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Book A Simple Method for Predicting Covariance Matrices of Financial Returns

Download or read book A Simple Method for Predicting Covariance Matrices of Financial Returns written by Kasper Johansson and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Simple Method for Predicting Covariance Matrices of Financial Returns makes three contributions. First, it proposes a new method for predicting the time-varying covariance matrix of a vector of financial returns, building on a specific covariance estimator suggested by Engle in 2002. The second contribution proposes a new method for evaluating a covariance predictor, by considering the regret of the log-likelihood over some time period such as a quarter. The third contribution is an extensive empirical study of covariance predictors. The authors compare their method to other popular predictors, including rolling window, exponentially weighted moving average (EWMA) and generalized autoregressive conditional heteroscedastic (GARCH) type methods. After an introduction, Section 2 describes some common predictors, including the one that this method builds on. Section 3 introduces the proposed covariance predictor. Section 4 discusses methods for validating covariance predictors that measure both overall performance and reactivity to market changes. Section 5 describes the data used in the authors' first empirical studies and the results are provided in Section 6. The authors then discuss some extensions of and variations on the method, including realized covariance prediction (Section 7), handling large universes via factor models (Section 8), obtaining smooth covariance estimates (Section 9), and using the authors' covariance model to generate simulated returns (Section 10).

Book Covariance Prediction in Large Portfolio Allocation

Download or read book Covariance Prediction in Large Portfolio Allocation written by Carlos Trucíos and published by . This book was released on 2019 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many financial decisions such as portfolio allocation, risk management, option pricing and hedge strategies are based on forecasts of the conditional variances, covariances and correlations of financial returns. The paper shows an empirical comparison of several methods to predict one-step-ahead conditional covariance matrices. These matrices are used as inputs to obtain out-of-sample minimum variance portfolios based on all stocks belonging to the S&P500 index from 2000 to 2017. When considering the standard deviation of out-of-sample portfolio returns as the main performance metric, we find that DCC-based models estimated by composite likelihood and the RiskMetrics 2006 methodology deliver the best performance for portfolios rebalanced on both daily and monthly frequencies.

Book Studies in Covariance Estimation and Applications in Finance

Download or read book Studies in Covariance Estimation and Applications in Finance written by Carl-Fredrik Arndt and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis examines estimation of covariance and correlation matrices. More specifically we will in the first part study dynamical properties of the top eigenvalue and eigenvector for sample estimators of covariance and correlation matrices. This is done under the assumption that the top eigenvalue is separated from the others, which is reasonable when the data comes from financial returns. We show exactly how these quantities behave when the true covariance or correlation is stationary and derive theoretical values of related quantities that can be useful when quantifying the amount of non-stationarity for real data. We also validate the results by using Monte-Carlo simulations. A major contribution from the analysis is that it shows how and under which regimes correlation matrices differ from covariance matrices from a dynamic viewpoint. This effect has been observed in financial data, but never explained. In the second part of the thesis we study modifications to covariance estimators that find the optimal estimator within a certain sub-class. This type of estimators is generally known as shrinkage estimators as they modify only eigenvalues of the original estimator. We will do this when the original estimator takes the form A1/2XBXT A1/2, where A and B are matrices and X is a matrix of i.i.d. variables. The analysis is done in the asymptotic limit where both the number of samples and variables approach infinity jointly so that random-matrix theory can be used. Our goal is to find the shrinkage estimator which minimizes expected value of the Frobenius norm between the estimator and the true covariance matrix. To do this we first derive a generalization to the Marchenko-Pastur equation for this class of estimators. This theorem allows us to calculate the asymptotic value of the projection of the sample eigenvectors onto the true covariance matrix. We then show how to use these to find the optimal covariance estimator. At last, we show with simulations that these estimators are close to the optimal bound when used on finite data sets.

