08/03/2017
Corporate Finance and
Financial Intermediation
Homework 2- Question 5
Names: Saaïdi Aymen and Liviello Antonio
PROGRAM: ECON2 MS/G
PROFESSOR: ALAIN DE CROMBRUGGHE
Question 5
What are the formal similarities between signaling and screening? What are
the economic differences?
Signaling and screening seem to be approximately close. But to differentiate them, we
will explain two models in which different results will emerge. We will demonstrate that the
intuition behind these two notions of economic theory are very similar. In fact, signaling and
screening are two different solutions in two models to remediate at the adverse selection
caused by the asymmetric information on markets. Despite the similarities, we will see that
there are some differences.
A model for signaling.
To introduce the signaling, let’s begin to describe one model of adverse selection. Let’s
assume two types of agent: the entrepreneurs and the investors. A large number of
entrepreneurs are endowed with a risky project that requires a fix investment. The
entrepreneurs have enough initial wealth (W0) for financing their project (W0 > 1). The
entrepreneurs are risk-averse. The investors are accessed to a low-cost technology and they
are risk-neutral.
About the projects, each one is risky and gives a random gross return denoted:
𝑅̃ (𝜃) = 1 + 𝑟̃ (𝜃). The net return of those investments follow a normal distribution of mean
𝜃 and of variance 𝜎 2 . This last is the same for all projects so the risk is the same.
Nevertheless, the mean 𝜃 differs across the projects: there are good ones with high 𝜃 being
bigger than the cut-off level 𝜃̃ , and bad ones if the contrary. The quality of the project is
observed privately by each entrepreneur but not by the investors. Here is the asymmetric
information.
𝜃 being a private information and the entrepreneurs indistinguishable by investors, the price P
of equity will be the same for all firms. The entrepreneurs have the choice between selling
their project on financial market to investors or self-financing. The bad projects will be sold
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on the market and the good will be self-financed. The proof is the following: if the project is
sold on the market, that gives 𝑢(𝑊0 + 𝑃). On the contrary, if the project is self-financed, that
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gives 𝐸𝑢(𝑊0 + 𝑟̃ (𝜃)) = 𝑢(𝑊0 + 𝜃 − 2 𝜌𝜎 2 ) where 𝜌 represents the constant absolute index
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of risk aversion1. By equalizing both we obtain: 𝜃̃ = 𝑃 + 2 𝜌𝜎 2 . If 𝜃 < 𝜃̃, the project will be
sold on the market because the project has a low expected return (“bad” project). Else, it will
be self-financed because it is the good project. The problem of the adverse selection results in
the choice of the investors to choose to invest in the bad project instead of investing in the
good one. The projects with a high expected return will choose to be self-financed because
their entrepreneurs don’t want to obtain the same price as projects with low expected returns.
But there is a solution to signal themselves that they offer the high-quality by self-financing
partially. Indeed, they can convince the investors that the low-quality entrepreneurs have no
incentive to mimic them. In consequence, the solution of signaling can resolve the adverse
selection problem: the investors viewing that the high-quality entrepreneurs signal themselves
by self-financing partially, they can offer them a high price 𝑃2 = 𝜃2 . On the other side, for
low-quality entrepreneurs, they offer a low price 𝑃1 = 𝜃1 . In conclusion, the signaling can
resolve the problem of adverse selection provoked by the asymmetric information.
A model for screening.
Now, let’s turn to screening. Let’s assume the model of heterogeneous borrowers with a highrisk borrower denoted by 𝜃 𝐻 and a low-risk borrower denoted by 𝜃 𝐿 where 𝜃 represents the
risk parameter. One lender can afford money in exchange of a repayment which depends on
the risk. Indeed, the repayment R will be higher for higher risks and lower for lower risks.
There is an asymmetric information in the sense that only borrowers can observe the 𝜃. All
borrowers would claim to be in the lowest-risk category in order to pay the minimum interest
rate. As a consequence, the lender would be bound to disregard the declaration of the
borrower and to charge a uniform interest rate. The lender can offer different loan contracts
with variable collateral requirements, the interest rate being a decreasing function of the
collateral. The investment of the lender can either fail (𝑦̅ = 0) or succeed (𝑦̅ = 𝑦). The risk
parameter discussed above represents the probability of failure. All agents are risk-neutral.
The borrowers can initially put down some collateral C. The lender can offer a menu of loan
contracts, where the repayment R in case of success depends on the collateral C put down by
the borrower. If the project fails, the lender can liquidate this collateral; the borrower loses C,
whereas the lender gets only 𝛿C. Thus, there is a cost of liquidation, (1 − 𝛿)C, which is
assumed to be proportional to the size of the collateral. On the other hand, the project
succeeds, there is no liquidation; the lender obtains R and the borrower gets (y – R).
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The entrepreneurs have an exponential utility function of their final wealth: 𝑢(𝑤)
= −𝑒 𝜌𝑤
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The problem of adverse selection in this model bears on the uniform interest rate and the
amount of collateral that the two borrowers have to face. In fact, the low-risk borrowers will
pay a too high interest rate and will put too much (costly) collateral compared to their risk. On
the other side, the lender which propose the contracts know that the liquidation is costly and is
better of when there is no collateral.
