Minimum variance portfolio pdf

Minimum variance portfolio pdf. 2024. Intuition: Recall that the covariance between portfolio return and the return of one of the underlying assets is the marginal contribution to risk of that asset (See Lecture 5). 1 However, even if investors decide to use the global minimum-variance portfolio, the estimation errors associated with the covariances can still lead to signi cant estimation errors in the portfolio weights, especially in a high-dimensional scenario. Sep 1, 2014 · Request PDF | Robust Minimum Variance Portfolio with L-infinity Constraints | Portfolios selected based on the sample covariance estimates may not be stable or robust, particularly so in May 20, 2022 · Mean-semivariance and minimum semivariance portfolios are a preferable alternative to mean-variance and minimum variance portfolios whenever the asset returns are not symmetrically distributed. Global Minimum Variance Portfolio In this section we present the GMV portfolio derived from the Markowitz model as well as the optimization procedure to create it. Highly Influential. For example α = −1, 1−α = 2 is possible . is the equally-weighted portfolio. Individual asset weights depend on systematic and idiosyncratic risk in all three risk-based portfolios, but systematic risk eliminates many investable assets in long-only constrained Minimum Variance and Maximum Diversification Mar 27, 2015 · In [13], the Global Minimum Variance Portfolio is studied and the authors show that applying an adapted estimation methodology based on the Shrinkage-Tyler M-estimator leads to achieving superior Aug 26, 2019 · The MVPO is an optimization problem, in finance, that includes allocating the assets in the portfolio in a way that reduces risk while achieving a desired expected return. Add to Favorites. Han Lin Shang Ruike Wu Yanrong Yang. (This is indeed the solution - I checked using the matrix algebra formula). min m p,m = s. 1σpm, = ′′Σ= m mm m1 This optimization problem can be solved easily using the solver with matrix algebra functions. txt) or read online for free. In view of this, few practical applications of VaR in portfolio A Robust Statistics Approach to Minimum Variance Portfolio Optimization. However, similarly to other portfolios based on downside risk measures, they are particularly affected by parameter uncertainty because the estimates of the necessary inputs are less reliable than the Oct 17, 2019 · Predicting the Global Minimum Variance Portfolio. Put simply each investment in a minimum variance portfolio is risky if traded The global minimum variance portfolio weights are x1 = 0. Jun 1, 2010 · The minimum-variance benchmark has the smallest market beta, which supports the results of Scherer (2011) and Clarke, de Silva, and Thorley (2006 Thorley ( , 2011): the minimum-variance portfolio 2. However, using VaR as a risk measure in portfolio optimization models leads to problems that are computationally hard to solve. Clarke, de Silva, andThorley derive an analytic solution for the long-only minimum-variance portfolio under the assumption of a single-factor covariance matrix. Minimum variance portfolio (MVP) seems to outperform the mean-variance optimized portfolio on a risk-adjusted basis. Suppose Harry follows a global minimum variance portfolio strategy. Here, W1 – First asset’s portfolio weight. algebra procedures that are needed to produce the minimum variance portfolio weights. t. A data-adaptive method to quantify the uncertainty with the help of a factor structure is proposed and Monte-Carlo Simulation is conducted to show the superiority of the method in high-dimensional cases. In this paper we define four min imum variance portfolio selection problems: two minimum variance portfolio selection problems which allow short -selling and two minimum variance problems that does not allow short-selling. The differences are statistically significant in the cases of the shortsale constraint minimum variance portfolio of Jagannathan and Ma (2003), and the equally weighted portfolio. e. 310, x2 = 0. All you have to do is to invest in two minimum variance portfolios (mutual funds) with the weight vectors w1 and w2 corresponding to two points on the frontier, and calculate the E cient frontier is de ned for a world with no risk-free assets It is the set of portfolios with minimum variance of return for each level of portfolio mean returns So, minimize portfolio variance XTV X subject to constraints: XT1 Feb 1, 2024 · Abstract. 