Lecture 2
BEEM119 Economics of Banking
Jan Auerbach
Department of Economics University of Exeter
Contents
1 Financial Institutions and Key Concepts
1 Institutions and Concepts.
2 Understanding Interest Rates.
3 The Risk and Term Structure of Interest Rates.
4 The Efficient Markets Hypothesis.
2 Money
1 What is Money?
2 The Money Supply Process.
3 Quantitative Theory, Inflation, and the Demand for Money.
3 Banking and Financial Intermediation
1 An Economic Analysis of Financial Structure.
2 Banking Industry: Structure and Competition.
4 Banking and Policy
1 Economic Analysis of Financial Regulation.
2 Financial Crises.
Interest rates
(Mishkin, chapter 4)
Interest Rate
Today, a dollar paid to you one year from now is less valuable than a dollar paid to you today.
Interest Rate: is the cost of borrowing–or the price paid for renting–funds.
If you deposit a dollar (i.e., rent it out to the bank), it earns interest.
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Interest Rate
Suppose the yearly interest rate is 10% and you deposit £100. How much money will you be paid back at the end of 1 year?
After 2 years?
(1 + 0.1)100 = 1.1 · 100 = 110.
(1 + 0.1)2100 = 1.12100 = 121.
3?
4?
What about after n years?
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Simple Present Value
Present Value: is the value today of goods or services that will be delivered or provided in the future.
Let
pv = today’s present value
cf = future cash flow payment
i = interest rate
n = number of time intervals after which the cash flow materializes
Then:
pv= cf . (1+i)n
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More Generally
Let
Then:
pv = today’s present value
cfj = future cash flow payment in time interval j i = interest rate
n = number of time intervals until maturity
pv=n cfj . j=1 (1+i)j
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Comparing cash flows
How do two investment opportunities compare? Say:
A Pays 110 next period and 121 the following period.
B Pays 115 next period and 115 the following period. Suppose the yearly interest rate is 20%. Then:
pvA = 253 =pvB. 1.22
What about any other interest rate?
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Types of Credit Market Instruments
1 Simple Loan: e.g. commercial loans
2 Fixed Payment Loan: e.g. mortgages
3 Coupon Bond: e.g. Treasury bonds.
• Coupon, or coupon rate • Face value
• Market value
• Maturity
4 Discount Bond: it is just a zero-coupon bond.
Yield to maturity: the interest rate that equates the present value of cash flow payments from a debt instrument with its value today.
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Simple loan
A single payment is made in, say, 1 year.
Then:
pv = amount borrowed = £100
cf = cash flow payment in 1 year = £110 n = number of years = 1
i = yield to maturity
£100= £110 ⇒ i=110−1=0.10=10%. (1 + i)1 100
For simple loans, the yield to maturity equals the simple interest rate.
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Fixed Payment Loan
The same payment is made every year until maturity.
Then:
lv = loan value
cf = cash flow payment in every year n = number of years to maturity
i = yield to maturity
lv= cf + cf + cf +…+ cf . (1+i) (1+i)2 (1+i)3 (1+i)n
c The interest rate i is the yield to maturity: it equates the present value of cash flow payments from the debt instrument with its value today.
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Fixed Payment Loan
Example: mortgage.
• the fixed payment is fp = 2000 monthly
• the yield to maturity is 0.5% per month
• number of periods until maturity: 30 years time 12 months: 360
What is the loan value? That is: How much is the lender giving to the borrower?
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Coupon bond
Similar to the fixed payment loan–but adding the bond’s face value.
p = price of the coupon bond
c = yearly coupon payment
f = face value of the bond
n = number of years to maturity i = yield to maturity
Then:
p=c+c+c+…+c+f. (1+i) (1+i)2 (1+i)3 (1+i)n (1+i)n
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Coupon bond
Yields to maturity on a 10%-coupon-rate bond maturing in 10 years, with face value £1, 000:
Price of the bond (£) 1,200
1,100
1,000
900
800
Yields to maturity (%) 7.13
8.48
10.00
11.75
13.81
• When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate
• The price of a coupon bond and the yield to maturity are negatively related
• The yield to maturity is greater than the coupon rate when the bond price is below its face value
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Consols
A bond that pays fixed coupon payments forever. (Also called perpetuity. The Bank of England still offers these in London today.)
