The test consists of two questions. Candidates must answer all questions.

Time allowed:    2 hours.

Question 1: (50 marks): Answer all parts (a), (b), and (c) of this question.

(a)  [10 marks] When the Central Bank purchases Government bonds held by banks, this:

I.       induces banks to increase their leverage

II.        makes banks less likely to grant loans to firms

III.       increases the mismatch of assets and liabilities of banks

IV.       makes banks more likely to grant loans to firms

V.       makes banks more fragile

Indicate which of the above is correct and briefly motivate your answer.

(b)  [10 marks] The presence of deposit insurance :

I.       Induces banks to hold excessive cash reserves

II.        Increases the possibility of having bank runs

III.        Induces banks to grant riskier loans

IV.       Lowers banks’ profits

V.       Implies that banks should not be regulated.

Indicate which of the above is correct and briefly motivate your answer.

(c)  [30 marks]  Suppose there are 50 investors. Each investor has savings equal to £200 at t=0 which he deposits in a bank, to be withdrawn either at t=1 or at t=2. It is known that a  fraction 0.1 of the depositors will have a liquidity shock and will then have to     withdraw at t=1.  Assume the bank promises to pay to the depositors who withdraw at t=1 the amount deposited.

What is the minimal number of depositors who will want to withdraw at t=1? And what is the amount of cash the bank must have available at t=1 to meet  these withdrawal requests?

Suppose the bank can use the cash received from investors at t=0 to make two- period loans to firms, yielding a net return of 10%. What is the maximal amount of money the bank can use at t=0 to make loans to firms, while having enough   cash at t=1 to meet the withdrawal requests you found in (i)?

What is the maximal interest rate the bank is able to offer to depositors who withdraw at t=2?

Suppose you are a depositor in the bank who did not experience a liquidity    shock. Given the interest rate you found in (iii), will you always prefer to wait and withdraw at t=2 or only under some conditions?

Suppose a 100% reserve requirement is imposed on banks. Explain in maximum three lines what are the costs and benefits of this measure.

Question 2: (50 marks): Answer all parts (a), (b), (c) and (d) of this question.

(a) [20 marks] Consider a bank with the following balance sheet at t=0. On the asset side it has a  two-year zero coupon bond, with a face value of £250,000, selling for £230,000; on the    liability side it has a one year zero coupon bond, with a face value of £230,000, selling at

£220,000.

-     What is the annual yield to maturity of the two-year bond?

-     What is the yield to maturity of the one-year bond? What is the level of bank equity at t=0?

-     Suppose in a year from now (at t=1) the central bank were to tighten monetary     policy so that the yield to maturity on one year bonds increases to 10%. What will be the value of the bank’s equity at t=1?