Finally. there is considerable evidence that suggests that daily stock
returns are too leptokurtic to be normally distributed. A possible alternative
that has been suggested is that daily returns are drawn from a t-distribution
with five degrees of freedom. Because of the law of large numbers, this would
effectively imply a lognormal return distribution for any period longer than a
few days. Therefore, in spite of the different assumed behavior of daily stock
price changes, it might well be inferred that the BlackPScholes option pricing
formula should still apply (with minor reservations). If this is so, then daily
hedge returns will be even more highly skewed than before and will be
negative roughly 75 :/, of the time. Still greater caution in evaluating crude tstatistics
would then seem appropriate and it would then seem even more
imperative either to adjust the t-statistics for skewness or to use the proper
distribution of the t-statistics given the assumed return generating process.