scholarly journals The GARCH (1, 1) Model As A Risk Predictor For International Portfolios

2011 ◽  
Vol 7 (11) ◽  
Author(s):  
Jean-François Laplante ◽  
Jean Desrochers ◽  
Jacques Préfontaine,
Keyword(s):  
Standard Deviation ◽  
Stock Returns ◽  
Covariance Matrix ◽  
Minimum Variance ◽  
Stock Index ◽  
Forecasting Model ◽  
Portfolio Risk ◽  
Volatility Forecasting ◽  
Forecasting Models ◽  
Minimum Variance Portfolio

This study pertains to forecasting portfolio risk using a GARCH (Generalized Autoregressive Conditional Heteroscedasticity) approach. Three models are compared to the GARCH model (1,1) i.e., random walk (RW), historical mean (HMM) and J.P. Morgans exponentially weighted moving average (EWMA). In recent years, many volatility forecasting models have been presented in the financial literature. Using the historical average of stock returns to determine the optimal portfolio is current practice in academic circles. However, we doubt the ability of this method to provide the best estimated portfolio variance. Moreover, an error in the estimated covariance matrix could result in a completely different portfolio mix. Consequently, we believe it would be relevant to examine the volatility forecasting model proposed in different studies to estimate the standard deviation of an efficient portfolio. With a view to building an efficient portfolio in an international context, we will analyze the forecasting models mentioned above. The purpose of this research is to determine whether a GARCH approach to forecasting the covariance matrix makes it possible to obtain a risk that most resembles the actual observed risk for a given return than the model traditionally used by practitioners and academic researchers. To this end, we selected six international stock indices. The study was conducted in a Canadian context and consequently, each stock index is converted into Canadian dollars. Initially, we estimate the covariance matrix for each forecasting model mentioned above. Then, we determine the proportions to invest in the portfolio and calculate the standard deviation of a minimum variance portfolio. Finally, the best model is selected based on the variances between estimated and actual risk by minimizing the root mean squared error (RMSE) for each forecasting model. Our results show that the GARCH (1,1) model is good for estimating risk in a minimum variance portfolio. As well, we find that it is statistically impossible to make a distinction between the accuracy of this model and the RW model. Lastly, our results show that based on the four statistical error measures used, the HMM is the least accurate for estimating portfolio risk. We therefore decided not to use this model and to rely instead on the GARCH approach or the RW, the simplest of all the models.

scholarly journals A Neutrosophic Forecasting Model for Time Series Based on First-Order State and Information Entropy of High-Order Fluctuation

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 455 ◽  
Author(s):  
Hongjun Guan ◽  
Zongli Dai ◽  
Shuang Guan ◽  
Aiwu Zhao
Keyword(s):  
Time Series ◽  
Information Entropy ◽  
Stock Exchange ◽  
Time Series Forecasting ◽  
High Order ◽  
Stock Index ◽  
Neutrosophic Set ◽  
Forecasting Model ◽  
Forecasting Models ◽  
Proposed Model

In time series forecasting, information presentation directly affects prediction efficiency. Most existing time series forecasting models follow logical rules according to the relationships between neighboring states, without considering the inconsistency of fluctuations for a related period. In this paper, we propose a new perspective to study the problem of prediction, in which inconsistency is quantified and regarded as a key characteristic of prediction rules. First, a time series is converted to a fluctuation time series by comparing each of the current data with corresponding previous data. Then, the upward trend of each of fluctuation data is mapped to the truth-membership of a neutrosophic set, while a falsity-membership is used for the downward trend. Information entropy of high-order fluctuation time series is introduced to describe the inconsistency of historical fluctuations and is mapped to the indeterminacy-membership of the neutrosophic set. Finally, an existing similarity measurement method for the neutrosophic set is introduced to find similar states during the forecasting stage. Then, a weighted arithmetic averaging (WAA) aggregation operator is introduced to obtain the forecasting result according to the corresponding similarity. Compared to existing forecasting models, the neutrosophic forecasting model based on information entropy (NFM-IE) can represent both fluctuation trend and fluctuation consistency information. In order to test its performance, we used the proposed model to forecast some realistic time series, such as the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), the Shanghai Stock Exchange Composite Index (SHSECI), and the Hang Seng Index (HSI). The experimental results show that the proposed model can stably predict for different datasets. Simultaneously, comparing the prediction error to other approaches proves that the model has outstanding prediction accuracy and universality.

scholarly journals Seleção de carteiras ótimas sob restrições nas normas dos vetores de alocação: uma avaliação empírica com dados da BM&FBOVESPA

