scholarly journals Explicit Value at Risk Goal Function in Bi-Level Portfolio Problem for Financial Sustainability

2021 ◽  
Vol 13 (4) ◽  
pp. 2315
Author(s):  
Todor Stoilov ◽  
Krasimira Stoilova ◽  
Miroslav Vladimirov
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Quantitative Measure ◽  
Goal Function ◽  
Financial Sustainability ◽  
Portfolio Risk ◽  
Optimal Weights ◽  
Portfolio Problem ◽  
Upper Level ◽  
Definition Of

The mean-variance (MV) portfolio optimization targets higher return for investment period despite the unknown stochastic behavior of the future asset returns. That is why a risk is explicitly considering, quantified by algebraic characteristics of volatilities and co-variances. A new probabilistic definition of portfolio risk is the Value at Risk (VaR). The paper makes explicit inclusion and minimization of VaR as a quantitative measure of financial sustainability of a portfolio problem. Thus, the portfolio weights as problem solutions will respect not only the MV requirements for risk and return, but also the additional minimization of risk defined by VaR level. The portfolio problem is defined in a new, bi-level form. The upper level minimizes and evaluates the VaR value. The lower level evaluates the optimal assets weights by minimizing portfolio risk and maximizing the return in MV form. The bi-level model allows to have extended set of portfolio solutions with the portfolio weights and the value of VaR. Graphical interpretation of this bi-level definition of the portfolio problem explains the differences with the MV portfolio definition. Thus, the bi-level portfolio problem evaluates the optimal weights, which makes maximization of portfolio return and minimization of the risk in its algebraic and probabilistic form of definition.

PENGUKURAN RISIKO PORTFOLIO DENGAN MENGGUNAKAN METODE VALUE AT RISK (VAR)

2013 ◽  
Author(s):  
Fajri Adrianto ◽  
Laela Susdiani
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Measurement Method ◽  
Simulation Method ◽  
Risk Measurement ◽  
Portfolio Risk ◽  
Historical Simulation ◽  
Stock Investment ◽  
Risk Investment

Value at Risk (VAR) is a risk measurement method that use in risk investment calculation. VAR shows risk in nominal. This research calculate risk portfolio of stock using VAR method and measure whether VAR value overvalued or underestimated. Using historical simulation method is found VAR value tend to decrease when stock investment consist more stocks in the portfolio. Risk investment calculation consistent with standar devistion as risk measurement, which the more investment diversified the less the risk in the investment. Then, using backtesting reveal that VAR tend too high in portfolio consisting small number of stocks. VAR value can accepted in the portfolio that consist many stocks or the more investment diversified the more accurate VAR value as risk measurement.

scholarly journals Estimation of the Portfolio Risk from Conditional Value at Risk Using Monte Carlo Simulation

2021 ◽  
Vol 17 (3) ◽  
pp. 370-380
Author(s):  
Ervin Indarwati ◽  
Rosita Kusumawati
Keyword(s):  
At Risk ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Risk Estimation ◽  
Conditional Value At Risk ◽  
Portfolio Risk ◽  
Portfolio Returns

