Interest Rates: Basic Determinants

1
Interest RatesBasic Determinants

• Week 5 September 28, 2005

2
Financial Asset Prices

• We have introduced the major players in financial
  markets
• Funds in financial institutions (banks, insurance
  companies, pension plans, etc.)
• Decision makers allocating those funds (bank
  managers, insurance company managers, asset
  managers under contract from pension-fund
  sponsors, etc.)
• Decision makers implementing plans interact in
  markets trading in similar securities
• Largest category of markets divides securities
  into fixed income and equities markets

3
Fixed Income Market
Fixed Income Market United States 2004 Fixed Income Market United States 2004
Issuer Amount
U. S. Treasury Issues 4,166.3
GSE Debt 2,697.7
GSE and Agency Pools 3,542.5
ABS Issuers 1,511.4
Municipal Debt 1,665.0
Non-Financial Corporate Debt 2,947.4
Financial Corporate Debt 3,679.0
Total of Debt Shown 20,209.3
Source FRB Flow of Funds, June, 2005
4
Fixed Income Returns

• Fixed income securities
• Bonds and notes
• Mortgages and other loan contracts (e.g. car
  loans)
• Money market instruments
• Business lending
• We will define and contrast contract rates,
  discount rates, yields to maturity, realized or
  holding period returns, and expected yields or
  expected returns

5
Contract rate

• Contract rate determines maximum future cash
  flows paid by borrower
• With bonds, contract or coupon rate determines
  periodic interest payments.
• E.g. 5-3/8 Feb 31 will pay 2-11/16 or .026875
  times the face value or principal of holdings
  every six months, or each February and August
  until February 2031(for about 26.5 years)
• If investor owns 1,000 in principle, pays
  semiannual 26.88, if 1,000,000, pays 26,875

6
Fixed Income Prices and Yields

• Fixed income cash flows are determined by the
  contracts underlying their issuances
• The price of a fixed-income security is the
  present value of the contractual cash flows
  calculated using the risk-adjusted discount rate
  investors apply to securities of that class of
  risk
• Given the cash flows, the price of a fixed income
  and its yield to maturity are two ways of looking
  at the same thing

7
Bond Prices

• Bonds are usually quoted as a percent of
  principal or face value, e.g. on September 22,
  2005, the Treasury maturing in February 2031
  (26.5 years) was quoted at 11326 ask, translated
  as 113-26/32 or 1.138125 times face value.
  Todays price?
• 1,000 face value cost 1,138.13 then
• 1,000,000 face value cost 1,138,125 then
• Examples of 1,000 face prices are rarely seen
• Bonds normally sell retail in blocks of 5,000
  but Wall Street Journal quotes are for 1 million
  face value amounts or over (institutional traders)

8
Bond Yield to Maturity

• The yield to maturity for a bond is the discount
  rate that makes the present value of coupon
  payments and redemption of principal equal to the
  current market price
• The relation of price to yield to maturity is
  given byfor y is yield to maturity, p is
  decimal price, c is coupon rate, is the yield to
  maturity, m (4.46 in our Treasury bond example)

9
Bond Yields (continued)

• Current yield is calculated asas is reported
  by Wall Street Journal for U.S Exchange traded
  corporate bonds (not Treasuries), but is not too
  useful
• Expected yield is less than the yield to maturity
  because yield to maturity assumes all payments
  are made on time (no default)

10
Bond Yields (continued)

• Holding period yield (HPY) is the actual cash
  realized yield over some holding period, usually
  stated as an annual yield.
• If you bought the 30-year Treasury in 2002 (5-3/8
  Feb 31) for 11014 ask (its price then) and sold
  it for 10403 in 2003 (its then bid price), HPY
  would have been

11
Relation between yields

• Expected yields for default risky bonds are below
  yields to maturity because yields to maturity do
  not allow for default or late payments
• Current yields are below yields to maturity
  because they ignore repayment of principle
• Expected yield should equal expected
  holding-period or realized yield over time in
  efficient markets

12
Interest rate components

• Real rate
• Inflation premium
• Term premium
• Risk premium

6/98
9/02
1/80
13
Theories of Interest Rates

• The Classical Theory of Interest Rates
• The Liquidity Preference or Cash Balances Theory
  of Interest Rates
• The Loanable Funds Theory of Interest
• The Rational Expectations Theory

14
Theory of Real Risk-free Rate

• Income and wealth (future income)
• Time preference
• Ability to exchange income through time or a
  financial market
• Exchange establishes rate of transformation
  between current and future consumption and
  depends on allocation of income and wealth
  between market participants

15
Exchange economy and real rate
Not an Equilibrium
As Income
Future Consumption
A Repays
Bs Utility
Bs Income
As Utility
B Lends
0
Present Consumption
A Borrows
16
Exchange and Investment
Future Consumption
Borrowing
0
Present Consumption
Investment
17
Alternative Views of Real Rate
The Equilibrium Rate of Interest In the Classical
Theory
18
Historical Perspective - T-Bills
19
Ex-post Real Rate 1950 to 2004
20
Ex-post Real Rate since 1980
21
Real Rate TIPS

• TIPS Treasury Inflation-Protected Securities
• Issued in 5-, 10-, and 30-year maturities,
  starting in January, 1997
• Principal value is adjusted daily using CPI index
  changes from three months earlier
• Problems
• CPI as measure of inflation and lags
• Taxation on increases in principal

22
Alternative Theories Money

• Liquidity preference theory assumes two assets,
  one of which is zero-interest earning money or
  cash balances
• Demand for money is composed of transactions,
  precautionary, and speculative components
• Interest rate is determined by price of bonds
  relative to demand for money

23
Total Demand for Money
24
Money and Interest Rates
The Equilibrium Interest Rate In the Liquidity
Preference Theory
25
Demand and Supply of Credit
The Equilibrium Interest Rate
26
Rational Expectations
27
Comparing Theories of Interest

• Liquidity theory focuses on money and bonds and
  not on real assets
• Loanable funds theory concentrates on primary
  sectors demands for funds which are linked to
  returns on investment in real assets
• Rational expectations is a powerful explanation
  of the relation between interest rates in
  efficient markets which we will draw on in
  discussing the term structure of interest rates

28
Next time October 1, 2005

• Read Chapter 7
• Read articles selected by students from trade
  publications on real rates and/or expected
  inflation
• Meet with your team and be prepared to define and
  refine your term project topic and discuss with me