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## Interest Rates

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**Interest Rates**Chapter 4**Valuing Debt**• In 1945, U.S. Treasury bills offered a return of 0.4%. At their 1981 peak, they offered a return of over 17%. • Why does the same security offer radically different yields at different times?**Valuing Debt**• In January 2000, the U.S. Treasury could borrow for 1 year at an interest rate of 6.2%, but it had to pay a rate of about 7% for 20-year loans. • Why do bonds maturing at different dates offer different rates of interest?**Valuing Debt**• In January 2000, the U.S. government could issue long-term bonds at a rate of about 7%. • You could not have borrowed at that rate. Why not?**INTEREST RATES SERVE AS A**YARDSTICK FOR COMPARING DIFFERENT TYPES OF SECURITIES AND MATURITIES.**5 Major Sources of Rate Differences in Bonds**• Term to maturity • Default risk • To default on a bond is to fail to pay the interest when interest is due or to fail to pay the principal at maturity • Bond ratings • Tax treatment • The value of the tax factors to the investor depends on the investor’s marginal income tax rate • After tax yield=Before tax yield (1-T)**Marketability**• time required to effect the sale • spread between the current market price and realized price at the time of the sale. • Special features • call option. • put option. • convertible option.**Characteristics of Bonds**• Details contained in the indenture. • Administered through a trustee. • Secured versus unsecured. • Mortgage/debenture • Senior or junior or subordinated. • Call features. • Bond rating.**Types of Bonds**• Coupon/Zero-coupon bonds • Municipal bonds • Revenue/General Obligation • Junk bonds • Consols • Eurobonds/Foreign bonds**Sources of Bond Information**• http://www.moodys.com • http://www.bondsonline.com/ • http://www.wsj.com • http://bonds.yahoo.com**Bond Features**• When a corporation (or government) wants to borrow money, it often sells a bond. • An investor gives the corporation money for the bond. • The corporation promises to give the investor: • Regular coupon payments every period until the bond matures. • The face value of the bond when it matures.**The Bond Pricing Formula**C1 C2 C3 Cn + Fn P = + + + … + (1 + r)1 (1 + r)2 (1 + r)3 (1 + r)T • The price of the bond today is the present value of all future cash flows (coupon payments and principal).**Bond Features**• Consider a bond with three years to maturity, a coupon rate of 8%, and a $1000 face value. If the current market rate is 10%, what is the price of the bond. $80 $80 $1080 P = + + (1.10)1 (1.10)2 (1.10)3 P=$80(0.9091)+$80(0.8264)+$1080(0.7513) P=$950.24**Bond Rates and Yields**• The coupon rate is the annual dollar coupon expressed as a percentage of the face value. Coupon rate = $80/$1000 = 8.0% • The current yield is the annual coupon divided by the price: Current yield = $80/$950.24 = 8.42% • The yield to maturity is the rate that makes the price of the bond just equal to the present value of its future cash flows. YTM = 10%**Example**• Bond A has 4 years remaining to maturity. Interest is paid annually; the bond has a $1,000 par value; and the coupon interest rate is 9%. • What is the current yield and yield to maturity at a current market price of $829? • What is the current yield and yield to maturity at a current market price of $1,104?**Par, Premium and Discount Bonds**• If a bond’s coupon rate is equal to the market rate of interest (the bond’s yield), the bond will always sell at par. • Bonds selling at below par are called discount bonds. • Bonds selling above par are called premium bonds.**Pure Discount Bond**• Zero-coupon bonds pay no coupon payment but promise a single payment at maturity. • Value of a pure discount bond: P = F / (1 + r)T**Perpetual Bonds**• A consol pays coupons forever. It never matures. • P=C/r**Bond Pricing Theorem I**• Bond prices and market interest rates move in opposite directions.**Bond Pricing Theorem II**• When coupon rate = YTM, price = par value. • When coupon rate > YTM, price > par value (premium bond) • When coupon rate < YTM, price < par value (discount bond)**Bond Pricing Theorem III**• A bond with longer maturity has higher relative (%) price change than one with shorter maturity when interest rate (YTM) changes. All other features are identical.**Bond Pricing Theorem IV**• A lower coupon bond has a higher relative (%) price change than a higher coupon bond when interest rate (YTM) changes. All other features are identical.**Bond Value**High Coupon Bond Discount Rate Low Coupon Bond Coupon Rate and Bond Price Volatility Consider two otherwise identical bonds. The low-coupon bond will have much more volatility with respect to changes in the discount rate**Interest Rate Risk**• Price Risk. • Reinvestment Risk. • Price Risk versus Reinvestment Risk. • Duration.