Portfolio risk shows the large deviations in portfolio returns from expected portfolio returns. Value at Risk (VaR) is one method for determining the maximum risk of loss of a portfolio or an asset based on a certain probability and time. There are three methods to estimate VaR, namely variance-covariance, historical, and Monte Carlo simulations. One disadvantage of VaR is that it is incoherent because it does not have sub-additive properties. Conditional Value at Risk (CVaR) is a coherent or related risk measure and has a sub-additive nature which indicates that the loss on the portfolio is smaller or equal to the amount of loss of each asset. CVaR can provide loss information above the maximum loss. Estimating portfolio risk from the CVaR value using Monte Carlo simulation and its application to PT. Bank Negara Indonesia (Persero) Tbk (BBNI.JK) and PT. Bank Tabungan Negara (Persero) Tbk (BBTN.JK) will be discussed in this study.  The  daily  closing  price  of  each  BBNI  and BBTN share from 6 January 2019 to 30 December 2019 is used to measure the CVaR of the two banks' stock portfolios with this Monte Carlo simulation. The steps taken are determining the return value of assets, testing the normality of return of assets, looking for risk measures of returning assets that form a normally distributed portfolio, simulate the return of assets with monte carlo, calculate portfolio weights, looking for returns portfolio, calculate the quartile of portfolio return as a VaR value, and calculate the average loss above the VaR value as a CVaR value. The results of portfolio risk estimation of the value of CVaR using Monte Carlo simulation on PT. Bank Negara Indonesia (Persero) Tbk and PT. Bank Tabungan Negara (Persero) Tbk at a confidence level of 90%, 95%, and 99% is 5.82%, 6.39%, and 7.1% with a standard error of 0.58%, 0.59%, and 0.59%. If the initial funds that will be invested in this portfolio are illustrated at Rp 100,000,000, it can be interpreted that the maximum possible risk that investors will receive in the future will not exceed Rp 5,820,000, Rp 6,390,000 and Rp 7,100,000 at the significant level 90%, 95%, and 99%

Risk Analysis of Portfolios Under Uncertainty: Minimizing Average Rates of Falling

2011 ◽  
Vol 15 (1) ◽  
pp. 56-62 ◽  
Author(s):  
Yuji Yoshida ◽  
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Asset Prices ◽  
Average Rate ◽  
Rate Of Return ◽  
Risk Of Falling ◽  
Average Value ◽  
Portfolio Problem ◽  
Proposed Model ◽  
Average Value At Risk

A portfolio model to minimize the risk of falling under uncertainty is discussed. The risk of falling is represented by the value-at-risk of rate of return. Introducing the perception-based extension of the average value-at-risk, this paper formulates a portfolio problem to minimize the risk of falling with fuzzy random variables. In the proposed model, randomness and fuzziness are evaluated respectively by the probabilistic expectation and the mean with evaluation weights and λ-mean functions. The analytical solutions of the portfolio problem regarding the risk of falling are given. This paper gives formulae to show the explicit relations among the following important parameters in portfolio: the expected rate of return, the risk probability of falling and bankruptcy, and the average rate of falling regarding the asset prices. A numerical example is given to explain how to obtain the optimal portfolio and these parameters from the asset prices in the stock market.

The risk analysis of Bitcoin and major currencies: value at risk approach

2019 ◽  
Vol 22 (1) ◽  
pp. 38-52 ◽  
Author(s):  
Umut Uyar ◽  
Ibrahim Korkmaz Kahraman
Keyword(s):  
At Risk ◽  
Risk Analysis ◽  
Value At Risk ◽  
Risk Measure ◽  
Risk Level ◽  
Portfolio Risk ◽  
Content Type ◽  
Historical Simulation ◽  
Digital Currency ◽  
Risk Approach

Purpose This study aims to compare investors of major conventional currencies and Bitcoin (BTC) investors by using the value at risk (VaR) method common risk measure. Design/methodology/approach The paper used a risk analysis named as VaR. The analysis has various computations that Historical Simulation and Monte Carlo Simulation methods were used for this paper. Findings Findings of the analysis are assessed in two different aspects of singular currency risk and portfolios built. First, BTC is found to be significantly risky with respect to the major currencies; and it is six times riskier than the singular most risky currency. Second, in terms of inclusion of BTC into a portfolio, which equally weights all currencies, it elevates overall portfolio risk by 98 per cent. Practical implications In spite of the remarkable risk level, it could be considered that investors are desirous of making an investment on BTC could mitigate their overall exposed risk relatively by building a portfolio. Originality/value The paper questions the risk level of Bitcoin, which is a digital currency. BTC, a matter of debate in the contemporary period, is seen as a digital currency free from control or supervision of a regulatory board. With the comparison of major currencies and BTC shows that how could be risky of a financial instrument without regulations. However, there is some advice for investors who would like to invest digital currencies despite the risk level in this study.

