Download Problem Set 3 Answers - University of Wisconsin–Madison

Economics 330
Fall 2006
University of Wisconsin-Madison
Menzie D. Chinn
Social Sciences 7418
Problem Set 3 Answers (rev’d 10/31)
Due in lecture on Monday, October 30th. No late submissions will be accepted. Make sure your name is
on your problem set, as well as the name of your (official) TA.
1. Consider the following information, drawn from the Economist, October 21-27 issue.
1.1 Using the Interest Parity Condition, calculate the expected annual rate of depreciation (or
appreciation) of the US dollar against the UK pound over the next two years.
Answer: Interest rate parity is given by:
1
itD − itF = −
Ete+1 − Et
Et
Substituting in the relevant interest rates on two year government bonds, one obtains:
0.0485 − 0.0502 = −0.0017
Or in words, the dollar is expected to appreciate at a 0.17 per cent per annum over the next two
years.
1.2 What is the exchange rate (UK pound per US dollar) expected one year from now, assuming the
interest parity condition holds.
Answer: Rearranging the above equation:
−
Ete+1
+ 1 = itD − itF
Et
Ete+1
− 1 = −(itD − itF )
Et
Ete+1 = Et − Et (itD − itF ) = 0.54 − 0.54 × (0.0485 − 0.0502) = 0.541
Note this indicates that the dollar is expected to be stronger against the pound in the next period.
2. Suppose the U.S. economy starts looking like it’s going into recession. What do you think will
happen to exchange rates? Be sure to use equation (6) from the handout in lecture of October
11th/18th in your answer.
Answer: Equation (6) is:
⎛ P F ⎞⎡ 1 D
⎤
⎟⎟ ⎢1 + [(it − π te+1 ) − (itF − π tF+1,e )]⎥
Et = ⎜⎜
⎦
⎝ P ⎠⎣ Θ
If the U.S. is expected to go into a recession, and inflation rates are not expected to rise, then the
U.S. real interest rate expected in the future falls, and the dollar depreciates. The intuition for this
is that a lower interest rate in the future implies that the value of dollars relative to a bundle of real
goods falls in the future. Since the value of a currency today depends upon how valuable that
currency is expected to be in the future, a decline in future interest rates should imply a weakeing
of the currency today.
3. Using equation (6), explain what happens to the Pound/Dollar exchange rate if the Fed decides
to raise rates by one percentage point when expected inflation has risen by one percentage point.
Answer: Equation (6) is:
⎛ PF
E t = ⎜⎜
⎝ P
⎞⎡ 1 D
⎤
⎟⎟ ⎢1 + [(it − π te+1 ) − (itF − π tF+1,e )]⎥
⎦
⎠⎣ Θ
If the U.S. interest rate is raised today by one percentage point, but inflationary expectations are
also rising simultaneously also by one percentage point, then the real interest rate stays constant,
and the dollar does not change value.
4. The Fed is the most independent of all U.S. government agencies. What is the main difference between
it and other government agencies that explains the Fed’s greater independence?
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Answer. The Fed governors are complete terms are for 14 years. Hence, once a governor is in
place, he/she can make decisions that might displease the Executive and Legislative branches
with relative impunity. In addition, the Federal Reserve Bank presidents are selected by the
member banks in each of the respective regions. This provides an additional layer of insulation
from the political process absent from other agencies within the U.S. Government.
5. What is the key monetary policy making group within the Federal Reserve System? Who makes the
decisions within this group?
Answer. The Federal Open Market Committee is the key monetary policy making group, with
powers to set the target Fed Funds Rate. The voting members include the 7 governors, and 5
bank presidents. Four of the presidents rotate membership, while the NY Fed president has a
permanent seat.
6. Do you think the lemons problem would be more severe for stocks traded on the NYSE or those traded
over the counter? Explain.
Answer: The lemons problem would be less severe for firms listed on the NYSE because they
are typically larger corporations which are better known in the market place. Therefore it is easier
for investors to get information about them and figure out whether the firm is of good quality or is
a lemon. This makes the adverse selection-lemons problem less severe.