**Interest Rate Risk Example**• Suppose you buy three securities: • A one-year bill with a face value of $10,000. • A 5-year strip with a face value of $10,000. • A 30-year strip with a face value of $10,000. • The market interest rate is 6%, so their prices are: • T-bill: P=$10,000/1.06=$9,434 • 5-year strip: P=$10,000/(1.06)5=$7,473 • 30-year strip: P=$10,000/(1.l06)30=$1,741**Example, continued**• After a year, you need your money and you must liquidate your portfolio. Suppose market rates have risen from 6% to 8%. • T-bill: P=$10,000 • 5-year strip: P=$10,000/(1.08)4=$7,350 • 30-year strip: P=$10,000/(1.08)29=$1,073**Reinvestment-Rate Risk**• Suppose that you do not need your money after one year but want to leave it invested until you retire in 30 years. • On the 30-year strip, the holding-period yield equals the market yield at the time you bought the bond. • How much you make on the other two investments will depend on how you reinvest the money when the bond matures.**Reinvestment-Rate Risk**• Reinvestment-rate risk • the risk associated with reinvestment at uncertain interest rates. • Considerations: • What is your time horizon? • Do you want to play it safe? • Do you think interest rates will rise or fall?**Lessons**• If you hold a bill or strip to maturity, the holding-period yield will equal the market yield at the time that you bought it. • If you sell a bill or strip before maturity, the holding-period yield depends on the market yield at the time of the sale. • The higher the market yield at the time of the sale, the lower the market price. • The greater the bill’s or the strip’s remaining time to maturity, the greater the sensitivity of its market price to market yield.**Return Versus Yield to Maturity**• Rate of return measures the cash flows received during a period relative to the amount invested at the beginning • For a bond held for one year, the return is computed as follows:**Nominal versus Real Rates**• The real rate of interest is the fundamental long-run interest rate in the economy. It is called the “real” rate of interest because it is determined by the real output of the economy. • It is estimated to be on average about 3 percent. It varies between 2 and 4 percent. • The nominal rate of interest is the observed rate of interest. • Nominal rate ~ Real rate + Inflation**Calculating Interest Rates**• Nominal Versus Real Interest Rates • Nominal Interest Rates—Money amount of interest received • Real Interest Rates—Purchasing power of interest received • Real interest rate is the nominal interest adjusted for inflation Real interest rate = Nominal rate – Inflation rate • Where: • “ex-ante” is based on the expected rate of inflation • “ex-post” is based on the actual or realized rate of inflation**Supply and Demand Determine the Interest Rate**• Interest rate is price of credit or borrowing money • Market for Credit or Loanable Funds • Supply of Funds—Upward sloping, lenders are willing to extend more credit at higher interest rates • Demand for Funds—Downward sloping, borrowers are willing to borrow less at higher interest rates • Equilibrium—Intersection of supply and demand, no tendency to change**Why Does the Interest Rate Fluctuate**• U.S. Treasury bond yields change day to day • Movement along a single curve—Changes in the interest rate results in a movement along a single demand or supply curve • Shifts of a Curve—Change in determinants of supply or demand (other than interest rate) causes the respective curve to shift • Changes in Equilibrium—Shift of either the supply or demand curve will reflect a change in the equilibrium interest rate**Borrowing (Demand)**• Business firms • finance inventory or buy capital equipment • Households • buy cars, consumer goods, or homes • State and local government • provide infrastructure or public services • Federal government • finance Federal Budget Deficit • INCREASES IN BORROWING • SHIFT DEMAND TO RIGHT AND RAISE INTEREST RATES**Lending or Credit (Supply)**• Financial institutions or individuals lend to market • Government authorities may restrict lending by banks • Ability of individuals to lend depends on their savings—less savings results in lower amount of lending • DECREASES IN LENDING • SHIFT SUPPLY TO LEFT AND RAISE INTEREST RATE**The Importance of Expectations**• Effect of a change in expectations of increasing inflation • Demand—Borrowers increase demand since they will be repaying in depreciated dollars and desire to purchase before the prices increase • Supply—Lenders decrease supply since they will be repaid with money of diminished purchasing power • SHIFTS OF THE DEMAND AND SUPPLY CURVE WILL CAUSE THE INTEREST RATE TO INCREASE**The Importance of Expectations**• Self-fulfilling Prophesies • If individuals and institutions expect inflation and interest rates to increase, they will alter behavior that causes the higher rates that were anticipated**Cyclical and Long-term Trends in Interest Rates**• Level of interest rates tends to rise during cyclical expansion and fall during recessions. • During economic expansion: • Firms and households increase borrowing—demand curve right • FED usually tightens credit during expansion—supply curve left**Cyclical and Long-term Trends in Interest Rates**• Level of interest rates on upward long-term trend between 1950 and 1981 • Large federal budget deficit forced US Treasury to increase borrowing—pushing up interest rates • Expectations of increasing inflation • Since 1981 rates have trended downward • Federal deficits continued to increase in 1980’s • Expectations of lower inflation has been major reason for fall of interest rates.