Lecture 9: Debt Markets and
Term Structure

Discount Bonds
• No coupon payments, just principal at maturity date (conventionally, $100).
• Initially sold at a discount (less than $100) and price rises through time, creating income.
• Term
T, Yield to Maturity (YTM) r
P t

( 1

1 r )
T
P t

1
( 1
 r / 2 )
2 T

Compound Interest
• If annual rate is r, compounding once per year, balance = (1+ r ) t after t years.
• If compounded twice per year, balance is
(1+ r /2) 2 t after t years.
• If compounded n times per year, balance is
(1+ r / n ) nt after t years.
• Continuous compounding, balance is e rt .

Price & Yield on T-Bills
• For buyer, Price = 100-Discount
• Discount = asked*(Days to Maturity/360).
• Yield = (Discount/Price)(365/(Days to
Maturity)). (Unless maturity > 6 months, in which case quadratic formula using semiannual compounding is required.)

Example Dec 18, 2000
• T-Bill maturing March 15, Asked=5.83%,
87 days to maturity.
• Discount = 5.83*87/360=1.40891
• Price=100-1.40891=98.59108
• Yield=(1.40891/98.59108)(365/87)=5.995%

Conventional Bonds Carry
Coupons
• Conventional Bond Issued at par (100), coupons every six months.
P t
 c (
1 r

( 1

1 r )
T
1
) r

100
( 1
 r )
T
P t
 c
2
( r /
1
2

( 1
 r
1
2
2 T r /
1
2
)

100
( 1
 r 2
2 T

Bond Yield Tables

Term Structure of Interest Rates
• Yield to maturity plotted against term
• Also called “The Yield curve”
• Usually upward sloping
• Inverted yield curve
• Hump shaped yield curve

0.1
Term Structure of Interest Rates, 1999 and 2004
7
Nov-00
6
5
4
3
2
1
0
1
Jan-04
10
Maturity in Years
100

Causes of Interest Rates
• Eugen von Böhm-Bawerk:
Capital and
Interest , 1884: technological progress, time preferences, advantages to roundaboutness
• Irving Fisher 1867-1947, wrote
Theory of
Interest 1930

Irving Fisher Yale ‘88

Irving Fisher Diary at Yale
• July 31, 1885 “it is neither politic nor right to study at the expense of one’s health.” Rowing.
• “When I fall in love she must be a girl of pure morality, broad culture and fine tastes.”
• “I have an earnest desire to be good and useful”
• April 4, 1886, roommate dies of a “cold.”
• May 29, 1887, “I take great satisfaction in my election to Bones for I felt it to be my first little conquest among men. As a freshman I was afraid of my own voice.”

Irving Fisher Diagram Today

Forward Rates
• Forward rates are interest rates that can be taken in advance using term structure
• J. R. Hicks
Value and Capital 1939
( 1
 r
2
)
2 
( 1
 r
1
)( 1
 f
2
)
( 1
 r k
) k 
( 1
 r k

1
) k

1
( 1
 f k
)

Example of Forward Rates
• Suppose I in 1925 expect to have £100 to invest in
1926, but want the money back by 1927. How can
I guarantee the interest rate on the £100 investment today (1925)?
• Buy in 1925 (1
+r
2
) 2 /( 1 +r
1
) 2-period discount bonds maturing at £100 in 1927. Cost: £1/(1+ r
1
)
• Short in 1925 one 1-period discount bond maturing at £100 in 1926. Receive: £1/(1+ r
1
)
• I have now locked in the interest rate 1+ f =(1 +r
2
)2 /
(1 +r
1
) between 1926 and 1927.

Expectations Theory
• Forward rates equal expected spot rates
• Slope of term structure indicates expected future change in interest rates.

Liquidity Preference Hypothesis
• Forward rates equal expected future spot rates plus a “risk premium.” (J. R. Hicks,
1939)
• Modigliani and Sutch: Risk premium could be either positive or negative. Preferred habitat hypothesis

Inflation and Interest Rates
• Nominal rate quoted in dollars, real rate quoted market baskets
• Nominal rate usually greater than real rate.
( 1
 r money
)

( 1
 r real
)( 1
 i ) r money
 r real
 i

Indexed Bonds
• Paul Revere, Massachusetts, 1780
• U. S. Treasury, 1997
• TIPS Treasury Inflation Protection
Securities, $115 billion outstanding 2000,
2% of US national debt
• UK Index-Linked Gilts 20% of debt
• France recently issued Euro Index bonds