Lecture 3
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 depend on…
1. Time to maturity:
Often, longer term securities have higher annual interest rates.
2. Borrower’s credit risk:
The less credit a borrower has, the higher is the interest rate.
3. Collateral value:
More valuable collateral induces lower interest rates.
4. Liquidity:
The easier it is to re-sell the security, the lower is the interest rate.
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Equilibrium interest rate
If any attribute of a given bond/loan changes, the implied interest rate (i.e., value of the bond/loan) also changes.
The credit risk goes up/down. The collateral value falls/rises.
In fact,
1 3-year bonds become 2-year bonds after 1 year.
2 Securitisation may lower the interest rates of mortgages, etc.
3 The bursting housing bubble affects house prices/mortgages.
4 Sovereigns run into trouble rolling over their debt.
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Equilibrium interest rate
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Equilibrium interest rate
Even if a bond’s attributes remain unchanged, its price is still affected by changes in demand and supply of these bonds in the market.
What happens if, e.g.,
1 Many “new” investors from “new” places enter.
2 Many investors move their funds into other “new” asset groups.
3 Fewer firms start new businesses.
4 More firms start new businesses.
Recall:
p=n cft . t=1 (1+i)t
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The Risk and Term Structure of Interest Rates
(Mishkin, chapter 6)
The Risk Structure of Interest Rates
Long-Term Bond Yields
Bonds with the same maturity have different interest rates. Why?
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Risk Structure of Interest Rates
1 Default risk
2 Liquidity
3 Tax considerations
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Risk Structure of Interest Rates
Default Risk
Default risk
is the probability that the issuer of the bond is unable or unwilling to make interest payments or pay off the face value.
Risk premium
is the spread between the interest rates on bonds with default risk and the interest rates on (same maturity) Treasury bonds.
(U.S. Treasury bonds are considered default free.)
Rating agencies
independently rate bonds to measure the issuer’s creditworthiness, or ability to make interest payments and repay principal.
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Risk Structure of Interest Rates
Default risk example:
• Bond 1: default free, face value 100, 1 year maturity.
• Bond 2: default probability 20%, face value 100, 1 year maturity. • Bond 3: default probability 20%, face value 200, 1 year maturity. • The interest rate is 0%.
• Prices equal the expected discounted payment.
Compute prices.
Now compute the yield to maturity. What do we notice?
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Equilibrium interest rate
What happens if, e.g.,
1 Investors become more risk-tolerant/the default risk decreases.
2 Investors become more risk-averse/the default risk increases.
What happens to the risk premium?
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Equilibrium interest rate
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Long-Term Bond Yields
Default risk is compensated by higher yields.
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Risk Structure of Interest Rates
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Risk Structure of Interest Rates
Default risk in country debt: See, e.g., Argentina as well as:
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Risk Structure of Interest Rates
In financial crisis, many securities are more prone to default.
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Risk Structure of Interest Rates
Liquidity
Liquidity
is the relative ease with which an asset can be converted into cash. Relates to, e.g.,
• the cost of selling a bond, e.g., institutions,
• the transaction costs involved in, e.g., information acquisition, • the number of buyers/sellers in a bond market,
• how widely and commonly a bond is traded.
Risk premium is a risk and liquidity premium.
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Risk Structure of Interest Rates
Income tax considerations
Income tax considerations
Investors take into account that different securities are taxed differently.
Example:
• The interest portion of payments to “mortgage” securities is subject to federal and state income tax.
• “Treasury” securities are exempt from state income tax.
• Two bonds with the same after-tax return, would imply different yields to maturity.
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Risk Structure of Interest Rates
Tax considerations example:
• Federal Tax = 0%.
• State Tax = 20%.
• Interest rate used to discount future = 5%.
• 1 year “Mortgage security”, face value 100, pays 12.50% interest. • 1 year “Treasury security”, face value 100, pays 10% interest.
What are the prices?
Do the yields to maturity differ?
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The Term Structure of Interest Rates
Term Structure of Interest Rates
Bonds with identical risk, liquidity, and tax characteristics may have different interest rates. Why?
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Term Structure of Interest Rates
Reason: the time remaining to maturity is different.
Yield curve:
a plot of the yield on bonds with differing terms to maturity but the
same risk, liquidity and tax considerations.
