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Mock exam online - Mock prac
Money, Credit and Banking (Erasmus Universiteit Rotterdam)
Studeersnel wordt niet gesponsord of ondersteund door een hogeschool of universiteit
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Money, Credit, and Banking
FEB13021
MOCK EXAM (ADJUSTED FEB 2015)
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Two remarks: 1) This exam was written for a 3-hour exam and
hence contains more questions than a 2-hour exam online 2) Because the exam material was slightly different in 2015, some questions were removed (from the original exam for display in this syllabus) and not all topics that we currently discuss are covered. The
online 2-hour exam can contain questions with regard to all materials discussed. The online 2-hour exam will consist of 15 multiple
choice questions and 2 open questions.
Question 1: Holmstrom & Tirole model (12 credits)
This question concerns the model of Holmstrom & Tirole (1997). Assume a
2-period model with firms (borrowers), uninformed investors and banks who
can monitor. Assume all parties are risk-neutral and protected by limited
liability. The firm has assets A and needs funding for its project of size
I > A. The firm’s project yields R in case of success and zero in case of
failure. The firm can choose between two projects: a less risky project, with
a probability of success of ps or a more risky project with a probability of
success of pr , where ps > pr .
The less risky project gives the firm a private benefit of s, whereas the
more risky project results in a private benefit of B, where s < B. The
project choice by the firm is unobservable by investors and the bank and
all projects are perfectly correlated. Both uninformed investors and banks
have an alternative investment option: they can choose to invest in the open
market and receive a return of γ. Only the less risky project is economically
viable: ps R > γI > pr R. Firms only differ in their publicly observable
starting capital A, where each firm needs external funds of size (I − A) for
their project and A ∈ [0, I). Uninformed investors are unable to monitor the
the firms.
We assume that the firm invests all its funds A and neither party is paid
anything if the project fails. We denote the return for the firm if the project
succeeds Rf and the return for uninformed investors Ru , where R = Rf + Ru .
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A. Calculate the condition, stated in the amount of capital of the firm A, under which
uninformed investors decide to invest in this firm directly. (4 credits)
Answer The firm will choose the save project if
ps R f + s ≥ pr R f + B
B−s
Rf ≥
ps − pr
To compensate the investors remains
Ru = R −
B−s
ps − pr
The expected revenue for investors with regard to the project is equal to
ps (R −
B−s
)
ps − pr
Investors choose to directly invest in the project if
B−s
) ≥ γ(I − A)
ps − pr
B−s
ps
)
Ā(γ) ≡ I − (R −
γ
ps − pr
ps (R −
The bank has the option to monitor the firm and decrease the private
benefit of the firm if it chooses the risky project to b, where s < b < B.
Monitoring is costly for the bank and depends on the height of the private
benefit b. The monitoring costs for the bank are equal to c = αb. Monitoring
cannot be done by uninformed investors.
We assume that the firm invests all its funds A and neither party is paid
anything if the project fails. We denote the return for the firm if the project
succeeds Rf , the return for uninformed investors Ru , and the return for the
bank Rb , where R = Rf + Ru + Rb . We assume the investment made by the
bank to be equal to I b .
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B. Calculate the condition, stated in the amount of capital of the firm A, under which
firms can invest in their project using indirect funding (6 credits)?
Answer The firm will choose the save project if
ps R f + s ≥ pr R f + b
b−s
Rf ≥
ps − pr
The bank will invest in the firm, if the return when monitoring is larger than
the return without monitoring
ps Rb − αb ≥ pr Rb
αb
Rb ≥
ps − pr
To compensate the investors remains
αb
b−s
−
ps − pr ps − pr
(1 + α)b − s
Ru = R −
ps − pr
Ru = R −
The expected revenue for investors with regard to the project is equal to
ps (R −
(1 + α)b − s
)
ps − pr
Investors choose to invest in the project if
(1 + α)b − s
) ≥ γ(I − I b − A)
ps − pr
(1 + α)b − s
ps
)
A(γ) ≡ I − I b − (R −
γ
ps − pr
ps (R −
The following picture is from the Holmstrom & Tirole (1997) article.
