Assuming the investor is uncertainty-aversion,the multiprior approach is applied to studying the problem of portfolio choice under the uncertainty about the expected return of risky asset based on the mean-variance mo...Assuming the investor is uncertainty-aversion,the multiprior approach is applied to studying the problem of portfolio choice under the uncertainty about the expected return of risky asset based on the mean-variance model. By introducing a set of constraint constants to measure uncertainty degree of the estimated expected return,it built the max-min model of multi-prior portfolio,and utilized the Lagrange method to obtain the closed-form solution of the model,which was compared with the mean-variance model and the minimum-variance model; then,an empirical study was done based on the monthly returns over the period June 2011 to May 2014 of eight kinds of stocks in Shanghai Exchange 50 Index. Results showed,the weight of multi-prior portfolio was a weighted average of the weight of mean-variance portfolio and that of minimumvariance portfolio; the steady of multi-prior portfolio was strengthened compared with the mean-variance portfolio; the performance of multi-prior portfolio was greater than that of minimum-variance portfolio. The study demonstrates that the investor can improve the steady of multi-prior portfolio as well as its performance for some appropriate constraint constants.展开更多
In order to study the effect of different risk measures on the efficient portfolios (fron- tier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper ...In order to study the effect of different risk measures on the efficient portfolios (fron- tier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.展开更多
Discussing results in asset pricing and efficient portfolio allocation,we show that mixed success and errors in these results often follow from a lack of information about the asset return distribution and wrong assum...Discussing results in asset pricing and efficient portfolio allocation,we show that mixed success and errors in these results often follow from a lack of information about the asset return distribution and wrong assumptions about its properties.Some mistakes in asset pricing come from the assumption of symmetry in return distributions.Some errors in efficient portfolio allocation follow from Markowitz’s approach when applying it to portfolio optimization of skewed asset returns.The Extended Merton model(EMM),generating skewed return distributions,demonstrates that(i)in skewed asset returns,the variance is not an adequate measure of risks and(ii)positive skewness in the asset returns comes together with a high default probability.Thus,the maximization of the mean portfolio returns and skewness with controlled variance used in mainstream papers can critically increase portfolio risks.We present the new settings of the optimal portfolio allocation problem leading to less risky efficient portfolios than the solutions suggested in all previous papers.展开更多
This paper is concerned with a study on the efficient frontier characters of portfolio with transaction cost. The conclusion is drawn that all portfolios are of positive correlation on the efficient frontier with tran...This paper is concerned with a study on the efficient frontier characters of portfolio with transaction cost. The conclusion is drawn that all portfolios are of positive correlation on the efficient frontier with transaction cost; the sufficient condition for the derivable efficient frontier has also been achieved. Meanwhile, in comparison with the position of the efficient frontier without transaction cost in the plane (σ 2,R), the conclusion has been made that the efficient frontiers with transaction cost drift and its opening shrinks correspondingly. With this study, the content of the efficient frontier is further enriched. It’s very constructive and important for the practical portfolio investment strategy.展开更多
In this paper, we consider an insurance company which has the option of investing in a risky asset and a risk-free asset, whose price parameters are driven by a finite state Markov chain. The risk process of the insur...In this paper, we consider an insurance company which has the option of investing in a risky asset and a risk-free asset, whose price parameters are driven by a finite state Markov chain. The risk process of the insurance company is modeled as a diffusion process whose diffusion and drift parameters switch over time according to the same Markov chain. We study the Markov-modulated mean-variance problem for the insurer and derive explicitly the closed form of the efficient strategy and efficient frontier. In the case of no regime switching, we can see that the efficient frontier in our paper coincides with that of [10] when there is no pure jump.展开更多
We establish, through solving semi-infinite programming problems, bounds on the probability of safely reaching a desired level of wealth on a finite horizon, when an investor starts with an optimal mean-variance finan...We establish, through solving semi-infinite programming problems, bounds on the probability of safely reaching a desired level of wealth on a finite horizon, when an investor starts with an optimal mean-variance financial investment strategy under a non-negative wealth restriction.展开更多