Book Empirical Asset Pricing

Download or read book Empirical Asset Pricing written by Wayne Ferson and published by MIT Press. This book was released on 2019-03-12 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory and methods of empirical asset pricing, integrating classical foundations with recent developments. This book offers a comprehensive advanced introduction to asset pricing, the study of models for the prices and returns of various securities. The focus is empirical, emphasizing how the models relate to the data. The book offers a uniquely integrated treatment, combining classical foundations with more recent developments in the literature and relating some of the material to applications in investment management. It covers the theory of empirical asset pricing, the main empirical methods, and a range of applied topics. The book introduces the theory of empirical asset pricing through three main paradigms: mean variance analysis, stochastic discount factors, and beta pricing models. It describes empirical methods, beginning with the generalized method of moments (GMM) and viewing other methods as special cases of GMM; offers a comprehensive review of fund performance evaluation; and presents selected applied topics, including a substantial chapter on predictability in asset markets that covers predicting the level of returns, volatility and higher moments, and predicting cross-sectional differences in returns. Other chapters cover production-based asset pricing, long-run risk models, the Campbell-Shiller approximation, the debate on covariance versus characteristics, and the relation of volatility to the cross-section of stock returns. An extensive reference section captures the current state of the field. The book is intended for use by graduate students in finance and economics; it can also serve as a reference for professionals.

Book Forecasting a Large Dimensional Covariance Matrix of a Portfolio of Different Asset Classes

Download or read book Forecasting a Large Dimensional Covariance Matrix of a Portfolio of Different Asset Classes written by Lillie Lam and published by . This book was released on 2009 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: In portfolio and risk management, estimating and forecasting the volatilities and correlations of asset returns plays an important role. Recently, interest in the estimation of the covariance matrix of large dimensional portfolios has increased. Using a portfolio of 63 assets covering stocks, bonds and currencies, this paper aims to examine and compare the predictive power of different popular methods adopted by i) market practitioners (such as the sample covariance, the 250-day moving average, and the exponentially weighted moving average); ii) some sophisticated estimators recently developed in the academic literature (such as the orthogonal GARCH model and the Dynamic Conditional Correlation model); and iii) their combinations. Based on five different criteria, we show that a combined forecast of the 250-day moving average, the exponentially weighted moving average and the orthogonal GARCH model consistently outperforms the other methods in predicting the covariance matrix for both one-quarter and one-year ahead horizons.

Book Introduction to Applied Linear Algebra

Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Book Volatility and Correlation

Download or read book Volatility and Correlation written by Riccardo Rebonato and published by John Wiley & Sons. This book was released on 2005-07-08 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over 80% new or fully reworked material and is a must have both for practitioners and for students. The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options. The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface. Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes. Praise for the First Edition: “In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.” —Professor Ian Cooper, London Business School “Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense.” —Anthony Neuberger, London Business School

Book Robust Estimation of a High Dimensional Integrated Covariance Matrix

Download or read book Robust Estimation of a High Dimensional Integrated Covariance Matrix written by Takayuki Morimoto and published by . This book was released on 2015 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we consider a robust method of estimating a realized covariance matrix calculated as the sum of cross products of intraday high-frequency returns. According to recent papers in financial econometrics, the realized covariance matrix is essentially contaminated with market microstructure noise. Although techniques for removing noise from the matrix have been studied since the early 2000s, they have primarily investigated a low-dimensional covariance matrix with statistically significant sample sizes. We focus on noise-robust covariance estimation under converse circumstances; that is, a high-dimensional covariance matrix possibly with a small sample size. For the estimation, we utilize a statistical hypothesis test based on the characteristic that the largest eigenvalue of the covariance matrix asymptotically follows a Tracy-Widom distribution. The null hypothesis assumes that log returns are not pure noises. If a sample eigenvalue is larger than the relevant critical value, then we fail to reject the null hypothesis. The simulation results show that the estimator studied here performs better than others as measured by mean squared error. The empirical analysis shows that our proposed estimator can be adopted to forecast future covariance matrices using real data.

Book Estimating a Covariance Matrix for Market Risk Management and the Case of Credit Default Swaps

Download or read book Estimating a Covariance Matrix for Market Risk Management and the Case of Credit Default Swaps written by Richard Neuberg and published by . This book was released on 2018 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze covariance matrix estimation from the perspective of market risk management, where the goal is to obtain accurate estimates of portfolio risk across essentially all portfolios--even those with small standard deviations. We propose a simple but effective visualization tool to assess bias across a wide range of portfolios. We employ a portfolio perspective to determine covariance matrix loss functions particularly suitable for market risk management. Proper regularization of the covariance matrix estimate significantly improves performance. These methods are applied to credit default swaps, for which covariance matrices are used to set portfolio margin requirements for central clearing. Among the methods we test, the graphical lasso estimator performs particularly well. The graphical lasso and a hierarchical clustering estimator also yield economically meaningful representations of market structure through a graphical model and a hierarchy, respectively.