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C. Explain certification according to the Holmstrom & Tirole model. (2 credits)
Answer This figure shows how the uninformed investors invest as independent investors, but only after the monitor has taken a large enough financial
interest in the firm that the investors can be assured that the firm will behave
diligently. In this interpretation the monitor resembles a venture capitalist, a
lead investment bank, or any other sophisticated investor whose stake in the
borrower certifies that the borrower is sound, allowing the firm to go to less
informed investors for additional capital. During the lecture we discussed the
example of the IPO, where a bank also supplies capital if the firm goes to the
stock exchange for the first time or a bank guarantee.
Question 2: Credit Rationing and Adverse Selection (10 credits)
Consider the case where there are only two types of firms in the economy. One
type, referred to as type a, participates in less risky activities, whereas type b
firms participate in more risky activities. If the activities of both firm types
turn out to be unsuccessful, the return for both types is zero. If the activities
of the firms turn out to be successful, the return is Ra or Rb respectively. The
probability of success of the activities are pa and pb respectively. We assume
Ra < Rb and pa > pb where pa Ra = pb Rb . Each firm requires a loan of size
1. The ratio of type a firms in the economy is equal to α (the ratio of type b
firms therefor equals (1 − α)).
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Assume type a firms can choose to receive funding from direct investors at an
interest rate ia , whereas type b firms can receive funding from direct investors
at an interest rate of ib . We assume ia < ib . Assume the cost of funding for
the bank is equal to c, but the bank has to bear the cost of funding regardless
of the success of the firm’s activities. The bank cannot distinguish between
type a and type b borrowers. The bank and firms are considered to be risk
neutral and have limited liability.
A. Calculate the expected return on one loan for the bank if it offers an interest rate
to the borrowers equal to r∗ < ia . (1 credit)
Answer If the bank offers an interest rate r∗ < ia , it will attract both type a
as type b firms, the expected return on a loan is equal to
(αpa r∗ ) + ((1 − α)pb r∗ ) − c
(αpa (1 + r∗ )) + ((1 − α)pb (1 + r∗ )) − (1 + c) also received the full points.
B. Calculate the expected return on one loan for the bank if it offers an interest rate
to the borrowers equal to ia < r∗∗ < ib . (1 credit)
Answer If the bank offers an interest rate r∗ < ia , it will attract both type a
as type b firms, the expected return on a loan is equal to
pb r∗∗ − c
(pb (1 + r∗∗ )) − (1 + c) also received the full points.
C. Under which condition stated in the probability of success for type a firms, pa , will
the banker offer an interest rate ia < r∗∗ < ib , instead of an interest rate r∗ < ia ? (3
credits)
Answer The banker will do so if the return on offering an interest rate
ia < r∗∗ < ib is higher than offering an interest rate r∗ < ia . Which is the
case if
pb r∗∗ − c > (αpa r∗ ) + ((1 − α)pb r∗ ) − c
αpa r∗ < pb r∗∗ − ((1 − α)pb r∗ )
αpa r∗ < αpb r∗ + pb (r∗∗ − r∗ )
(r∗∗ − r∗ ) b
a
p < (1 +
)p
αr∗
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If you calculated (pb (1 + r∗∗ )) − (1 + c) > (αpa (1 + r∗ )) + ((1 − α)pb (1 + r∗ )) −
(1 + c), you also received the full points.
Now assume that each type of a firm can supply collateral of size ca to the
banker, whilst type b firms cannot.
D. Calculate the interest rate(s) the banker will charge the firms. (2 credits)
Answer The banker can now offer two different contracts to the firms. One
contract that includes an interest rate of
pa r∗ + (1 − pa )ca − c ≥ 0
c − ca
+ ca
r∗ ≥
a
p
and collateral of size ca . So contract a = {r∗ , ca }. And another contract that
offers an interest of
pb r∗∗ − c ≥ 0
c
r∗∗ ≥ b
p
This contract matches b = {r∗∗ , 0}. The banker can use collateral to distinguish between both type of firms.
E. Describe in your own words what credit rationing is. Explain how the use of
collateral can be used to prevent credit rationing. (3 credits)
Answer
Credit rationing is a situation in which a lender limits the supply of credit to
borrowers, although borrowers are willing to pay the prevailing price. Credit
rationing can be the result of adverse selection or moral hazard and is caused
by two countervailing effects on a banks profit: if a bank raises its interest rate,
the expected profit for the bank increases if loan demand would be inelastic,
but on the other hand if the bank raises its interest rate adverse selection and
/ or moral hazard also increase, causing the expected profit of the bank to
decrease. Collateral can be used as a screening tool for firms that apply for
a loan. Collateral mitigates adverse selection and would in the most extreme
case (as is shown in the papers of Bester (1985) and Hansen and Thatcher
(1983)) prevent a situation of credit rationing to occur.
