A model of investor sentiment Barberis, Shleifer & Vishny Journal of Financial Economics,1998 Cedric Foucart Dries Heyman

Anomalies  Underreaction to news: E(r t+1 |z t =G)> E(r t+1 |z t =B) Empirical evidence:  Cutler et al (1991): positive autocorrelation in excess returns over months period  Bernard (1992): past earnings announcement return predicts future (60 days) return  Jegadeesh and Titman (1993)  Rouwenhorst (1997)

Anomalies (2)  Overreaction to a series of news: E(r t+1 |z t =G, z t-1 =G, z t-j =G)< E(r t+1 |z t =B, z t-1 =B, z t-j =B) (j≥1) Empirical evidence:  Cutler et al (1991): slightly negative autocorrelation over 3-5 year period  De Bondt and Thaler (1985):Losers outperform winners  Zarowin (1989)

Modelling over- and underreaction  Representative, risk neutral investor  Earnings follow random walk  Investor beliefs: two regime world  Regime 1: mean reverting  Regime 2: trending  Regimes capture two psychological phenomena: conservatism and representativeness

Conservatism and representativeness  Individuals change beliefs too slow → leads to underreaction  Mean reverting regime = conservatism  People think they see patterns in truly random sequences → Leads to overreaction  Trending regime = representativene ss

Regime switching model  Underlying switching process follows a Markov process  Switches are rare  Most likely to be in model 1 (mean reverting)  Bloomfield, Hales (2002): Experimental evidence supports regime-shifting beliefs

Earnings forecast  Determine model that governs earnings  Probability of being in model 1(q t ) depends on → previous probability of being in model 1 → new earnings observation → transition probabilities  Earnings reversals increase q t  Same earnings decrease q t

Pricing  If random walk: P t =N t /δ  If regime switching model: P t =N t /δ + y t (p 1 – p 2 q t ) → Mispricing: y t (p 1 – p 2 q t ) <0: underreaction >0: overreaction  Both underreaction and overreaction are possible (depending on parameters)

Simulation  Earnings generation: random walk  2000 firms over six years  2 portfolios: positive and negative realisations  N= 1 to 4  Compute returns in year after formation  Difference between returns Results confirm expectations

Conclusion  Model of investor sentiment  Explain both over- and underreaction  Makes use of conservatism and representativeness  Simulation results confirm expectations