BERND PAPE Asset Allocation, Multivariate Position Based Trading ...

ACTA WASAENSIA 19& Scheinkman (1987) regularly reject the null hypothesis of independence of equityreturns as of financial returns in general 13 .Even swift visual inspections of plots of equity return series as of financial return seriesin general reveal Heteroscedasticity as the most obvious violation of the assumption ofindependently and identically distributed returns: volatility as measured by absoluteor squared returns is not constant through time.Heteroscadasticity was first noted by Mandelbrot (1963) in daily returns of cottonprices. Fielitz (1971) investigated the returns of 200 stocks listed at the New York StockExhange (NYSE) from 1963-68 and found that almost half of the stocks investigatedexhibited significant variation in realized volatility of the daily returns. For weeklyreturns the fraction with statistically significant heteroscedasticity was one quarter 14 .Schwert (1989) reports volatility estimates of monthly stock returns in 1857-1987 varyingfrom 2% in the early 1960’s to 20% in the early 1930’s. Haugen, Talmor & Torous(1991) identify more than 400 significant changes in volatility of the daily price changesin the Dow Jones Index in 1887-1988.Volatility is not only fluctuating but also correlated through time. Again this facthas first been noted by Mandelbrot for daily returns of cotton prices in his famousstatement thatlarge changes tend to be followed by large changes–of either sign–andsmall changes tend to be followed by small changes.(Mandelbrot 1963: page 418).Fama (1965) finds an increased conditional probablility of large price changes on stockswith large price changes on the preceding day in a sample of 10 randomly selected US13 see Scheinkman & LeBaron (1989); Hsieh (1991); Brock, Hsieh & LeBaron (1991); Bollerslev,Engle & Nelson (1994); Pagan (1996).14 Further early illustrative examples of heteroscedasticity in equity returns include Wichern, Miller& Hsu (1976) and Hsu (1977, 1979a, 1982).