2 Global Minimum Variance Portfolios The global minimum variance (GMV) portfolio is a special case of mini-mum variance portfolios that contain only risky assets and satisfy the full-investment constraint that the portfolio weights sum to one, but there is no other constraint and in particular no limit on short sales. Feb 3, 2020 · 2. May 4, 2021 · The global minimum variance portfolio (GMVP) is the starting point of the Markowitz mean-variance efficient frontier. Taylor Peery Professor of Finance at Brigham Young University in Provo, UT. Jan 10, 2022 · Motivated by the recent theoretical rehabilitation of mean-variance analysis, the authors revisit the question of whether minimum variance (MinVar) or maximum Sharpe ratio (MaxSR) investment weights are preferable in practical portfolio formation. Over the past 20 years, several attempts to include VaR in the portfolio selection process have been proposed. Because shorting is allowed, one of these weights might be negative. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning Oct 31, 2006 · In the minimum-variance portfolio, far to the left on the efficient frontier, security weights are independent of expected security returns. = 1. The objective function is minimi-zation of ex ante portfolio risk, irrespective of forecasted returns, so that the minimum-variance portfolio lies on the left-most tip of the ex ante efficient frontier. Scherer (2011) conjectures that the MVP tilts toward low beta and low idiosyncratic risk assets. Key Words: Tangent portfolio, global minimum variance portfolio, mean-variance spanning. Key ndings: 1. al. Set global minimum variance portfolio = first frontier portfolio. steven. This paper proposes a new time-varying minimum variance portfolio (TV-MVP) in a large investment universe of assets. ” Consequently, this paper formulates the global minimum variance portfolio as a regression problem with added penalties. When Consequently, the return associated with the least variance so-lution is µ min-var = mTΣ−1e eTΣ−1e. Let L be an arbitrary p × k matrix of constants, p < k, and define (4 The analytic expression for a minimum variance portfolio can be used to show that any minimum variance portfolio can be created as a linear combination of any two minimum variance portfolios with different target expected returns. Oct 20, 2023 · This paper introduces a dynamic minimum variance portfolio (MVP) model using nonlinear volatility dynamic models, based on high-frequency financial data. argue that “shortsale-constrained minimum-variance portfolios [\(\dots \)] tend to assign a weight different from zero to only a few of the assets”, while it is noted by Clarke et al. However, the minimum-variance approach may also have certain Jul 1, 2015 · For instance, with the 100FF data set, the robust portfolio always achieves out-of-sample variances lower than those of the minimum variance portfolios considered. Portfolio Optimization Using Minim um Variance Line Approach: (A case study of. thorley@byu. 58. 3 Variance De nition 14. Doku-Amposah. To evaluate the dynamic MVP model, we estimate the inverse volatility matrix using the constrained $\\ell_1 Indeed, the op- weighting coefficients and the shrinkage intensity defining the timal mean-variance solution has been empirically observed to minimum variance portfolio implementation, can be optimized so be significantly sensitive to deviations from the true input pa- as to minimize the realized variance while taken into account the rameters. If the standard deviation of returns of Asset A is 18% and that of Asset B is 10%, determine the overall variance of the portfolio considering that the However, if. Step 3 Open Solver (from the “Tools” menu). In this paper we take a more general setup by considering arbitrary linear combinations of the GMV portfolio weights. covariances), the weights corresponding to the minimum-variance portfolio. This work analyzes the asymptotic convergence of the risk measure of sample minimum variance portfolios of arbitrarily high dimension and proposes a generalized consistent estimator of the out-of-sample portfolio variance that only depends on the set of observed returns. Abstract This paper studies the estimation of high-dimensional minimum variance portfolio (MVP) based on the high frequency returns which can exhibit heteroscedasticity and possibly be contaminated by Feb 10, 2010 · The equation for optimal security weights has a simple and intuitive form that provides several insights on minimum variance portfolio composition. Modern portfolio theory ( MPT ), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. 