This paper tests the Arbitrage Pricing Theory (APT) by estimating the factor loadings that are consistent between two industry groups of securities. One of the pitfalls in the study by Roll and Ross is that the factors estimated in one group may not be the same with the factors estimated in another group. This raises some concerns on the acceptability of their conclusions. For our study, we employ inter‐battery factor analysis which enables us to estimate factor loadings by constraining the factors to be the same between two different groups. Our results show that there seem to be five or six inter‐group common factors that generate daily returns for two industry groups of securities, and these inter‐group common factors do not seem to depend on the size of groups. Also, based on our cross‐sectional tests on the risk premia, we conclude that the APT should not be rejected.

This paper investigates the month‐by‐month stability of (a) daily returns and correlation coefficients of stock returns, (b) correlation and covariance matrices, (c) number of return‐generating factors, and (d) the APT pricing relationship. The results show that there is a January effect and a small‐firm effect in stock returns. Correlation matrices are more stable than covariance matrices, but both types of matrices are not stable across months and across the sample groups. The number of return‐generating factors is rather stable most of the time and for most of the sample groups, but there is some significant instability that is related to the average correlation coefficients among stocks. The APT pricing relationship does not seem to be supported by the two‐stage process using the maximum‐likelihood factor analysis.

This paper investigates the month-by-month stability of (a) daily returns and correlation coefficients of stock returns, (b) correlation and covariance matrices, (c) number of return-generating factors, and (d) the APT pricing relationship. The results show that there is a January effect and a small-firm effect in stock returns. Correlation matrices are more stable than covariance matrices, but both types of matrices are not stable across months and across the sample groups. The number of return-generating factors is rather stable most of the time and for most of the sample groups, but there is some significant instability that is related to the average correlation coefficients among stocks. The APT pricing relationship does not seem to be supported by the two-stage process using the maximum-likelihood factor analysis.

In this paper, we test the arbitrage pricing theory (APT) in an international setting. Inter‐battery factor analysis is used to estimate the international common factors and the Chow test is used in testing the validity of the APT. Our inter‐battery factor analysis results show that the number of common factors between a pair of countries ranges from one to five, and our cross‐sectional test results lead us to reject the joint hypothesis that the international capital market is integrated and that the APT is internationally valid. Our results, however, do not rule out the possibility that the APT holds locally or regionally in segmented capital markets. Finally, the basic results of both the inter‐battery factor analysis and the cross‐sectional tests are largely invariant to the numeraire currency chosen.

This paper introduces an estimator of stock price volatility that eliminates, at least asymptotically, the biases that are caused by the discreteness of observed stock prices. Assuming that the observed stock prices are continuously monitored, an estimator is constructed using the notion of how quickly the price changes rather than how much the price changes. It is shown that this estimator has desirable asymptotic properties, including consistency and asymptotic normality. Also, through a simulation study, the authors show that it outperforms natural estimators for the low‐ and middle‐priced stocks. Furthermoret, he simulation study demonstratest hat the proposed estimator is robust to certain misspecifications in measuring the time between price changes.

This paper introduces an estimator of stock price volatility that eliminates, at least asymptotically, the biases that are caused by the discreteness of observed stock prices. Assuming that the observed stock prices are continuously monitored, an estimator is constructed using the notion of how quickly the price changes rather than how much the price changes. It is shown that this estimator has desirable asymptotic properties, including consistency and asymptotic normality. Also, through a simulation study, the authors show that it outperforms natural estimators for the low- and middle-priced stocks. Furthermoret, he simulation study demonstratest hat the proposed estimator is robust to certain misspecifications in measuring the time between price changes.

D. Chinhyung Cho, Edwin J. Elton, Martin J. Gruber, On the Robustness of the Roll and Ross Arbitrage Pricing Theory, The Journal of Financial and Quantitative Analysis, Vol. 19, No. 1 (Mar., 1984), pp. 1-10