Systematic risk has been measured traditionally using the CAPM beta estimated by applying the market model developed by Sharpe. However, it is generally accepted by practitioners as well as researchers that stock prices are influenced by a number of different economic factors. Thus, the Arbitrage Pricing Theory (APT) assuming the stock return to be a linear function of a certain number of economic factors has received increased attention in recent years. It has been shown by numerous studies that conditional variances and covariances of returns are time-varying. Most of the APT tests ignore those properties of financial time series. The variability of variances of factors and variances and covariances of asset returns may significantly influence the results of the APT tests. The APT model with the factor GARCH covariance structure, which is able to capture those properties of asset returns, is presented in the paper. In the empirical part of the paper, a test of the APT model is performed for sectors quoted on the WSE. Factors were extracted by principal component analysis for economic variables: stock indices - WIG, S&P 500, DAX, BUX, currency rates -USD/PLN, EUR/PLN, yield on the 52-week Polish Treasury Bills, 1 month WIBOR rate, US 10-year note yield, prices of raw materials - crude oil, copper, gold, CRB index. A two-stage estimation procedure with a multivariate GARCH model in the second stage is used and the number of factors is tested. Risk connected with seven factors is priced in the market. Presented model significantly better explained variability of conditional variances and covariances of stock returns than variability of returns. Two new modifications of procedures for construction of the APT with factor GARCH model are proposed. Many financial processes have common conditional volatility, which can be described by factor GARCH model, however it is not very probable, that considered factors explained the whole variability of conditional variances and covariances. The first proposed modification is extension of the model, which captures unexplained variability of asset returns conditional covariance matrix. The second one is estimation of the market risk premia and conditional variances of factors in the first stage by applying a model with the threshold GARCH-M effect instead of applying the traditional GARCH-M model. The threshold GARCH-M model assumes that the relation between expected return and variance can be different, depending on the sign of the exogenous variable, in this analysis returns of the S&P 500 index.The results of tests indicate the advantage of the model constructed by this procedure
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