EC372: ECONOMICS OF FINANCIAL MARKETS
Takehome assignment:
1. [30 marks] An entrepreneur has the following technology: if she invests £1 the
technology yields £A with probability q and nothing (0) with probability 1 - q. The
probability q of success depends on the unobservable level of effort exerted by the
borrow £1 from a bank. ( ) = 2
entrepreneur. Effort is costly: to induce a probability q of success the entrepreneur
incurs a disutility cost of 1 2. The entrepreneur has no funds and must then
The bank charges an interest rate r to the firm (so the firm needs to repay £(1 + r) when it borrows £1 from the bank). Let x be the cash obtained by the entrepreneur from the yield of the project, after repaying the bank. The entrepreneur benefits from limited liability (that is, cannot pay the bank a greater amount than the income generated by the project). The entrepreneur’s utility is then qx-c(q).
(i) [10 marks] The entrepreneur can’t commit to exert effort. For a given level of r, find the level of q chosen by the entrepreneur. Find the expected value of the amount repaid by the entrepreneur to the bank.
(ii) [10 marks] Find the value of r for which the bank makes zero profits (that is, the expected value of the amount repaid by the entrepreneur equals the amount borrowed, £1). What is the level of q chosen by the entrepreneur for this value of r?
(iii) [10 marks] How does the level of A affects the values of q and r found in (ii)? Explain.
2. [15 marks] Multiple choice questions:
A. [5 marks] The sequential service constraint feature in a deposit contract implies that:
i. the amount that the bank pays to a withdrawing depositor depends on what was promised by the bank and on his place in the queue of depositors wishing to withdraw.
ii. the amount that the bank pays to a withdrawing depositor depends on what was promised by the bank and how long the queue of withdrawing depositors is.
iii. the amount that the bank pays to a withdrawing depositor depends only on what the bank promised.
iv. the amount that the bank pays to a withdrawing depositor depends only on how much money the bank has at the time.
v. None of the above
B. [5 marks] The trade-off faced by a goldsmith when deciding to print more receipts than the amount of gold available is
i. between insolvency risk and interest rate risk
ii. between profitability and interest rate risk
iii. between interest rate risk and credit risk
iv. between profitability and credit risk
v. between profitability and insolvency risk
C. [5 marks] Duration is different from maturity because duration reflects
i. intermediate cash flows instead of principal value
ii. the current yield rather than the yield to maturity
iii. the timing of all cash flows that accrue to the asset holder
iv. investors’ expectations about future interest rates
v. all of the above
3. [35 marks] Consider a bank operating over a period of three years, t=0,1,2. The bank has an obligation of £750 after one year from today (that is, at t=1) and £550 after two years (that is, at t=2). The bank has at year t=0 an amount £1,528.93 to invest and can choose between a zero-coupon bond or a coupon bond. The coupon bond matures in two years, pays an annual coupon of £100, and has a balloon payment of £1,400. The zero-coupon bond has a balloon payment of £1,610 at the end of the second year. Suppose at t=0 the
default-free yield on a one-year bond is 10%, and the annualized yield on a two-year bond is also 10%.
(i) [5 marks] What is the present value at t=0 of the bank’s equity (that is, the difference between the cash held and the present value of its liability)?
(ii) [10 marks] What is the duration of the bank’s liability?
(iii) [10 marks] Suppose the bank at t=0 uses all its funds to purchase the zero coupon bond. How many units of the bond does the bank purchase at t=0 [note: the bank can also hold fractions of a unit]? Suppose at t=1 the default-free yield on one-year bonds becomes 8%. What will be the bank’s equity at t=1? Suppose instead at t=1 the default -free yield on one -year bonds becomes 12%; what will be the value of bank equity at t=1 in this case?
(iv) [10 marks] Consider next the case where the bank at t=0 uses all its funds to purchase the coupon bond. How many units of the bond does the bank purchase at t=0? Suppose at t=1 the default-free yield on one-year bonds becomes 8%, what will be the bank’s equity at t=1? Suppose instead the default-free yield on one-year bonds becomes 12%; what will be the value of bank equity at t=1 in this case?
4. [20 marks] You earn £12000.at your current delivery job. But you need to drive in order to work. Each year you can have an accident with probability p = 0.1. In this case, your income loss is L = 6000. You can purchase insurance and each unit of income insured
costs 0.2 [note that at this price you may also sell insurance, in which case per unit sold you have to pay one unit of income if you have the accident( and)= inv return you receive a
payment of 0.2). Suppose you are risk averse with utility .
(i) [10 marks] What is your expected utility when you buy (or sell) insurance for A units of income?
(ii) [10 marks] How much insurance will you buy (or sell)?
USA 
India