Bonds, bond prices and interest rates Bonds, bond prices and interest rates Bond prices and yields...

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