apoorva javadekar - ratings quality under ’investor-pay model

Ratings Quality Under ’Investor-Pay Model’

Apoorva JavadekarBoston University

September 13, 2013

A. Javadekar () Investor Pay Model September 13, 2013 1 / 15

Motivation

Recent crises - also a ’ratings crises’ (Benmelech, Dlugosz)

’Inflations Ratings’ Phenomenon - Risky securities rated AAA

Fallen Angels: 60% of the initially AAA rated products during2005-07, rated below investment grade by 2009 for S&P (IMF, GFSR,2009)

Reasons - conflict of interest, ratings shopping, lack of effectivemonitoring, faulty risk models etc.

Conflict of interest - Result of ’Issuer pay system’fees contingent upon ratings (Ratings shoppings)CRA’s trade off - current income vs future reputation


Reforms

Reforms suggested - Cuomo Commission, Dodd Frank Act,European Union Commission

Examples - Non - contingent fee under issuer pay, Investor Paysystem, Platform system, rotation scheme, discloser norms

Investor Pay systemInvestors pays a non - contingent fee to CRA for ratingsEliminates ’conflict of interest’Possible problems - free riding, regulatory arbitrage (Acharya,Calomiris)

Objective: Understand the incentives of CRA under Investor paysystem and shed light on possible issues/problems


Main Findings of the paper

CRA’s incentive to ’lie’? - CRA acts ’truthfully’, given the signal

Stable ratings quality over business cycles?- Counter Cyclical-Lower in expansions

Incentives of reputed firms to maintain quality? - Optimal qualitydecreases after a reputational level

’Reputation Cycles’? - Yes! Reputation is built in recessions andconsumed in expansion

Implications and Reasons:

’Ratings inflation’ problem replaced by ’Ratings deflation’

Why? Costly to make an error in a bad state


Literature Review

Isaac and Shapiro (2012) - Cyclicality result under issuer paymodel; Considers cyclical issue ignoring opportunistic behavior

Mathis et al (2009) - Reputational concerns work only when otherincome is dominant

Skreta, veldKamp (2008) - Higher asset complexity induces ratingsShoppings

Bolton, Frexias, Shapiro (2012) - ratings shopping + naiveinvestors implies ratings inflation

Becker, Milbourn (2010) - Competition reduced the quality ofratings post entry of FITCH

What this paper adds?First model to analyze Investor pay systemCyclicality result under very weak assumption as compared to Isaac andShapiro (2012)Sheds light on possible problems with investor pay model


Model Time Line

At the beginning of period t1 State at time t is realized

st ∈ {g , b}follows a Markov process (could be persistent or IID)

2 Project arrivesgood with probability of λstReturns = π > 1 if good, 0 if bad, with probability 1.λg > λb - only distinguishing feature between a good and a bad state

3 Investor pays a non-contingent fee to CRA4 CRA choses the effort level to identify quality of the project:

E = {e1, e2, ..., en}Efforts are costly and costs could be state dependent

5 CRA receives a ’noisy signal’ about quality of the project. A(.) isthe accuracy of the signal.

A(et) =1

2+

1

2

√et (1)

6 CRA rates the product truthfully according to the signal andinvestment takes place if rating is good


Model Time Line

At the end of period t

1 Project success or failure is known publicly zt ∈ {S ,F ,N}2 Beliefs about CRA’s accuracy are updated based on the outcome

Belief at t - A distribution φt over EExpected Accuracy of ratings or reputation

A(φ) =∑e∈E

φ(e)A(e) (2)

Update - φt+1 = B(φt , st , zt)Example: Bayesian Update if A(e) is known

φt+1(e)|(zt = S) =λstφ

t(e)A(e, st)∑e′∈E φ

t(e′)A(e′, st)λst(3)

If A(.) is unknown - Arbitrary rules to update the reputationExample: z = S ⇒ reward, z = F ⇒ penalty s.t reputation hits lowerbound (zero fees), z = N ⇒ no update


Properties of Belief updates

Bayesian UpdateReward for success and penalty for failure is same irrespective of thestate for any given beliefBad rating in bad times ⇒ upward update, Bad rating in good times⇒ downward update

Arbitrary Rules - Designed to follow similar patterns, but may havehigher penalties and counter cyclical rewards

Example of Arbitrary Rule - Lower Bound Penalty, Grim - TriggerStrategy (Abreu 1986, Isaac Shapiro (2012))


Equilibrium Fee and Equilibrium Concept

Risk neutral investors operate in a competitive markets

Equilibrium fee is such that given the beliefs, expected profits net offees are zero for investors

f (st , φt) = λst (π − 1)A(φt)− (1− λst )(1− A(φt)) (4)

Fee is increasing in reputation and higher in a good state

Definition

Given φ0 ∈ Φ, an equilibrium with Bayesian update for this economy is asequence of fee schedules, optimal efforts {f (st , φ

t), e(st , φt)}∞t=0 and a

sequence of beliefs {φt}∞t=0, such that for every t,

1 f (st , φt) is determined competitively

2 e(st , φt) solves the revenue maximization program of the CRA.

3 φt+1 = B(φt , st , zt).


Value functions

Maximization Problem for CRA

max(U) = maxet

Et

∞∑t=0

βt f (st , φt) (5)

subject to φt+1 = B(φt , st , zt).Starting from a good state, after earning the current fee

Vg (φt) = maxet

(−c(et , g) + βpggEt(Vg (φt+1) + f (φt+1, g))

+ β(1− pgg )Et(Vb(φt+1) + f (φt+1, b)))(6)

Starting from a bad state after earning the current fee

Vb(φt) = maxet

(−c(et , b) + β(1− pbb)Et(Vg (φt+1) + f (φt+1, g))

+ βpbbEt(Vb(φt+1) + f (φt+1, b)))

(7)

Expectation is with respect to future beliefs - choice of e induces adistribution over φt+1


Optimal Policy Under Bayesian Beliefs

Figure : Optimal Policy Under Bayesian Update


Simulation Results Under Lower Bound Penalty

Table : Simulation Results: Lower Bound Penalty

Statistic Persistence IID Mean Reversion

ρ(Rt , st) -0.40 -0.004 0.30ρ(st , et) -0.80 -0.89 -0.87

ρ(Rt ,Rt−1) 0.63 0.41 0.24Mean et , st = g 0.53 0.49 0.48Mean et , st = b 0.69 0.74 0.73Mean Rt , st = g 0.48 0.56 0.64Mean Rt , st = b 0.61 0.57 0.54Mean At , st = g 0.87 0.82 0.84Mean At , st = b 0.91 0.94 0.92


Discussion of Results

Cyclical AsymmetryResults from asymmetric cost of making errorsBad State - Most likely Error ⇒ bad project rated as good ⇒ highpenalty to reputationGood State - Most likely Error ⇒ good project rated as bad ⇒ lowerpenalty to reputation⇒ higher incentive in a bad state to keep quality of ratings high

Non-Monotone effort choice in a good stateGood State - Cost of error lower + Marginal gain low at higher levelsof reputation ⇒ Decreasing efforts in reputationBad State - Cost of error high enough to keep quality high even whenmarginal gain from higher quality is limited

Ratings Deflation - Good projects turned down in expansion


Extensions

Introducing other Income - Not much impact (already solved)

Analytical results - Solving two period problem (obtained cyclicalresults)

Competition - Horse race between Issuer pay and Investor pay modelto acquire market share - cyclical credibility of each business modelcould be different

Long Lived Projects - Endogenous upgrades and downgrades


Acknowledgments

Thank You for coming !


apoorva javadekar - ratings quality under ’investor-pay model

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