Interest Rates: Basic Determinants

1. Interest Rates:Basic 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

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 couponrate 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 113:26 ask, translated as 113-26/32% or 1.138125 times face value. Today’s 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 by:for 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 110:14 ask (its price then) and sold it for 104:03 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 A’s Income Future Consumption A Repays B’s Utility B’s Income A’s Utility B Lends 0 Present Consumption A Borrows

16. Exchange and Investment Future Consumption Borrowing 0 Present Consumption Investment

17. Interest Rate Investment Savings rE  Savings & Investment QE 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. Interest Rate Money Supply Equilibrium interest rate  Total Demand Quantity of Money / Cash Balances QE Money and Interest Rates The Equilibrium Interest Rate In the Liquidity Preference Theory

25. Interest Rate Supply rE  Demand Amount of Loanable Funds QE 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