Mean-variance portfolio optimization models are sensitive to uncertainty in risk-return estimates,which may result in poor out-of-sample performance.In particular,the estimates may suffer when the number of assets con...Mean-variance portfolio optimization models are sensitive to uncertainty in risk-return estimates,which may result in poor out-of-sample performance.In particular,the estimates may suffer when the number of assets considered is high and the length of the return time series is not sufficiently long.This is precisely the case in the cryptocur-rency market,where there are hundreds of crypto assets that have been traded for a few years.We propose enhancing the mean-variance(MV)model with a pre-selection stage that uses a prototype-based clustering algorithm to reduce the number of crypto assets considered at each investment period.In the pre-selection stage,we run a prototype-based clustering algorithm where the assets are described by variables representing the profit-risk duality.The prototypes of the clustering partition are auto-matically examined and the one that best suits our risk-aversion preference is selected.We then run the MV portfolio optimization with the crypto assets of the selected cluster.The proposed approach is tested for a period of 17 months in the whole cryp-tocurrency market and two selections of the cryptocurrencies with the higher market capitalization(175 and 250 cryptos).We compare the results against three methods applied to the whole market:classic MV,risk parity,and hierarchical risk parity methods.We also compare our results with those from investing in the market index CCI30.The simulation results generally favor our proposal in terms of profit and risk-profit financial indicators.This result reaffirms the convenience of using machine learning methods to guide financial investments in complex and highly-volatile environments such as the cryptocurrency market.展开更多
This paper studies the multi-period mean-variance(MV)asset-liability portfolio management problem(MVAL),in which the portfolio is constructed by risky assets and liability.It is worth mentioning that the impact of gen...This paper studies the multi-period mean-variance(MV)asset-liability portfolio management problem(MVAL),in which the portfolio is constructed by risky assets and liability.It is worth mentioning that the impact of general correlation is considered,i.e.,the random returns of risky assets and the liability are not only statistically correlated to each other but also correlated to themselves in different time periods.Such a model with a general correlation structure extends the classical multiperiod MVAL models with assumption of independent returns.The authors derive the explicit portfolio policy and the MV efficient frontier for this problem.Moreover,a numerical example is presented to illustrate the efficiency of the proposed solution scheme.展开更多
This paper considers a continuous-time mean-variance portfolio selection with regime-switching and random horizon.Unlike previous works,the dynamic of assets are described by non-Markovian regime-switching models in t...This paper considers a continuous-time mean-variance portfolio selection with regime-switching and random horizon.Unlike previous works,the dynamic of assets are described by non-Markovian regime-switching models in the sense that all the market parameters are predictable with respect to the filtration generated jointly by Markov chain and Brownian motion.The Markov chain is assumed to be independent of Brownian motion,thus the market is incomplete.The authors formulate this problem as a constrained stochastic linear-quadratic optimal control problem.The authors derive closed-form expressions for both the optimal portfolios and the efficient frontier.All the results are different from those in the problem with fixed time horizon.展开更多
Portfolio selection is one of the major capital allocation and budgeting issues in financial management, and a variety of models have been presented for optimal selection. Semi-variance is usually considered as a risk...Portfolio selection is one of the major capital allocation and budgeting issues in financial management, and a variety of models have been presented for optimal selection. Semi-variance is usually considered as a risk factor in drawing up an efficient frontier and the optimal portfolio. Since semi-variance offers a better estimation of the actual risk portfolio, it was used as a measure to approximate the risk of investment in this work. The optimal portfolio selection is one of the non-deterministic polynomial(NP)-hard problems that have not been presented in an exact algorithm, which can solve this problem in a polynomial time. Meta-heuristic algorithms are usually used to solve such problems. A novel hybrid harmony search and artificial bee colony algorithm and its application were introduced in order to draw efficient frontier portfolios. Computational results show that this algorithm is more successful than the harmony search method and genetic algorithm. In addition, it is more accurate in finding optimal solutions at all levels of risk and return.展开更多
In this paper we generalize the single-period Markowitz Mean-Variance portfolio selection problem. The Markowitz’s model requires that after choosing the number of each security which constructs the portfolio in the ...In this paper we generalize the single-period Markowitz Mean-Variance portfolio selection problem. The Markowitz’s model requires that after choosing the number of each security which constructs the portfolio in the beginning of the investment period, these numbers remain constant during and at the end of the investment period. We drop this as-sump- tion and consider an investment model in which the number of each security can vary randomly during the in-vestment period. Indeed we consider a single-period investment with the property that the initial weight of each security is not equal to the final weight of that security. We redefine the notion of the rate of return of each security and show that the return of the investment in a cash account is not certain. We investigate some alternatives among risky securi-ties which acts similar to cash accounts. For this we introduce the notion of free security and relate free securities to a riskless se- curity.展开更多
This paper studied cardinality constrained portfolio with integer weight.We suggested two optimization models and used two genetic algorithms to solve them.In this paper,after finding well matching stocks,according to...This paper studied cardinality constrained portfolio with integer weight.We suggested two optimization models and used two genetic algorithms to solve them.In this paper,after finding well matching stocks,according to investor’s target by using first genetic algorithm,we gave optimal integer weight of portfolio with well matching stocks by using second genetic algorithm.Through numerical comparisons with other feasible portfolios,we verified advantages of designed portfolio with two genetic algorithms.For a numerical comparison,we used a prepared data consisted of 18 stocks listed in S&P 500 and numerical example strongly supported the designed portfolio in this paper.Also,we made all comparisons visible through all feasible efficient frontiers.展开更多
This paper is a revised and expanded version of a paper entitled “The static and dynamic criteria of building an investment asset portfolio” presented at International Conference on Applied Economics (ICOAE, 2014), ...This paper is a revised and expanded version of a paper entitled “The static and dynamic criteria of building an investment asset portfolio” presented at International Conference on Applied Economics (ICOAE, 2014), Chania, 3-5 July 2014 and published at Procedia Economics and Finance, Volume 14, Pages 575-584 (2014) [1]. At the previous research, it showed the significance to go beyond the scope of selecting one or another metric of static efficiency. And the attention was paid to the dynamic efficiency criteria. The ICOAE 2015 research gives brief results of that work, which is only one of applied areas of polydimensional efficiency measurement model (PEMM). Research work on PEMM conceptual and methodical elaboration has been started in the author’s dissertation study [2] and continued in the practical activity and materialized in Innovative LLC (limited liability company) creating project. The research is concentrating on the real economic benefit of 3D PEMM (thee criterial PEMM version) implementation. In the first part of ICOAE 2015 empirical study, the dynamic component of 3D PEMM on the industrial level was tested. Next, the company economic profit changes and dynamic-market 3D PEMM components correlation was estimated. Finally, the economic benefit of 3D PEMM functional operationalization in the framework of management systems development was calculated.展开更多
This paper analyzes the portfolio with inflation and transaction cost by broadening mean-variance model assumption. Based on the comparison between efficient frontier with and without transaction cost and inflation, t...This paper analyzes the portfolio with inflation and transaction cost by broadening mean-variance model assumption. Based on the comparison between efficient frontier with and without transaction cost and inflation, the conclusion is drawn that the new efficient frontier is revolving and the new investment strategy changes. Furthermore, we provide a numerical example based on real world data.展开更多
