We investigate quantitatively the so-called "leverage effect," which corres
ponds to a negative correlation between past returns and future volatility.
For individual stocks this correlation is moderate and decays over 50 days
, while for stock indices it is much stronger but decays faster. For indivi
dual stocks the magnitude of this correlation has a universal value that ca
n be rationalized in terms of a new "retarded" model which interpolates bet
ween a purely additive and a purely multiplicative stochastic process. For
stock indices a specific amplification phenomenon seems to be necessary to
account for the observed amplitude of the effect.