The yield to maturity is
where
i=c, p
i = yield to maturity
c = consol payment
p = current price of the coupon bond.
The yield to maturity is: consol payment divided by the bond price.
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Current yield
The current yield calculated as
ic = c,
where
p
i = yield to maturity
c = consol payment
p = current price of the coupon bond.
is an approximation for the yield of maturity on long term coupon bonds.
Why? Long time horizon and discounting.
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Discount/Zero-coupon Bond
A bond that pays no coupon but only its face value in one year. i=f−p,
where
p
i = yield to maturity
f = face value of the discount bond
p = current price of the discount bond.
The yield to maturity is the increase in price over the year divided by the initial price.
As with the coupon bond, the yield to maturity is negatively related to the current price.
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Real and Nominal Interest Rates
Nominal interest rate: is the rate that you usually read in newspapers. Real interest rate: is the nominal interest rate adjusted for changes in
price level.
The real interest rate reflects more accurately the cost of borrowing.
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Fisher Equation
The fisher equation postulates a relation between the nominal and real interest rates.
where
i = r + πe,
i = nominal interest rate
r = real interest rate
πe = expected inflation rate.
(In fact, this is an approximation for small rate. The actual equivalence relation is (1 + i) = (1 + r)(1 + πe).)
The real interest rate is a better indicator of the incentives to borrow or lend: the lower it is, the “cheaper” it is to borrow and the less “profitable” it is to lend.
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The inflation rate
Inflation is a sustained rise in the price level.
The inflation rate is the rate at which the price level increases.
Deflation is a sustained decline in the price level–it corresponds to a negative inflation rate.
What should the definition of the price level be?
We typically use two indices: the GDP deflator and the consumer price index (CPI).
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The inflation rate–GDP and Prices
Gross domestic product (GDP) is the value of the final goods and services produced in the economy during a given period.
If the value is calculated at current prices, it is called nominal GDP. If the value is calculated at fixed prices, it is called real GDP.
There are 3 equivalent definitions of GDP.
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The inflation rate–GDP and Prices
Example
Wood company Revenues from sales Expenses
Wages
Profit
Book shelves company Revenues from sales Expenses
Wages Wood purchases
Profit
£50
£30 £30
£20
£150
£120 £70
£50
£30
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The inflation rate–GDP and Prices
1. GDP is the value of the final goods and services produced in the economy during a given period.
Final goods: Goods sold directly to consumers, e.g., book shelves. Intermediate goods: Goods used in the production of another
good, e.g., wood used in the production of book shelves.
Counting the value of the wood, would be counting part of the value of the book shelves twice: The value of the book shelf includes the costs of buying the wood to be used in its production.
(There are goods that are both intermediate goods and final goods.)
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The inflation rate–GDP and Prices
The GDP in our example economy equals the value of the book shelves sold, i.e., £150.
Think of one firm producing both the wood and the shelves (i.e., the two companies merged). Wages add up to £70 + £30 = £100. The only good sold is book shelves.
Book shelves company Revenues from sales £150 Expenses (Wages) £100
Profit £50
That firm makes profits £20 + £30 = £50.
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The inflation rate–GDP and Prices
2. GDP is the sum of value added in the economy during a given period.
Value added: The value added by a firm is the value of its production minus the value of the intermediate goods used in production.
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The inflation rate–GDP and Prices
The wood company does not use intermediate goods: it adds £50 in value.
The book shelves company does use intermediate goods: it add value equal to the value of the book shelf it sells minus the value of the wood it uses in production, i.e., £150 − £50 = £100.
Total value added (GDP) equals £50 + £100 = £150.
In case of the single firm, there would be no intermediate goods and
the value added would equal the value of the book shelves, £150.
The value of final goods and services equals the value added by all firms in the economy.
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The inflation rate–GDP and Prices
3. GDP is the sum of incomes in the economy during a given period.
The wood company pays £30 in wages–which is labour income; the firm retains £20 as capital income.
The books shelves company pays £70 in wages as labour income; the firm retains £30 as capital income.
For the economy, labor income is £30 + £70 = £100 and capital income is £20 + £30 = £50. GDP equals £100 + £50 = £150.
Aggregate production and aggregate income are always equal!
