scholarly journals Mean-Variance Portfolio Selection with Tracking Error Penalization

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1915
Author(s):  
William Lefebvre ◽  
Grégoire Loeper ◽  
Huyên Pham
Keyword(s):  
Portfolio Selection ◽  
Tracking Error ◽  
Efficient Frontier ◽  
Minimum Variance ◽  
Sharpe Ratio ◽  
Portfolio Strategy ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance ◽  
Variance Criterion

This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in the case of misspecified parameters, by “fitting" it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean–Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio.

scholarly journals Continuous-Time Mean-Variance Portfolio Selection under the CEV Process

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Hui-qiang Ma
Keyword(s):  
Portfolio Selection ◽  
Continuous Time ◽  
Stock Price ◽  
Efficient Frontier ◽  
Optimal Portfolio ◽  
Portfolio Strategy ◽  
Cev Process ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance

We consider a continuous-time mean-variance portfolio selection model when stock price follows the constant elasticity of variance (CEV) process. The aim of this paper is to derive an optimal portfolio strategy and the efficient frontier. The mean-variance portfolio selection problem is formulated as a linearly constrained convex program problem. By employing the Lagrange multiplier method and stochastic optimal control theory, we obtain the optimal portfolio strategy and mean-variance efficient frontier analytically. The results show that the mean-variance efficient frontier is still a parabola in the mean-variance plane, and the optimal strategies depend not only on the total wealth but also on the stock price. Moreover, some numerical examples are given to analyze the sensitivity of the efficient frontier with respect to the elasticity parameter and to illustrate the results presented in this paper. The numerical results show that the price of risk decreases as the elasticity coefficient increases.

scholarly journals ON TIME CONSISTENCY FOR MEAN-VARIANCE PORTFOLIO SELECTION

2020 ◽  
Vol 23 (06) ◽  
pp. 2050042 ◽  
Author(s):  
ELENA VIGNA
Keyword(s):  
Portfolio Selection ◽  
Optimal Strategy ◽  
Time Consistency ◽  
Time Inconsistency ◽  
Selection Problem ◽  
Portfolio Selection Problem ◽  
The Mean ◽  
Optimal Approach ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper addresses a comparison between different approaches to time inconsistency for the mean-variance portfolio selection problem. We define a suitable intertemporal preferences-driven reward and use it to compare three common approaches to time inconsistency for the mean-variance portfolio selection problem over [Formula: see text]: precommitment approach, consistent planning or game theoretical approach, and dynamically optimal approach. We prove that, while the precommitment strategy beats the other two strategies (that is a well-known obvious result), the consistent planning strategy dominates the dynamically optimal strategy until a time point [Formula: see text] and is dominated by the dynamically optimal strategy from [Formula: see text] onwards. Existence and uniqueness of the break even point [Formula: see text] is proven.

Mean-variance portfolio selection with an uncertain exit-time in a regime-switching market

2019 ◽  
Vol 53 (4) ◽  
pp. 1171-1186
Author(s):  
Reza Keykhaei
Keyword(s):  
Portfolio Selection ◽  
Regime Switching ◽  
Exit Time ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Homogeneous Markov Chain ◽  
Investment Strategies ◽  
Special Cases ◽  
Mean Variance Portfolio ◽  
Mean Variance

In this paper, we deal with multi-period mean-variance portfolio selection problems with an exogenous uncertain exit-time in a regime-switching market. The market is modelled by a non-homogeneous Markov chain in which the random returns of assets depend on the states of the market and investment time periods. Applying the Lagrange duality method, we derive explicit closed-form expressions for the optimal investment strategies and the efficient frontier. Also, we show that some known results in the literature can be obtained as special cases of our results. A numerical example is provided to illustrate the results.

Prescriptive portfolio selection: a compromise between fast and slow thinking

2017 ◽  
Vol 9 (2) ◽  
pp. 98-116 ◽  
Author(s):  
Omid Momen ◽  
Akbar Esfahanipour ◽  
Abbas Seifi
Keyword(s):  
Portfolio Selection ◽  
Stock Exchange ◽  
Efficient Frontier ◽  
Fast System ◽  
Content Type ◽  
The Mean ◽  
Selection For ◽  
Mean Variance ◽  
Prescriptive Analysis

PurposeThe purpose of this paper is to develop a prescriptive portfolio selection (PPS) model based on a compromise between the idea of “fast” and “slow” thinking proposed by Kahneman. Design/methodology/approach“Fast” thinking is effortless and comfortable for investors, while “slow” thinking may result in better performance. These two systems are related to the first two types of analysis in the decision theory: descriptive, normative and prescriptive analysis. However, to compromise between “fast” and “slow” thinking, “overconfidence” is used as a weighting parameter. A case study including a sample of 161 active investors in Tehran Stock Exchange (TSE) is provided. Moreover, the feasibility and optimality of the model are discussed. FindingsResults show that the PPS recommendations are efficient with a shift from the mean-variance efficient frontier; investors prefer PPS portfolios over the advisor recommendations; and investors have no significant preference between PPS and their own expectations. Research limitations/implicationsTwo assumptions of this study include: first, investors follow their “fast” system of thinking by themselves. Second, the investors’ “slow” system of thinking is represented by advisor recommendations which are simple expected value of risk and return. Therefore, considering these two assumptions for any application is the main limitation of this study. Moreover, the authors did not have access to more investors in TSE or other financial markets. Originality/valueThis is the first study that includes overconfidence in modeling portfolio selection for the purpose of achieving a portfolio that has a reasonable performance and one that investors are comfortable with.

