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