OPTIMAL CONSTANT-REBALANCED PORTFOLIO INVESTMENT STRATEGIES FOR DYNAMIC PORTFOLIO SELECTION

2006 ◽  
Vol 09 (06) ◽  
pp. 951-966 ◽  
Author(s):  
ZHONG-FEI LI ◽  
KAI W. NG ◽  
KEN SENG TAN ◽  
HAILIANG YANG
Keyword(s):  
Risk Measure ◽  
Efficient Frontier ◽  
Investment Strategy ◽  
Investment Strategies ◽  
Variance Model ◽  
Optimal Constant ◽  
Black Scholes ◽  
Dynamic Portfolio ◽  
Portfolio Optimization Problem ◽  
Mean Variance

In this paper we propose a variant of the continuous-time Markowitz mean-variance model by incorporating the Earnings-at-Risk measure in the portfolio optimization problem. Under the Black-Scholes framework, we obtain closed-form expressions for the optimal constant-rebalanced portfolio (CRP) investment strategy. We also derive explicitly the corresponding mean-EaR efficient portfolio frontier, which is a generalization of the Markowitz mean-variance efficient frontier.

scholarly journals Time-Consistent Strategies for Multi-Period Portfolio Optimization with/without the Risk-Free Asset

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Zhongbao Zhou ◽  
Xianghui Liu ◽  
Helu Xiao ◽  
TianTian Ren ◽  
Wenbin Liu
Keyword(s):  
Empirical Studies ◽  
Lagrange Function ◽  
Investment Strategy ◽  
Open Loop ◽  
Investment Strategies ◽  
Variance Model ◽  
Risky Assets ◽  
Consistent Solution ◽  
Mean Variance Portfolio ◽  
Mean Variance

The pre-commitment and time-consistent strategies are the two most representative investment strategies for the classic multi-period mean-variance portfolio selection problem. In this paper, we revisit the case in which there exists one risk-free asset in the market and prove that the time-consistent solution is equivalent to the optimal open-loop solution for the classic multi-period mean-variance model. Then, we further derive the explicit time-consistent solution for the classic multi-period mean-variance model only with risky assets, by constructing a novel Lagrange function and using backward induction. Also, we prove that the Sharpe ratio with both risky and risk-free assets strictly dominates that of only with risky assets under the time-consistent strategy setting. After the theoretical investigation, we perform extensive numerical simulations and out-of-sample tests to compare the performance of pre-commitment and time-consistent strategies. The empirical studies shed light on the important question: what is the primary motivation of using the time-consistent investment strategy.

scholarly journals Modified Mean-Variance Risk Measures for Long-Term Portfolios

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 111
Author(s):  
Hyungbin Park
Keyword(s):  
Risk Measures ◽  
Risk Measure ◽  
Investment Strategy ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Volatility Model ◽  
Variance Risk ◽  
Investment Portfolios ◽  
Mean Variance

This paper proposes modified mean-variance risk measures for long-term investment portfolios. Two types of portfolios are considered: constant proportion portfolios and increasing amount portfolios. They are widely used in finance for investing assets and developing derivative securities. We compare the long-term behavior of a conventional mean-variance risk measure and a modified one of the two types of portfolios, and we discuss the benefits of the modified measure. Subsequently, an optimal long-term investment strategy is derived. We show that the modified risk measure reflects the investor’s risk aversion on the optimal long-term investment strategy; however, the conventional one does not. Several factor models are discussed as concrete examples: the Black–Scholes model, Kim–Omberg model, Heston model, and 3/2 stochastic volatility model.

A time consistent derivative strategy

2020 ◽  
Vol 07 (01) ◽  
pp. 2050004
Author(s):  
Walter Mudzimbabwe
Keyword(s):  
Nash Equilibrium ◽  
Utility Function ◽  
Stochastic Volatility ◽  
Efficient Frontier ◽  
Equation System ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Game Theoretic ◽  
Time Inconsistent ◽  
Mean Variance

In this paper, we derive a time consistent investment strategy for an investor who can invest not only in a bond and stock but in a derivative as well. In order to capture typical features shown by stocks, the stock and by extension the derivative depends on stochastic volatility. We assume that the investor is interested in maximizing a mean–variance utility function. Since the problem is time-inconsistent, we formulate the problem in game theoretic way and seek a subgame Nash equilibrium as the strategy. By solving an extended HJB equation system, we derive explicit time-consistent strategy and the corresponding efficient frontier. In order to show efficiency of the derivative strategy, we compare it with a strategy for the case of a market without a derivative. Our results show that efficient frontier for an investor with a derivative is higher than without derivative.

