scholarly journals Maximum Varma Entropy Distribution with Conditional Value at Risk Constraints

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 663
Author(s):  
Chang Liu ◽  
Chuo Chang ◽  
Zhe Chang
Keyword(s):  
At Risk ◽  
Maximum Entropy ◽  
Power Law ◽  
Value At Risk ◽  
Conditional Value At Risk ◽  
Investment Bank ◽  
Lagrangian Multipliers ◽  
Variance Model ◽  
The Mean ◽  
Mean Variance

It is well known that Markowitz’s mean-variance model is the pioneer portfolio selection model. The mean-variance model assumes that the probability density distribution of returns is normal. However, empirical observations on financial markets show that the tails of the distribution decay slower than the log-normal distribution. The distribution shows a power law at tail. The variance of a portfolio may also be a random variable. In recent years, the maximum entropy method has been widely used to investigate the distribution of return of portfolios. However, the mean and variance constraints were still used to obtain Lagrangian multipliers. In this paper, we use Conditional Value at Risk constraints instead of the variance constraint to maximize the entropy of portfolios. Value at Risk is a financial metric that estimates the risk of an investment. Value at Risk measures the level of financial risk within a portfolio. The metric is most commonly used by investment bank to determine the extent and occurrence ratio of potential losses in portfolios. Value at Risk is a single number that indicates the extent of risk in a given portfolio. This makes the risk management relatively simple. The Value at Risk is widely used in investment bank and commercial bank. It has already become an accepted standard in buying and selling assets. We show that the maximum entropy distribution with Conditional Value at Risk constraints is a power law. Algebraic relations between the Lagrangian multipliers and Value at Risk constraints are presented explicitly. The Lagrangian multipliers can be fixed exactly by the Conditional Value at Risk constraints.

scholarly journals O Princípio da Máxima Entropia e a Moderna Teoria das Carteiras

2003 ◽  
Vol 1 (2) ◽  
pp. 271
Author(s):  
Ailton Cassetari
Keyword(s):  
At Risk ◽  
Maximum Entropy ◽  
Value At Risk ◽  
Capital Allocation ◽  
Systematic Comparison ◽  
Principle Of Maximum Entropy ◽  
The Mean ◽  
Mean Variance ◽  
Principle Of Maximum ◽  
Risk Concept

In this work, a capital allocation methodology base don the Principle of Maximum Entropy was developed. The Shannons entropy is used as a measure, concerning the Modern Portfolio Theory, are also discuted. Particularly, the methodology is tested making a systematic comparison to: 1) the mean-variance (Markovitz) approach and 2) the mean VaR approach (capital allocations based on the Value at Risk concept). In principle, such confrontations show the plausibility and effectiveness of the developed method.

The Risk Parity Approach Applied to Agricultural Commodities

2017 ◽  
pp. 222-257
Author(s):  
Denis Veliu
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Conditional Value At Risk ◽  
Agricultural Commodities ◽  
Risk Parity ◽  
The Mean ◽  
Risk Contribution ◽  
Mean Variance ◽  
Data Estimation ◽  
Special Case

The recent years were hard for commodities, with most suffering of high losses. The uncertainty of the financial markets after the 2008 crisis has pushed in the interest of finding new way of diversification. With the Risk Parity or Equally Weighted Risk Contribution strategy, Maillard, Roncalli, and Teiletche (2008) suggested a method that maximize the diversification. These authors have applied this strategy to the volatility (standard deviation). In this chapter, the author describes how to apply Risk Parity to the Conditional Value at Risk using historical data estimation. Passing to CVaR, a coherent measure, the model can benefit from its properties with the needed assumptions. As a special case, the author has applied this method to an agricultural portfolio, compared the Risk Parity strategies with each other and with the Mean Variance and Conditional Value at Risk. An important part is the analysis of the riskiness, the diversification and the turnover. A portfolio with a certain numbers of agricultural commodities may have particular specified that an investor requires.

scholarly journals Robust Optimization-Based Commodity Portfolio Performance

2020 ◽  
Vol 8 (3) ◽  
pp. 54
Author(s):  
Ramesh Adhikari ◽  
Kyle J. Putnam ◽  
Humnath Panta
Keyword(s):  
At Risk ◽  
Robust Optimization ◽  
Value At Risk ◽  
Optimization Technique ◽  
Practical Importance ◽  
Optimization Techniques ◽  
Commodity Futures ◽  
Conditional Value At Risk ◽  
Holding Period ◽  
Mean Variance

This paper examines the performance of a naïve equally weighted buy-and-hold portfolio and optimization-based commodity futures portfolios for various lookback and holding periods using data from January 1986 to December 2018. The application of Monte Carlo simulation-based mean-variance and conditional value-at-risk optimization techniques are used to construct the robust commodity futures portfolios. This paper documents the benefits of applying a sophisticated, robust optimization technique to construct commodity futures portfolios. We find that a 12-month lookback period contains the most useful information in constructing optimization-based portfolios, and a 1-month holding period yields the highest returns among all the holding periods examined in the paper. We also find that an optimized conditional value-at-risk portfolio using a 12-month lookback period outperforms an optimized mean-variance portfolio using the same lookback period. Our findings highlight the advantages of using robust optimization for portfolio formation in the presence of return uncertainty in the commodity futures markets. The results also highlight the practical importance of choosing the appropriate lookback and holding period when using robust optimization in the commodity portfolio formation process.

