Analytical Closed-form Parameterizations for Bounded Rationality of either of Overconfidence or Underconfidence

This study establishes analytical closed-form mathematical parameterizations for each of overconfidence or underconfidence that boundedly are rational. Given that, feasibly `boundedly rational overconfident (BRoverconfident)' agents revert, over time, to `boundedly rational underconfidence (BRunderconfidence)', but not vice versa, there exist specifications of BRoverconfidence that rationalize `patterns' of stock return momentum and reversals. For concreteness, whereas, emergence of `boundedly irrational overconfidence', which, necessarily reverts to `boundedly irrational underconfidence', and vice versa induces {positive,negative;...positive,negative} return sequences; with all agents boundedly rational, feasibly emergence of BRoverconfidence induces {positive,negative,positive;...positive,negative,positive} return sequences in markets. Corroborating the formal theory, but yet with the boundedly irrational pattern parameterized by better goodness-of-it, the same underlying stock portfolio return data supports the two dichotomous - boundedly rational vis-a-vis boundedly irrational - patterns for return momentum and reversals. Boundedly irrational investing swamps, as such boundedly rational investing