1 generation of private signals by analysts eaa2006, dublin, eire
TRANSCRIPT
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Generation of Private Signals by Analysts
EAA2006, Dublin, Eire
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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
?
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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
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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
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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 ?
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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
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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
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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
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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
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Method
Extend D&F by endogenising: cost quality of the private signal
I derive additional comparative statics (not for this paper)
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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
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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”)
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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
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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].
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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
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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)
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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
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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)
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1.2
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6400
1200
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1760
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2320
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2880
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4560
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5120
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5680
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6240
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6800
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7360
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7920
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8480
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9040
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9600
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1016
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1072
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1128
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1184
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1240
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1296
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1352
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1408
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1464
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1520
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1576
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1632
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1688
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1744
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1800
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1856
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1912
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1968
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DF replication with price=2500
DF replication with price=500
price and analyst noise both optimised
Region 3
Region 1
Region 2
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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)
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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 ?
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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
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Empirics - Sample
start with all IBES quarterly forecast summaries
remove data where– no announcement date available– EPS unavailable– “confounded”
25 075 data points
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Empirics - Approach
just use extreme quintiles on ENOISE
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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
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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)
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Stuff I need to do
What is the analyst following in the various quintiles?
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Intuition Slides
to be used if necessary
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Solving for Equilibrium (7) – Intuition
It1 against sigma2squared
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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
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Solving for Equilibrium (6) – Intuition
Profit against sigma2squared
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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