1

Generation of Private Signals by Analysts

EAA2006, Dublin, Eire

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

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 R2 between firm return and market returnincreases for firms with low following (i.e. low competition) where return variability has declined in firms with regulated disclosure

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

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

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

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

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

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

Method

Extend D&F by endogenising: cost quality of the private signal

I derive additional comparative statics (not for this paper)

11

The Model

4 dates, 1 (monopolist) analyst

t=0 investors endowed with wealth; have a negative exponential utility function: u(w)=-e-bw

t=1 a private signal y1 is generated by the analyst. This signal is y2 + noise.

trade occurs - supply is uncertain

t=2 the public signal y2 is released. y2=x+noise

trade occurs - supply is uncertain

t=3 realisation occurs

All stochastic variables are assumed normalVariances are known but not outcomes

12

The Model – what happens ?

the t=1 signal, y1 : 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 y2 (the “earnings announcement”)

13

Endogenisation of the analyst

The analyst sells signal y1 into the market at a price c.

He chooses the quality of the signal, σ12

Can capture revenue directly proportional to the number of purchasers, R = λc – k /σ1

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 [σ12, c].

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=2 everyone has the same expectations

at t=1 informed 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

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/σ22) of public signal y2

determine optimum:a search algorithm that finds the

-maximising [σ12, c] pair for each value of .

Solving for Equilibrium (2)– Process

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

0

2000

4000

6000

8000

10000

12000

800

6400

1200

0

1760

0

2320

0

2880

0

3440

0

4000

0

4560

0

5120

0

5680

0

6240

0

6800

0

7360

0

7920

0

8480

0

9040

0

9600

0

1016

00

1072

00

1128

00

1184

00

1240

00

1296

00

1352

00

1408

00

1464

00

1520

00

1576

00

1632

00

1688

00

1744

00

1800

00

1856

00

1912

00

1968

00

analyst noise fixed for DF replication

price and analyst noise both optimised

Region 3

Region 1

Region 2

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

opt_cost against sigma2squared

0

1000

2000

3000

4000

5000

6000

80

0

72

00

13

60

0

20

00

0

26

40

0

32

80

0

39

20

0

45

60

0

52

00

0

58

40

0

64

80

0

71

20

0

77

60

0

84

00

0

90

40

0

96

80

0

10

32

00

10

96

00

116

00

0

12

24

00

12

88

00

13

52

00

14

16

00

14

80

00

15

44

00

16

08

00

16

72

00

17

36

00

18

00

00

18

64

00

19

28

00

19

92

00

opt_cost+DF500

opt_cost+DF2500

opt_cost+opt c

opt_cost+opt c,s1s

opt_cost+opt & k

opt_cost+opt c (s1s=1k)

c is optimised with s1s=10000

c and s1s are optimised

both c and s1s are optimised

c is optimised with s1s=1000

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

0

0.2

0.4

0.6

0.8

1

1.2

800

6400

1200

0

1760

0

2320

0

2880

0

3440

0

4000

0

4560

0

5120

0

5680

0

6240

0

6800

0

7360

0

7920

0

8480

0

9040

0

9600

0

1016

00

1072

00

1128

00

1184

00

1240

00

1296

00

1352

00

1408

00

1464

00

1520

00

1576

00

1632

00

1688

00

1744

00

1800

00

1856

00

1912

00

1968

00

DF replication with price=2500

DF replication with price=500

price and analyst noise both optimised

Region 3

Region 1

Region 2

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

Empirics – Measures (Figure 5)

σ12 measured by deviation of forecast from

earnings ultimately announced

FNOISE = [ (y0acteps-mean) / y0acteps ]2

σ22 ENOISE 1/R2 from Foster (1977) model

of earnings (+other measures)

Logic ?

21

Empirics – Controls

LMKVALQ – size

URET = is the unsystematic return for the firm’s 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

Empirics - Sample

start with all IBES quarterly forecast summaries

remove data where– no announcement date available– EPS unavailable– “confounded”

25 075 data points

23

Empirics - Approach

just use extreme quintiles on ENOISE

24

Results

Variable Param. Predicted Param. Est.

t Value p

Intercept 04.8661 16.495 0.0000

ENOISE 1 1 <0 -0.2049 -1.702 0.0889

ENOISE HIQUINT 2 1+2 ≥ 0 0.2077 1.700 0.0892

LMKVALQ 1-0.4508 -11.475 0.0000

URET 2-0.7744 -0.733 0.4635

NEWRET 3-0.3056 -0.567 0.5710

PERFORM 40.0701 0.226 0.8214

NEWINFO 5-0.1438 -0.333 0.7393

Table 4, Panel A

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

Stuff I need to do

What is the analyst following in the various quintiles?

28

Intuition Slides

to be used if necessary

29

Solving for Equilibrium (7) – Intuition

It1 against sigma2squared

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

800

7200

1360

0

2000

0

2640

0

3280

0

3920

0

4560

0

5200

0

5840

0

6480

0

7120

0

7760

0

8400

0

9040

0

9680

0

1032

00

1096

00

1160

00

1224

00

1288

00

1352

00

1416

00

1480

00

1544

00

1608

00

1672

00

1736

00

1800

00

1864

00

1928

00

1992

00

It1+DF500

It1+DF2500

It1+opt c

It1+opt c,s1s

It1+opt & k

It1+opt c (s1s=1k)

optimise c, s1s optimise c, s1s with k is slightly lower

optimise c, s1s=1000

DF2500

DF500

optimise c

30

Solving for Equilibrium (6) – Intuition

Profit against sigma2squared

0

100

200

300

400

500

600

700

800

Profit+DF500

Profit+DF2500

Profit+opt c

Profit+opt c,s1s

Profit+opt & k

Profit+opt c (s1s=1k)

DF2500

DF500

c is optimised, s1s=10000

optimise both c and s1s; andboth optimised with cost functionAlthough the difference is not visible on the chart, the latter is slightly lower than the former.

c optimised, s1s=1000