1. We start on this problem next. Jun 1, 2016 · The global minimum variance portfolio (GMVP) is the starting point of the Markowitz mean‐variance efficient frontier. Motivated by both 2 Mar 1, 2018 · Abstract. Regularized minimum-variance portfolios using asset group information By Marcelo Fernandes, Guilherme Rocha, and Thiago Souza Regularized minimum-variance portfolios obtained by restricting the norm of the portfolio-weights vector to be smaller than a certain value often have better out-of-sample performance than unrestricted ones. Asset A weighs 30% of the portfolio, while Asset B weighs 70%. The estimation of the GMVP weights is therefore of much importance for Moreover, as Brodie et. In other words: Var(X) = E (X E(X))2 Note: The square root of variance is the standard deviation and is denoted ˙(X) or ˙ X or just ˙. Empirical results illustrate the practical value of large-scale numerical optimizations using However, the open outcry mechanism has higher market quality (or smaller variance of the pricing error) on the basis of Hasbrouck's (1993) model. TLDR. When weights are all positive, the minimum value for the diversification proxy D (w)−1 is 1 and its maximum value is N. A novel dynamic approach to forecast the weights of the global minimum variance portfolio (GMVP) for the conditional covariance matrix of asset returns using a recursive least squares (RLS) scheme as well as by generalized autoregressive score (GAS) type dynamics. In terms of individual asset selection, minimum-variance and (more recently) maximum diversification objective functions have been explored Sep 1, 2021 · Long-only minimum-variance portfolio. Minimum Variance Portfolio - Weights - Free download as Word Doc (. . Equivalently, it corresponds to the portfolio Jul 11, 2023 · The primary objective of a minimum-variance portfolio is to reduce the overall risk of the investment portfolio. , 2021; Lee and Seregina, 2020), we consider the dynamics of the optimal portfolio and study the time-varying population covariance matrix. 3. Portfolio allocation is one of the most important investment decisions in financial markets. The estimation of the GMVP weights is therefore of much importance for We would like to show you a description here but the site won’t allow us. Keywords: Carbon, climate change, risk factor, carbon beta, carbon intensity, minimum variance portfolio. SSNIT) N. Considering the shortcomings of the traditional sample covariance matrix estimation, this paper proposes an review of minimum-variance portfolios, which have been defined and analyzed from the start of modern portfolio theory in the 1960s. g. Jun 1, 2019 · Under certain sparsity assumptions on the precision matrix, estimators of the MVP are proposed and it is proved that the portfolios asymptotically achieve the minimum variance in a sharp sense. Equivalently, it corresponds to the portfolio Jun 14, 2014 · DeMiguel et al. Of course, large institutional portfolio investors which pursue dynamic volatility timing strategies are interested to hold the original GMVP weights ω t as Jun 1, 2010 · Minimum-Variance Portfolio Composition. 011. The signi cance of the mutual fund theorem is that if you want to construct a portfolio with a required , you don't have to build from scratch to pick all the individual securities according to the weight w . , 2020). , 2013; Ding et al. , DeMiguel et al. The variance of a random variable X, denoted Var(X), is the long-term average of the square of the di erence between the variable and its long-term average. 196 and x3 = 0. The most left point on the minimum variance set is called the minimum variance point . Dec 31, 2017 · Page 1 of 17. ,The authors answer this question with a focus on mainstream investors which can be modeled by a metric can be used to build minimum variance strategies and how they impact their portfolio construction. Minimum Variance Portfolio = W12σ12 + W22σ22 + 2W1W2Cov1,2. 3 Minimal variance when n = 2 When n = 2 the weights can be described by one number α where α 1 = α and α 2 = 1 − α. So, the GMV portfolio is the portfolio with the lowest possible variance for a given universe of assets. May 1, 2016 · Request PDF | Sparse Weighted-Norm Minimum Variance Portfolios | We propose to impose a weighted l1 and squared l2 norm penalty on the portfolio weights to improve out-of-sample (OOS) performances What is the definition of minimum variance portfolio? This leverages the risk of each individual asset with an offsetting investment, thus hedging the total portfolio risk for the level of risk accepted with respect to the expected rate of portfolio return. Oct 20, 2023 · Based on the realized non-normalized MVP weight estimator, we propose the dynamic MVP model, which we call the dynamic realized minimum variance portfolio (DR-MVP) model. The aim of May 1, 2021 · We propose a high dimensional minimum variance portfolio estimator under statistical factor models, and show that our estimated portfolio enjoys sharp risk consistency. Mathematics, Business. The screen shot of the portfolio tab below shows how to set‐up this optimization problem in Excel. with expected returns greater than the minimum variance portfolio’s expected return, R mv say, are said to lie on the e cient frontier. The early researchers investigating this matter usually applied a simple plug-in estimator for estimating the weights and paid very little attention to the distributional property of the estimator. Exercise 2 Let w 1 and w 2 be (mean-variance) e cient portfolios corresponding to expected Strategy for Plotting Portfolio Frontier. Estimating the precision matrix is a key step that often generates misspecification which translates to resulting portfolio weights, directly affecting the GMVP out-of-sample Nov 9, 2017 · According to standard portfolio theory, the tangency portfolio is the only efficient stock portfolio. Find asset μ0 = max( that has highest expected return. Expand. The analysis of the investment decision problem as an optimization problem that seeks to maximize the expected return of the portfolio while minimizing its risk, i. TOPICS: Portfolio construction, statistical methods, analysis of individual factors/risk premia. Our method extends the existing literature of minimum variance portfolio by allowing for time-varying factor loadings, which is the facilitator to capture the dynamics of asset returns' covariance structure (hence the optimal investment strategy in a dynamic setting). In STEP 1, the Dec 14, 2021 · We use the Minimum Regularised Covariance Determinant Estimator (MRCD) to limit weights’ misspecification within the Global Minimum Variance Portfolio (GMVP) framework. May 4, 2021 · On the contrary, zero-correlation GMVP weights in (ii) could be seen as a possibility for a robust and feasible portfolio selection, primarily for small private minimum variance investors. Specifically, we impose an autoregressive dynamic structure on MVP processes, which helps capture the MVP dynamics directly. that their long-only minimum variance “portfolio averages about 120 long securities, i. We denote the set of weights associated with the minimum vari-ance solution ¯w by w min-var as well. Pretty cool, huh? Using the Solver to find the tangency portfolio Mar 27, 2015 · In [13], the Global Minimum Variance Portfolio is studied and the authors show that applying an adapted estimation methodology based on the Shrinkage-Tyler M-estimator leads to achieving superior Jan 1, 2013 · PDF | The global minimum variance portfolio computed using the sample covariance matrix is known to be negatively affected by parameter uncertainty. Unlike existing literature of minimum variance portfolio estimators under statistical factor models (Fan et al. 1Primer on Financial Data. Jul 1, 2020 · Introduction. Aug 1, 2020 · The global minimum variance portfolio (GMVP) is the starting point of the Markowitz mean‐variance efficient frontier. Jan 1, 2017 · The sample estimator of the GMV portfolio weights is constructed by replacing Σ with S in (2) and it is given by (3) w ^ G M V = S − 1 1 1 T S − 1 1. 6), and compute = m0μ and 2 = m0Σm. JEL classi cation: C61, G11. Most indices can be used as building blocks as part of a greater portfolio and need to be used as such, being unsuitable for standalone allocations. 3. 495 and the variance of the portfolio is 0. As seen in [23] [24] [25 manner. Apr 4, 2024 · Each variance is further adjusted with its covariance. and compute μp,m =. pdf), Text File (. It is important to note that a uniformly minimum variance unbiased estimator may not always exist, and even if it does, we may not be able to find it. global minimum-variance portfolio (GMV), as this does not depend on ex-pected returns. This selection and appropriate proportion of fund allocation, paper discusses the estimates Value-at-Risk and minimum portfolio risk can be reduced to a minimum level [13]. To evaluate the dynamic MVP model, we estimate the inverse volatility matrix using the constrained $\\ell_1 May 1, 2021 · This paper proposes a new time-varying minimum variance portfolio (TV-MVP) in a large investment universe of assets. = (1 /N , . , about 12 % of the 1000-security investable set”. Finally, enter the definition of portfolio return in cell I26, again using. We begin by deriv- May 7, 2023 · Value-at-risk is one of the most popular risk management tools in the financial industry. We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. Chapm an-Wardy, and K. , Var Y[bθMV UE(Y)] ≤ Var Y[θe(Y)], (2) for all estimators eθ(Y) ∈ Λ and all parameters θ ∈ Λ. Ultimately, investors ensure that overall portfolio variance is lower than the weighted average of individual variances. the weights given in cells C26 and D26 and the information on expected returns that we entered in Step 1. Compute the efficient portfolio x by with target expected return equal to the maximum expected return of the assets under consideration. His portfolio comprises two assets, A and B. Finally observe that is the minimum variance weights w min-var are feasible for M, that is, if mTw min-var ≥ µ b, then w min-var By stock produces the same level of profit, but with minimum risk. The daily historical prices of the stocks are scraped from Yahoo Finance website from January 1, 2016, to December 31, 2020. point out, the Markowitz optimization scheme, “is empirically