7. How can a sharp rise in interest rates provoke a financial crisis?
Answer: A sharp increase in interest rates can increase the adverse selection problem
dramatically because individuals and firms with the riskiest investment projects are the ones who
are most willing to pay higher interest rates. A sharp rise in interest rates which increases
adverse selection means that lenders will be more reluctant to lend, leading to a financial crisis in
which financial markets do not work well and thus to a declining economy.
8. Suppose the bank you own has the following balance sheet, in millions:
Assets
Liabilities
Reserves $1600 Deposits
$10000
Loans
$10400 Bank Capital $2000
If the bank suffers a deposit outflow of $1 billion with a required reserve ratio on deposits of
10%, what actions must you take to keep you bank from failing?
Answer:
Required reserves: 10% of $10000 = $1000
Excess reserve: $1600-$1000 = $600
Deposit outflow of $1 billion.
Balance sheet becomes:
Assets
Liabilities
Reserves
Loans
$600
$10400
Deposits
$9000
Bank
$2000
Capital
Required reserves: 10% of $9000 = $900
Excess reserve: $600-$900= -$300
Insufficient reserves. To eliminate shortfall the bank has 4 basic options to acquire reserves to
meet deposit outflow:
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1.
borrowing them from other banks in the Fed funds market or corporations (cost: interest
rates on the loans)
2.
sell some of its securities (cost: transaction costs)
3.
borrowing from the Fed (cost: 1.interest rate on loan; 2. non-explicit cost of increased
scrutiny and Fed’s discouragement of too much borrowing)
4.
reducing loans by this amount (cost: lose customers, very costly)
Option 1:
Assets
Reserves
Loans
Liabilities
$900
$10400
Deposits
Borrowing
from other
banks
or
corporations
Bank
Capital
$9000
$300
$2000
Option 2: no securities owned
Option 3:
Assets
Reserves
Loans
Liabilities
$900
$10400
Option 4:
Assets
Reserves
Loans
Deposits
Discount
loans from
Fed
Bank
Capital
$9000
$300
$2000
Liabilities
$900
$10100
Deposits
Bank
Capital
$9000
$2000
9. Consider the “High Capital Bank” in the middle of page 231 (8/e) [213 (7/e)]. Suppose further that the
return on assets (ROA) is 2%.
9.1
Calculate the ROE.
Answer:
ROE = (net profit after taxes)/(equity capital)
= ROA*EM
EM
= (assets)/(equity capital)
= $100/$10
= 10
ROE = 2%*10=20%
9.2
Suppose the owners’ bank equity rises to $30.00. Assuming the ROA is fixed, what happens to
ROE?
Answer: Assuming ROA stays fixed, and deposits stay constant at $90, then ROE = 2%*(120/30)
= 8%.
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9.3
What are the benefits of this option?
Answer: The likelihood of having a shock to assets that makes the bank go insolvent is reduced.
10. Consider the case of a manager of a bank that is attempting to reduce the risk associated with interest
rate changes. The bank has $30 million of fixed-rate assets, $20 million of rate-sensitive assets, $10
million of fixed-rate liabilities, and $40 million of rate-sensitive liabilities. If the bank manager conducts
a gap analysis for the bank, show what would happen to bank profits if interest rates rise by 2 percentage
points. What actions could the bank manager take to reduce the bank’s interest rate risk, if he/she so
decided?
Answer: The sensitivity of bank profits to changes in interest rates is given by
(rate-sensitive assets – rate-sensitive liabilities)* (change in interest rates)
($20-$40)*(2%) = -$20*2%=-$10*0.02=-$0.4
If interest rates rise by 2% the bank’s profits falls by $0.4 million.
Actions to reduce bank’s interest rate risk:
1.
shorten the duration of the bank’s assets to increase their rate sensitivity
2.
lengthen the duration of the bank’s liabilities to reduce their rate sensitivity
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