CN106251217A - Portfolio Optimization method based on historical analogy method WCVaR Risk Model - Google Patents
Portfolio Optimization method based on historical analogy method WCVaR Risk Model Download PDFInfo
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- CN106251217A CN106251217A CN201610218853.1A CN201610218853A CN106251217A CN 106251217 A CN106251217 A CN 106251217A CN 201610218853 A CN201610218853 A CN 201610218853A CN 106251217 A CN106251217 A CN 106251217A
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Abstract
The invention discloses a kind of Portfolio Optimization method based on historical analogy method WCVaR Risk Model, the Risk Model of WCVaR based on historical analogy method first has to determine the holding period historical return of investment combination, then being ranked up holding period historical return, finally choosing minima is WCVaR value.Portfolio Optimization method based on this model comprises the following steps: step one, random initializtion investment combination each target ratio between investments；Step 2, calculates WCVaR value according to model；Step 3, is optimized ratio between investments, until WCVAR value is optimal, and corresponding ratio between investments i.e. optimal Portfolio ratio.Step 3 quickly can be realized by algorithm.Present invention achieves the risk measurement under extreme case and risk averse, it is possible to be effectively applied in financial risk management and investment practice.
Description
Technical field
The present invention relates to financial modeling optimization method field, specifically a kind of based on historical analogy method WCVaR risk measurement
The Portfolio Optimization method of model.
Background technology
Along with constantly improving and development of China's financial market, increasing finance and spin-off thereof are developed.
The financial market of China is the most in line with international standards, presents more and more open situation.Meanwhile, investment channel is relative
Lacking but grows to even greater heights to the enthusiasm of financial investment with the domestic common people defines no small contrast.But financial investment is excessive risk
With high yield the patterns of investment deposited, the most effectively measure and avoid risk, while risk minimization, realizing income
Bigization, is one of the key problem of modern finance theory.
Due to complexity and the fertile tail in financial market itself, the most conventional Risk Measurement Method to quantile below
Risk is paid attention to not, and common method is the most less suitable for the tolerance of this kind of risk.It is true that because " black Swan " event prediction and control
Difficulty processed is big, destructive the most catastrophic with impact.Economic globalization, knowledge huge explosion etc. provide more preferable for us
Products & services while, various uncertain factors are also with wherein, and the probability that unexpected incidents occur also is substantially improved,
How to predict and to measure unexpected incidents risk more and more important.
Because the complexity in financial market, traditional linear programming cannot solve the nonlinear problem of complexity, in a large number
Intelligent optimization algorithm is employed wherein.Traditional particle swarm optimization algorithm process such issues that when barely satisfactory, although
Ability of searching optimum is strong, but it is low to be easily absorbed in local optimum, search precision and search efficiency, solves problem above to evading and controlling
Unexpected incidents risk is significant.
Summary of the invention
It is an object of the invention to effectively overcome tradition Risk Measurement Method deficiency in extreme circumstances, it is provided that Yi Zhongji
In the Portfolio Optimization method of historical analogy method WCVaR Risk Model, to the risk measurement under extreme case and risk
A kind of new method of offer is provided, can be considered and VaR is supplemented and perfect.
In order to achieve the above object, the technical solution adopted in the present invention is:
Portfolio Optimization method based on historical analogy method WCVaR Risk Model, it is characterised in that: first determine
The holding period historical return of investment combination, and set up WCVaR Risk Model, then holding period historical return is carried out
Sequence, chooses the holding period historical return minima optimal WCVaR value with acquisition WCVaR Risk Model, finally according to
Optimal WCVaR value tries to achieve the optimal solution of WCVaR Risk Model, and detailed process is as follows:
(1) WCVaR Risk Model, is set up as shown in Equation (1):
In formula (1), X=(x1, x2..., xm) it is the ratio between investments of each investment target, R=(r1, r2..., rn) it is
Earning rate in n holding period of investment combination, A is the gain matrix of m investment target n holding period；
(2), target ratio between investments is respectively invested in random initializtion investment combination；
(3) the minimum yield rate, in contrast holding period, and be optimized and make it maximum, until WCVaR Risk Model
WCVaR value optimal, thus change into the Solve problems of the X met under maximal condition, now corresponding each investment target is thrown
Money ratio is the optimal solution of WCVaR Risk Model.
Described Portfolio Optimization method based on historical analogy method WCVaR Risk Model, it is characterised in that: ask
The algorithm steps of the optimal solution taking WCVaR Risk Model is as follows:
(1), t=0 time, solution space randomly generates n initial solution, t represents current iteration number of times；
(2), by the p of i-th particleiIt is set to the current location of particle, piRepresent the locally optimal solution of particle；pgFor planting
The position of optimal solution in Qun；
(3), the position of more new particle i, and judge xiWhether belong to feasible zone, if the more upper bound, then take the upper bound；If under more
Boundary, then take off boundary；
(4), the fitness of particle i is calculated, if being better than the fitness of individual extreme value, with current particle seat xiSubstitute pi；
If being better than the fitness of global extremum, with current particle seat xiSubstitute global extremum pg；
(5), algorithm reaches stop condition, output globally optimal solution pgWith global optimum matter f (pg)；Otherwise return step (3)
Continue iteration.
