Bonds, bond prices and interest Bonds, bond prices and interest ratesrates Bonds, bond prices and interest Bonds, bond prices and interest ratesrates

• Bond prices and yields

• Bond market equilibrium

• Bond risks

• Bond prices and yields

• Bond market equilibrium

• Bond risks

Bonds: 4 typesBonds: 4 typesBonds: 4 typesBonds: 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 e.g. Tbills

• fixed payment loans e.g. mortgages, car loans

• coupon bonds e.g. Tnotes, Tbonds

• consols

Zero coupon bondsZero coupon bondsZero coupon bondsZero coupon bonds

• discount bonds purchased price less than face

value

-- F > P face value at maturity no interest payments

• discount bonds purchased price less than face

value

-- F > P face value at maturity no interest payments

exampleexampleexampleexample

• 91 day Tbill,

• P = $9850, F = $10,000

• YTM solves

• 91 day Tbill,

• P = $9850, F = $10,000

• YTM solves

36591

)1(

000,10$9850$

i

36591

)1(

000,10$9850$

i

9850

100001 365

91 i

91365

9850

100001

i

%25.619850

10000 91365

i

yield on a discount basis (127)yield on a discount basis (127)yield on a discount basis (127)yield on a discount basis (127)

• how Tbill yields are actually quoted

• approximates the YTM• how Tbill yields are actually quoted

• approximates the YTM

idb = F - P

Fx

360d

exampleexampleexampleexample

• 91 day Tbill,

• P = $9850, F = $10,000

• discount yield =

• 91 day Tbill,

• P = $9850, F = $10,000

• discount yield =

%93.591

360

000,10$

150$

• idb < YTM

• why? F in denominator 360 day year

• 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

• fixed-payment loan loan is repaid with equal (monthly)

payments each payment is combination of

principal and interest

example 2: fixed pmt. loanexample 2: fixed pmt. loanexample 2: fixed pmt. loanexample 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?

• $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

• 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

602 1

500...

1

500

1

50020000

mmm iii

im=1.44%

i=(1+. 0144)12 – 1 =18.71%

%28.17120144. APR

• how to solve for i? trial-and-error table financial calculator spreadsheet

• how to solve for i? trial-and-error table financial calculator spreadsheet

• (chapter 4)• (chapter 4)

Coupon bondCoupon bondCoupon bondCoupon bond

Bond YieldsBond YieldsBond YieldsBond Yields

• Yield to maturity (YTM) chapter 4

• Current yield

• Holding period return

• Yield to maturity (YTM) chapter 4

• Current yield

• Holding period return

Yield to Maturity (YTM)Yield to Maturity (YTM)Yield to Maturity (YTM)Yield to Maturity (YTM)

• a measure of interest rate

• interest rate where• a measure of interest rate

• interest rate where

P = PV of cash flows

Current yieldCurrent yieldCurrent yieldCurrent yield

• approximation of YTM for coupon bonds• approximation of YTM for coupon

bonds

ic =annual coupon payment

bond price

• better approximation when maturity is longer P is close to F

• better approximation when maturity is longer P is close to F

example example example example

• 2 year Tnotes, F = $10,000

• P = $9750, coupon rate = 6%

• current yield

• 2 year Tnotes, F = $10,000

• P = $9750, coupon rate = 6%

• current yield

ic =600

9750= 6.15%

• current yield = 6.15%

• true YTM = 7.37%

• lousy approximation only 2 years to maturity selling 2.5% below F

• current yield = 6.15%

• true YTM = 7.37%

• lousy approximation only 2 years to maturity selling 2.5% below F

Holding period returnHolding period returnHolding period returnHolding period return

• sell bond before maturity

• return depends on holding period interest payments resale price

• sell bond before maturity

• return depends on holding period interest payments resale price

exampleexampleexampleexample

• 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.

• 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.

221

3009900

21

3009750

ii

i/2 = 3.83%i = 7.66%

• why i/2?

• interest compounds annually not semiannually

• why i/2?

