  We consider the role of finite size effects on the value of the effective
Hurst exponent H. This problem is motivated by the properties of the high
frequency daily stock-prices. For a finite size random walk we derive some
exact results based on Spitzer's identity. The conclusion is that finite size
effects strongly enhance the value of H and the convergency to the asymptotic
value (H=1/2) is rather slow. This result has a series of conceptual and
practical implication which we discuss.