scholarly journals Pengukuran Value at Risk pada Aset Perusahaan dengan Metode Simulasi Monte Carlo

Jurnal MIPA ◽  
2013 ◽  
Vol 2 (1) ◽  
pp. 5
Author(s):  
Leony P. Tupan ◽  
Tohap Manurung ◽  
Jantje D. Prang
Keyword(s):  
At Risk ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Value At Risk ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Monte Carlo Data ◽  
Closing Price ◽  
The Mean ◽  
Mean Variance

Telah dilakukan penelitian untuk mengukur Value at Risk (VaR) pada aset perusahaan PT. Indo Tambangraya Megah Tbk (ITMG), PT. Bank Mandiri Tbk (BMRI), dan PT. Astra International Tbk (ASII) serta portofolio yang dapat dibentuk oleh ketiga aset tersebut menggunakan metode simulasi Monte Carlo. Data yang digunakan adalah data return harian diperoleh dari harga penutupan (closing price) saham harian ketiga perusahaan tersebut selama periode tahun 2011. Bobot masing-masing portofolio ditentukan dengan metode Mean Variance Efficient Portofolio. Hasil pengukuran menunjukan bahwa jika dana yang diinvestasikan sebesar Rp 100.000.000,00 dengan tingkat kepercayaan 95% dengan periode adalah 1 hari, maka VaR ITMG sebesar Rp 4.103.963,33, VaR BMRI sebesar Rp 4.060.096,67, dan VaR ASII sebesar Rp 3.353.913,33. Sedangkan VaR portofolio1 (terdiri dari aset ITMG dan BMRI) adalah Rp 3.726.543,33. VaR portofolio2 (terdiri dari aset ITMG dan ASII) adalah Rp 3.233.133,33. VaR portofolio3 (terdiri dari aset BMRI dan ASII) adalah Rp 3.278.933,33. VaR portofolio4 (terdiri dari aset ITMG, BMRI, dan ASII) adalah Rp 3.218.906,67. Nilai VaR portofolio yang lebih rendah dari VaR aset tunggal disebabkan karena adanya efek diversifikasi.Research has been conducted to measure the Value at risk (VaR) at assets PT. Indo Tambangraya Megah Tbk (ITMG), PT. Bank Mandiri Tbk (BMRI), and PT. Astra International Tbk (ASII) and portfolios that can be formed by the three assets using Monte Carlo simulation method. The data used daily return data by the three assets obtained from the closing price of daily stock over a period in 2011. The weight of each portfolio is determined by the Mean Variance Efficient Portfolio method. If the funds invested amounting to Rp 100.000.000,00 with 95% confidence level and the period is 1 day, then the results from measurement VaR ITMG is Rp 4.103.963,33, VaR BMRI is Rp 4.060.096,67 and VaR ASII is Rp 3.353.913,33. While VaR portofolio1 (consists of ITMG and BMRI asset) is Rp 3.726.543,33. VaR portofolio2 (consists of ITMG and ASII asset) Rp 3.233.133,33. VaR portofolio3 (consists of BMRI and ASII asset) is Rp 3.278.933,33. VaR portofolio4 (consists of ITMG, BMRI and ASII asset) is Rp 3.218.906,67. VaR portfolios are lower than VaR of each single asset due to diversification effects.

scholarly journals A Novel Framework for Portfolio Selection Model Using Modified ANFIS and Fuzzy Sets

Computers ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 57 ◽  
Author(s):  
Chanchal Kumar ◽  
Mohammad Najmud Doja
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Portfolio Selection ◽  
Layered Structure ◽  
Value At Risk ◽  
Conditional Value At Risk ◽  
Variance Model ◽  
Portfolio Selection Model ◽  
Mean Variance ◽  
Existing Structure

This paper proposes a novel framework for solving the portfolio selection problem. This framework is excogitated using two newly parameters obtained from an existing basic mean variance model. The scheme can prove entirely advantageous for decision-making while using computed values of these significant parameters. The framework combines effectiveness of the mean-variance model and another significant parameter called Conditional-Value-at-Risk (CVaR). It focuses on extracting two newly parameters viz. αnew and βnew, which are demarcated from results obtained from mean-variance model and the value of CVaR. The method intends to minimize the overall cost, which is computed in the framework using quadratic equations involving these newly parameters. The new structure of ANFIS is designed by changing existing structure of ANFIS and this new structure contains six layers instead of existing five-layered structure. Fuzzy sets are harnessed for the design of the second layer of this new ANFIS structure. The output parameter acquired from the sixth layer of the new ANFIS structure serves as an important index for an investor in the decision-making. The numerical results acquired from the framework and the new six-layered structure is presented and these results are assimilated and compared with the results of the existing ANFIS structure.

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