as in the process 10 uses the unique fluctuation factor εit obtained in the process 8 and the unique fluctuation factor Eit considering the time structure. And ask for:

[0033]

[Equation 8]

When the stock price is neither in the rising period nor in the falling period, the past price-earnings ratio data is regarded as the corrected data git as in the process 11.

The process 12 is based on the corrected price-earnings ratio data, and the sample variance covariance σij is calculated according to the following equation.
To estimate. Here, E () represents an expected value and is calculated using a sample average.

[0036]

[Equation 9]

From the sample covariance matrix thus obtained,
The variance σp of the portfolio is calculated by the following (Equation 10), and this variance is minimized using a non-linear optimization method.
The optimal investment ratio ci for individual securities is determined.

[0038]

[Equation 10]

[0039]

The portfolio optimization method of the present invention has the following effects.

When the stock market is in a steady rising period such as 1989, the portfolio optimization method according to this method
The value of the portfolio when the investment ratio for the portfolio constituents is determined is an average value increase of 5% compared to when the investment ratio is determined by the conventional method. Contrary to the stock price rising period such as 1989, the portfolio value when the investment ratio for the portfolio constituents is determined by the portfolio optimization method by the method is also for the steady stock price falling period. It has been confirmed that the average value increase is 5% compared to the case where the investment ratio is determined by the conventional method.

[Brief description of drawings]

FIG. 1 is a block diagram of a portfolio optimization method according to an embodiment of the present invention.

FIG. 2 is a block diagram of an estimation method of a variance-covariance matrix between portfolio constituents.

Claims (2)

[Claims] 1. A portfolio construction method, in which portfolio constituents are designated, and variance and covariance among the constituents is estimated based on a stock price model and a stock market price trend,
A portfolio optimizing method characterized by determining the investment ratio of each issue in the portfolio composition by minimizing the portfolio variance calculated based on the variance covariance. 2. The structure according to claim 1, the structure of which is estimated from the stock price of the stock based on a stock price model composed of an observation equation and a state equation described from the stock price profit ratio of the portfolio constituent stock and the common variable factor variable, It is characterized by correcting the past price-earnings ratio data from the original variable factor term that is not explained only by the common variable factor determined from the model, and estimating the variance-covariance among stocks based on this corrected data. Portfolio optimization method.