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

14 ACTA WASAENSIA2.2 Absence of Serial CorrelationThe fact that stock price changes appear to be uncorrelated was already noted by King(1930). Kendall & Hill (1953) provide the first rigorous analysis of the time series ofstock indices. They find only small (and usually positive) autocorrelations in the weeklyreturn series of 19 British stock indices in 1928-38, half of them insignificant. Even thehighest measured autocorrelation coefficients stay below 0.24, implying predictability(R 2 ) of less then 6% of a weeks return by the return of the preceding week.Fama (1965) investigated in his doctoral thesis both daily and weekly returns of individualstocks in 1957-62. He found small predominantly positive autocorrelations(usually below 0.1) at daily and even smaller predominantly negative autocorrelations(usually above -0.05) at weekly frequency. A rapid decline of the autocorrelation abovethe first lag has since then be confirmed in many studies for both stocks and stockindices, 4 and even for high frequency data, 5 making absence of autocorrelations in returnsa well accepted working hypothesis for all horizons despite its marginal rejectionat the first lag.2.3 Excess KurtosisReturns of stocks and stock indices, like the returns of many other financial assets, arebell shaped similar to the normal distribution, but contain more mass in the peak andthe tail than the Gaussian. Such distributions are called leptokurtic. Leptokurtosisbecomes visually evident as a curve shaped as an elongated S in so called QQ-plots, inwhich the quantiles of an empirical distribution are plotted against the correspondingquantiles of a normal distribution with mean and variance identical to those of theempirical distribution.4 see for example Fama (1970, 1976); Taylor (1986); Ding, Granger & Engle (1993) and referencestherein.5 see Gopikrishnan et al. (1999).