What happens when the stock markets are closed?


Abstract


The normality of the log-return of stock prices is often assumed by the market players in order to use some useful results, as for instance, the Black-Scholes formula for pricing European options. However, several studies regarding different indexes have shown that the normality assumption of the returns usually fails. In this paper we analyse the normality assumption for intra-day and inter-day log-returns, comparing opening prices and/or closing prices for a large number of companies quoted in the Nasdaq Composite index. We use the Pearson's Chi-Square, Kolmogorov-Smirnov, Anderson-Darling, Shapiro-Wilks and Jarque-Bera goodness-of-fit tests to study the normality assumption.We find that the failure rate in the normality assumption for the log-return of stock prices is not the same for intra-day and inter-day prices, is somewhat test dependent and strongly dependent on some extreme price observations. To the best of our knowledge, this is the first study on the normality assumption for the log-return of stock prices dealing simultaneously with a large number of companies and normality tests, and at the same time considering various scenarios of intra-day, inter-day prices and data trimming.

DOI Code: 10.1285/i20705948v12n2p405

Keywords: Data Trimming, Inter-day prices, Intra-day prices, Log-return, Normality Tests

References


Anderson, T. and Darling, D. (1952). Asymptotic theory of certain goodness-of-fit criteria based on stochastic processes. Annals of Mathematical Statistics, 23(2):193-212.

Anderson, T. and Darling, D. (1954). A test of goodness of fit. Journal of the American Statistical Association, 49(268):765-769.

Birnbaum, Z. (1952). Numerical tabulation of the distribution of kolmogorov's statistic for finite sample size. Journal of the American Statistical Association, 47(259):425-441.

Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3):637-654.

Jarque, C. and Bera, A. (1987). A test for normality of observations and regression residuals. International Statistical Review, 55(2):163-172.

Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12(2-3):231-254.

Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models. Econometrica, 59(6):1551-1580.

Kolmogorov, A. (1933). Sulla determinazione empirica di una legge di distribuzione (on the empirical determination of a distribution law). Giornale dell'Istituto Italiano degli Attuari, 4:83-91.

Lewis, P. (1961). Distribution of the anderson-darling statistic. Annals of Mathematical Statistics, 32(4):1118-1124.

Lilliefors, H. (1967). On the kolmogorov-smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association, 62(318):399-402.

Massey, F. (1951). The kolmogorov-smirnov test for goodness of fit. Journal of the American Statistical Association, 6(253):68-78.

Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine Series 5, 50(302):157-175.

Royston, J. (1982). An extension of shapiro and wilk's w test for normality to large samples. Journal of the Royal Statistical Society. Series C (Applied Statistics), 31(2):115-124.

Royston, J. (1983). A simple method for evaluating the shapiro-francia w' test of non-normality. Journal of the Royal Statistical Society. Series D (The Statistician), 32(3):297-300.

Shapiro, S. and Francia, R. (1972). An approximate analysis of variance test for normality. Journal of the American Statistical Association, 67(337):215-216.

Shapiro, S. and Wilk, M. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3/4):591-611.

Stephens, M. (1974). Edf statistics for goodness of fit and some comparisons. Journal of the American Statistical Association, 69(347):730-737.

Stephens, M. (1976). Asymptotic results for goodness-of-fit statistics with unknown parameters. Annals of Statistics, 4(2):357-369.


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