2015 ◽  
Vol 13 (3) ◽  
pp. 504
Author(s):  
Paulo Ferreira Naibert ◽  
João Caldeira
Keyword(s):  
Stock Market ◽  
Covariance Matrix ◽  
Portfolio Selection ◽  
Stock Exchange ◽  
Minimum Variance ◽  
Average Risk ◽  
Short Sale ◽  
Performance Indexes ◽  
Out Of Sample ◽  
Minimum Variance Portfolio

In this paper, we study the problem of minimum variance portfolio selection based on a recent methodology for portfolio optimization restricting the allocation vector proposed by Fan et al. (2012). To achieve this, we consider different conditional and unconditional covariance matrix estimators. The main contribution of this paper is one of empirical nature for the brazilian stock market. We evaluate out of sample performance indexes of the portfolios constructed for a set of 61 different stocks traded in the São Paulo stock exchange (BM&FBovespa). The results show that the restrictions on the norms of the allocation vector generate substantial gains in relation to the no short-sale portfolio, increasing the average risk-adjusted return (larger Sharpe Ratio) and lowering the portfolio turnover.

scholarly journals Índices Valor-Coppead, Carteiras de Ponderação Igualitária e de Mínima Variância

2016 ◽  
Vol 14 (1) ◽  
pp. 45
Author(s):  
Ricardo Pereira Câmara Leal ◽  
Carlos Heitor Campani
Keyword(s):  
Literature Review ◽  
Selection Criterion ◽  
Efficient Frontier ◽  
Minimum Variance ◽  
Sharpe Ratio ◽  
Stock Index ◽  
Stock Selection ◽  
Stock Indices ◽  
Minimum Variance Portfolio ◽  
Complex Methods

This article presents a literature review that justified the creation of the equally weighed and minimum variance Valor-Coppead stock indices and offers details about its calculation. There was no Brazilian stock index with these simple portfolio formation rules attainable by the non-sophisticated investor. An index that uses the minimum variance portfolio in the efficient frontier, with limits on the weights, offers an optimized portfolio less affected by errors in estimates. Equally weighed portfolios with up to 20 stocks displayed a performance superior to that of the majority of Brazilian stock funds and comparable to that of the minimum variance portfolio with constrained weights, but portfolios optimized with more complex methods, may outclass equally weighed portfolios. The previous three or four months Sharpe ratio stock selection criterion is relevant. The literature reviewed supported that the Valor-Coppead indices may become relevant benchmarks for non-sophisticated investors.

scholarly journals PERHITUNGAN VaR PORTOFOLIO SAHAM MENGGUNAKAN DATA HISTORIS DAN DATA SIMULASI MONTE CARLO

2012 ◽  
Author(s):  
WAYAN ARTHINI ◽  
KOMANG DHARMAWAN ◽  
LUH PUTU IDA HARINI
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Standard Deviation ◽  
Stock Returns ◽  
Value At Risk ◽  
Time Horizon ◽  
Historical Data ◽  
Portfolio Risk ◽  
Simulation Data ◽  
Risk And Return

Value at Risk (VaR) is the maximum potential loss on a portfolio based on the probability at a certain time.  In this research, portfolio VaR values calculated from historical data and Monte Carlo simulation data. Historical data is processed so as to obtain stock returns, variance, correlation coefficient, and variance-covariance matrix, then the method of Markowitz sought proportion of each stock fund, and portfolio risk and return portfolio. The data was then simulated by Monte Carlo simulation, Exact Monte Carlo Simulation and Expected Monte Carlo Simulation. Exact Monte Carlo simulation have same returns and standard deviation  with historical data, while the Expected Monte Carlo Simulation satistic calculation similar to historical data. The results of this research is the portfolio VaR  with time horizon T=1, T=10, T=22 and the confidence level of 95 %, values obtained VaR between historical data and Monte Carlo simulation data with the method exact and expected. Value of VaR from both Monte Carlo simulation is greater than VaR historical data.

Improving Minimum-Variance Portfolios by Alleviating Overdispersion of Eigenvalues

2019 ◽  
Vol 55 (8) ◽  
pp. 2700-2731
Author(s):  
Fangquan Shi ◽  
Lianjie Shu ◽  
Aijun Yang ◽  
Fangyi He
Keyword(s):  
Covariance Matrix ◽  
General Framework ◽  
Minimum Variance ◽  
Risk Minimization ◽  
Portfolio Risk ◽  
Computationally Efficient ◽  
Estimation Errors ◽  
Inverse Covariance Matrix ◽  
Sample Covariance ◽  
Out Of Sample

In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. Yet the eigenvalues of the sample covariance matrix are often overdispersed, leading to severe estimation errors in the inverse covariance matrix. To deal with this problem, we propose a general framework by shrinking the sample eigenvalues based on the Schatten norm. The proposed framework has the advantage of being computationally efficient as well as structure-free. The comparative studies show that our approach behaves reasonably well in terms of reducing out-of-sample portfolio risk and turnover.