In reality,when facing a multi-period asset-liability portfolio selection problem,the risk aversion attitude of a mean-variance investor may depend on the wealth level and liability level.Thus,in this paper,we propose...In reality,when facing a multi-period asset-liability portfolio selection problem,the risk aversion attitude of a mean-variance investor may depend on the wealth level and liability level.Thus,in this paper,we propose a state-dependent risk aversion model for the investor,in which risk aversion is a linear function of current wealth level and current liability level.Due to the time inconsistency of the resulting multi-period asset-liability mean-variance model,we investigate its time-consistent portfolio policy by solving a nested mean-variance game formulation.We derive the analytical time-consistent portfolio policy,which takes a linear form of current wealth level and current liability level.We also analyze the influence of the risk aversion coefficients on the time-consistent portfolio policy and the investment performance via a numerical example.展开更多
基金National Natural Science Foundations of China(Nos.71271003,71171003)Programming Fund Project of the Humanities and Social Sciences Research of the Ministry of Education of China(No.12YJA790041)
文摘Assuming the investor is uncertainty-aversion,the multiprior approach is applied to studying the problem of portfolio choice under the uncertainty about the expected return of risky asset based on the mean-variance model. By introducing a set of constraint constants to measure uncertainty degree of the estimated expected return,it built the max-min model of multi-prior portfolio,and utilized the Lagrange method to obtain the closed-form solution of the model,which was compared with the mean-variance model and the minimum-variance model; then,an empirical study was done based on the monthly returns over the period June 2011 to May 2014 of eight kinds of stocks in Shanghai Exchange 50 Index. Results showed,the weight of multi-prior portfolio was a weighted average of the weight of mean-variance portfolio and that of minimumvariance portfolio; the steady of multi-prior portfolio was strengthened compared with the mean-variance portfolio; the performance of multi-prior portfolio was greater than that of minimum-variance portfolio. The study demonstrates that the investor can improve the steady of multi-prior portfolio as well as its performance for some appropriate constraint constants.
基金Supported by the NNSF of China (10571141) the Key Project of the NNSF of China (70531030).
文摘In order to study the effect of different risk measures on the efficient portfolios (fron- tier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.
文摘Discussing results in asset pricing and efficient portfolio allocation,we show that mixed success and errors in these results often follow from a lack of information about the asset return distribution and wrong assumptions about its properties.Some mistakes in asset pricing come from the assumption of symmetry in return distributions.Some errors in efficient portfolio allocation follow from Markowitz’s approach when applying it to portfolio optimization of skewed asset returns.The Extended Merton model(EMM),generating skewed return distributions,demonstrates that(i)in skewed asset returns,the variance is not an adequate measure of risks and(ii)positive skewness in the asset returns comes together with a high default probability.Thus,the maximization of the mean portfolio returns and skewness with controlled variance used in mainstream papers can critically increase portfolio risks.We present the new settings of the optimal portfolio allocation problem leading to less risky efficient portfolios than the solutions suggested in all previous papers.
文摘This paper is concerned with a study on the efficient frontier characters of portfolio with transaction cost. The conclusion is drawn that all portfolios are of positive correlation on the efficient frontier with transaction cost; the sufficient condition for the derivable efficient frontier has also been achieved. Meanwhile, in comparison with the position of the efficient frontier without transaction cost in the plane (σ 2,R), the conclusion has been made that the efficient frontiers with transaction cost drift and its opening shrinks correspondingly. With this study, the content of the efficient frontier is further enriched. It’s very constructive and important for the practical portfolio investment strategy.
基金supported by National Basic Research Program of China(973 Program)(2007CB814905)the National Natural Science Foundation of China(10871102)the Research Fund for the Doctorial Program of Higher Education
文摘In this paper, we consider an insurance company which has the option of investing in a risky asset and a risk-free asset, whose price parameters are driven by a finite state Markov chain. The risk process of the insurance company is modeled as a diffusion process whose diffusion and drift parameters switch over time according to the same Markov chain. We study the Markov-modulated mean-variance problem for the insurer and derive explicitly the closed form of the efficient strategy and efficient frontier. In the case of no regime switching, we can see that the efficient frontier in our paper coincides with that of [10] when there is no pure jump.
文摘We establish, through solving semi-infinite programming problems, bounds on the probability of safely reaching a desired level of wealth on a finite horizon, when an investor starts with an optimal mean-variance financial investment strategy under a non-negative wealth restriction.
