Stock Portfolio Optimization Using Mean-Variance and Mean Absolute Deviation Model Based On K-Medoids Clustering by Dynamic Time Warping

The tendency of investors to choose investments with maximum return and minimal risk causes the need for diversification in a portfolio to form an optimal portfolio. A lot of research on stock portfolio optimization has been conducted extensively, but not many have tried to apply machine learning concepts such as clustering analysis to accelerate the establishment of a model that can have a positive effect on the time and cost efficiency of portfolio management. However, clustering is only limited to determining the optimal stock candidate, so it is necessary to add another optimization model to calculate the portfolio weight. Based on these problems, this study carried out portfolio optimization using Mean-Variance (MV) and Mean Absolute Deviation (MAD) model based on K-Medoids Clustering by Dynamic Time Warping approach using Monte Carlo-Expected Tail Loss for risk analysis. Based on the analysis results, the MAD portfolio is more optimal than the MV portfolio by the MAD portfolio consists of five stocks, namely BMRI shares with a weight of 0.06243, UNTR shares of 0.08658, BBRI shares of 0.10285, BBCA of 0.53623, and KLBF shares of 0.21191 are the best optimal portfolios. The optimal portfolio of the MAD model has a rate of return of 87.836% in May 2017 - December 2022 with a portfolio performance of 0.03704, while the resulting risk level based on Carlo-Expected Tail Loss is 2.2416%.  Kecenderungan investor untuk memilih investasi dengan return maksimal dan risiko minimal mengakibatkan perlunya diversifikasi dalam suatu portofolio untuk membentuk portofolio optimal. Salah satu alternatif optimasi portofolio dapat dilakukan menggunakan analisis pengelompokan (clustering). Namun, clustering hanya terbatas untuk menentukan kandidat saham optimal, sehingga perlu ditambah metode atau model optimasi lain untuk menghitung bobot portofolio. Model pembentukan portofolio optimal seperti model Mean-Variance (MV) dan Mean Absolute Deviation (MAD) menggunakan asumsi bahwa preferensi investor didasarkan pada tingkat expected return dan risiko dari portofolio, tetapi cara memilih saham untuk model tersebut tidak didiversifikasi secara detail, sehingga dalam penelitian ini, dilakukan penggabungan metode pembentukan portofolio optimal antara model optimasi MV dan MAD dengan analisis pengelompokan (clustering) saham menggunakan metode K-Medoids Clustering dengan pendekatan ukuran jarak Dynamic Time Warping (DTW). Idealnya, dalam pembentukan portofolio optimal juga disertai dengan perhitungan estimasi risiko yang akan diperoleh investor. Alternatif pengestimasian risiko yang digunakan dalam penelitian ini adalah metode Expected Tail Loss (ETL) berdasarkan hasil Simulasi Monte Carlo. Variabel yang digunakan dalam penelitian ini adalah data saham yang konsisten terdaftar dalam Indeks SRI-KEHATI periode 1 Mei 2017 hingga 31 Desember 2022 dan tingkat suku bunga IndONIA sebagai aset bebas risiko (risk free rate). Berdasarkan analisis yang telah dilakukan, portofolio MAD merupakan portofolio yang lebih optimal dibandingkan portofolio MV dengan portofolio MAD yang tersusun atas lima saham yaitu saham BMRI dengan bobot sebesar 0,06243, saham UNTR sebesar 0,08658, saham BBRI sebesar 0,10285, saham BBCA sebesar 0,53623, dan saham KLBF sebesar 0,21191 menjadi portofolio optimal yang terbaik. Portofolio optimal model MAD memiliki tingkat pengembalian (return) sebesar 87,836% dalam kurun waktu Mei 2017 – Desember 2022 dengan kinerja portofolio sebesar 0,03704, sedangkan tingkat risiko yang dihasilkan berdasarkan Monte Carlo-Expected Tail Loss adalah sebesar 2,2416%

Expected Utility Maximization and Conditional Value-at-Risk Deviation-based Sharpe Ratio in Dynamic Stochastic Portfolio Optimization

In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation ($CVaRD$) based Sharpe ratio for measuring risk-adjusted performance of a dynamic portfolio. We compute optimal strategies for a portfolio investment problem motivated by the German DAX 30 Index and we evaluate and analyze the dependence of the $CVaRD$-based Sharpe ratio on the utility function and the associated risk aversion level

Tracking Error: a multistage portfolio model

We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.

