Week 6
1. Suppose that you are the manager of a bank whose $100 billion of assets have an average duration of four years and whose $90 billion of liabilities have an average duration of six years. Conduct a duration analysis for the bank, and show what will happen to the net worth of the bank if interest rates rise by five percentage points. What actions could you take to reduce the bank's interest-rate risk?
2. Suppose that you are the manager of a bank that has $15 million of fixed-rate assets, $30 million of rate-sensitive assets, $25 million of fixed-rate liabilities, and $20 million of rate-sensitive liabilities. Conduct a gap analysis for the bank, and show what will happen to bank profits if interest rates rise by five percentage points. What actions could you take to reduce the bank's interest rate risk?
3. The following question illustrates how Gresham's Law need not arise in an economy in which coins of two different qualities circulate. The setup of the problem is exactly the same as that in question 2 of the week 3 problems, except the valuations chart is as follows:
|
Coin Quality
|
# of coins
|
Value to buyer
|
Value to seller
|
|
High
|
4
|
$2,400
|
$1,800
|
|
Low
|
1
|
$1,000
|
$800
|
a) If neither the coin buyer nor the coin seller knows the quality of the coins (that is, they know that there is one high quality coin and one low quality coin, but not which of the two is high quality - they are indistinguishable to both parties), what is the range of possible market prices (in other words, what dollar value of goods will the coin buyer have to exchange for the coin(s))? How many high quality coins will change hands? How many low quality coins will change hands?
b) Suppose now that this coin market is characterized by asymmetric information. More specifically, the coin maker knows which of the coins available for sale is the high quality coin and which is the low quality coin, but the coin buyer does not know which is which (again, he knows there is one high quality coin and one low quality coin but cannot distinguish between the two). What is the range of possible equilibrium prices in this market? How many high quality coins will be change hands? How many low quality coins will change hands? What is the issue here?