Exercises for tutorial 1 in Financial Intermediation - Lehrstuhl für ...

UNIVERSITÄT HOHENHEIM
INSTITUT FÜR BETRIEBSWIRTSCHAFTSLEHRE
LEHRSTUHL FÜR BANKWIRTSCHAFT UND
FINANZDIENSTLEISTUNGEN
PROF. DR. HANS-PETER BURGHOF
Exercises for tutorial 1 in Financial Intermediation
Exercise 1: (Chapter 1.2: „Banks as liquidity providers“, page 4.)
a)
Given is a random number of 2 types of depositors.
T1 realises with probability π1=0.5. The demand for consumption is short term (i.e. t1).
T2 realises with probability π2=0.5. The demand for consumption is long term (i.e. t2).
In t0 the depositors have to make their investment decision. Thereby they don’t know
their type. It is assumed that depositors put their fortune of 1 in the bank (financial
intermediary). It is assumed that the bank knows frequencies π1 and π2.
Given a depositor in autarchy there are following terms:
ln ; 0.8; 1.3; 0.5; 0.8
The depositor maximizes his expected utility by long term production technology and
liquidation option.
max
∗ ∗∗ s.t.
111 10.2
11 10.3
Determine a value for investment I that enables optimal quantities of
∗ ∗
consumption , in autarchy.
Determine the optimal quantities of consumption in autarchy.

)
Now depositors can put their money in a bank. They can either get an amount of c1
in t1 or an amount of c2 in t2.
∗ ∗ Determine the maximum quantities of consumption , a bank could offer
without suffering an expected loss.
Comment your result.
The bank maximizes the utility of all depositors respectively the expected utility of an
average depositor.
max ∗ ∗∗
s.t.
1
Bank’s view: Payout will be amount with probability of or with probability of
.
Depositors’ view: A depositor „invests“ the amount of 1 in the bank. Hence, the
expected return has to be at least 1.
c)
Repeat your calculation from exercise b). Differing, assume a rate of time
preference of 0.5.
Comment your result in view of stability of the bank.

Exercise 2: (Chapter 1.2: „Banks as liquidity providers“, page 11.)
Given are the following business opportunities of a bank:
1. 130 monetary unit credit (margin: 3%), subsequent payment of 40 monetary
units with probability of 12%
2. 110 monetary units deposit (margin: 1%), premature payout in of 30 monetary
unit with probability of 8%
3. borrowing at capital market (margin: 0%)
4. investment in cash (margin: -4%)
5. costs for short term acquisition of liquidity: 40%
Liquidity shocks are correlated as followed:
Demand in liquidity of particular states
withdrawal no withdrawal
additional loans 70 (p=0.05) 40 (p=0.07)
no additional loans 30 (p=0.03) 0 (p=0.85)
Assuming following conditions determine the return of a bank balance:
i) Pure financing corporation (only credit business, no deposit business).
(With and without liquidity buffer. Assume a liquidity buffer that offsets every
expected loss.)
ii) Bank with deposit business and credit business.
(With and without liquidity buffer. Assume a liquidity buffer that offsets every
expected loss.
Can you mention an alternative liquidity buffer that increases the profit of the bank?)