Described Portfolio Optimization method based on historical analogy method WCVaR Risk Model, it is characterised in that: step
Suddenly in (3), particle iterative formula as shown in Equation (2): (particle iterative formula here is step (3) in algorithm？)
In formula (2), ω is inertia weight, inertia weight ω as shown in Equation (3):
ω=μmin+(μmax-μmin) × rand ()+σ × randn () (3),
In formula (3): μminIt is the minima of Stochastic inertia weight, μmaxIt it is the maximum of Stochastic inertia weight；rand()
For ［ 0,1 ］ uniform random number, randn () is the random number of normal distribution, variances sigma be used for measure stochastic variable weights omega with
Departure degree between its mathematic expectaion i.e. average；
In formula (2), C1、C2Studying factors respectively, as shown in Equation (4):
In formula (4), C1ini、C2iniRepresent Studying factors C respectively1、C2Initial value, C1fin、C2finRepresent study respectively
Factor C1、C2Iteration final value, t represents current iteration number of times, TmaxRepresenting maximum iteration time, value is 1000 here.
Advantage of the present invention is:
The WCVaR Risk Model based on historical analogy method of the present invention and Portfolio Optimization method, be determined by
The holding period historical return of investment combination, is ranked up holding period historical return, and choosing minima is WCVaR value.Again
On the basis of this, counter pushing away is applied to Portfolio Optimization, first random initializtion investment combination target ratio between investments, calculates should
The WCVaR value of ratio between investments, then continues to optimize ratio between investments, until WCVaR value is optimum, solves and obtains optimum throwing
Capital's case.Whole process is realized by algorithm, effectively solves the risk measurement under the conditions of extreme risk and risk averse problem, right
Availability risk tolerance and risk averse model and method are well to supplement.
Accompanying drawing explanation
Fig. 1 is comparison diagram in specific embodiment.
Detailed description of the invention
Portfolio Optimization method based on historical analogy method WCVaR Risk Model, it is first determined investment combination
Holding period historical return, and set up WCVaR Risk Model, then holding period historical return is ranked up, chooses
Holding period historical return minima is to obtain the optimal WCVaR value of WCVaR Risk Model, finally according to optimal WCVaR
Value tries to achieve the optimal solution of WCVaR Risk Model, and detailed process is as follows:
(1) WCVaR Risk Model, is set up as shown in Equation (1):
In formula (1), X=(x1, x2..., xm) it is the ratio between investments of each investment target, R=(r1, r2..., rn) it is
Earning rate in n holding period of investment combination, A is the gain matrix of m investment target n holding period；
(2), target ratio between investments is respectively invested in random initializtion investment combination；
(3) the minimum yield rate, in contrast holding period, and be optimized and make it maximum, until WCVaR Risk Model
WCVaR value optimal, thus change into the Solve problems of the X met under maximal condition, now corresponding each investment target is thrown
Money ratio is the optimal solution of WCVaR Risk Model.
The algorithm steps of the optimal solution asking for WCVaR Risk Model is as follows:
(1), t=0 time, solution space randomly generates n initial solution, t represents current iteration number of times；
(2), by the p of i-th particleiIt is set to the current location of particle, piRepresent the locally optimal solution of particle；pgFor planting
The position of optimal solution in Qun；
(3), the position of more new particle i, and judge xiWhether belong to feasible zone, if the more upper bound, then take the upper bound；If under more
Boundary, then take off boundary；
(4), the fitness of particle i is calculated, if being better than the fitness of individual extreme value, with current particle seat xiSubstitute pi；
If being better than the fitness of global extremum, with current particle seat xiSubstitute global extremum pg；
(5), algorithm reaches stop condition, output globally optimal solution pgWith global optimum matter f (pg)；Otherwise return step (3)
Continue iteration.
In step (3), particle iterative formula as shown in Equation (2): (particle iterative formula here be in algorithm walk
Suddenly (3)？)
In formula (2), ω is inertia weight, inertia weight ω as shown in Equation (3):
ω=μmin+(μmax-μmin) × rand ()+σ × randn () (3),
In formula (3): μminIt is the minima of Stochastic inertia weight, μmaxIt it is the maximum of Stochastic inertia weight；rand()
For ［ 0,1 ］ uniform random number, randn () is the random number of normal distribution, variances sigma be used for measure stochastic variable weights omega with
Departure degree between its mathematic expectaion i.e. average；
In formula (2), C1、C2Studying factors respectively, as shown in Equation (4):
In formula (4), C1ini、C2iniRepresent Studying factors C respectively1、C2Initial value, C1fin、C2finRepresent study respectively
Factor C1、C2Iteration final value, t represents current iteration number of times, TmaxRepresenting maximum iteration time, value is 1000 here.
