Download Money and Prices

Money and Prices
Chapter 12
The Bond Market
Chapter 22
Objective





Calculate price indexes and inflation rates.
Calculate a discount bond yields using
discount bond prices.
Calculate Bond Returns using interest rates.
Use the Expectations Theory of the Term
Structure to deconstruct the yield curve.
Calculate the demand for money balances
using nominal GDP and interest rates.
Money



Money is a tool for conducting transactions and, like
all tools, is subject to technological advance.
Barter was replaced by commodity money, precious
metal with intrinsic value.
Problems (Issues) with commodity money
–
–
–
Commodities used as money can’t be used for other
purposes.
Supply of money determined by availability of resources.
Government must share the revenues from the creation of
money (Perhaps only a problem from governments point of
view).
Fiat Money



Fiat money is intrinsically valueless commodity (typically paper)
widely accepted as payment rendered (by government
command.
First paper money circulated in Szechwan province during the
Northern Sung dynasty. Szechwan had iron coins which are
heavy and rusty. Banks issued receipts for the coins called
chiao-tzu which circulated as the origins of paper money.
In 1161, under the Southern Sung dynasty, the government
developed a paper called hui-tzu which eventually developed
into first nationwide paper money.
Decade-by-Decade History of Hui-tzu



Observations
For many years, inflation
lags money growth rate.
Money growth rate
accelerates near turn of the
century.
During final years of
dynasty, inflation is faster
than money growth.
Why?
(Cite: F. Lui, JPE 1983)
Years
Money Growth
Inflation
1165-75
7.13%
1175-85
0.94%
1185-95
13.06%
1195-1205
5.47%
1205-15
4.96%
1215-25
1.60%
1225-1240
3.91%
-1.43%
2.13%
5.39%
4.20%
0.01%
1.80%
16.58%
What is Inflation?


Define Inflation as the
growth rate of prices.
The Greek letter π is
often used as a symbol
of inflation
Pt
1 t 
Pt 1
Pt  Pt 1
 1
Pt 1
Aggregate Prices
We also might want a
measure of average
prices.
Aggregate price measures
are weighted averages of
the prices of a set of
goods n = 1..N relative to
their price in a base year
B.
Two main types of
measures



1.
2.
Price Indices
Price Deflators
w1
pt ,1
pB ,1
 w2
pt , 2
pB , 2
 ....  wN
w1  w2  ....  wN  1
pt , N
pB , N
Price Indices



Most commonly used price index is the Consumer
Price Index (CPI)
In constructing the CPI, statisticians calculate the
total expenditure of the average household during a
benchmark year.
The weight on good n in the CPI is the share of
expenditure in the base year that was on good n.
Price Deflator




Another type of price aggregate
is the deflator which is
calculated simultaneously with
a real quantity aggregate.
The deflator uses weights
which change over time.
The weight for good n in the
GDP deflator is the ratio of the
quantity of that good relative to
real GDP.
The GDP deflator is also the
ratio of nominal GDP to real
GDP. Deflators can be
constructed for any subcategory of GDP.
p t,1 p B,1q t,1
p B,1

Qt

p t,2 p B,2 q t,2
p B,2
p t,N p B, N q t,N
p B, N
 Pt
PQt

Qt
Qt
Qt
 ....
HK Price Aggregates
(Base Year 2000)
120
110
100
90
80
70
60
50
40
30
86
88
90
92
CPI
94
96
98
GDP Deflator
00
02
Adjusting for Inflation/Converting Current
Price Series into Constant Price Series


One may have a time series of a nominal
aggregate, Nt, (in current prices) without
the microeconomic data necessary to
construct a corresponding real aggregate.
We can use some price index to “adjust for
inflation” effectively converting into a real
variable.
1.
2.
Select a reference or base year.
Series measured in base year dollars is
PB
N  Nt 
Pt
B
t
Role of Money

1.
2.
3.
Money has 3 roles
Medium of Exchange – Money is a
technology for engaging in transactions.
Unit of Account – Value of most goods and
assets is measured in money.
Store of Value – Money is an asset. It can
be exchanged for goods in the future.
Monetary Aggregates




Real world Different
assets have different
levels of usefulness in
transactions.
Money is measured in
sums of these assets.
M2 & M3 include less
liquid assets and are
called broad money.
M1 is the most liquid
type of money.
Assets
M1
Currency in
Circulation+
Checking Deposits
M2
M1 + Other Deposits
(Savings, Time, CD’s)
at Fully Licensed
Banks
M3
M2 + Deposits at
Finance Companies
Monetary Aggregates in HK
(Nov. 2002)
Million HK$
M3
M2
Million HK$
M1
0
500000 1000000 1500000 2000000 2500000 3000000 3500000 4000000
Velocity/Liquidity



Define the ratio of transactions to the supply of
money as ‘Velocity’, the speed with which money
circulates.
The value of transactions is nominal GDP.
PY
V 
 V  M  P Y
M
The inverse of velocity is the willingness to hold
money between transactions or the willingness to
hold a liquid position, L
1 M
L 
V PY
Rules of Thumb

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If Z = X×Y, then gZ = growth rate of z
gZ ≈ g X + g Y
Example: Z = Nominal GDP = P×Y
gZ ≈ g P + g Y = π + g Y
Growth rate of Nominal GDP is approximately
equal to inflation plus growth rate of real GDP.
If Z = Y/X, then
g Z ≈ gY - g X
Example: Z = Per Capita Real GDP = Y/POP
gZ ≈ gY - gPOP
Growth rate of per capita real GDP is growth rate
of real GDP minus the growth rate of population.
Quantity Theory & Inflation


Using the definition of velocity, we can say
gY + π ≈ gM + gV = gM - gL
This gives us an equation for inflation.
–
–

π ≈ (gM - gY ) + gV
π ≈ (gM - gY ) - gL
Inflation (the growth rate of prices {money per good})
is equal to the growth rate of money minus growth
rate of goods unless there are significant changes in
the willingness to hold money.
Sung Dynasty


In the early years of the introduction of huitzu, there was likely an increasing willingness
to hold new form of money,
gL > 0 → π < (gM - gY )
In the final years of the Sung Dynasty, there
was a reduced willingness to hold Sung
money,
gL > 0 → π > (gM - gY )
Ordinary Determinants of Velocity



What determines the willingness of people to hold
money or conversely what determines the speed
with which they spend money.
Money is an asset that does not pay interest. When
you hold money, opportunity cost is lost interest. The
higher is the interest rate, the greater is the
opportunity cost.
Some forms of money, (e.g. savings and time
deposits) pay interest, however, they are lower than
the interest rate on bonds.
Nominal Interest Rate


The nominal interest
rate is the ratio of
money you get in the
future relative to the
money you give up
today, i.e. the time
value of money.
If you give the bank $1,
they will give you $1+i
after one period.


i ≡ Net Nominal Interest
Rate
Liquidity demand is a
negative function of the
nominal interest rate.
L(i-)
Money Demand Curve



Write the Quantity Equation as a money
demand curve
MD = L(i)∙PY
Given the level of nominal GDP, the nominal
interest rate will determine the demand for
money.
We write this as a downward sloping
relationship between MD and i.
i
MD
M
Money Demand
Q: Why does the money
demand curve slope
down?
A: The greater is the
nominal interest rate,
the greater is the
opportunity cost of
holding money.
Q: What shifts the money
demand curve?
A: An increase in the nominal
GDP will increase the need
for money for transactions.
This will shift the demand
curve out. A reduction in
nominal GDP will shift the
demand curve in.
Money Supply

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
Central banks in large economies (the US, Euroland)
typically set an interest rate target though they
directly control the money supply.
Relationship between interest rates and money
demand give them tools to control interest rate.
Set money supply as straight line indicating central
bank control.
Given nominal GDP, interest rate will set money
supply equal to money demand.
MS
i
iEQ
MD
M
Reaching Equilibrium


If i > iEQ, then money demand will be less
than money supply. People will buy bonds
which will reduce the interest rates that
borrowers must offer.
If i<iEQ, then money demand will be greater
than money supply. People will sell bonds to
get money. This will increase the interest rate
that bond issuers must sell.
Open Market Operations

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
The government authority controlling the money supply is the
central bank. In Hong Kong, this is Hong Kong Monetary
Authority (HKMA)
Central banks typically (though not in HK) change the money
supply through open market operation (OMO). An OMO is the
purchase or sale of government bonds by the central bank.
In an open market purchase, the central bank prints new money
and uses it to buy bonds. This increases the supply of money in
the short run.
In an open market sale, the central bank sells some of its stock
of bonds and receives existing money in exchange. This
reduces the supply of money in the short run.
Interest Targets



When the central bank selects an interest rate target,
they will instruct their bond department to conduct
OMO’s to keep interest rate in some market (typically
interbank lending market) inside some target zone.
If money demand increases, the bond dept. will do
an open market purchase.
If money demand falls, the dept. will do an open
market sale.
MS
1.
i
Increase in money demand
due to increase in GDP
iEQ
MD’
2. Open Market Purchase
increases money supply
MD
M
Liquidity Effect

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

In the very short run (less than 3 months or so), open market
operations can be thought of as having little effect on nominal
GDP.
An unexpected increase in the money supply growth will
increase the available liquidity. This will lead to increased
demand for bonds and reduced interest rates.
An unexpected decrease in the money supply will reduce
available liquidity, causing sales of bonds and upward pressure
on interest rates.
The negative short-run relationship between money supply and
interest rate is called the liquidity effect.
MS
i
MS’
1. Open Market Purchase
increases money supply
iEQ
Excess Liquidity causes
interest rates to fall
iEQ’
MD
M
Long-run Neutrality of Money


Hypothesis: In the long run, real production
and relative prices of different goods do not
depend on the level or growth rate of money.
Reason: Money is of intrinsically no value.
Money prices are just an arbitrarily chosen
value. In short run, money may matter due to
market imperfections, but cannot matter in
long run.
Real Interest Rate




The price level of goods is Pt
and the interest rate is it.
If you buy $1 worth of bonds
you will give up opportunity to
by 1/Pt goods.
You will get $1+i in the future
which will allow you to buy
1+i/Pt+1 goods in the future.
The payoff of future goods
relative to foregone current
goods is the goods interest rate
or the real interest rate.
1  it
Pt 1
1 i
1  rt 

1
Pt 1
Pt
Pt

1  it
1   t 1
rt  it   t 1
Ex Ante vs. Ex Post Real Interest Rates


The future inflation rate, πt+1, is not known at
the time a bond is purchased.
Ex Ante Real Interest Rate is the interest rate
less the expected inflation rate, πEt+1.
rAt = it - πEt+1

Ex Post Real Interest Rate is the interest rate
less the actual realized inflation rate
rPt = it - πt+1
HK Interest Rates
1 Year HK Government Bond Rates
20
15
10
5
0
-5
-10
1992
1994
1996
Nominal Rate
1998
2000
Ex Post Real Rate
2002
Fisher Effect



In the long run, the money growth rate does
not affect the real interest rate.
Money growth affects the interest rate
through its affect on inflation.
The higher is future inflation, the higher is the
interest rate.
Long Run Inflation and Interest Rate
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
Assume there is a long run money growth rate, gM , and long run
output growth rate, gY. Also assume there is a stable real interest
rate, r.
If there is a stable long run inflation rate, then there is a stable
nominal interest rate.
If there is a stable nominal interest rate, then velocity is stable, gV =
0.
If velocity is stable, then π = gM – gY
If there is a stable inflation rate, then nominal interest rate is i=r+ gM
– gY.
An increase in the money growth rate will increase inflation in the
long run. Given a target real interest rate, this will increase the
nominal interest rate demanded by lenders.
Money and Interest Rates



In short run, there is a negative relationship between
interest rates and an increase in money growth.
In the long run, there is a positive relationship
between an increase in money growth and the long
run interest rate.
This dichotomy is often manifested in the yield curve,
the difference between a long-term interest rate and
a short-term interest rate.
Deflation



Deflation is defined simply as negative
inflation or falling prices over time.
Nominal Interest Rate has a lower bound.
Since money pays 0% rate, bonds that pay
less than 0% cannot be sold. Thus, the lower
bound of the nominal interest rate is 0%
When interest rate reaches lower bound (as
in HK now) deflation pushes up real interest
rate.
Long-term Interest Rates


Bonds are sold with different maturities. For
example, there are Hong Kong government
bonds with maturities as long as 10 years.
An expansion in money growth will have
different effects on interest rates on longterm bonds and short-term bonds

Consider two strategies which should
have the same expected pay-off.
Starting with $1.
Buy a two year discount bond and hold it
for two years. Payoff:
(1  i2 ) 2  (1  2  i2  i22 )  1  2  i2
2. Buy a 1 year bond. After 1 year, invest
pay-off in another 1 year bond. Payoff:
(1  i1 )  (1  i1e, 1 )  1  i1  i1e, 1  (i1  i1e, 1 )  1  i1  i1e, 1
1.

Equal pay-offs imply that yield on a
two year bond is equal to the expected
average yield of 1 year ebonds over the
next two years. i  i1  i1, 1
2
2

In general, if the pay-off for investing in
an n period bond should be the same as
the pay-off from rolling over 1 year
bonds for n periods:
(1  in )n  (1  i1 )  (1  i1e, 1 )  (1  i1e, 2 )  ...  (1  i1e,  n1 )

Then a n period bond yield is
(approximately) equal to the average
expected yield on 1 period bonds
between today and date n.
e
e
e
in 
i1  i1, 1  i1, 2  ...  i1,  n 1
n
On average, longer term bonds have higher interest
rates than short-term bonds.
Mean Yield Curve
Maturity

8
7.5
7
6.5
6
Series1
1 Year 2 Year 3 Year 5 Year
Yield
10
Year
Discount Bonds



There are many types of bonds. The simplest type of
bond is a discount bond. The issuer of a discount
bond makes a single payment (called the face value)
at some designated time T periods from now.
The standard unit of bonds are in $100 of face value.
So if a bond price is quoted at PB, this is the price
per $100 worth of face value.
Ex. If a bond had a face value of $10,000 and you
were quoted a price of 90, you would have to pay
$9000 for this bond.
What is a Bond




Bonds are a promise to repay certain amounts of
money at specific dates in future.
Most bonds specify specific amounts of currency
units that will be repaid (unlike stocks which entitle
owner to a share of profits).
Bonds unlike bank loans can be traded on securities
markets.
Since governments cannot issue equity, they rely on
bonds for financing. Government bonds are a large
share of world bond market.
HK Dollar Bond Market
Listed HK$ Bonds
Total: HK$ Million 607962
State-owned
12%
Supranational
7%
Bank
7%
Corporate
23%
State
51%
Bond Prices and Interest Rates

The interest rate quoted on a discount bond of
maturity date T is calculated as P  (1 100
i )
If you put PB into a bank account that offered and
interest rate of it,T for T years, you would have a final
balance of 100.
This interest rate is the average return you will get
on your bond if you hold it for T periods which is
referred to as the yield to maturity or the yield.
Holding interest rates constant, the price of a
discount bond gets closer to 100 as the bond
matures.
B
t ,T
T
t ,T



Implications



There is an inverse relationship between the
price of a bond and the interest yield on the
bond.
When a bond is relatively cheap, an investor
can earn a high return by buying it and
holding it until maturity.
When interest rates rise, bond prices fall.
Implications


Long-term bond prices are
more sensitive to a
persistent increase in
interest rates because they
are held for many periods.
The percentage change in
discount bond prices are
approximately equal to the
negative maturity level.
P
 T  i
P
B
T
B

Example: Interest rates at all
maturities change from 2%
to 3%: Δi=.01
–
–
–
The % change in a two year
bond price will be
approximately -2%.
The % change in a 3 year
bond price will be
approximately -3%
The % change in a 10 year
bond price will be
approximately -10%.
Ex Ante Yields vs. Ex Post Returns



Yields are the average returns that a bond
holder can expect to earn in the future.
Ex post returns are the returns that someone
has earned by holding bonds over a past
period.
For discount bonds, the annual ex post bond
return, Rt, will be the change in the price level
over the period
Pt B  Pt B1
Rt 
Pt 1
B
Inflation: Enemy of Bondholders



A surprise increase in money growth may
reduce short-term interest rates through the
liquidity effect, but it can be expected to
increase long-term interest rates through the
Fisher effect.
Therefore, an increase in money growth is
likely to increase long-term bond yields.
This will reduce long-term bond prices and
lead to negative nominal returns to bonds.
Costs of Expected Inflation


Shoe Leather Costs – Money is a technology
for engaging in transactions. The greater is
inflation, the greater the cost for individuals
of holding money. Individuals must make
efforts as a substitute for the convenience of
holding money.
Menu Costs – Firms must engage in costs of
changing posted prices.
Costs of Unexpected Inflation


When actual inflation is greater than
expected inflation, ex post real interest rates
are less than actual interest rates.
Inflation is a double whammy for long-term
bond holders. A rise in inflation increases
interest rates reducing returns, then reduces
the real value of those returns.
Bond Investment



An Indian investor decided to invest Rp.1,000,000 in
Indian bonds in 1970. The strategy will be to buy
bonds in 1970 and roll over all payments of principal
and interest back into a bond fund.
The average return on Indian bonds during this
period was 6%
In 1990, the Indian investor would have Rp.
3,253,992.04 in savings, tripling his money in twenty
years.
Real Returns



However, the average Indian inflation rate
during this period was 8.3%.
Thus, in 1990, the pay-off of the savers bond
investment would only buy the same amount
of goods as Rp.$622,394 would have bought
in 1970.
Investing in Indian bonds has cut the
purchasing power of savings nearly in half!
Inflation Risk




Unexpected inflation is bad for long-term
bond holders.
Volatile inflation is a source of risk for bond
buyers.
Extra risk pushes up interest rates, pushes
down bond prices.
Inflation risk premium can lead to higher
interest rates.
Floating Rate Bonds




Bond holders who are sensitive to inflation
risk often purchase floating rate bonds.
If some benchmark interest rate rises, the
holders of floating rate bonds receive an
extra payment.
Most mortgages are floating rate loans.
Government debt is typically fixed rate.
HK$ Bond Market: Fixed vs.
Floating
Floating Rate Bonds as a % of HK Dollar Bond Market (excl. Ex.
Fund)
% of Issues w/ Floating Rates
45.00%
40.00%
35.00%
30.00%
25.00%
20.00%
15.00%
10.00%
5.00%
0.00%
< 3Years
3 to 5 Years
Maturity Date
> 5 Years
Seignorage




If inflation is so bad, why is it so common?
When governments print money, they can use it to
finance government spending.
Seignorage – Revenue raised by a central bank
through printing money due to the difference
between the face value of money and the cost of
production.
For paper money, cost of production is very small.
Seignorage & Real Seignorage



When the government prints
new money, they can buy
more goods = Mt – Mt-1.
The real value of
government money printing
is proportional to real GDP.
Factor of proportion is
function of the money
growth rate and demand for
liquidity.
M t  M t 1
Pt

M t  M t 1 M t 1 M t


M t 1
M t Pt
gM

 LY
M
1 g
Inflation Tax


Who pays for seignorage? The ordinary
household whose value loses real money
overtime.
Obtaining revenues through seignorage has
diminishing returns.
–
The higher is the money growth rate, the faster is
inflation. The higher is inflation, the higher is the
nominal interest rate. The higher is the nominal
interest rate the less money holding there will be.
Relative Price Changes




Overall, inflation measures often mask
changes in relative prices.
Housing prices in HK have been more
volatile than other types of prices.
When inflation is high, rent inflation is higher
than average.
When inflation is low, rent inflation is lower
than average
HK Inflation: 1991-1997
HK Inflation: 1998-2001
12.00%
0.00%
Appliances
-1.00%
10.00%
-2.00%
8.00%
-3.00%
6.00%
-4.00%
-5.00%
4.00%
-6.00%
2.00%
-7.00%
0.00%
Appliances
Rent
-8.00%
Rent