• Upward-sloping: long-term rates are above short-term rates • Flat: short- and long-term rates are the same
• Inverted: long-term rates are below short-term rates
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Term Structure of Interest Rates
Yield Curves for U.S. Bonds
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Term Structure of Interest Rates
Some facts:
• Interest rates on bonds of different maturities move together over time.
• When the short-term rates are high (low) yield curves likely slope downwards (upwards).
• Yield curves almost always slope upward.
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Expectations Theory
The Expectations Theory holds that:
Bond holders consider bonds with different maturities to be perfect
substitutes (i.e., they don’t prefer one over the other).
This implies that the interest rate on a long-term bond will equal an average of the short-term interest rates that people expect to occur over the life of the long-term bond.
The expected return on substitutable bonds must be equal!
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Expectations Theory
Example
• Let the current interest rate on a 1-year bond be 6%.
• You expect the interest rate on a 1-year bond to be 8% next year.
• Then, $1 buying two 1-year bonds, returns (1.06)(1.08).
• Both bonds will be held only if $1 returns the same. Why?
• The interest rate on a two-year bond must be approximately 7% (or, 6.995327%) for you to be willing to purchase it.
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Expectations Theory
Offers explanations for why
• the term structure of interest rates changes at different times
• interest rates on bonds with different maturities move together over time (the same expectations are used to price them):
increase in short term interest rates lead to higher expected short term interest rates in the future–whose average gives a higher long term interest rate
• upward sloped yield curves are likely if short-term rates are low: Short-term rates are expected to decreases to a normal (lower)
level–whose average gives a higher long term interest rate
Does not offer an explanation for why yield curves usually slope upward: increases and decreases of short term rates are equally likely.
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Segmented Markets Theory
Assumes that bonds with different maturities aren’t substitutes at all.
Investors prefer certain maturities due to, e.g., fixed holding periods.
Markets for bonds of different maturities are segmented.
The yields are determined by supply and demand in those markets without interaction with other markets.
Yield curves: differences in supply and demand in those markets.
Can explain fact 3: short-term bonds carry less interest risk–risk averse investors desire short holding periods; so that there is more demand for short term bonds.
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Liquidity Premium Theory
The interest rate on a long-term bond will equal
• an average of short-term interest rates expected to occur over the life of the long-term bond plus
• a liquidity premium that responds to supply and demand conditions for that bond.
Bonds of different maturities are partial (not perfect) substitutes.
Longer maturity bonds are less liquid (you need to find somebody to sell it to).
Investors prefer shorter terms (interest rate risk)–and thus require a liquidity premium (a higher yield) to hold longer term bonds.
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Term Structure of Interest Rates
Yield Curves for U.S. Bonds
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Neely: “The Mysterious Greek Yield Curve”
The yield curve for Greek government debt has recently developed a pronounced hump-shaped pattern. 28 / 31
Neely: “The Mysterious Greek Yield Curve”
What economic conditions cause this very unusual shape?
• Observers expected a program to reduce the bond payoffs (face value) in exchange for a lower likelihood of outright default.
• In that case, every bond redeemed after the restructuring date would be redeemed for only half its original face value.
• The hump in the Greek yield curve exists because the calculated yields assume that the bonds will pay off at their full value but market prices incorporate expectations that the payoff will be much lower.
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Neely: “The Mysterious Greek Yield Curve”
Example:
• Bond 1: A 2-year zero-coupon bond with a nominal payoff of 100 euros and a price of 80 euros.
• Bond 2: A 1-year zero-coupon bond with the same face value and yield.
• Bond 3: 10-year zero-coupon bond with the same face value and yield.
What would happen if suddenly the market expect that all payoffs would be cut to half in 2 years?
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Neely: “The Mysterious Greek Yield Curve”
Bond
1 year bond
2 year bond 10 year bond
State
Face Value Price Yield
original expected restructuring
100 100
89.4 89.4
original expected restructuring
100 50
80 40
original expected restructuring
100 32.8 50 16.4
11.8% 11.8% 11.8% 58.1% 11.8% 19.8%
Yields for bonds that mature before the expected restructuring are unaffected.
There is a hump around the expected date of restructuring.
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