Minimum Variance Portfolio Selection for Large Number of Stocks – Application of Time-Varying Covariance Matrices

An evaluation of the efficiency of different methods of the minimum variance portfolio selection was performed for seventy stocks from the Warsaw Stock Exchange. Eight specifications of multivariate GARCH models and six other methods were used. The application of all considered GARCH-class models was more efficient in stocks allocation than the implementation of the other analyzed methods. The simple specifications of multivariate GARCH models, whose parameters were estimated in two stages, like the DCC and CCC models were the best performing models.W pracy dokonano oceny efektywności różnych metod tworzenia portfeli o minimalnej wariancji, w tym przede wszystkim z wykorzystaniem różnych specyfikacji wielorównaniowych modeli GARCH. Badanie zostało przeprowadzone dla 70 spółek notowanych na GPW w Warszawie. Zastosowano osiem parametryzacji modelu GARCH: skalarny BEKK, zintegrowany, CCC, ortogonalny dla 70 czynników, DCC, zintegrowany DCC, DECO-DCC, skalarny BEKK z warunkowym rozkładem t Studenta oraz sześć innych metod: równe udziały dla wszystkich aktywów, bezwarunkowa macierz kowariancji stóp zwrotu, ruchoma macierz kowariancji, ruchoma macierz kowariancji ze stałą wygładzania równą 25, metoda wyrównywania wykładniczego dla macierzy kowariancji oraz metoda wyrównywania wykładniczego dla macierzy kowariancji z parametrem wygasania równym 0,94

Konstrukcja portfeli efektywnych z zastosowaniem wielorownaniowych modeli

The purpose of this paper is to present dynamic approach to selection of efficient port folios using a forecasts of variances and covar iances from the multivaria te GARCH models. Evaluation of efficiency for different methods of asset allocation is also performed for stocks from the WSE. Twelve specif ications o f the multivariate GARCH models, the univariate GARCH model and six other covariance matrix estimation methods are used. Taking in to consideration time varying variances and covariances of stock returns in portfolio selections increases, with some exceptions , efficiency of asset allocation process. Simple specifications of the multivariateGARCH models, which parame ters are estimated in one stage, are the best performing models. From economic point of view, the differences between the models are not significant, with exception of the factor and orthogonal models. RiskMetrics methodology commonly used by practitioners does not give good results for constructions of efficient portfolios

Range-based DCC models for covariance and value-at-risk forecasting

The dynamic conditional correlation (DCC) model by Engle (2002) is one of the most popular multivariate volatility models. This model is based solely on closing prices. It has been documented in the literature that the high and low prices of a given day can be used to obtain an efficient volatility estimation. We therefore suggest a model that incorporates high and low prices into the DCC framework. We conduct an empirical evaluation of this model on three datasets: currencies, stocks, and commodity exchange traded funds. Regardless of whether we consider in-sample fit, covariance forecasts or value-at-risk forecasts, our model outperforms not only the standard DCC model, but also an alternative range-based DCC model.publishedVersio

Modelowanie liczby transakcji dokonywanych przy użyciu gotówki i kart płatniczych na rynku polskim

The work deals with an analysis of factors determining the intensity of usage of payment methods by Polish customers. The study covers the 3 main payment methods used in physical Points-of-Sale: cash, debit cards and credit cards. In order to describe the number of payments count data models: Poisson regression, negative binomial regression, Poisson hurdle model, negative binomial hurdle model, ZIP and ZINB were applied. The results obtained in the study revealed a significant effect of many demographic factors, as well as the use of financial and telecommunication services. A substitution effect between payments by credit and debit cards has been shown. The study demonstrated a strong impact of customers’ concerns about security on the usage of cards. A significant barrier to the development of card payments are also the preferences of society for maintaining the anonymity of payment transactions.W artykule dokonano analizy czynników determinujących intensywność wykorzystania przez polskich klientów trzech głównych metod płatności stosowanych w fizycznych punktach sprzedaży: gotówki, karty debetowej oraz karty kredytowej. Do opisu liczby płatności zastosowano 6 modeli zmiennych licznikowych, między innymi model ujemny dwumianowy i ZINB. Uzyskane wyniki wykazały wpływ wielu czynników demograficznych i ekonomicznych oraz istnienie efektu substytucyjnego. Wykorzystanie kart jest także silnie uzależnione od poczucia bezpieczeństwa oraz preferencji odnośnie anonimowości płatności