To remain this adverse selection, the lender has to ask one question: “Do you want to be a
collateral C that you will not fail, against a reduction in interest rates?”. So Only low-risk
borrowers will take that bet. The contract with low-risk is represents by:
(1 − 𝜃 𝐿 )(𝑦 − 𝑅 𝐿 ) − 𝜃 𝐿 ≥ 𝑈 𝐿 2
But the high-risk borrower, which don’t take the bet, prefer the contract with high rate instead
of having collateral:
(1 − 𝜃 𝐻 )(𝑦 − 𝑅 𝐻 ) ≥ (1 − 𝜃 𝐻 )(𝑦 − 𝑅) − 𝜃 𝐻 C
Thus, the role of collateral is to allow for self-selection between the two types of risks. The
design of self-selection mechanism above represents the solution of the problem of adverse
selection caused by the asymmetric information.
Similarities and economic differences.
In order to compare signaling and screening, we will first talk about similarities in these two
models presented above and then we will emphasize the main economic differences.
First, the two models show clearly a problem of asymmetric information. Indeed, the first one
tells us about entrepreneurs knowing their types of risk against investors, the second one tells
us about two borrowers knowing their types of risk again face to a lender. The two results in
the phenomenon of adverse selection: the hidden information encourages the investor/lender
to make a uniform choice (payment or interest rate) to remediate at this risk-difference. In
consequence, that provokes a wrong equilibrium on the market because the low-risk
borrower/entrepreneurs have the same repayment or investment than high-risk people. Here is
the similarity between signaling and screening: to fight adverse selection by fighting the nontruthfulness of the high-risk people, a tool must be used to remove the incentive to mimic the
low-risk people. Entrepreneurs signal their high-quality by self-financing partially while
lender screens low-risk borrower by putting down more collateral against a reduce in interest
rate for the repayment. In the first model, the investment demand side removes the incentive
to be mimicked. In the second one, this is the investment supply side that removes this last.
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The outside opportunities of borrowers are represented by their reservation utilities 𝑈 𝑘 , 𝑘
= 𝐿, 𝐻
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There is in this sentence a first economic difference in a similarity. Signaling and screening
remove both the incentive to lie without having a big cost (signaling cost or liquidation cost
for collateral). But the former resides in the demand side whereas the latter resides in the
supply side.
An other difference resides in the assumptions of the models. The model of signaling tells us
that the entrepreneurs are risk-averse while the model of screening tells us that the borrowers
are risk-neutral. In the first case, if the entrepreneurs were risk-neutral, they would have the
need to sell their projects because of the risky nature of these last. In consequence, all
wouldn’t have the need to require financial market and thus they would self-finance to have
money for their project. No signaling shouldn’t be needed to solve an inexistent adverse
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selection. In fact the risk premium 2 𝜌𝜎 2 would be equal to 0 (because the risk-aversion
index 𝜌 is 0) and : 𝜃̃ = 𝑃. Thus, no adverse selection would exist in this type of world. In the
second case, the agents were risk-neutral. If they would be risk-averse like the first case, the
high-risk borrowers wouldn’t demand an investment if the probability of default would be
high. Only low-risk borrower would ask an investment and there would be no requirement of
screening to detect who tell the truth.
One difference needed to be added is about the risk management behind the two models. In
the signaling model, the investor know that the two projects are risky but tends to invest into
the high expected return project. Indeed, why should we take the low expected return instead
of the high expected return if the risk 𝜎 2 is the same for all projects? But in the screening
model, the risk is not the same: the low-risk borrower is a better project but offers a lower
repayment due to lower interest rate. The high-risk borrower offers a higher repayment due to
higher interest rate but is a riskier project and tends to be costly at the liquidation if the project
fails. Thus, the investors in the first model tends to invest into high-quality entrepreneurs if
they are rational, but in the second one, the lender tends to get a mixed portfolio composed by
a low-risk borrower with low interest rate and more collateral and a high-risk borrower with
high interest rate and no collateral.
This difference leads us to the last one and is about the correlation between risk and return. In
the second model with borrowers and lender, the risk and the return are positively correlated.
Indeed, the high-risk borrower offers a bigger repayment compared to the low-risk borrower
but the risk of project failure is higher. Moreover, we could say that the repayment increases
with the risk of failure. But in the first model, we observed that there are two different levels
of return for the same risk. The high-quality entrepreneur offers a higher expected return than
the low-quality entrepreneur for the same risk.
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Conclusion.
In conclusion, after having introduced signaling and screening through two simple model, we
observed that both seem to be very close. In fact, the adverse selection provoked by the
asymmetric information presented on the market could be resolved by remove the incentive of
people to lie about their type and to mimic the higher quality or the lower risk. Despite these
similarities, we emphasize some economic and financial differences hidden behind the two
notions. The risk-aversion or neutrality assumption modified could decrease the need of those
solutions on market if there is no adverse selection. Then, in an economical point of view, the
solution resides on two different sides on the market: signaling is used by the demand side
whereas screening is used by the supply side. Afterwards, if the people are rational, the risk
management is not the same in the sense that the signaling makes a discrimination incentive
to put only investments into the high-quality projects while the screening aimed to have a
mixed portfolio with high and low risk borrowers. Finally, the correlation between risk and
return is not always positive if we look to the first model where there are two different levels
of returns with the same risk.
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Reference
FREIXAS, X., ROCHET, J.C. (2008), Microeconomics of Banking, Chapters II and IV,
2nd ED., Cambridge: MIT Press.
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