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The inflation rate–GDP and Prices
Nominal GDP: sum of quantities of final goods produced times their current price.
Over time, production and prices of most goods change (increase).
How do we compare GDP over time? What do changes in GDP mean?
To measure changes in production, we have to eliminate price changes!
Real GDP: sum of quantities of final goods produced times a constant price.
Our example economy: multiply today’s production with yesterday’s price to compare GDP today and yesterday.
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The inflation rate–GDP and Prices
Our book shelf economy:
Year Quantity Price 2010 100 150 2011 120 175 2012 130 200
Nom. GDP £15000 £21000 £26000
% change
– £17500
40 £21000 24 £22750
% change – 20 8
Real GDP
Real GDP uses 2011 prices. Percentage changes are approximate. In the real world, there are very many final goods.
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The inflation rate–GDP and Prices
In the real world, there are very many final goods.
Real GDP is a weighted average of the output of all final goods. What should the weights be?
Relative prices: Baskets of consumption goods.
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The inflation rate–GDP and Prices
Real GDP: aggregate output.
It measures the economic size of a country.
Real GDP per capita: ratio of real GDP to population.
It measures the average standard of living.
GDP growth: rate of growth of real GDP.
It measures the economy’s performance.
Expansion: periods of positive GDP growth. Recession: periods of negative GDP growth.
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The inflation rate–GDP deflator
If nominal GDP increases faster than real GDP, then prices must increase!
GDP deflator in year t, Pt, is given by
Pt = Nominal GDPt = £Yt ,
Real GDPt Yt
i.e., the ratio of nominal GDP to real GDP in year t. Pt is an index number. It equals 1 in the base year. Its level has no economic interpretation.
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The inflation rate–GDP deflator
But its rate of change does!
πt ≡ Pt −Pt−1 Pt−1
is the rate of inflation, i.e., the rate at which the general price level increases over time.
In our book shelf economy:
Year 2010 2011 2012
GDP deflator Pt 0.86
1
1.14
πt × 100% – 16% 14%
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The inflation rate–GDP deflator
Rearranging the GDP deflator definition, we get that nominal GDP is equal to the GDP deflator times real GDP:
£Yt =PtYt.
The rate of growth in nominal GDP (approximately) equals the rate of inflation plus the rate of growth in real GDP.
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The inflation rate–CPI
Consumers care about the average price of consumption. Consumers generally don’t buy, use, consume machine tools. Consumers consume imported goods.
The consumer price index measures the cost of living.
The GDP deflator and the CPI mostly move together and are close.
Differences arise because the CPI measures the price of goods consumed in a country while the GDP deflator measures the price of goods produced in that country.
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The inflation rate
Interpretations of inflation:
• Things are getting more expensive.
• Each £1 is losing its purchasing power.
• Money is getting less valuable.
• Money is getting cheaper (in terms of actual goods).
What about deflation?
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The inflation rate
Why do we care?
• Inflation
• Inflation
are fixed
• Inflation
• Inflation incomes.
affects the income distribution.
affects relative prices causing distortions (some prices by regulation).
thus increases uncertainty affecting investment decisions. may interact with taxation to decrease after tax
Deflation creates problems that are very similar in nature.
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Treasury Inflation Protected Securities (TIPS)
Suppose you buy a TIPS with
• face value $1000, • 1 year maturity, • and a 5% coupon
at $1000.
Suppose inflation during that first year was 10%.
The TIPS would adjust upward:
• the face value would increase by 10%, to $1,100
• the coupon payment, which is based on face value, would be $55.
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Treasury Inflation Protected Securities (TIPS)
TIPS are useful:
• If you save in bonds, and hold them to maturity, you know what the return is going to be in currency. But you don’t know (there is uncertainty) how many consumption goods you will be able to buy with that currency.
• If you save in TIPS, you know what the return is going to be in terms of consumption goods, not currency.
• They can be used to compute inflation expectations.
• The difference between nominal and real yields of the same maturity is referred to as the breakeven inflation rate (BEI).
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Treasury Inflation Protected Securities (TIPS)
As an example, 1-year bonds with zero coupon and face value $100:
• treasury bond at the price $97. The YTM is 3%. • TIPS at the price $99. The YTM is 1%.
• Expected inflation in the previous example is 2%.
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