Transcript Chapter 4. Understanding Interest Rates

Bonds, bond prices and interest
rates
• Bond prices and yields
• Bond market equilibrium
• Bond risks
Bonds: 4 types
• zero coupon bonds
•
•
•
 e.g. Tbills
fixed payment loans
 e.g. mortgages, car loans
coupon bonds
 e.g. Tnotes, Tbonds
consols
Zero coupon bonds
• discount bonds
 purchased price less than face
value
-- F > P
 face value at maturity
 no interest payments
example
• 91 day Tbill,
• P = $9850, F = $10,000
• YTM solves
$9850 
$10,000
(1  i )
91
365
$9850 
$10,000
(1  i )
1  i 
91
365
91
365
10000

9850
 10000 
1 i  

 9850 
 10000 
i 

 9850 
365
91
365
91
 1  6.25%
yield on a discount basis (127)
• how Tbill yields are actually quoted
• approximates the YTM
idb =
F-P
F
x
360
d
example
• 91 day Tbill,
• P = $9850, F = $10,000
• discount yield =
 $150   360 


  5.93%
 $10,000   91 
• idb < YTM
• why?
 F in denominator
 360 day year
• fixed-payment loan
 loan is repaid with equal (monthly)
payments
 each payment is combination of
principal and interest
example 2: fixed pmt. loan
• $20,000 car loan, 5 years
• monthly pmt. = $500
• so $15,000 is price today
• cash flow is 60 pmts. of $500
• what is i?
•
•
•
•
•
•
i is annual rate
 (effective annual interest rate)
but payments are monthly, &
compound monthly
(1+im)12 = i
im= i1/12-1
im is the periodic rate
note: APR = im x 12
500
500
500
20000 

 ... 
2
60
1  im  1  im 
1  im 
im=1.44%
i=(1+. 0144)12 – 1 =18.71%
APR  .0144 12  17.28%
• how to solve for i?
 trial-and-error
 table
 financial calculator
 spreadsheet
Coupon bond
• (chapter 4)
Bond Yields
• Yield to maturity (YTM)
•
•
 chapter 4
Current yield
Holding period return
Yield to Maturity (YTM)
• a measure of interest rate
• interest rate where
P = PV of cash flows
Current yield
• approximation of YTM for coupon
bonds
ic =
annual coupon payment
bond price
• better approximation when
 maturity is longer
 P is close to F
example
• 2 year Tnotes, F = $10,000
• P = $9750, coupon rate = 6%
• current yield
600
ic =
9750
= 6.15%
• current yield = 6.15%
• true YTM = 7.37%
• lousy approximation
 only 2 years to maturity
 selling 2.5% below F
Holding period return
• sell bond before maturity
• return depends on
 holding period
 interest payments
 resale price
example
• 2 year Tnotes, F = $10,000
• P = $9750, coupon rate = 6%
• sell right after 1 year for $9900
 $300 at 6 mos.
 $300 at 1 yr.
 $9900 at 1 yr.
300 9900  300
9750 

2
i
i
1
1

2
2

i/2 = 3.83%
i = 7.66%

• why i/2?
• interest compounds annually not
semiannually
The Bond Market
• Bond supply
• Bond demand
• Bond market equilibrium
Bond supply
• bond issuers/ borrowers
• look at Qs as a function of price,
yield
• lower bond prices
•
 higher bond yields
 more expensive to borrow
 lower Qs of bonds
so bond supply slopes up with price
Bond
price
S
Q of bonds
• Changes in bond price/yield
•
 Move along the bond supply curve
What shifts bond supply?
Shifts in bond supply
• Change in government borrowing
 Increase in gov’t borrowing
• Increase in bond supply
• Bond supply shifts right
P
S
S’
Qs
•
a change in business conditions
 affects incentives to expand
production
exp.
profits
supply of
bonds
(shift rt.)
 exp. economic expansion shifts
bond supply rt.
• a change in expected inflation
 rising inflation decreases real cost
of borrowing
exp.
inflation
supply of
bonds
(shift rt.)
Bond Demand
• bond buyers/ lenders/ savers
• look at Qd as a function of bond
price/yield
Bond
yield
Qd of
bonds
price
of bond
Qd of
bonds
• so bond demand slopes down with
respect to price
Bond
price
D
Quantity of bonds
• Changes in bond price/yield
•
 Move along the bond demand
curve
What shifts bond demand?
• Wealth
 Higher wealth increases asset
demand
• Bond demand increases
• Bond demand shifts right
P
D
D
Qd
• a change in expected inflation
 rising inflation decreases real
return
inflation
expected
to
demand for
bonds
(shift left)
• a change in exp. interest rates
 rising interest rates decrease value
of existing bonds
int. rates
expected
to
demand for
bonds
(shift left)
• a change in the risk of bonds relative
to other assets
relative
risk of
bonds
demand for
bonds
(shift left)
• a change in liquidity of bonds
relative to other assets
relative
liquidity
of bonds
demand for
bonds
(shift rt.)
Bond market equilibrium
• changes when bond demand shifts,
•
and/or bond supply shifts
shifts cause bond prices AND
interest rates to change
Example 1: the Fisher effect
• expected inflation 3%
• exp. inflation rises to 4%
 bond demand
-- real return declines
-- Bd decreases
 bond supply
-- real cost of borrowing declines
-- Bs increases
• bond price falls
• interest rate rises
Fisher effect
• expected inflation rises,
nominal interest rates rise
Example 2: economic slowdown
• bond demand
•
 decline in income, wealth
 Bd decreases
 P falls, i rises
bond supply
 decline in exp. profits
 Bs decreases
 P rises, i falls
• shift Bs > shift in Bd
• interest rate falls
Why shift Bs > shift Bd?
• changes in wealth are small
• response to change in exp. profits is
large
 large cyclical swings in investment
• interest rate is pro-cyclical
Why are bonds risky?
• 3 sources of risk
 Default
 Inflation
 Interest rate
Default risk
• Risk that the issuer fails to make
•
•
•
promised payments on time
Zero for U.S. gov’t debt
Other issuers: corporate, municipal,
foreign have some default risk
Greater default risk means a greater
yield
Inflation risk
• Most bonds promise fixed dollar
•
•
payments
 Inflation erodes the real value of
these payments
Future inflation is unknown
Larger for longer term bonds
Interest rate risk
• Changing interest rates change the
•
value (price) of a bond in the
opposite direction.
All bonds have interest rate risk
 But it is larger for the long term
bonds