EC372-6-SP ECONOMICS OF FINANCIAL MARKETS Final Year Examinations 2021
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EC372-6-SP
Final Year Examinations 2021
ECONOMICS OF FINANCIAL MARKETS
Section A
1. Answer all parts (a), (b), (c), (d) and (e) of this question.
a) [10 marks] The vulnerability of the fractional banking system is due to
I. the volatility of interest rates
II. the nature of demand deposits
III. the illiquidity of loans
IV. the risk of theft or loss of funds deposited
V. the incentives of bank managers to seek profitable opportunities
Indicate which of the above are correct (could be more than one) and briefly motivate your answer.
II an d III
This text applies to all remaining questions b)-e).
Suppose there are 100 consumers. Each consumer has savings of £1,000 at t=0, which she deposits in a bank. The bank incurs a safeguarding cost of £0.02 per pound kept in its vault.
A fraction 0.2 of the depositors will face a liquidity shock and need then to withdraw the funds they deposited at t= 1. The rest of the depositors will withdraw their funds at t=2.
Suppose the bank can use the funds deposited to lend money to merchants. Each merchant needs to borrow £15,000 at t=0 to invest in a project. The project generates a revenue of £20,000 at t=2, but if prematurely liquidated at t=1 the project only yields £8,000. The bank charges the merchant an interest rate on the loan of20%.
b) [5 marks] What is the revenue the bank expects to receive at t=2 from each loan?
18,000
c) [ 15 marks] Suppose the bank offers depositors who choose to withdraw at t=1 the amount deposited less the safeguarding costs incurred by the bank. What is the size of the cash reserves the bank needs to keep to meet the expected withdrawal requests at t=1? What are then the funds the bank can use to make loans to merchants? How many merchants can the bank lend to at t=1?
1,000 X 0.98 X 20 =19600
80,000
5
d) [10 marks] Consider the total amount lent to merchants at t=0 you found in c). Given this amount of loans made at t=0 and the amount paid to depositors who withdraw at t=1, what are the funds the bank has available in period 2? If all these funds are paid to depositors who withdraw in period 2, what is the interest rate they receive? Is it higher than the interest rate paid to depositors who withdraw at t=1?
75,000 X 1,2 + 5,000 X 0.98 = 94,900
18.625%
YES
e) [10 marks] Compare the amount (found in d) paid to each depositor who withdraws at t=2 with the one paid to each depositor who withdraws in t=1: will a depositor not subject to a liquidity shock prefer to withdraw at
t=1 or t=2? Will the situation be different if now all other depositors choose to withdraw at t=1? When does a bank run occur?
At t=2
Yes, prefers to withdraw at t=1
2. Answer all parts a), b), c), d), e) of this question.
a) [10 marks] A possible solution to reduce the vulnerability of the fractional
banking system is that the central bank acts as lender of last resort, but this in turn induces banks:
I. to reduce their loans and increase their cash reserves
II. to increase their loans and reduce their cash reserves
III. to issue more equity
IV. to lend to riskier firms
V. to lend to safer firms
Indicate which of the above are correct (could be more than one) and briefly motivate your answer.
II, IV
This text applies to all remaining questions b)-e).
Suppose there are 100 consumers. Each consumer has an amount of £100 to invest at date t=0 to provide for her future consumption (at t=1 or t=2). The consumer can invest £100 in an illiquid project, yielding £160 at t = 2. If the project is liquidated at date t=1, it only yields £50. The consumer knows that with probability 0.2 she will receive a liquidity shock, forcing her to consume at t=1: in that event her utility for consumption will be 1 . With the remaining probability 0.8 the consumer receives no liquidity shock and is then indifferent between consuming at t=1 or t=2: her utility for consumption in that case is 1 + 2 .
b) [5 marks] What the consumer ’s expected utility when she invests directly all her funds in the illiquid project. Is the consumer risk neutral or risk averse?
0.2 X 500.5+ 0. 8 X 1600.5 = 11.534
Risk averse
c) [ 10 marks] Suppose now all the 100 consumers deposit all their funds in a bank. The bank uses the funds deposited to invest in the illiquid project. How many projects can the bank invest in? 100
Suppose the bank offers consumers a deposit contract which promises to pay £60 to a consumer who withdraws at date t=1 and £X to a consumer who withdraws at t=2. How many projects need to be liquidated by the bank at t=1 to meet all the requests for date 1 withdrawals coming from consumers who suffer a liquidity shock at t=1?
24
d) [15 marks] What is the maximal value of X the bank can credibly promise to pay depositors who withdraw at t=2?
76 x 160 / 80 = 152
I. II. III.
160
50
145
IV. 152
V. 146
Briefly motivate your answer.
Is the level of the consumer’s expected utility with this deposit contract higher or lower than the level found in b) (when the consumer invests directly in the project)? Explain your finding.
0.2 X 600.5+ 0. 8 X 1520.5=11.412
If the bank has also access a t=0 to a storage technology, allowing to keep funds in its vault at no cost, would it be able to offer a deposit contract with better terms for consumers?
Yes, no need to liquidate the project at a loss
e) [10 marks] Suppose you are a consumer with no liquidity shock at t=1 and must decide whether to withdraw at t=1 or t=2. If you believe that all other consumers with no liquidity shock choose to withdraw at t=2, how much do you expect to receive if you also withdraw at t=2?