Evaluating Greek equity funds using data envelopment analysis

This study assesses the relative performance of Greek equity funds employing a non-parametric method, specifically Data Envelopment Analysis (DEA). Using an original sample of cost and operational attributes we explore the e¤ect of each variable on funds' operational efficiency for an oligopolistic and bank-dominated fund industry. Our results have significant implications for the investors' fund selection process since we are able to identify potential sources of inefficiencies for the funds. The most striking result is that the percentage of assets under management affects performance negatively, a conclusion which may be related to the structure of the domestic stock market. Furthermore, we provide evidence against the notion of funds' mean-variance efficiency

Multi-Period Trading via Convex Optimization

We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets. We then describe a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the first one executed, using estimates of future quantities that are unknown when the trades are chosen. The single-period method traces back to Markowitz; the multi-period methods trace back to model predictive control. Our contribution is to describe the single-period and multi-period methods in one simple framework, giving a clear description of the development and the approximations made. In this paper we do not address a critical component in a trading algorithm, the predictions or forecasts of future quantities. The methods we describe in this paper can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software library that implements many of the ideas and methods described in the paper

Fuzziness and Funds Allocation in Portfolio Optimization

Each individual investor is different, with different financial goals, different levels of risk tolerance and different personal preferences. From the point of view of investment management, these characteristics are often defined as objectives and constraints. Objectives can be the type of return being sought, while constraints include factors such as time horizon, how liquid the investor is, any personal tax situation and how risk is handled. It's really a balancing act between risk and return with each investor having unique requirements, as well as a unique financial outlook - essentially a constrained utility maximization objective. To analyze how well a customer fits into a particular investor class, one investment house has even designed a structured questionnaire with about two-dozen questions that each has to be answered with values from 1 to 5. The questions range from personal background (age, marital state, number of children, job type, education type, etc.) to what the customer expects from an investment (capital protection, tax shelter, liquid assets, etc.). A fuzzy logic system has been designed for the evaluation of the answers to the above questions. We have investigated the notion of fuzziness with respect to funds allocation.Comment: 21 page

Export diversification and resource-based industrialization: the case of natural gas

For resource-rich economies, primary commodity specialization has often been considered to be detrimental to growth. Accordingly, export diversification policies centered on resource-based industries have long been advocated as effective ways to moderate the large variability of export revenues. This paper discusses the applicability of a mean-variance portfolio approach to design these strategies and proposes some modifications aimed at capturing the key features of resource processing industries (presence of scale economies and investment lumpiness). These modifications help make the approach more plausible for use in resource-rich countries. An application to the case of natural gas is then discussed using data obtained from Monte Carlo simulations of a calibrated empirical model. Lastly, the proposed framework is put to work to evaluate the performances of the diversification strategies implemented in a set of nine gas-rich economies. These results are then used to formulate some policy recommendations

A review of portfolio planning: Models and systems

In this chapter, we first provide an overview of a number of portfolio planning models which have been proposed and investigated over the last forty years. We revisit the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. A piecewise linear approximation of the problem through a reformulation involving diagonalisation of the quadratic form into a variable separable function is also considered. A few other models, such as, the Mean Absolute Deviation (MAD), the Weighted Goal Programming (WGP) and the Minimax (MM) model which use alternative metrics for risk are also introduced, compared and contrasted. Recently asymmetric measures of risk have gained in importance; we consider a generic representation and a number of alternative symmetric and asymmetric measures of risk which find use in the evaluation of portfolios. There are a number of modelling and computational considerations which have been introduced into practical portfolio planning problems. These include: (a) buy-in thresholds for assets, (b) restriction on the number of assets (cardinality constraints), (c) transaction roundlot restrictions. Practical portfolio models may also include (d) dedication of cashflow streams, and, (e) immunization which involves duration matching and convexity constraints. The modelling issues in respect of these features are discussed. Many of these features lead to discrete restrictions involving zero-one and general integer variables which make the resulting model a quadratic mixed-integer programming model (QMIP). The QMIP is a NP-hard problem; the algorithms and solution methods for this class of problems are also discussed. The issues of preparing the analytic data (financial datamarts) for this family of portfolio planning problems are examined. We finally present computational results which provide some indication of the state-of-the-art in the solution of portfolio optimisation problems