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.

scholarly journals MEAN-VARIANCE VERSUS MEAN–EXPECTED SHORTFALL MODELS: AN APPLICATION TO WHEAT VARIETY SELECTION

2016 ◽  
Vol 48 (2) ◽  
pp. 148-172 ◽  
Author(s):  
KUNLAPATH SUKCHAROEN ◽  
DAVID LEATHAM
Keyword(s):  
Risk Measure ◽  
Management Strategies ◽  
Wheat Variety ◽  
Expected Shortfall ◽  
Wheat Varieties ◽  
Variance Model ◽  
Variety Selection ◽  
Risk Management Strategies ◽  
The Mean ◽  
Mean Variance

AbstractOne of the most popular risk management strategies for wheat producers is varietal diversification. Previous studies proposed a mean-variance model as a tool to optimally select wheat varieties. However, this study suggests that the mean–expected shortfall (ES) model (which is based on a downside risk measure) may be a better tool because variance is not a correct risk measure when the distribution of wheat variety yields is multivariate nonnormal. Results based on data from Texas Blacklands confirm our conjecture that the mean-ES framework performs better in term of selecting wheat varieties than the mean-variance method.

Characterization of efficient frontier for mean–variance model with a drawdown constraint

2013 ◽  
Vol 220 ◽  
pp. 770-782 ◽  
Author(s):  
Haixiang Yao ◽  
Yongzeng Lai ◽  
Qinghua Ma ◽  
Huabao Zheng
Keyword(s):  
Efficient Frontier ◽  
Variance Model ◽  
Drawdown Constraint ◽  
Mean Variance

scholarly journals Open-loop equilibrium mean-variance reinsurance, new business and investment strategies with constraints

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Liming Zhang ◽  
Rongming Wang ◽  
Jiaqin Wei
Keyword(s):  
Convex Set ◽  
Investment Strategy ◽  
Open Loop ◽  
Equilibrium Strategy ◽  
Investment Strategies ◽  
Risky Investment ◽  
New Business ◽  
New Policies ◽  
Risk Processes ◽  
Mean Variance

<p style='text-indent:20px;'>In this paper, we study a general mean-variance reinsurance, new business and investment problem, where the claim processes of original and new businesses are modeled by two different risk processes and the safety loadings of reinsurance and new business are different. The retention level of the insurer is constrained in <inline-formula><tex-math id="M1">\begin{document}$ [0,1] $\end{document}</tex-math></inline-formula> and the controls of new business and risky investment are required to be non-negative. This model relaxes the limitations of those in existing research. By using the projection onto the convex set controls valued in, we obtain an open-loop equilibrium reinsurance-new business-investment strategy explicitly. We also show that the obtained equilibrium strategy is the optimal one among all deterministic strategies in the sense that it yields the smallest mean-variance cost. In the case where original and new businesses are the same, the equilibrium strategy is given in closed-form and its sensitivities to safety loadings are shown by numerical examples. At last, by comparing with the case where acquiring new business is prohibited, we show that allowing writing new policies indeed improves the performance of the insurer's risk management.</p>

scholarly journals Investment strategy performance under tracking error constraints

2019 ◽  
Vol 16 (1) ◽  
pp. 239-257 ◽  
Author(s):  
Carig Evans ◽  
Gary van Vuuren
Keyword(s):  
Performance Indicators ◽  
Tracking Error ◽  
Efficient Frontier ◽  
Investment Strategy ◽  
Risk Return ◽  
Portfolio Strategies ◽  
Investment Opportunities ◽  
Strategy Performance ◽  
Relationship Of ◽  
Mean Variance

Recent (2018) evidence identifies the increased need for active managers to facilitate the exploitation of investment opportunities found in inefficient markets. Typically, active portfolios are subject to tracking error (TE) constraints. The risk-return relationship of such constrained portfolios is described by an ellipse in mean-variance space, known as the constant TE frontier. Although previous work assessed the performance of active portfolio strategies on the efficient frontier, this article uses several performance indicators to evaluate the outperformance of six active portfolio strategies over the benchmark – subject to various TE constraints – on the constant TE frontier.

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