اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio
326
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, new results in random matrix theory are derived which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage target is determined as the holding portfolio estimated from previous data. The theoretical findings are applied to develop theory for dynamic estimation of the GMV portfolio, where the new estimator of its weights is shrunk to the holding portfolio at each time of reconstruction. Both cases with and without overlapping samples are considered in the paper. The non-overlapping samples corresponds to the case when different data of the asset returns are used to construct the traditional estimator of the GMV portfolio weights and to determine the target portfolio, while the overlapping case allows intersections between the samples. The theoretical results are derived under weak assumptions imposed on the data-generating process. No specific distribution is assumed for the asset returns except from the assumption of finite $4+varepsilon$, $varepsilon>0$, moments. Also, the population covariance matrix with unbounded spectrum can be considered. The performance of new trading strategies is investigated via an extensive simulation. Finally, the theoretical findings are implemented in an empirical illustration based on the returns on stocks included in the S&P 500 index.
قيم البحث
اقرأ أيضاً
In this study, we construct two tests for the weights of the global minimum variance portfolio (GMVP) in a high-dimensional setting, namely, when the number of assets $p$ depends on the sample size $n$ such that $frac{p}{n}to c in (0,1)$ as $n$ tends
to infinity. In the case of a singular covariance matrix with rank equal to $q$ we assume that $q/nto tilde{c}in(0, 1)$ as $ntoinfty$. The considered tests are based on the sample estimator and on the shrinkage estimator of the GMVP weights. We derive the asymptotic distributions of the test statistics under the null and alternative hypotheses. Moreover, we provide a simulation study where the power functions and the receiver operating characteristic curves of the proposed tests are compared with other existing approaches. We observe that the test based on the shrinkage estimator performs well even for values of $c$ close to one.
We introduce simplicial persistence, a measure of time evolution of network motifs in subsequent temporal layers. We observe long memory in the evolution of structures from correlation filtering, with a two regime power law decay in the number of per
sistent simplicial complexes. Null models of the underlying time series are tested to investigate properties of the generative process and its evolutional constraints. Networks are generated with both TMFG filtering technique and thresholding showing that embedding-based filtering methods (TMFG) are able to identify higher order structures throughout the market sample, where thresholding methods fail. The decay exponents of these long memory processes are used to characterise financial markets based on their stage of development and liquidity. We find that more liquid markets tend to have a slower persistence decay. This is in contrast with the common understanding that developed markets are more random. We find that they are indeed less predictable for what concerns the dynamics of each single variable but they are more predictable for what concerns the collective evolution of the variables. This could imply higher fragility to systemic shocks.
The only input to attain the portfolio weights of global minimum variance portfolio (GMVP) is the covariance matrix of returns of assets being considered for investment. Since the population covariance matrix is not known, investors use historical da
ta to estimate it. Even though sample covariance matrix is an unbiased estimator of the population covariance matrix, it includes a great amount of estimation error especially when the number of observed data is not much bigger than number of assets. As it is difficult to estimate the covariance matrix with high dimensionality all at once, clustering stocks is proposed to come up with covariance matrix in two steps: firstly, within a cluster and secondly, between clusters. It decreases the estimation error by reducing the number of features in the data matrix. The motivation of this dissertation is that the estimation error can still remain high even after clustering, if a large amount of stocks is clustered together in a single group. This research proposes to utilize a bounded clustering method in order to limit the maximum cluster size. The result of experiments shows that not only the gap between in-sample volatility and out-of-sample volatility decreases, but also the out-of-sample volatility gets reduced. It implies that we need a bounded clustering algorithm so that maximum clustering size can be precisely controlled to find the best portfolio performance.
In this paper, using the shrinkage-based approach for portfolio weights and modern results from random matrix theory we construct an effective procedure for testing the efficiency of the expected utility (EU) portfolio and discuss the asymptotic beha
vior of the proposed test statistic under the high-dimensional asymptotic regime, namely when the number of assets $p$ increases at the same rate as the sample size $n$ such that their ratio $p/n$ approaches a positive constant $cin(0,1)$ as $ntoinfty$. We provide an extensive simulation study where the power function and receiver operating characteristic curves of the test are analyzed. In the empirical study, the methodology is applied to the returns of S&P 500 constituents.
We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of available marke
t returns is often of similar order to the number of assets, so that the sample covariance matrix performs poorly as a covariance estimator. Additionally, financial market data often contain outliers which, if not correctly handled, may further corrupt the covariance estimation. We address these shortcomings by studying the performance of a hybrid covariance matrix estimator based on Tylers robust M-estimator and on Ledoit-Wolfs shrinkage estimator while assuming samples with heavy-tailed distribution. Employing recent results from random matrix theory, we develop a consistent estimator of (a scaled version of) the realized portfolio risk, which is minimized by optimizing online the shrinkage intensity. Our portfolio optimization method is shown via simulations to outperform existing methods both for synthetic and real market data.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
