Chapter 6. Bonds, bond prices and interest rates

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Chapter 6. Bonds, bond prices and interest rates

• Bond prices and yields
• Bond market equilibrium
• Bond risks

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Bonds 4 types

• zero coupon bonds
• e.g. Tbills
• fixed payment loans
• e.g. mortgages, car loans
• coupon bonds
• e.g. Tnotes, Tbonds
• consols

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Zero coupon bonds

• discount bonds
• purchased price less than face value
• -- F gt P
• face value at maturity
• no interest payments

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example

• 91 day Tbill,
• P 9850, F 10,000
• YTM solves

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yield on a discount basis (127)

• how Tbill yields are actually quoted
• approximates the YTM

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example

• 91 day Tbill,
• P 9850, F 10,000
• discount yield

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• idb lt YTM
• why?
• F in denominator
• 360 day year

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• fixed-payment loan
• loan is repaid with equal (monthly) payments
• each payment is combination of principal and
  interest

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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?

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• i is annual rate
• (effective annual interest rate)
• but payments are monthly, compound monthly
• (1im)12 i
• im i1/12-1
• im is the periodic rate
• note APR im x 12

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im1.44
i(1. 0144)12 1 18.71
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• how to solve for i?
• trial-and-error
• table
• financial calculator
• spreadsheet

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Coupon bond

• (chapter 4)

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Bond Yields

• Yield to maturity (YTM)
• chapter 4
• Current yield
• Holding period return

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Yield to Maturity (YTM)

• a measure of interest rate
• interest rate where

P
PV of cash flows
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Current yield

• approximation of YTM for coupon bonds

annual coupon payment
ic
bond price
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• better approximation when
• maturity is longer
• P is close to F

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example

• 2 year Tnotes, F 10,000
• P 9750, coupon rate 6
• current yield

600
ic
6.15
9750
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• current yield 6.15
• true YTM 7.37
• lousy approximation
• only 2 years to maturity
• selling 2.5 below F

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Holding period return

• sell bond before maturity
• return depends on
• holding period
• interest payments
• resale price

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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.

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i/2 3.83 i 7.66
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• why i/2?
• interest compounds annually not semiannually

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The Bond Market

• Bond supply
• Bond demand
• Bond market equilibrium

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Bond supply

• bond issuers/ borrowers
• look at Qs as a function of price, yield

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• lower bond prices
• higher bond yields
• more expensive to borrow
• lower Qs of bonds
• so bond supply slopes up with price

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Bond price
Q of bonds
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• Changes in bond price/yield
• Move along the bond supply curve
• What shifts bond supply?

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Shifts in bond supply

• Change in government borrowing
• Increase in govt borrowing
• Increase in bond supply
• Bond supply shifts right

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P
Qs
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• a change in business conditions
• affects incentives to expand production

supply of bonds (shift rt.)
exp. profits

• exp. economic expansion shifts bond supply rt.

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• a change in expected inflation
• rising inflation decreases real cost of borrowing

supply of bonds (shift rt.)
exp. inflation
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Bond Demand

• bond buyers/ lenders/ savers
• look at Qd as a function of bond price/yield

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Bond yield
Qd of bonds
price of bond
Qd of bonds

• so bond demand slopes down with respect to price

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Bond price
Quantity of bonds
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• Changes in bond price/yield
• Move along the bond demand curve
• What shifts bond demand?

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• Wealth
• Higher wealth increases asset demand
• Bond demand increases
• Bond demand shifts right

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• a change in expected inflation
• rising inflation decreases real return

inflation expected to
demand for bonds (shift left)
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• a change in exp. interest rates
• rising interest rates decrease value of existing
  bonds

int. rates expected to
demand for bonds (shift left)
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• a change in the risk of bonds relative to other
  assets

relative risk of bonds
demand for bonds (shift left)
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• a change in liquidity of bonds relative to other
  assets

relative liquidity of bonds
demand for bonds (shift rt.)
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Bond market equilibrium

• changes when bond demand shifts,
• and/or bond supply shifts
• shifts cause bond prices AND interest rates to
  change

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Example 1 the Fisher effect

• expected inflation 3

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• exp. inflation rises to 4
• bond demand
• -- real return declines
• -- Bd decreases
• bond supply
• -- real cost of borrowing declines
• -- Bs increases

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• bond price falls
• interest rate rises

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Fisher effect

• expected inflation rises,
• nominal interest rates rise

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Example 2 economic slowdown
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• bond demand
• decline in income, wealth
• Bd decreases
• P falls, i rises
• bond supply
• decline in exp. profits
• Bs decreases
• P rises, i falls

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• shift Bs gt shift in Bd
• interest rate falls

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Why shift Bs gt shift Bd?

• changes in wealth are small
• response to change in exp. profits is large
• large cyclical swings in investment

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• interest rate is pro-cyclical

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Why are bonds risky?

• 3 sources of risk
• Default
• Inflation
• Interest rate

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Default risk

• Risk that the issuer fails to make promised
  payments on time
• Zero for U.S. govt debt
• Other issuers corporate, municipal, foreign have
  some default risk
• Greater default risk means a greater yield

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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

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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