Specific embodiment:
As a example by 40 stocks of Hang Seng's Hang Seng China Enterprises Index, stock code is as shown in table 1:
40 stock index tables of state-owned enterprise of table 1 Hang Seng
Choose the closing price data of on February 29,2 year 485 day of trade 3 days to 2016 March in 2014, by based on going through
The Risk Model of the WCVaR of history simulation method, uses algorithm to solve it so that the investment group that 40 stock is constituted
Close least risk, i.e. make WCVaR value maximum.The optimum combination weight obtained is as shown in table 2:
Table 2 optimum combination weight table
As it is shown in figure 1, by with Hang Seng China Enterprise Index to contrast, it was demonstrated that model is in terms of risk measurement and risk averse
Effectively.
Claims (3)
1. Portfolio Optimization method based on historical analogy method WCVaR Risk Model, it is characterised in that: first determine throwing
The holding period historical return of money combination, and set up WCVaR Risk Model, then holding period historical return is arranged
Sequence, chooses holding period historical return minima to obtain the optimal WCVaR value of WCVaR Risk Model, finally according to
Good WCVaR value tries to achieve the optimal solution of WCVaR Risk Model, and detailed process is as follows:
(1), set up shown in WCVaR Risk Model such as formula (1):
In formula (1), X=(x1, x2..., xm) it is the ratio between investments of each investment target, R=(r1, r2..., rn) for investing
Combining the earning rate in n holding period, A is the gain matrix of m investment target n holding period；
(2), target ratio between investments is respectively invested in random initializtion investment combination；
(3) the minimum yield rate, in contrast holding period, and be optimized and make it maximum, until WCVaR Risk Model
WCVaR value is optimal, thus changes into the Solve problems of the X met under maximal condition, now corresponding each investment target investment
Ratio is the optimal solution of WCVaR Risk Model.
Portfolio Optimization method based on historical analogy method WCVaR Risk Model the most according to claim 1, its
It is characterised by: the algorithm steps of the optimal solution asking for WCVaR Risk Model is as follows:
(1), t=0 time, solution space randomly generates n initial solution, t represents current iteration number of times；
(2), by the p of i-th particleiIt is set to the current location of particle, piRepresent the locally optimal solution of particle；pgFor in population
The position of optimal solution；
(3), the position of more new particle i, and judge xiWhether belong to feasible zone, if the more upper bound, then take the upper bound；If more lower bound, then take
Lower bound；
(4), the fitness of particle i is calculated, if being better than the fitness of individual extreme value, with current particle seat xiSubstitute pi；If it is excellent
Fitness in global extremum then uses current particle seat xiSubstitute global extremum pg；
(5), algorithm reaches stop condition, output globally optimal solution pgWith global optimum matter f (pg)；Otherwise return step (3) to continue
Iteration.
Portfolio Optimization method based on historical analogy method WCVaR Risk Model the most according to claim 2, its
Being characterised by: in step (3), particle iterative formula is as shown in formula (2): (particle iterative formula here is in algorithm
Step (3)？)
In formula (2), ω is inertia weight, shown in inertia weight ω such as formula (3):
ω=μmin+(μmax-μmin) × rand ()+σ × randn () (3),
In formula (3): μminIt is the minima of Stochastic inertia weight, μmaxIt it is the maximum of Stochastic inertia weight；Rand () be [0,
1] uniform random number, randn () is the random number of normal distribution, and variances sigma is used for measuring stochastic variable weights omega and its number
Departure degree between term prestige i.e. average；
In formula (2), C1、C2Studying factors respectively, as shown in formula (4):
In formula (4), C1ini、C2iniRepresent Studying factors C respectively1、C2Initial value, C1fin、C2finRepresent Studying factors respectively
C1、C2Iteration final value, t represents current iteration number of times, TmaxRepresenting maximum iteration time, value is 1000 here.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2019192134A1 (en) * | 2018-04-03 | 2019-10-10 | 平安科技（深圳）有限公司 | Portfolio optimization method, device, and storage medium |
| CN110852888A (en) * | 2019-10-18 | 2020-02-28 | 浙江工业大学 | Particle filter-based security investment portfolio optimization method |
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2016
- 2016-04-07 CN CN201610218853.1A patent/CN106251217A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2019192134A1 (en) * | 2018-04-03 | 2019-10-10 | 平安科技（深圳）有限公司 | Portfolio optimization method, device, and storage medium |
| CN110852888A (en) * | 2019-10-18 | 2020-02-28 | 浙江工业大学 | Particle filter-based security investment portfolio optimization method |
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Application publication date: 20161221 |