A model of investor sentiment

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

2. Anomalies • Underreaction to news: E(rt+1|zt=G)> E(rt+1|zt=B) Empirical evidence: • Cutler et al (1991): positive autocorrelation in excess returns over 1-12 months period • Bernard (1992): past earnings announcement return predicts future (60 days) return • Jegadeesh and Titman (1993) • Rouwenhorst (1997)

3. Anomalies (2) • Overreaction to a series of news: E(rt+1|zt=G, zt-1=G, zt-j=G)< E(rt+1|zt=B, zt-1=B, zt-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)

4. 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

5. 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 = representativeness Conservatism and representativeness

6. 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

7. Earnings forecast • Determine model that governs earnings • Probability of being in model 1(qt) depends on → previous probability of being in model 1 → new earnings observation → transition probabilities • Earnings reversals increase qt • Same earnings decrease qt

8. Pricing • If random walk: Pt=Nt/δ • If regime switching model: Pt=Nt/δ + yt(p1 – p2qt) →Mispricing: yt(p1 – p2qt) <0: underreaction >0: overreaction • Both underreaction and overreaction are possible (depending on parameters)

9. 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

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