Internet Appendix “Conviction and volume: Measuring the information content of hedge fund trading” C Maximum likelihood estimation

C Maximum likelihood estimation C.1 Building the likelihoood function Let Θ = (Θ1; Θ2) = (σ , σ η, σ u, π; β1, λ1, β2, λ2, φ) be the vector of parameters. Let X = (x1,s,t, x2,s,t, r1,s,t, r2,s,t) be the vector of observables, with r2 = p2− p1 and r1 = p1. Let 1(x) be an indicator variable equal to 1 if the event x has occured, and 0 otherwise. Let g(x) be the standard normal PDF and G(x) the standard normal CDF. Solve for the probability of X given Θ. s indexes stocks, t indexes information episodes (rather than quarters), and the subscript of 1 (subscript of 2) denotes the first (second) quarter in each episode. The likelihood function for observing X given Θ, with x1 and x2 censored below at xc and information publicly released after quarter 1 (as opposed to after quarter 2) if x1 > xc and x2 ≤ xc, is: