Homework Assignment 1
Economics 4334: Money and Banking
Assigned: September 15th, 2015
Due: September 22nd, 2015
1. The oldest central bank in the world is the Riksbank, the central bank of Sweden.
Its monetary policy operations are described at this website. What are the main
instruments that the Riksbank uses to implement monetary operations? What is
the operating target (see here)? Write a short paragraph describing how they use
the instruments to guide the interbank rate. How does the instrument relate to the
interbank interest rate?
The Riksbank uses a number of tools to control short-term liquidity. The Riksbank
has a weekly repo operation to adjust liquidity. These repo operations are
conducted at the policy rate, called the repo rate. In addition, the central bank
conducts fine-tuning operations to keep the operating target, the overnight rate,
near the policy rate. Further, the central bank operates standing deposit and
lending facilities to create an interest rate corridor which keeps the overnight rate
within those bounds.
2. The Bank of Thailand provides liquidity to commercial banks with a daily reverse
auction at the Base Rate. There are also standing loan and deposit facilities at
rates 50 basis points above and 50 basis points below the base rate. The interbank
rate is called BIBOR for Bangkok Interbank Offered Rate.
a. Construct a graph depicting the interbank market immediately after the
morning refinancing operation.
The supply of reserves automatically shifts out to meet the demand for
reserves as the bank fills orders for reserves at the base rate.
iLF
iBASE
iDF
b. Assume that an increase in political uncertainty during the afternoon
sharply increases commercial banks demand for liquidity. Assume the
BoT does no fine tuning operations. Demonstrate what happens to the
market. What is the maximum interest rate that will be observed?
Demonstrate.
As demand for liquidity rises,banks will want to hold more reserves. The
lack of lenders in the market will raise BIBOR. Ultimately, the interest
rate will rise to the lending facility rate. Banks seeking liquidity will
borrow from the lending faciloity. Thus, interest rates will not rise above
the lending facility rate.
Borrowed Reserves
iLF
iBASE
iDF
3. During summer of 2006, China increased their reserve requirement for the
banking system while maintaining a fixed target for the interbank lending rate.
Draw a graph of the interbank market when a central bank increases the reserve
ratio while maintaining a fixed interest rate. What effect would such a policy have
on the monetary base? Assuming no excess reserves, what effect would such a
policy have on the money multiplier? Can we say what would be the effect on the
money supply?
The increase in the reserve ratio will increase the demand for reserves at any
level of deposits. If the central bank wants to keep the interbank interest rate from
rising, they will need to do an open market purchase to make more reserves
available.
iIBOR
D
D'
2
S
ITGT
1
\The monetary base would increase as reserves increase. However, the money
C  Q 1
multiplier D D
would fall. The effect on the money supply (i.e. the money
C R
D
D
multiplier times the money base) is therefore ambiguous.
4. The following table lists data (from IMF’s International Financial Statistics) on
economic and monetary aggregates in Hong Kong. Calculate the M2 money
multiplier for Hong Kong for years 2001-2014. What is the lowest level? What is
the highest level? Calculate the M2 money velocity. Compare the level of velocity
in Hong Kong with that in the USA. Would M2 growth targets be a useful
monetary policy guide for Hong Kong? Explain.
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
Gross
Domestic Money
Product Supply:
Base
(GDP)
M2
Money
1321.14 3550.06
229.98
1297.34 3518.33
246.56
1256.67 3813.44
293.03
1316.95 4166.71
295.43
1412.13 4379.06
284.23
1503.35 5054.48
296.25
1650.76 6106.35
320.56
1707.49 6268.06
507.46
1659.25 6602.31 1010.96
1776.33 7136.27 1039.81
1934.43 8057.53
1073.3
2037.06
8950 1219.14
2138.66 10056.4 1255.77
2255.63 11014.4 1346.06
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
Velocity
0.372146
0.368737
0.329537
0.316065
0.322473
0.297429
0.270335
0.272411
0.251314
0.248916
0.240077
0.227604
0.212667
0.204789
Multiplier
15.43639
14.26967
13.01382
14.10388
15.40675
17.06154
19.04901
12.35183
6.530733
6.863052
7.507249
7.341241
8.008154
8.182696
We can calculate the money multiplier as the ratio of the money supply to the
monetary base. The money multiplier in Hong Kong has ranged between 6.5 and 19.
The M2 velocity is the ratio of GDP to M2. This number ranges between .37 in 2001
down to .2 today. The velocity in the US is much larger, ranging from 1.5 to 2.2.
Both the multiplier and the velocity seems quite volatile, which might make a money
target not that useful for stabilizing the economy.
5. You go to the Hong Kong Monetary Authority Website and get data from Table
5.3.1 Link for February 28, 2015. Assume that the expectations theory of the term
structure is true. Use the yield curve to calculate the market’s expectation of some
future interest rates.
%
1
2
3
4
5
0.09
0.48
0.75
1.02
1.39
28-Feb-15
28-Feb-16
28-Feb-17
28-Feb-18
Expecation of One year rates
Approximate Net
Exact
%
1+i
0.09
1.0009
0.866
1.0087
1.288
1.0129
1.844
1.0185
Expecation of Two year rates
Approximate
Exact
%
1+i
2.363
1.0237
a. Calculate the market’s expectation of the 1 year yield to maturity on
February 28, 2016 (1 year from now), February 28, 2017 (2 years from
now), and February 28, 2018 (3 years from now).
Under the expectations theory, the 2 year yield is the geometric average of the 1
year yield and expectations of the 1 year yield in 1 year
1  i 1  i   1  i 
1  i2 
e
1, 1
1
1  i 

