The Impacts of Kurtosis on Risk Stationarity: Some Empirical Evidence - WU, Chunchi (Institutional Knowledge at Singapore Management University, 1985)
An analysis is performed of the impact of kurtosis on the stationarity of the standard deviation and beta risk. To test the intertemporal stationarity of variance estimates, monthly returns for 464 securities on the CRSP monthly return file, having no missing observations during the period January 1959-December 1979, were gathered. Data are grouped into 3 nonoverlapping periods: 1959-1965, 1966-1972, and 1973-1979, yielding 84 return observations for each period. Analysis indicates that the standard deviation is significantly affected by the kurtosis of the returns distribution. It is also shown that the nonstationarity of beta is neither the result of using ordinary least squares regression nor a statistical phenomenon in the presence of a leptokurtic returns distribution. Finally, it appears that, in using the option pricing model, the 4th moment of the returns distribution should probably be considered to adjust the estimated standard deviation.