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 Inflation1165-75 7.13% -1.43%1175-85 0.94% 2.13%1185-95 13.06% 5.39%1195-1205 5.47% 4.20%1205-15 4.96% 0.01%1215-25 1.60% 1.80%1225-1240 3.91% 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 1

1

1

1

1

t

tt

t

tt

P

PP

P

P

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. Price Indices2. Price Deflators

1....

....

21

,

,

2,

2,2

1,

1,1

N

NB

NtN

B

t

B

t

www

p

pw

p

pw

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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 sub-category of GDP. t

t

t

Q

PQ

P

t

Nt,NB,

NB,

Nt,

t

t,2B,2

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HK Price Aggregates(Base Year 2000)

30

40

50

60

70

80

90

100

110

120

86 88 90 92 94 96 98 00 02

CPI GDP Deflator

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. Select a reference or base year.2. Series measured in base year dollars is

t

Bt

Bt P

PNN

Role of Money

Money has 3 roles

1. Medium of Exchange – Money is a technology for engaging in transactions.

2. Unit of Account – Value of most goods and assets is measured in money.

3. 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$

0 500000 1000000 1500000 2000000 2500000 3000000 3500000 4000000

M1

M2

M3

Million HK$

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.

The inverse of velocity is the willingness to hold money between transactions or the willingness to hold a liquid position, L

YPMVM

PYV

PY

M

VL

1

Rules of Thumb

If Z = X×Y, then gZ = growth rate of z gZ ≈ gX + gY

Example: Z = Nominal GDP = P×YgZ ≈ gP + gY = π + gY

Growth rate of Nominal GDP is approximately equal to inflation plus growth rate of real GDP.

If Z = Y/X, then gZ ≈ gY - gX

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 saygY + 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 hui-tzu, 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

M

MD

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

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.

i

M

MD

MS

iEQ

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

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.

i

M

MD

MS

iEQ

MD’

1. Increase in money demand

due to increase in GDP

2. Open Market Purchase increases money supply

Liquidity Effect

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.

i

M

MD

MS

iEQ

MS’

1. Open Market Purchase increases money supply

iEQ’

Excess Liquidity causes interest rates to fall

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.

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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, πE

t+1.

rAt = it - πE

t+1

Ex Post Real Interest Rate is the interest rate less the actual realized inflation rate rP

t = it - πt+1

HK Interest Rates

-10

-5

0

5

10

15

20

1992 1994 1996 1998 2000 2002

Nominal Rate Ex Post Real Rate

1 Year HK Government Bond Rates

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

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 long-term bonds and short-term bonds

Consider two strategies which should have the same expected pay-off. Starting with $1.

1. Buy a two year discount bond and hold it for two years. Payoff:

2. Buy a 1 year bond. After 1 year, invest pay-off in another 1 year bond. Payoff:

Equal pay-offs imply that yield on a two year bond is equal to the expected average yield of 1 year bonds over the next two years.

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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:

Then a n period bond yield is (approximately) equal to the average expected yield on 1 period bonds between today and date n.

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On average, longer term bonds have higher interest rates than short-term bonds.

Mean Yield Curve

66.5

77.5

8

1 Year 2 Year 3 Year 5 Year 10Year

Yield

Mat

urity Series1

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$ BondsTotal: HK$ Million 607962

Bank7%

Corporate23%

State51%

State-owned12%

Supranational7%

Bond Prices and Interest Rates

The interest rate quoted on a discount bond of maturity date T is calculated as

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.

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BTt i

P)1(

100

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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.

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%. iT

P

PB

BT

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

Bt

Bt

Bt

tP

PPR

1

1

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)

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

45.00%

< 3Years 3 to 5 Years > 5 Years

Maturity Date

% o

f Is

sues

w/

Flo

atin

g R

ates

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.

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g

P

M

M

M

M

MM

P

MM

M

M

t

t

t

t

t

tt

t

tt

1

1

1

1

1

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: 1998-2001

-8.00%

-7.00%

-6.00%

-5.00%

-4.00%

-3.00%

-2.00%

-1.00%

0.00%Appliances Rent

HK Inflation: 1991-1997

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

Appliances Rent