scholarly journals Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

2019 ◽  
Vol 12 (1) ◽  
pp. 48 ◽  
Author(s):  
Ruili Sun ◽  
Tiefeng Ma ◽  
Shuangzhe Liu ◽  
Milind Sathye
Keyword(s):  
Covariance Matrix ◽  
Portfolio Selection ◽  
Factor Model ◽  
Minimum Variance ◽  
Risk Measurement ◽  
Financial Data ◽  
Portfolio Risk ◽  
Matrix Estimation ◽  
Measurement Moment ◽  
Portfolio Selection Model

The literature on portfolio selection and risk measurement has considerably advanced in recent years. The aim of the present paper is to trace the development of the literature and identify areas that require further research. This paper provides a literature review of the characteristics of financial data, commonly used models of portfolio selection, and portfolio risk measurement. In the summary of the characteristics of financial data, we summarize the literature on fat tail and dependence characteristic of financial data. In the portfolio selection model part, we cover three models: mean-variance model, global minimum variance (GMV) model and factor model. In the portfolio risk measurement part, we first classify risk measurement methods into two categories: moment-based risk measurement and moment-based and quantile-based risk measurement. Moment-based risk measurement includes time-varying covariance matrix and shrinkage estimation, while moment-based and quantile-based risk measurement includes semi-variance, VaR and CVaR.

scholarly journals Does GMVP Strategy Reduce Risk? A Global Asset Approach

2014 ◽  
Vol 30 (6) ◽  
pp. 1873
Author(s):  
Arben Zibri ◽  
Agim Kukeli
Keyword(s):  
Risk Reduction ◽  
Covariance Matrix ◽  
Minimum Variance ◽  
Portfolio Constraints ◽  
Stock Portfolios ◽  
Sample Covariance ◽  
Out Of Sample ◽  
Bond Portfolios ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio

<p>This paper studies the out of sample risk reduction of global minimum variance portfolio. The analysis are drown from the discussions of Jagannathan and Ma (2003) regarding the risk reduction in US stock portfolios using portfolio constraints. We estimate the covariance matrix using the sample covariance matrix approach and derive optimal minimum variance portfolios considering upper/lower bounds and no restrictions. Results are shown under different revision frequency and transaction costs assumed. The data used are monthly indices of stocks, bonds, gold oil and spreads from 1996 until 2013. Unconstrained GMVPs result in the lowest out of sample variance, while unconstrained GMVPs of global bond portfolios performs the best in terms of risk reduction. Diversification through global asset classes result in a better strategy than international stock diversification regarding risk, as suggested by the literature.</p>

scholarly journals PORTFOLIO RHO-PRESENTATIVITY

2019 ◽  
Vol 22 (07) ◽  
pp. 1950034
Author(s):  
TRISTAN FROIDURE ◽  
KHALID JALALZAI ◽  
YVES CHOUEIFATY
Keyword(s):  
Covariance Matrix ◽  
Regularity Condition ◽  
Minimum Variance ◽  
Finite Union ◽  
Local Regularity ◽  
Maximum Weight ◽  
Common Framework ◽  
Minimum Variance Portfolio ◽  
Vector Formula ◽  
The Impact

Given an investment universe, we consider the vector [Formula: see text] of correlations of all assets to a portfolio with weights [Formula: see text]. This vector offers a representation equivalent to [Formula: see text] and leads to the notion of [Formula: see text]-presentative portfolio, that has a positive correlation, or exposure, to all assets. This class encompasses well-known portfolios, and complements the notion of representative portfolio, that has positive amounts invested in all assets (e.g. the market-cap index). We then introduce the concept of maximally [Formula: see text]-presentative portfolios, that maximize under no particular constraint an aggregate exposure [Formula: see text] to all assets, as measured by some symmetric, increasing and concave real-valued function [Formula: see text]. A basic characterization is established and it is shown that these portfolios are long-only, diversified and form a finite union of polytopes that satisfies a local regularity condition with respect to changes of the covariance matrix of the assets. Despite its small size, this set encompasses many well-known and possibly constrained long-only portfolios, bringing them together in a common framework. This also allowed us characterizing explicitly the impact of maximum weight constraints on the minimum variance portfolio. Finally, several theoretical and numerical applications illustrate our results.

Properties of the beta coefficient of the global minimum variance portfolio

2020 ◽  
Vol 8 (1) ◽  
pp. 11-21
Author(s):  
S. M. Yaroshko ◽  
◽  
M. V. Zabolotskyy ◽  
T. M. Zabolotskyy ◽  
◽  
...  
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Global Minimum ◽  
Asset Returns ◽  
Minimum Variance ◽  
Benchmark Portfolio ◽  
Beta Coefficient ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio ◽  
Daily Returns

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.

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