unstable,” making, “the classic Markowitz portfolio optimization an ill-posed (or ill-conditioned) inverse problem. , 2007) due to its capacity to achieve both lower risk and higher return, and to avoid the estimation of expected returns (Cai et al. Jan 1, 2021 · Request PDF | On Jan 1, 2021, Qingliang Fan and others published Time-varying Minimum Variance Portfolio | Find, read and cite all the research you need on ResearchGate Jun 2, 2014 · TLDR. Empirical studies document that equity portfolios constructed to have the lowest possible risk have surprisingly high average returns. The e cient frontier is plotted as the upper blue curve in Figure 1 ar alternatively, the blue curve in Figure 2. Our approach relies on properly integrating ℓ 1 constraint on portfolio weights with an appropriate covariance matrix estimator. This approach leads to a shrinkage-type STEVEN THORLEY is the H. Feb 1, 2008 · The global minimum variance portfolio (GMVP) is the starting point of the Markowitz mean‐variance efficient frontier. Analytic solutions to Minimum Variance, Maximum Diversification, and Risk Parity portfolios provide helpful intuition about their properties and construction. 1 f1 Introduction Following the pioneering work on the mean-variance trade-off in Markowitz (1952) the ques- tion of mean-variance efficiency of an asset or a set of proposed asset-pricing factors has been of great importance In this paper we define four min imum variance portfolio selection problems: two minimum variance The efficient frontiers for various portfolio selection portfolio selection problems which allow short -selling problems have been studied by many authors under a and two minimum variance problems that does not allow variety of assumptions. May 21, 2020 · The “boxed” areas in bold labeled “STEP 1” and “STEP 2” refer to the matrix. The benefits of this approach include potentially lower portfolio volatility, improved risk-adjusted returns, and increased resilience during periods of market turbulence. Inventory control considerations also affect the electronic market Apr 16, 2024 · Example #2. Furthermore, employing the Hasbrouck (1991) model, we show that trades in the open outcry market have higher information content. The purpose of this section is to study the properties of β L and prove the correctness of the formulas (5) and (6). But little is known about the distributions of 2. The minimum variance portfolio formula is as follows. m0μ. To estimate a large number of parameters, we employ the least absolute shrinkage and selection operator (LASSO) and predict the future MVP and establish its asymptotic properties. If the expected return on the resulting portfolio is greater than the expected return on the global minimum 14. Consequently, the MVP capitalizes on both the beta anomaly and the idiosyncratic risk anomaly. 1 Multi-objective portfolio selection problems. Aug 8, 2023 · The simulation of real and synthetic data shows that the proposed improved global minimum variance portfolio model and named spectral corrected and regularized global minimumvariance portfolio (SCRGMVP) is better than the traditional risk model and has lower computational complexity. as an optimization problem with multiple conflicting objectives, highlights the multi-objective nature of the portfolio selection problem. ABSTRACT: The main motive of 2 Characteristics of a minimum variance portfolio (MVP) There is a common misconception that minimum variance indices are just another “smart beta” product, but we would argue differently. Our method extends the existing literature on minimum variance portfolios by allowing for time-varying factor loadings, which facilitates the capture of the dynamics of the covariance structure of asset returns (and Jul 1, 2015 · The global minimum variance portfolio computed using the sample covariance matrix is known to be negatively affected by parameter uncertainty, an important component of model risk. The estimation of the GMVP weights is therefore of much importance for Jul 30, 2015 · The results show that covered bonds have a role in the minimum-variance portfolio because of the reduced risk, which is an indication of diversification benefits. doc), PDF File (. The minimum variance (MV) portfolio strategy has received growing attention over the last decade (e. However, empirical studies show that an investment in the global minimum variance portfolio often yields better out-of-sample results than does an investment in the tangency portfolio and suggest investing in the global minimum variance portfolio. Estimation risk tends to affect the optimal weight calculation noticeably, especially when a large number of assets are considered. This work develops a consistent estimator of (a scaled version of) the realized portfolio risk, which is minimized by optimizing online the shrinkage intensity, and is shown via