1. 1 Generation of Private Signals by Analysts EAA2006, Dublin, Eire

2. 2 Background Empirical regularities regarding analyst behaviour have been documented Much of this is atheoretical, in particular – there is no modelling of the equilibrium e.g. what came first: – the analyst – or an informationally rich market ?

3. 3 Empirical regularities - Following inversely related to price variability around announcements associated with speed with which forecast info. is incorporated in prices increasing (Bhushan 1989b) / decreasing (Rock et al 2001) in ownership concentration decreases in lines of business increasing in R 2 between firm return and market return increases for firms with low following (i.e. low competition) where return variability has declined in firms with regulated disclosure

4. 4 Empirical regularities - Forecasts related to price changes revisions reflect prior returns Analyst superiority vs TS models of positively related to size Trading Volume related to forecast revision

5. 5 The Issue How do analysts decide on signal quality ? Is the quality of the analyst-generated signal a function of the quality of the information environment (upcoming public signal) ? Other effects (not part of this paper) : if we model analysts as responding to public info quality, does this change our predictions regarding market metrics ?

6. 6 Caveats My focus is on supply ("sell-side") analysts Motivations are more complex than buy-side analysts ??? As information intermediaries, how do they interplay with other sources of information

7. 7 The approach Noisy Rational Expectations and cognate signalling literature models simple markets where a signal is generated in a semi-game- theoretic way, i.e. actors have rational, linear expectations Given an objective function, expected characteristics of the signal can be modelled

8. 8 Potential Frameworks Kyle (1985) noise comes from uninformed demand a market maker clears the market investors are risk neutral Grossman & Stiglitz (1980) noise due to supply a less artificial setting risk-averse investors self-fulfilling conjectures about price linearity in signals Kim & Verrecchia (1991) there are multiple private signals; implications for differential informedness; Demski & Feltham (1994) a single private signal is purchasable by investors

9. 9 Demski and Feltham (1994) … allow for the purchase of a private signal (i.e. costly acquisition of private information) … have derived some testable comparative statics (not relevant for this paper): Analysts can be included as producers of the private signal

10. 10 Method Extend D&F by endogenising: cost quality of the private signal I derive additional comparative statics (not for this paper)

11. 11 The Model 4 dates, 1 (monopolist) analyst t=0investors endowed with wealth; have a negative exponential utility function: u(w)=-e -bw t=1a private signal y 1 is generated by the analyst. This signal is y 2 + noise. trade occurs - supply is uncertain t=2the public signal y 2 is released. y 2 =x+noise trade occurs - supply is uncertain t=3realisation occurs All stochastic variables are assumed normal Variances are known but not outcomes

12. 12 The Model – what happens ? the t=1 signal, y 1 : is available to investors at a cost c. investors purchase the signal (so 1- remain "uninformed"); they weigh expected utility of the signal against expect utility of observing price this signal can be thought of as an analyst forecast of signal y 2 (the earnings announcement)

13. 13 Endogenisation of the analyst The analyst sells signal y 1 into the market at a price c. He chooses the quality of the signal, σ 1 2 Can capture revenue directly proportional to the number of purchasers, R = λc – k /σ 1 2 key assumptions – R is increasing in. – analyst faces a cost function preventing infinitely precise info – cost is linear in precision The analyst's choice variables are [σ 1 2, c].

14. 14 Investors demands are a function of information available. price works out to be linear in information available (i.e. posterior of informed, posterior of uninformed) and supply noise. Why is price linear in information ? A (convenient) outcome of assuming normality at t=2everyone has the same expectations at t=1informed investors have posterior expectations of true value of x uninformed investors make assessment of what they think the informed investors know We can ascribe linear price conjectures to the market, and show that such conjectures are self-fulfilling. This allows us to solve for price and other variables. Solving for Equilibrium (1) – Approach

15. 15 Price at t=1 is a function of, since P1 results from a weighting of the posterior expectations of the informed and uninformed. itself is a function of the cost and quality of the private signal. The optimum c cannot be derived algebraically Simulation: Vary quality (1/ σ 2 2 ) of public signal y 2 determine optimum: a search algorithm that finds the -maximising [ σ 1 2, c] pair for each value of. Solving for Equilibrium (2) – Process

16. Solving for Equilibrium (3) – Basic Result (Figure 2)

17. Solving for Equilibrium (4) – Intuition (~Figure 3)

18. Solving for Equilibrium (5) – Intuition (Figure 4)

19. 19 Empirics – Data Earnings forecasts from I/B/E/S International Inc. Income statement data and release dates from Standard and Poor's Compustat service Price and volume data from Center for Research in Security Prices (CRSP)

20. 20 Empirics – Measures (Figure 5) σ 1 2 measured by deviation of forecast from earnings ultimately announced FNOISE = [ (y 0 acteps-mean) / y 0 acteps ] 2 σ 2 2 ENOISE 1/R 2 from Foster (1977) model of earnings (+other measures) Logic ?

21. 21 Empirics – Controls LMKVALQ – size URET= is the unsystematic return for the firms ordinary stock between the forecast and the earnings announcement NEWRET= is the return from the previous forecast summary to the current forecast summary for this firm (oops) PERFORM= recent returns prior to forecast NEWINFO= (NUMUP+NUMDOWN) / NUMEST Horizon– controlled by selection

22. 22 Empirics - Sample start with all IBES quarterly forecast summaries remove data where – no announcement date available – EPS unavailable – confounded 25 075 data points

23. 23 Empirics - Approach just use extreme quintiles on ENOISE

24. 24 Results

25. VariableParam.PredictedParam. Est. t Value p Intercept 0 4.866116.4950.0000 ENOISE 1 1 <0 -0.2049-1.7020.0889 ENOISE HIQUINT 2 1 + 2 0 0.20771.7000.0892 LMKVALQ 1 -0.4508-11.4750.0000 URET 2 -0.7744-0.7330.4635 NEWRET 3 -0.3056-0.5670.5710 PERFORM 4 0.07010.2260.8214 NEWINFO 5 -0.1438-0.3330.7393 Table 4, Panel A

26. 26 Results removing insignificant controls makes no difference (Table 4, Panel B) adding analyst following makes no difference (Table 5) regression by size quintiles – all the action is happening in quintiles 2 and 3 (Table 6, change heading)

27. 27 Stuff I need to do What is the analyst following in the various quintiles?

28. 28 Intuition Slides to be used if necessary

29. 29 Solving for Equilibrium (7) – Intuition

30. 30 Solving for Equilibrium (6) – Intuition