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Bonds, bond prices and interest rates • 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 • discount bonds purchased price less than face value -- F > P face value at maturity no interest payments example • 91 day Tbill, • P = $9850, F = $10,000 • YTM solves $9850 $10,000 (1 i ) 91 365 $9850 $10,000 (1 i ) 1 i 91 365 91 365 10000 9850 10000 1 i 9850 10000 i 9850 365 91 365 91 1 6.25% yield on a discount basis (127) • how Tbill yields are actually quoted • approximates the YTM idb = F-P F x 360 d example • 91 day Tbill, • P = $9850, F = $10,000 • discount yield = $150 360 5.93% $10,000 91 • 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 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? • • • • • • 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 12 500 500 500 20000 ... 2 60 1 im 1 im 1 im im=1.44% i=(1+. 0144)12 – 1 =18.71% APR .0144 12 17.28% • how to solve for i? trial-and-error table financial calculator spreadsheet Coupon bond • (chapter 4) Bond Yields • Yield to maturity (YTM) • • chapter 4 Current yield Holding period return Yield to Maturity (YTM) • a measure of interest rate • interest rate where P = PV of cash flows Current yield • approximation of YTM for coupon bonds ic = annual coupon payment bond price • better approximation when maturity is longer P is close to F example • 2 year Tnotes, F = $10,000 • P = $9750, coupon rate = 6% • current yield 600 ic = 9750 = 6.15% • 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 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. 300 9900 300 9750 2 i i 1 1 2 2 i/2 = 3.83% i = 7.66% • why i/2? • interest compounds annually not semiannually The Bond Market • Bond supply • Bond demand • Bond market equilibrium Bond supply • 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 Bond price S Q of bonds • 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 P S S’ Qs • 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 exp. inflation supply of bonds (shift rt.) Bond Demand • 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 D Quantity of bonds • 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 P D D Qd • 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 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 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 • bond price falls • interest rate rises Fisher effect • 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 • 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 • interest rate is pro-cyclical Why are bonds risky? • 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 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 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