simulations to outperform existing methods both for synthetic and real market data. The left boundary of a feasible region is called the minimum variance set . σ2 m0Σm m01. The global minimum variance portfolio (GMVP) is the starting point of the Markowitz mean‐variance efficient frontier. the smallest variance of all possible estimators over all possible values of θ, i. The Global Minimum Variance Portfolio The global minimum variance portfolio solves the optimization problem 2 min s. Sep 1, 2021 · The minimum-variance portfolio (MVP) has become an essential part of modern portfolio theory, largely due to the availability of its analytical formula and its good out-of-sample performance. We first prove the existence of β L. Nkum, A. 2Modeling the Returns. In addition, efficient frontier is the combination of all other feasible portfolios which have higher standard deviations and higher expected return. Mar 1, 2016 · In this study, for the first time, the portfolio selection problem has been modeled based on mean-semi variance with transaction cost and minimum transaction lots considering functional Optimizations that go back to 1968 reveal that the long-only minimum-variance portfolio has about three-fourths the realized risk of the capitalization-weighted market portfolio, with higher average returns. Then, use this definition of portfolio variance to specify the portfolio StD, in cell H26. Sep 26, 2017 · Abstract and Figures. The estimation of the GMVP weights is therefore of much importance for financial…. Set target return to μ ) and solve: σ2. Download PDF. Measuring carbon risk is di erent if we consider a fundamental-based approach by Sample and realized minimum variance portfolios: Estimation, statistical inference, and tests. While high idiosyncratic risk can lead to a low security weight, high systematic risk takes the large majority of investable securities out of long-only solutions. Global minimum variance portfolio (GMVP) is the portfolio with lowest variance among all other feasible portfolios. Feb 1, 2024 · Abstract. 3Portfolio Basics. variance on an investment portfolio. Note that the formula remains meaningful even for negative weights. , 1 /N , ) then D (w)−1 = N and the portfolio is fully diversified. The estimation of the GMVP weights is therefore of much importance for financial investors. edu Portfolio construction techniques based on predicted risk, without expected returns, have become popular in the last decade. In terms of covariance matrix estimation, we Mar 11, 2022 · The popularity of modern portfolio theory has decreased among practitioners because of its unfavorable out-of-sample performance. Lotsi, C. Nov 1, 2021 · Abstract. Portfolios can be constructed using only the estimated security covariance matrix, without reference to equilibrium expected or actively forecasted returns. To overcome these issues, many methods have been proposed in recent years, but only a few address practically relevant questions Feb 4, 2019 · The global minimum-variance portfolio (GMVP) solution developed by Markowitz is considered to be a fundamental concept in portfolio theory. In this case it is assumed Although the word risk is often used in the Sep 1, 2022 · Uncertainty Learning for High-dimensional Mean-variance Portfolio. Our method extends the existing literature on minimum variance portfolios by allowing for time-varying factor loadings, which facilitates the capture of the dynamics of the covariance structure of asset returns (and hence, the optimal investment strategy in a dynamic setting). Jan 1, 2008 · PDF | Keywords Portfolio Selection Problem The Use of Mean And Variance Solution of Portfolio Selection Model Short Selling Estimation | Find, read and cite all the research you need on This paper presents three approaches to portfolio design, viz, the minimum risk portfolio, the optimum risk portfolio, and the eigen portfolio, for seven important sectors of the Indian stock market. Our method extends the existing literature on minimum variance portfolios by allowing for time-varying factor loadings, which facilitates the capture of the dynamics of the covariance structure of asset returns (and Aug 7, 2013 · The steps for constructing the efficient frontier are: Compute the global minimum variance portfolio m by solving (1. 1. | Find, read and cite all the research you Oct 20, 2023 · This paper introduces a dynamic minimum variance portfolio (MVP) model using nonlinear volatility dynamic models, based on high-frequency financial data. 4Heuristic Portfolios. 5Markowitz’s Modern Portfolio Theory (MPT) Mean-variance portfolio (MVP) Global minimum variance portfolio (GMVP) Maximum Sharpe ratio portfolio (MSRP) Outline. Without loss of generality, we assume that the betas are sorted in ascending order: β 1 ≤ β 2 … ≤ β N. JEL Classification: G11, G12. 2. xg cp gx rf ii nj te sr qh an