This paper investigates the uneven mean reverting pattern of monthly return indexes of the NYSE, AMEX and NASDAQ, using asymmetric non-linear smooth-transition (ANST) GARCH models. It also evaluates the extent to which time-varying volatility in the index returns support the stock market overreaction hypothesis. The models illuminate patterns of asymmetric mean reversion and risk decimation. Between 1926:01 and l997:12, not only did negative returns reverse to positive returns quicker than positive returns reverted to negative ones, but negative returns, in fact, reduced risk premiums from predictable high volatility. The findings support the market overreaction hypotheses. The asymmetry is due to the mispricing behavior on the part of investors who overreact to certain market news. The findings also corroborate arguments for the “contrarian” portfolio strategy.