scholarly journals Multi-period mean-variance portfolio optimization with markov switching parameters

2008 ◽  
Vol 19 (2) ◽  
pp. 138-146
Author(s):  
Oswaldo L. V. Costa ◽  
Michael V. Araujo
Keyword(s):  
Optimal Control ◽  
Portfolio Selection ◽  
Regime Switching ◽  
Efficient Frontier ◽  
Control Policy ◽  
Control Law ◽  
Numerical Examples ◽  
Markov Random ◽  
Mean Variance Portfolio ◽  
Mean Variance

In this paper we deal with a multi-period mean-variance portfolio selection problem with the market parameters subject to Markov random regime switching. We analytically derive an optimal control policy for this mean-variance formulation in a closed form. Such a policy is obtained from a set of interconnected Riccati difference equations. Additionally, an explicit expression for the efficient frontier corresponding to this control law is identified and numerical examples are presented.

CONTINUOUS-TIME MEAN–VARIANCE OPTIMIZATION FOR DEFINED CONTRIBUTION PENSION FUNDS WITH REGIME-SWITCHING

2019 ◽  
Vol 22 (06) ◽  
pp. 1950029
Author(s):  
ZHIPING CHEN ◽  
LIYUAN WANG ◽  
PING CHEN ◽  
HAIXIANG YAO
Keyword(s):  
Brownian Motion ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Regime Switching ◽  
Efficient Frontier ◽  
Defined Contribution ◽  
Risky Assets ◽  
Mean Variance Portfolio ◽  
Mean Variance

Using mean–variance (MV) criterion, this paper investigates a continuous-time defined contribution (DC) pension fund investment problem. The framework is constructed under a Markovian regime-switching market consisting of one bank account and multiple risky assets. The prices of the risky assets are governed by geometric Brownian motion while the accumulative contribution evolves according to a Brownian motion with drift and their correlation is considered. The market state is modeled by a Markovian chain and the random regime-switching is assumed to be independent of the underlying Brownian motions. The incorporation of the stochastic accumulative contribution and the correlations between the contribution and the prices of risky assets makes our problem harder to tackle. Luckily, based on appropriate Riccati-type equations and using the techniques of Lagrange multiplier and stochastic linear quadratic control, we derive the explicit expressions of the optimal strategy and efficient frontier. Further, two special cases with no contribution and no regime-switching, respectively, are discussed and the corresponding results are consistent with those results of Zhou & Yin [(2003) Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model, SIAM Journal on Control and Optimization 42 (4), 1466–1482] and Zhou & Li [(2000) Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization 42 (1), 19–33]. Finally, some numerical analyses based on real data from the American market are provided to illustrate the property of the optimal strategy and the effects of model parameters on the efficient frontier, which sheds light on our theoretical results.

scholarly journals Mean-Variance Portfolio Selection for Defined-Contribution Pension Funds with Stochastic Salary

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chubing Zhang
Keyword(s):  
Portfolio Selection ◽  
Closed Form Solution ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Pension Funds ◽  
Form Solution ◽  
Defined Contribution ◽  
Time Dynamic ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier.

Markowitz Theory in Portfolio Optimization for Heavy Tailed Assets

2019 ◽  
Vol 1 (3) ◽  
pp. 1-14
Author(s):  
Wong Ghee Ching ◽  
Che Mohd Imran Che Taib
Keyword(s):  
Portfolio Optimization ◽  
Composite Index ◽  
Minimum Variance ◽  
Optimization Techniques ◽  
Expected Return ◽  
Markowitz Model ◽  
The Mean ◽  
Heavy Tailed ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper aims at solving an optimization problem in the presence of heavy tail behavior of financial assets. The question of minimizing risk subjected to a certain expected return or maximizing return for a given expected risk are two objective functions to be solved using Markowitz model. The Markowitz based strategies namely the mean variance portfolio, minimum variance portfolio and equally weighted portfolio are proposed in conjunction with mean and variance analysis of the portfolio. The historical prices of stocks traded at Bursa Malaysia are used for empirical analysis. We employed CAPM in order to investigate the performance of the Markowitz model which was benchmarked with risk adjusted KLSE Composite Index. We performed a backtesting study of portfolio optimization techniques defined under modern portfolio theory in order to find the optimal portfolio. Our findings showed that the mean variance portfolio outperformed the other two strategies in terms of performance of investment for heavy tailed assets.

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