Download (and the previous equation) that entrepreneur with

Nicolas Prélat
Alyssa Ouattara
March 8, 2017
HOMEWORK 02: ON LENDING AND
ASYMMETRIC INFORMATION
Question: Can you write a simpler model for section 2.3 using the assumptions on the lenders,
the borrowers and the probabilities of section 4.6? Explain how you would work and what
would be gained (simplicity) and lost.
We saw in the model from section 2.3 that very much like in Akerlof’s “Market for lemon, only entrepreneurs with
a relatively low expected return will issue equity (sell their project) while entrepreneur with a high expected return
will choose to finance their project with their own money. This is simply due to the fact that they are seeking their
own personal interest and will simply choose the most profitable alternative.
Indeed, if they are self-financing, they will get
Meanwhile, if they were to sell their project on the market, they would get the expected value of a random project
on the market (ie
). It is important to stress that only the entrepreneur knows the
expected return for his own particular project. What is available to investor is only the statistical distribution of the
return for project. Therefore, the entrepreneur will only sell his project if the expected return of his project is
lower than the expected return of a random project in the market, that is
This will lead to only lower return securities being available to investor and is a perfect illustration of adverse
selection. Furthermore, given that investors are risk-neutral and entrepreneur risk-averse, efficiency is only
reached when all entrepreneur fully finance their project by selling equity. For that to happens, it would require
that the risk premium to be superior to the adverse selection effect.
In the section 4.6 which is about lending, we saw that a menu of contract with varying level of interest rate and
collateral requirement could induce self-selection in a panel of heterogeneous borrowers.
The borrower are entrepreneurs that have varying level of failure probability of their project.
Entrepreneur that have a respectively higher likelihood of failure for their project would be willing to pay a higher
interest rate in exchange for not having to offer a collateral.
The expected payoff for the entrepreneur is
Where
is the probability of failure
is the Repayment (ie principal + interest)
Is the amount of collateral (which would be lost if failure were to occur)
It is obvious from the equation that both the repayment and the collateral adversely impact the utility of the
borrowers regardless of the risk of the project.
However, it can be seen in the following graph (and the previous equation) that entrepreneur with more risky
project are relatively more affected by an increase in collateral requirement (That is simply because they have a
higher probability of losing it). Meanwhile, low-risk project manager are relatively more affected by the interest
rate (Again, that is because they have a higher probability of success and thus of having to pay the interest rate).
Nicolas Prélat
Alyssa Ouattara
March 8, 2017
To create an improved model for the section 2.3, we could use the incentive that induce self-selection in section
4.6 to create signals about the quality of the project and solve the adverse selection problem.
Indeed, probability of failure is a major component of the expected return. By observing the choice of plan of the
borrower, we could draw conclusion about the risk of the project and thus its expected return. By exposing
themselves to an increased potential loss of their collateral. However, this could prove problematic if the benefit of
mimicking the strategy of high-quality project manager outweighs the increased risk of loss of collateral because
there would still be incentive to lie for the low-quality project manager. In other words, the adverse selection can
be avoided if risk premium is larger than adverse selection effect:
½ρσ2 ≥ π1 (θ2 – θ1).
Another way to solve the problem would be to allow the manager to offer collateral against a promised expected
return.