Bonds, bond prices and interest rates Bonds, bond prices and interest rates Bond prices and yields Bond market equilibrium Bond risks 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  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 discount bonds  purchased price less than face value -- F > P  face value at maturity  no interest payments

exampleexample 91 day Tbill, P = $9850, F = $10,000 YTM solves 91 day Tbill, P = $9850, F = $10,000 YTM solves

yield on a discount basis (127) how Tbill yields are actually quoted approximates the YTM how Tbill yields are actually quoted approximates the YTM i db = F - P F x 360 d

exampleexample 91 day Tbill, P = $9850, F = $10,000 discount yield = 91 day Tbill, P = $9850, F = $10,000 discount yield =

i db < YTM why?  F in denominator  360 day year i db < 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. 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+i m ) 12 = i i m = i 1/12 -1 i m is the periodic rate note: APR = i m x 12 i is annual rate  (effective annual interest rate) but payments are monthly, & compound monthly (1+i m ) 12 = i i m = i 1/12 -1 i m is the periodic rate note: APR = i m x 12

i m =1.44% i=( ) 12 – 1 =18.71%

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) Coupon bond

Bond 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) a measure of interest rate interest rate where a measure of interest rate interest rate where P =PV of cash flows

Current yield approximation of YTM for coupon bonds i c = 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

exampleexample 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 i c = = 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 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

exampleexample 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.

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 Market Bond supply Bond demand Bond market equilibrium Bond supply Bond demand Bond market equilibrium

Bond 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 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 of bonds (shift 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 of bonds (shift rt.)

Bond 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 of bonds price of bond Qd of bonds 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 D D

a change in expected inflation  rising inflation decreases real return 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 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 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 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 effect expected inflation rises, nominal interest rates rise 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 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? 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

Why are bonds risky? 3 sources of risk  Default  Inflation  Interest rate 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 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 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 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