interest rates: basic determinants

J. K. Dietrich - FBE 524 - Fall, 2005

Interest Rates:Basic Determinants

Week 5 – September 28, 2005


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


Fixed Income MarketFixed 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


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


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


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


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)


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)

mm yyy

cp

)1(

1)

)1(

11(0


Bond Yields (continued) Current yield is calculated as

as 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)

%722.4138125.1

05375.

p

cyieldcurrent


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:

%736.104375.1

104375.10425.105375.HPY


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


-4

-2

0

2

4

6

8

10

12

14

16

1 2 3

Real Rate Inflation Premium on 90-Day T-BillTerm Premium on 10-Y. Treasury Baa Bond Risk Premium

Interest rate components

Real rate Inflation

premium Term

premium Risk

premium

1/806/98 9/02


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


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


Exchange economy and real rate

Present Consumption

Fut

ure

Con

sum

ptio

n

0

A’s Income

B’s Income

A’s Utility

B’s Utility

A Borrows

B Lends

Not an EquilibriumA

Rep

ays


Exchange and Investment

Present Consumption

Fut

ure

Con

sum

ptio

n

0

Investment

Borrowing


Alternative Views of Real RateThe Equilibrium Rate of Interest In the Classical Theory

InterestRate

Savings &Investment

rE

QE

Investment Savings


Historical Perspective - T-Bills

0

4

8

12

16

20

35 40 45 50 55 60 65 70 75 80 85 90 95 00

TBILL90DAY

90-Day T-Bill Rate 1935 to 2004


Ex-post Real Rate 1950 to 2004

-20

-15

-10

-5

0

5

10

15

50 55 60 65 70 75 80 85 90 95 00

REALRATE


Ex-post Real Rate since 1980

-10

-5

0

5

10

15

80 82 84 86 88 90 92 94 96 98 00 02 04

REALRATE

Real Rate Since 1980


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


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


Total Demand for Money


Money and Interest RatesThe Equilibrium Interest Rate

In the Liquidity Preference TheoryInterest

Rate

Quantity ofMoney / Cash

Balances

Equilibrium interest rate Total

Demand

QE

MoneySupply


Demand and Supply of Credit

The Equilibrium Interest Rate

InterestRate

Amount ofLoanable Funds

rE

QE

Demand

Supply


Rational Expectations


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


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

interest rates: basic determinants

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