1  i 
2
2
1
1.00482

 1.0087
1.009
e
1, 1
.
We can approximate this relationship by saying that the net 2 year yield is equal
to the arithmetic average of the net yield of a 1 year bond and the markets
expectations of the net yield of a 1 year bond in 1 year
i1  i1,e 1
i2 
 i1,e 1  2  i2  i1  0.00866 . Notice the approximation is very close.
2
The yield on the three year bond is the geometric average of the expected interest
rates on 1 year bonds over their life.
1  i3 
3
1  i 1  i 1  i 
1  i 
1  i 
  1 i 1 i 
 
 1  i 
e
1, 1
1
e
1, 2
3

 1  i1,e 2
3
1
3
3
e
1, 1
2
2

1.00753
 1.0129
1.00482
We could also write the net 3 year yield as the arithmetic average of three net
i1  i1,e 1  i1,e 2
i3 
 i1,e 2  3i3  i1  i1e 
3
interest rates.  3i3  2i2
i1,e 2  3  .0075  2  .0048  0.01288
In general, we can write,
i1,e  n 1  (n)  in  (n  1)  in 1
1  in 
(1  i1, n 1 ) 
n 1
1  in1 
n
.
For example, if n = 4, and n-1=3
i1,e  n 1  (4)  i4  (3)  i3  .01844
1  i4   1.0102 
(1  i1,3 ) 
3
3
1  i3  1.0075
4
4
 1.0185
b. Calculate the market’s expectation of the yield to maturity on a 2 year note
on February 28, 2018 (3 years from now).
The yields on the 3 & 5 year bond are the geometric average of the 1 year interest
rates over the life of the bond.
1  i   1  i 1  i 1  i 1  i 1  i 
1  i   1  i 1  i 1  i 
1  i 
 1  i 1  i   1  i  
1  i 
1  i   1.0139   1.0237
1  i  
1  i  1.0102 
5
5
e
1, 1
1
3
3,t
e
1, 2
e
1, 1
1
e
1, 3
e
1, 4
e
1, 2
5
e
1, 3
e
1, 4
e
2, 3
2
5
3
3
e
2, 3
5
5
3
3
5
3
Approximately.
(5)  i5  (3)  i3 5  .0139  3  .0102
i2,e 3 

 0.02363
2
2