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.

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 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 Comparison of Conventional Deterministic and Entropy-Based Methods for Predicting Sediment Concentration in Debris Flow

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 439 ◽  
Author(s):  
Zhongfan Zhu ◽  
Hongrui Wang ◽  
Bo Pang ◽  
Jie Dou ◽  
Dingzhi Peng
Keyword(s):  
Debris Flow ◽  
Maximum Entropy ◽  
Shannon Entropy ◽  
Sediment Concentration ◽  
Tsallis Entropy ◽  
Principle Of Maximum Entropy ◽  
General Index ◽  
Deterministic Methods ◽  
The Mean ◽  
Principle Of Maximum

In this study, the distribution of sediment concentration and the mean sediment concentration in debris flow were investigated using deterministic and probabilistic approaches. Tsallis entropy and Shannon entropy have recently been employed to estimate these parameters. However, other entropy theories, such as the general index entropy and Renyi entropy theories, which are generalizations of the Shannon entropy, have not been used to derive the sediment concentration in debris flow. Furthermore, no comprehensive and rigorous analysis has been conducted to compare the goodness of fit of existing conventional deterministic methods and different entropy-based methods using experimental data collected from the literature. Therefore, this study derived the analytical expressions for the distribution of sediment concentration and the mean sediment concentration in debris flow based on the general index entropy and Renyi entropy theories together with the principle of maximum entropy and tested the validity of existing conventional deterministic methods as well as four different entropy-based expressions for the limited collected observational data. This study shows the potential of using the Tsallis entropy theory together with the principle of maximum entropy to predict sediment concentration in debris flow over an erodible channel bed.

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 To Be or to Have Been Lucky, That Is the Question

Philosophies ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 57
Author(s):  
Antony Lesage ◽  
Jean-Marc Victor
Keyword(s):  
High Risk ◽  
Maximum Entropy ◽  
Chronic Diseases ◽  
Statistical Test ◽  
Low Risk ◽  
Principle Of Maximum Entropy ◽  
Ex Ante ◽  
Social Opportunities ◽  
Global Population ◽  
Principle Of Maximum

Is it possible to measure the dispersion of ex ante chances (i.e., chances “before the event”) among people, be it gambling, health, or social opportunities? We explore this question and provide some tools, including a statistical test, to evidence the actual dispersion of ex ante chances in various areas, with a focus on chronic diseases. Using the principle of maximum entropy, we derive the distribution of the risk of becoming ill in the global population as well as in the population of affected people. We find that affected people are either at very low risk, like the overwhelming majority of the population, but still were unlucky to become ill, or are at extremely high risk and were bound to become ill.

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