• interest compounds annually not semiannually

The Bond MarketThe Bond MarketThe Bond MarketThe Bond Market

• Bond supply

• Bond demand

• Bond market equilibrium

• Bond supply

• Bond demand

• Bond market equilibrium

Bond supplyBond supplyBond supplyBond supply

• bond issuers/ borrowers

• look at Qs as a function of price, yield

• 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

• lower bond prices higher bond yields more expensive to borrow lower Qs of bonds

• so bond supply slopes up with price

Bond price

Q of bonds

S

• Changes in bond price/yield Move along the bond supply curve

• What shifts bond supply?

• Changes in bond price/yield Move along the bond supply curve

• What shifts bond supply?

Shifts in bond supplyShifts in bond supplyShifts in bond supplyShifts in bond supply

• Change in government borrowing Increase in gov’t borrowing• Increase in bond supply• Bond supply shifts right

• Change in government borrowing Increase in gov’t borrowing• Increase in bond supply• Bond supply shifts right

P

Qs

S

S’

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

affects incentives to expand production

exp.profits

supply ofbonds(shift rt.)

exp. economic expansion shifts bond supply rt. exp. economic expansion shifts bond supply rt.

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

rising inflation decreases real cost of borrowing

exp.inflation

supply ofbonds(shift rt.)

Bond DemandBond DemandBond DemandBond Demand

• bond buyers/ lenders/ savers

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

• bond buyers/ lenders/ savers

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

Bond yield

Qd ofbonds

priceof bond

Qd of bonds

• so bond demand slopes down with respect to price• so bond demand slopes down with

respect to price

Bond price

Quantity of bonds

D

• Changes in bond price/yield Move along the bond demand

curve

• What shifts bond demand?

• 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

• Wealth Higher wealth increases asset

demand• Bond demand increases• Bond demand shifts right

P

Qd

DD

• a change in expected inflation rising inflation decreases real

return

• a change in expected inflation rising inflation decreases real

return

inflationexpected to

demand forbonds(shift left)

• a change in exp. interest rates rising interest rates decrease value

of existing bonds

• a change in exp. interest rates rising interest rates decrease value

of existing bonds

int. ratesexpected to

demand forbonds(shift left)

• a change in the risk of bonds relative to other assets• a change in the risk of bonds relative

to other assets

relativerisk of bonds

demand forbonds(shift left)

• a change in liquidity of bonds relative to other assets• a change in liquidity of bonds

relative to other assets

relative liquidityof bonds

demand forbonds(shift rt.)

Bond market equilibriumBond market equilibriumBond market equilibriumBond market equilibrium

• changes when bond demand shifts,

and/or bond supply shifts

• shifts cause bond prices AND interest rates to change

• changes when bond demand shifts,

and/or bond supply shifts

• shifts cause bond prices AND interest rates to change

Example 1: the Fisher effectExample 1: the Fisher effectExample 1: the Fisher effectExample 1: the Fisher effect

• expected inflation 3%• expected inflation 3%

• exp. inflation rises to 4% bond demand

-- real return declines

-- Bd decreases bond supply

-- real cost of borrowing declines

-- Bs increases

• 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• bond price falls

• interest rate rises

Fisher effectFisher effectFisher effectFisher effect

• expected inflation rises,

nominal interest rates rise• expected inflation rises,

nominal interest rates rise

Example 2: economic slowdownExample 2: economic slowdownExample 2: economic slowdownExample 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

• 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• shift Bs > shift in Bd

• interest rate falls

Why shift Bs > shift Bd?Why shift Bs > shift Bd?Why shift Bs > shift Bd?Why shift Bs > shift Bd?

• changes in wealth are small

• response to change in exp. profits is large large cyclical swings in investment

• changes in wealth are small

• response to change in exp. profits is large large cyclical swings in investment

• interest rate is pro-cyclical• interest rate is pro-cyclical

Why are bonds risky?Why are bonds risky?Why are bonds risky?Why are bonds risky?

• 3 sources of risk Default Inflation Interest rate

• 3 sources of risk Default Inflation Interest rate

Default riskDefault riskDefault riskDefault 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

• 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 riskInflation riskInflation riskInflation risk

• Most bonds promise fixed dollar payments Inflation erodes the real value of

these payments

• Future inflation is unknown

• Larger for longer term bonds

• 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 riskInterest rate riskInterest rate riskInterest 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

• 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