Optimizing Stock Portfolio with Markowitz Method as a Reference for Investment Community Decisions

An investor who wants to invest by avoiding risk makes investors tend to choose investments with the same expected return and the smallest or lowest possible risk. Therefore, investors expect to be able to maximize profits and minimize risk at the same time in investing. In a stock portfolio, it can be done by investing the funds owned by investors into several stocks so that it can reduce the risk of losses that will occur simultaneously. In choosing the right company to invest in with consideration of expected return and risk, a multi-objective optimization with multivariate objects can be used so that it can meet the expectations of investors. The portfolio concept introduced by Markowitz is a portfolio optimization intended for standard investors because it only refers to one explanation of portfolio returns. The Markowitz method can produce an optimal stock portfolio by considering the expected return and risk simultaneously so that the maximum profit can be obtained without eliminating the existing risk

A superior active portfolio optimization model for stock exchange

Due to the vast number of stocks and the multiple appearances of developing investment portfolios, investors in the financial market face multiple investment opportunities. In this regard, the investor task becomes extremely difficult as investors define their preferences for expected return and the amount to which they want to avoid potential investment risks. This research attempts to design active portfolios that outperform the performance of the appropriate market index. To achieve this aim, technical analysis and optimization procedures were used based on a hybrid model. It combines the strong features of the Markowitz model with the General Reduced Gradient (GRG) algorithm to maintain a good compromise between diversification and exploitation. The proposed model is used to construct an active portfolio optimization model for the Iraq Stock Exchange (ISX) for the period from January 2010 to February 2020. This is applied to all 132 companies registered on the exchange. In addition to the market portfolio, two methods, namely, Equal Weight (EW) and Markowitz were used to generate active portfolios to compare the research findings. After a thorough review based on the Sharpe ratio criterion, the suggested model demonstrated its robustness, resulting in maximizing earnings with low risks

Multi-period mean–variance portfolio optimization based on Monte-Carlo simulation

We propose a simulation-based approach for solving the constrained dynamic mean– variance portfolio managemen tproblem. For this dynamic optimization problem, we first consider a sub-optimal strategy, called the multi-stage strategy, which can be utilized in a forward fashion. Then, based on this fast yet sub-optimal strategy, we propose a backward recursive programming approach to improve it. We design the backward recursion algorithm such that the result is guaranteed to converge to a solution, which is at leas tas good as the one generated by the multi-stage strategy. In our numerical tests, highly satisfactory asset allocations are obtained for dynamic portfolio management problems with realistic constraints on the control variable

On pre-commitment aspects of a time-consistent strategy for a mean-variance investor

In this paper, a link between a time-consistent and a pre-commitment investment strategy is established. We define an implied investment target, which is implicitly con- tained in a time-consistent strategy at a given time step and wealth level. By imposing the implied investment target at the initial time step on a time-consistent strategy, we form a hybrid strategy which may generate better mean-variance efficient frontiers than the time-consistent strategy. We extend the numerical algorithm proposed in Cong and Oosterlee (2016b) to solve constrained time-consistent mean-variance optimization pro- blems. Since the time-consistent and the pre-commitment strategies generate different terminal wealth distributions, time-consistency is not always inferior to pre-commitment

Comonotonic approximations for optimal portfolio selection problems.

We investigate multiperiod portfolio selection problems in a Black & Scholes type market where a basket of 1 riskless and m risky securities are traded continuously. We look for the optimal allocation of wealth within the class of 'constant mix' portfolios. First, we consider the portfolio selection problem of a decision maker who invests money at predetermined points in time in order to obtain a target capital at the end of the time period under consideration. A second problem concerns a decision maker who invests some amount of money (the initial wealth or provision) in order to be able to fullfil a series of future consumptions or payment obligations. Several optimality criteria and their interpretation within Yaari's dual theory of choice under risk are presented. For both selection problems, we propose accurate approximations based on the concept of comonotonicity, as studied in Dhaene, Denuit, Goovaerts, Kaas & Vyncke (2002 a,b). Our analytical approach avoids simulation, and hence reduces the computing effort drastically.Approximation; Choice; Comonotonicity; Criteria; Decision; Market; Optimal; Optimal portfolio selection; Portfolio; Problems; Risk; Selection; Simulation; Theory; Time;

Mathematical Analysis in Investment Theory: Applications to the Nigerian Stock Market

This thesis intends to optimise a portfolio of assets from the Nigerian Stock Exchange (NSE) using mathematical analysis in the investment theory to model the Nigerian financial market data better. In this work, we analysed the 82 stocks which were consistently traded in the NSE throughout 4years from August 2009 to August 2013. We attempt to maximise the expected return and minimise the variance of the portfolio by using Markowitz's portfolio selection model and a three-objective linear programming model allocating different percentages of weight to different assets to obtain an optimal/feasible portfolio of the financial sector of the NSM. The mean and the standard deviation served as constraints in the three-objective model used, and we constructed portfolios with the aims of maximising the returns and the Sharpe ratio and minimising the Standard Deviation (Variance) respectively. In another development, we use Random Matrix Theory (RMT) to analyse the Eigen-structure of the empirical correlations, apply the Marchenko-Pastur distribution of eigenvalues of a purely random matrix to investigate the presence of investment-pertinent information contained in the empirical correlation matrix of the selected stocks. We use a hypothesised standard normal distribution of eigenvector components from RMT to assess deviations of the empirical eigenvectors to this distribution for different eigenvalues. We also use the Inverse Participation Ratio to measure the deviation of eigenvectors of the empirical correlation matrix from RMT results. These preliminary results on the dynamics of asset price correlations in the NSE are essential for improving risk-return trade-offs associated with Markowitz's portfolio optimisation in the stock exchange, which we achieve by cleaning up the correlation matrix. Since the variance-covariance method underestimates risk, we employ Monte-Carlo simulations to estimate Value-at-Risk (VaR) and copula for a portfolio of 9 stocks of NSE. The result compared with historical simulation and variance-covariance data. Finally, with the outcome of our simulation and analysis, we were able to select the assets that form the optimal portfolio and the weights allocation to each stock. We were able to provide advice to the investors and market practitioners on how best to invest in the sector of NSE. We propose to measure the extent of closeness or otherwise in selected sectors of the NSE and the Johannesburg Stock Exchange (JSE) in our future work