How much do you expect to receive if instead you withdraw at t=1? When do you then prefer to withdraw in this case?
Briefly explain what is a bank run.
Section B
3. Answer all parts a), b), c) and d) of this question.
a) [10 marks] Interest rate risk is:
I. the risk that arises from lending to a borrower below the market interest rate
II. the risk that arises from the movement of general interest rates which cause the bank’s publicly traded assets and liabilities to be revalued by the market.
III. the risk that the depositors get a smaller amount when they withdraw their deposits
IV. the risk that borrowers are unable to repay the loans they received from the bank
V. the risk that depositors withdraw their funds from the bank. Indicate which of the above is correct and briefly motivate your answer.
II.
This text applies to all remaining questions b)-d)
Consider a bank with the following assets and liabilities. The assets are given by a coupon bond which matures in two years (t=2), pays a yearly coupon of £100 and has a balloon payment of £ 500. The liabilities entail an obligation to make a payment of £500 after one year (t=1) and of £100 after two years. Suppose that currently the interest rate on a one-year bond is 2% and the annualized yield on a two-year bond is also 2%.
b) [ 10 marks] What is the current value (at t=0) of the bank’s assets? And of its liabilities? What is then the current level of bank equity?
Assets: 100/1.02 + 600/1.022= 98.039+576.701=674.74
Liabilities: 500/1.02 + 100/1.022= 490.196 +96.117 =586.313
Equity: 88.427
c) [15 marks] What is the duration of the bank assets?
D of assets: 0.145+ 2 X 0.855 = 1.85
And of its liabilities?
D= 0.836 + 2 X 0.164 = 1.164
Compare the two values: do you think such a bank is exposed to interest rate risk?
d) [15 marks] Suppose after one year (at t=1) the interest rate on one year bonds jumps to 40%. What is the value of the bank’s assets and liabilities at t=1?
Assets: 100 + 600/1.4= 528.57
Liabilities: 500 + 100/1.4= 571.43
Equity: -42.86
And the value of bank’s equity?
Briefly explain why you find that equity declines.
What can a bank do to prevent this from happening?
4. Answer all parts (a), (b), (c), (d) of this question.
a) [10 marks] Consider a bank facing a pool of borrowers, some with low risk projects, others with high risk project. If the risk profile of a borrower is not observable, to separate the different types of borrowers the bank can offer:
I. loan contracts with different interest rates but otherwise identical conditions.
II. loan contracts with higher interest rates to firms who partly fund their project with equity and with lower interest rates to firms who fund their project entirely with debt.
III. loan contracts with lower interest rates to firms who partly fund their project with equity and with higher interest rates to firms who fund their project entirely with debt.
IV. loan contracts with higher interest rates to firms who fund their project with a single large loan and with lower interest rates to firms who fund their project with several smaller loans.
V. loan contracts with lower interest rates to firms who adopt environmentally friendly technologies and with lower interest rates to firms who adopt less environmentally friendly projects.
.
Indicate which of the above is correct and briefly motivate your answer.
III.
This text applies to questions b)-d).
Consider a bank with £ 90,000 to lend. The bank faces a pool of 150 loan applicants, 75 of them are low risk (L) and the remaining 75 high risk (H). Each applicant is applying for a £1,200 loan. A low risk (L) borrower will use the funds to invest in a project that yields £2,600 with probability 0.8 and zero with probability 0.2. A high risk (H) borrower will use the funds to invest in a project that pays £3,400 with probability 0.4 and zero with probability 0.6. The bank is a monopolist and chooses the interest rate it charges to loan applicants so as to maximize its profits. Assume a loan applicant will agree to borrow at the rate set by the banker if, in the event her project succeeds (that is, has a strictly positive yield), she is left with a revenue of at least £ 400 (after repaying the loan).
b) [10 marks] Suppose the bank is unable to identify the type of a loan applicant. What is the highest interest rate the bank can charge so that both the L and the H type of borrowers are willing to apply? What is the total amount of funds requested by loan applicants at this rate? Show the bank has insufficient funds to accommodate all loan applications received at this rate and hence must ration applicants. Comment.
Repayment: 2200, g. int. rate: 2200/1200-1=1.83
1200 X 150 = 180,000
c) [10 marks] Find the highest interest rate the bank can charge so that the demand for loans by borrowers equals the funds available to the bank (that is, such that there is no rationing).
Repayment: 3200, g. int rate: 3200/1200= 2.67
d) [10 marks] Compare the profits of the bank in the situation described in b) and in c): when are profits higher? Briefly explain your finding.
In b: 1.83 X (0.5 X 0. 8 + 0. 5 X 0.4)= 1.1
In c: 2.67 X 0.4 = 1.067
e) [10 marks] Consider a bank which can use its funds to finance risky projects. Projects may be good (succeed with probability 0.9) or bad (succeed with probability 0.5). The bank may screen projects, paying an effort cost e>0. Screening allows to perfectly identify good projects. The bank will have a greater incentive to screen projects
I. when the bank manager receives a higher compensation
II. when the bank manager receives a lower compensation.
III. when the banks raises the funds to finance the projects only using deposits.
IV. when the bank finances the projects at least partly with own equity and the rest using deposits.
V. When depositors are risk averse.
.
Indicate which of the above is correct and briefly motivate your answer
IV.
2022-05-24