基金supported by the European Union’s H2020 Coordination and Support Actions CA19130 under Grant Agreement Period 2.
文摘Mean-variance portfolio optimization models are sensitive to uncertainty in risk-return estimates,which may result in poor out-of-sample performance.In particular,the estimates may suffer when the number of assets considered is high and the length of the return time series is not sufficiently long.This is precisely the case in the cryptocur-rency market,where there are hundreds of crypto assets that have been traded for a few years.We propose enhancing the mean-variance(MV)model with a pre-selection stage that uses a prototype-based clustering algorithm to reduce the number of crypto assets considered at each investment period.In the pre-selection stage,we run a prototype-based clustering algorithm where the assets are described by variables representing the profit-risk duality.The prototypes of the clustering partition are auto-matically examined and the one that best suits our risk-aversion preference is selected.We then run the MV portfolio optimization with the crypto assets of the selected cluster.The proposed approach is tested for a period of 17 months in the whole cryp-tocurrency market and two selections of the cryptocurrencies with the higher market capitalization(175 and 250 cryptos).We compare the results against three methods applied to the whole market:classic MV,risk parity,and hierarchical risk parity methods.We also compare our results with those from investing in the market index CCI30.The simulation results generally favor our proposal in terms of profit and risk-profit financial indicators.This result reaffirms the convenience of using machine learning methods to guide financial investments in complex and highly-volatile environments such as the cryptocurrency market.
基金partially supported by the National Natural Science Foundation of China under Grant Nos.72201067,12201129,and 71973028the Natural Science Foundation of Guangdong Province under Grant No.2022A1515010839+1 种基金the Project of Science and Technology of Guangzhou under Grant No.202102020273the Opening Project of Guangdong Province Key Laboratory of Computational Science at Sun Yat-sen University under Grant No.2021004。
文摘This paper studies the multi-period mean-variance(MV)asset-liability portfolio management problem(MVAL),in which the portfolio is constructed by risky assets and liability.It is worth mentioning that the impact of general correlation is considered,i.e.,the random returns of risky assets and the liability are not only statistically correlated to each other but also correlated to themselves in different time periods.Such a model with a general correlation structure extends the classical multiperiod MVAL models with assumption of independent returns.The authors derive the explicit portfolio policy and the MV efficient frontier for this problem.Moreover,a numerical example is presented to illustrate the efficiency of the proposed solution scheme.
基金supported by the Natural Science Foundation of China under Grant Nos.11831010,12001319 and 61961160732Shandong Provincial Natural Science Foundation under Grant Nos.ZR2019ZD42 and ZR2020QA025+2 种基金The Taishan Scholars Climbing Program of Shandong under Grant No.TSPD20210302Ruyi Liu acknowledges the Discovery Projects of Australian Research Council(DP200101550)the China Postdoctoral Science Foundation(2021TQ0196)。
文摘This paper considers a continuous-time mean-variance portfolio selection with regime-switching and random horizon.Unlike previous works,the dynamic of assets are described by non-Markovian regime-switching models in the sense that all the market parameters are predictable with respect to the filtration generated jointly by Markov chain and Brownian motion.The Markov chain is assumed to be independent of Brownian motion,thus the market is incomplete.The authors formulate this problem as a constrained stochastic linear-quadratic optimal control problem.The authors derive closed-form expressions for both the optimal portfolios and the efficient frontier.All the results are different from those in the problem with fixed time horizon.
文摘Portfolio selection is one of the major capital allocation and budgeting issues in financial management, and a variety of models have been presented for optimal selection. Semi-variance is usually considered as a risk factor in drawing up an efficient frontier and the optimal portfolio. Since semi-variance offers a better estimation of the actual risk portfolio, it was used as a measure to approximate the risk of investment in this work. The optimal portfolio selection is one of the non-deterministic polynomial(NP)-hard problems that have not been presented in an exact algorithm, which can solve this problem in a polynomial time. Meta-heuristic algorithms are usually used to solve such problems. A novel hybrid harmony search and artificial bee colony algorithm and its application were introduced in order to draw efficient frontier portfolios. Computational results show that this algorithm is more successful than the harmony search method and genetic algorithm. In addition, it is more accurate in finding optimal solutions at all levels of risk and return.