scholarly journals Analisis Value At Risk Dalam Pembentukan Portofolio Optimal (Studi Kasus Perusahaan Perbankan Di Indonesia)

2020 ◽  
Vol 10 (2) ◽  
pp. 124-136
Author(s):  
Yohanna Thresia Nainggolan ◽  
Ahmad Juliana ◽  
Citra Aziya Alantina
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Portfolio Risk ◽  
Business World ◽  
Long Period ◽  
Closing Price ◽  
Differences Of Opinion ◽  
High Return ◽  
Expected Benefits ◽  
Almost All

ABSTRAK Dalam dunia bisnis investor akan menghadapi resiko ketika investor akan berinvestasi. Oleh karena itu, untuk bahan pertimbangan bagi investor dalam berinvestasi dibutuhkan suatu perhitungan resiko.Untuk menghindari hal tersebut investor harus bisa mengantisipasi tingkat risiko dengan return yang tinggi. Untuk memperkecil resiko dan mendapatkan keuntungan yang diharapkan salah satu cara yang dapat dilakukan seorang investor adalah dengan membentuk suatu portofolio. Penelitian ini dilakukan untuk dilakukan untuk menghitung risiko dalam pembentukan portoflio optimal mernggunakan metode varians kovarians.Penelitian ini juga dilatarbelakangi masih banyaknya perbedaan pendapat dari para peneliti dan dianggap masih belum banyak penelitan yang menggunakan metode varians-kovarians pada perusahaan perbankan di Indonesia.Rumusan masalah dalam penelitian adalah bagaiman pembentukan portofolio optimal dari saham-saham perbankan di Indonesia berdasarkan metode Markowitz dan pengukuran Value at Risk pada portofolio dengan metode varians-kovarians pada harga penutupan saham-saham Perbankan di Indonesia.Keterbaharuan dalam penelitian ini adalah menggunnakan jangka waktu lama pada harga penutupan saham harian dan menggunakan metode varian kovarians dalam menanalisis Value at Risk dengan objek lebih dari dua perusahaan dalam satu portofolio.Hasil penelitian menunjukkan bahwa pada tingkat kepercayaan 95% perhitungan portofolio VaRmenunjukkan rata-rata nilai VaR0,044956. Keadaan tersebutmenunjukkan ada keyakinan 95% bahwa kerugian yang akan ditanggung oleh investor tidak akan melebihi Rp.449,560,891.Dengan kata lain bahwa ada kemungkinan sebesar 5% kerugian yang akan diderita investortidak akan melebihi Rp.449.560,891.    Kata-kata Kunci : Risiko Portofolio, Varians Kovarians, Value at Risk   ABSTRACT In the business world, almost all investments have risks. There for there is a need for a risk calculation that can be a judgment for investors in investing.To avoid that investors must be able to anticipate the level of risk with a high return. One way that an investor can do to minimize risk and get the expected benefits is to form a portfolio. There for this study was conducted to calculate the risk in the formation of an optimal portfolio using the covariance variance method.This study is also focused on the fact that the researchers still have several differences of opinion, and it is known that there is still not much study using the variance-covariance approach in Indonesian banking companies. The question proposed in this research is how to construct an optimum portfolio of banking stocks in Indonesia based on the Markowitz method and the portfolio calculation of Value at Risk using the variance-covariance method at the closing price of banking shares in Indonesia.The novelty of this study is use a long period of time at the closing price of the daily stock and using the covariance variance method in analysis Value at Risk with objects more than two companies in one portfolio.The results shown that calculation of the VaR portfolio At a confidence level of 95%, it produces an average VaR value of 0.044956. This can be defined is a confidence as much as 95 % that would suffer losses that investors wo not be more than rp 449.560,891.In other words, there is a chance that Rp.449,560,891 would not surpass 5 per cent of the losses suffered by investors in portfolio.  Keywords : Portfolio Risk, Covariance Variance, Value at Risk