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Question 3: Deposit Insurance & Limited Liability (8 credits)
Consider a depositor with funds of size X. This depositor has the choice to
make a deposit on a deposit account at two different banks:
1. Bank A which offers an interest rate of α per year
2. Bank B which offers an interest rate of β per year
where α > 21 β. The probability of default of bank A, being p, is higher than
the probability of default of bank B, being 21 p, that is p > 21 p. Assume there is
no deposit insurance installed by the government. When the bank defaults,
the depositor will loose his deposit and does not receive interest. Assume
the depositor is risk neutral, has limited liability and no alternatives beside
making a deposit at bank A or B.
A. Under which condition, expressed in the probability of default of bank A, that is
p, will the depositor choose to issue a deposit account at bank A? (2 credits)
Answer The depositor will make a deposit at bank A if the return on his
deposit at bank A is higher than the return on his deposit at bank B, that is
1
1
(1 − p) × (1 + α) × X + p × 0 > (1 − p) × (1 + β) × X + p × 0
2
2
1
(1 − p)(1 + α) > (1 − p)(1 + β)
2
1
−p(1 + α) + p(1 + β) > (1 + β) − (1 + α)
2
1 1
p(− + β − α) > (β − α)
2 2
α−β
p<
α − 21 β + 12
Now consider the case where the government installs deposit insurance. A
fixed amount of units deposit per depositor is insured through deposit insurance. Assume the deposit of size X is fully insured by deposit insurance.
If bank A or bank B defaults, the depositor will receive back its principal
without interest from the government.
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B. Under which condition, expressed in the probability of default of bank A, that is
p, will the depositor choose to issue a deposit account at bank A now the government
has installed fixed deposit insurance? (2 credits)
Answer The depositor will make a deposit at bank A if the return on his
deposit at bank A is higher than the return on his deposit at bank B, that is
1
1
(1 − p) × (1 + α) × X + p × X > (1 − p) × (1 + β) × X + p × X
2
2
1
1
(1 − p)(1 + α) + p > (1 − p)(1 + β) + p
2
2
1
( β − α)p > β − α
2
α−β
p<
α − 21 β
Now consider the case where the government installs risk-based deposit insurance instead of fixed amount deposit insurance. The risk-based deposit
insurance insures the deposit at bank A of amount X only for 50% of the
deposited amount (without interest). While if the depositor opens a deposit
account at bank B, his full deposit of size X is insured (without interest).
C. Under which condition, expressed in the probability of default of bank A, that is
p, will the depositor choose to issue a deposit account at bank A now the government
has installed risk-based deposit insurance? (2 credits)
Answer The depositor will make a deposit at bank A if the return on his
deposit at bank A is higher than the return on his deposit at bank B, that is
1
1
1
(1 − p) × (1 + α) × X + p × X > (1 − p) × (1 + β) × X + p × X
2
2
2
1
1
1
(1 − p)(1 + α) + p > (1 − p)(1 + β) + p
2
2
2
1
1
( β − α − )p > β − α
2
2
α−β
p<
α − 21 β + 12
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D. Use the answers of question A (no deposit insurance), B (fixed deposit insurance)
and C (risk-based deposit insurance) to explain the influence of deposit insurance on
limited liability. (2 credits)
α−β
Answer If you compare answer A to answer B: α−α−β
1
1 . So if fixed
1 <
α−
β+
2
2
2β
base deposit insurance is present (answer question B) the depositor will more
likely choose bank A, in comparison to when no deposit insurance is present
(answer question A). Risk-based deposit insurance (answer question C) perfectly mimics the case when there would be no deposit insurance present (answer question A). Fixed base deposit insurance limits the liability of the depositor, the more likely a risk-neutral depositor is to choose the bank A (the
more risky bank). The probability of choosing the risky bank is highest under
full-coverage of fixed deposit insurance (B), this form of deposit insurance
limits the liability of the depositor most. If the depositor is fully (limited to
his principal amount) liable for his choice (A) and no deposit insurance is
installed, or under risk-based deposit insurance the depositor is least likely to
choose the risky bank.
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