文摘In this paper we generalize the single-period Markowitz Mean-Variance portfolio selection problem. The Markowitz’s model requires that after choosing the number of each security which constructs the portfolio in the beginning of the investment period, these numbers remain constant during and at the end of the investment period. We drop this as-sump- tion and consider an investment model in which the number of each security can vary randomly during the in-vestment period. Indeed we consider a single-period investment with the property that the initial weight of each security is not equal to the final weight of that security. We redefine the notion of the rate of return of each security and show that the return of the investment in a cash account is not certain. We investigate some alternatives among risky securi-ties which acts similar to cash accounts. For this we introduce the notion of free security and relate free securities to a riskless se- curity.
文摘This paper studied cardinality constrained portfolio with integer weight.We suggested two optimization models and used two genetic algorithms to solve them.In this paper,after finding well matching stocks,according to investor’s target by using first genetic algorithm,we gave optimal integer weight of portfolio with well matching stocks by using second genetic algorithm.Through numerical comparisons with other feasible portfolios,we verified advantages of designed portfolio with two genetic algorithms.For a numerical comparison,we used a prepared data consisted of 18 stocks listed in S&P 500 and numerical example strongly supported the designed portfolio in this paper.Also,we made all comparisons visible through all feasible efficient frontiers.
文摘This paper is a revised and expanded version of a paper entitled “The static and dynamic criteria of building an investment asset portfolio” presented at International Conference on Applied Economics (ICOAE, 2014), Chania, 3-5 July 2014 and published at Procedia Economics and Finance, Volume 14, Pages 575-584 (2014) [1]. At the previous research, it showed the significance to go beyond the scope of selecting one or another metric of static efficiency. And the attention was paid to the dynamic efficiency criteria. The ICOAE 2015 research gives brief results of that work, which is only one of applied areas of polydimensional efficiency measurement model (PEMM). Research work on PEMM conceptual and methodical elaboration has been started in the author’s dissertation study [2] and continued in the practical activity and materialized in Innovative LLC (limited liability company) creating project. The research is concentrating on the real economic benefit of 3D PEMM (thee criterial PEMM version) implementation. In the first part of ICOAE 2015 empirical study, the dynamic component of 3D PEMM on the industrial level was tested. Next, the company economic profit changes and dynamic-market 3D PEMM components correlation was estimated. Finally, the economic benefit of 3D PEMM functional operationalization in the framework of management systems development was calculated.
文摘This paper analyzes the portfolio with inflation and transaction cost by broadening mean-variance model assumption. Based on the comparison between efficient frontier with and without transaction cost and inflation, the conclusion is drawn that the new efficient frontier is revolving and the new investment strategy changes. Furthermore, we provide a numerical example based on real world data.
基金This research was supported by the National Natural Science Foundation of China(Nos.71601107,71671106 and 71201094)Shanghai Pujiang Program(No.15PJC051)+1 种基金the State Key Program in the Major Research Plan of National Natural Science Foundation of China(No.91546202)Program for Innovative Research Team of Shanghai University of Finance and Economics.
文摘In reality,when facing a multi-period asset-liability portfolio selection problem,the risk aversion attitude of a mean-variance investor may depend on the wealth level and liability level.Thus,in this paper,we propose a state-dependent risk aversion model for the investor,in which risk aversion is a linear function of current wealth level and current liability level.Due to the time inconsistency of the resulting multi-period asset-liability mean-variance model,we investigate its time-consistent portfolio policy by solving a nested mean-variance game formulation.We derive the analytical time-consistent portfolio policy,which takes a linear form of current wealth level and current liability level.We also analyze the influence of the risk aversion coefficients on the time-consistent portfolio policy and the investment performance via a numerical example.