Book Handbook of Financial Time Series

Download or read book Handbook of Financial Time Series written by Torben Gustav Andersen and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 1045 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view. There are many fine contributions, and a preamble by Nobel Prize winner Robert F. Engle.

Book Dynamics of Top Eigenvalues of Empirical Covariance Matrices of Financial Data

Download or read book Dynamics of Top Eigenvalues of Empirical Covariance Matrices of Financial Data written by Lijia Wang and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Covariance matrices of financial data and their inverses play an important role in algorithmic portfolio optimization and risk management. For example, PCA (principal component analysis) based strategies in algorithmic portfolio trading, and Markowitz portfolio theory in risk control and portfolio construction. However, since the true covariance matrix is neither perfectly known nor constant in time, the dynamics of the empirical covariance covariances is of great importance, as the volatilities and correlations evolve with time. It is obviously too heavy to carry the whole empirical covariance matrices all the time, especially when they contain a lot of noise. As PCA strategies suggest, most of the meaningful economic information is contained in the large eigenvalues and eigenvectors of covariance matrices, especially, the largest eigenvalue and eigenvector correspond to a collective market mode. As also suggested in risk control, the largest eigenvalue and eigenvector represent the most risky direction in a financial context. The largest eigenvalue of the empirical covariance matrix and the corresponding eigenvector are of considerable importance and we want to analyze their stability over time and characterize their fluctuations. We thus study the dynamics of the top eigenvalues and eigenvectors, instead of the whole matrices. In the thesis, we use a one factor continuous time model and study the dynamics of the top eigenvalues of the empirical covariance matrices. We first model the dynamics of stock returns and construct the empirical covariance matrices through an exponential moving average of the returns. We then derive a stochastic differential equation for the deviation part of the empirical covariance matrix from the true covariance matrix. We also establish a weak convergence result for the top eigenvalue of the deviation matrix at the equilibrium level, and show that the dynamics of the top eigenvalues of the deviation matrices satisfies in probability a reflecting stochastic differential equation for large N (size of covariance matrix) and a large true top eigenvalue. Numerical results are presented at the end to validate our theoretical results.

Book A Test of Covariance Matrix Forecasting Methods

Download or read book A Test of Covariance Matrix Forecasting Methods written by Valeriy Zakamulin and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a more accurate covariance matrix forecast can substantially improve the performance of optimized portfolios. Using out-of-sample tests, in this paper, we evaluate alternative covariance matrix forecasting methods by looking at (1) their forecast accuracy, (2) their ability to track the volatility of the minimum-variance portfolio, and (3) their ability to keep the volatility of the minimum-variance portfolio at a target level. We find large differences between the methods. Our results suggest that shrinkage of the sample covariance matrix improves neither the forecast accuracy nor the performance of minimum-variance portfolios. In contrast, switching from the sample covariance matrix forecast to a multivariate GARCH forecast reduces forecasting error and portfolio tracking error by at least half. Our findings also reveal that the exponentially weighted covariance matrix forecast performs only slightly worse than the multivariate GARCH forecast.

Book Consistent Covariance Matrix Estimation with Cross Sectional Dependence and Heteroskedasticity in Cross Sectional Financial Data

Download or read book Consistent Covariance Matrix Estimation with Cross Sectional Dependence and Heteroskedasticity in Cross Sectional Financial Data written by Kenneth A. Froot and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a simple method to account for heteroskesdasticity and cross-sectional dependence in samples with large cross sections and relatively few time series observations. The estimators we derive are motivated by cross-sectional regression studies in finance and accounting. Simulation evidence suggests that the estimators are dependable in small samples and may be useful when generalized least squares is infeasible, unreliable, or computationally too burdensome. The approach allows a relatively small number of time series observations to yield a rich characterization of cross-sectional correlations. We also consider efficiency issues and show that in principle asymptotic efficiency can be improved using a technique due to Cragg (1983).