scholarly journals VALUE AT RISK OF MOMENTUM INVESTMENT STRATEGY: INDONESIA'S LIQUID STOCKS PORTFOLIO

2019 ◽  
Vol 19 (1) ◽  
pp. 30
Author(s):  
A.Rowland Bismark Fernando Pasaribu
Keyword(s):  
At Risk ◽  
Risk Reduction ◽  
Value At Risk ◽  
Stock Exchange ◽  
Investment Strategy ◽  
Selection Method ◽  
Portfolio Risk ◽  
Result Show ◽  
Risk Approach

The capability of momentum investment strategy was explore through portfolio risk reduction by value at risk method at liquid shares in Indonesia stock exchange period 2008-2016. The purpose of this study are to analyse the value of momentum investment strategy risk reduction with the Value at Risk approach to historical-volatility approach and examine differences in risk reduction performance by winner and loser portfolios formed from a collection of liquid shares in the Indonesia stock exchange for the period 2008-2016. The stocks selection method in forming winners and losers portfolio done by Jegadesh and Titman procedure (1993) followed by calculation of risk reduction with the VaR-HisVol approach. The result show for quarterly and semester period winner portfolio has superior capacity of portfolio risk reduce than loser. Keywords—Investment; Strategy; Portfolio, VaR. Abstrak Kemampuan strategi investasi momentum dieksplorasi dalam teminologi pengurangan risiko portofolio dengan metode value at risk pada portofolio saham saham likuid di Bursa Efek Indonesia periode 2008-2016. Metode pemilihan saham pembentuk portofolio pemenang dan pecundang dilakukan dengan prosedur Jegadesh dan Titman (1993) dilanjutkan dengan kalkulasi pengurangan risiko dengan pendekatan VaR-HisVol. Hasil menunjukkan untuk portofolio pemenang periode triwulanan dan semester memiliki kapasitas superior mengurangi risiko portofolio daripada pecundang. Kata kunci— Investasi, Strategi, Portofolio, VaR

Risk-Based Loan Pricing: Portfolio Optimization Approach with Marginal Risk Contribution

2020 ◽  
Vol 66 (8) ◽  
pp. 3735-3753 ◽  
Author(s):  
So Yeon Chun ◽  
Miguel A. Lejeune
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Optimization Approach ◽  
Portfolio Risk ◽  
Loan Pricing ◽  
Acceptance Probability ◽  
Risk Contribution ◽  
Marginal Risk

We consider a lender (bank) that determines the optimal loan price (interest rate) to offer to prospective borrowers under uncertain borrower response and default risk. A borrower may or may not accept the loan at the price offered, and both the principal loaned and the interest income become uncertain because of the risk of default. We present a risk-based loan pricing optimization framework that explicitly takes into account the marginal risk contribution, the portfolio risk, and a borrower’s acceptance probability. Marginal risk assesses the incremental risk contribution of a prospective loan to the bank’s overall portfolio risk by capturing the dependencies between the prospective loan and the existing portfolio and is evaluated with respect to the value-at-risk and conditional value-at-risk measures. We examine the properties and computational challenges of the formulations. We design a reformulation method based on the concavifiability concept to transform the nonlinear objective functions and to derive equivalent mixed-integer nonlinear reformulations with convex continuous relaxations. We also extend the approach to multiloan pricing problems, which feature explicit loan selection decisions in addition to pricing decisions. We derive formulations with multiple loans that take the form of mixed-integer nonlinear problems with nonconvex continuous relaxations and develop a computationally efficient algorithmic method. We provide numerical evidence demonstrating the value of the proposed framework, test the computational tractability, and discuss managerial implications. This paper was accepted by Chung Piaw Teo, optimization.

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