Bài giảng Financial Markets - Lecture 9: Debt Markets and Term Structure

Discount Bonds No coupon payments, just principal at maturity date (conventionally, $100). Initially sold at a discount (less than $100) and price rises through time, creating income.

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Lecture 9: Debt Markets and Term StructureDiscount BondsNo coupon payments, just principal at maturity date (conventionally, $100).Initially sold at a discount (less than $100) and price rises through time, creating income.Term T, Yield to Maturity (YTM) rCompound InterestIf annual rate is r, compounding once per year, balance = (1+r)t after t years.If compounded twice per year, balance is (1+r/2)2t after t years.If compounded n times per year, balance is (1+r/n)nt after t years.Continuous compounding, balance is ert.Price & Yield on T-BillsFor buyer, Price = 100-DiscountDiscount = asked*(Days to Maturity/360).Yield = (Discount/Price)(365/(Days to Maturity)). (Unless maturity > 6 months, in which case quadratic formula using semi-annual compounding is required.) Example Dec 18, 2000T-Bill maturing March 15, Asked=5.83%, 87 days to maturity.Discount = 5.83*87/360=1.40891Price=100-1.40891=98.59108Yield=(1.40891/98.59108)(365/87)=5.995%Conventional Bonds Carry CouponsConventional Bond Issued at par (100), coupons every six months.Term is time to maturity.Bond Yield TablesTerm Structure of Interest RatesYield to maturity plotted against termAlso called “The Yield curve”Usually upward slopingInverted yield curveHump shaped yield curveTerm Structure of Interest Rates, 1999 and 2004Causes of Interest RatesEugen von Böhm-Bawerk: Capital and Interest, 1884: technological progress, time preferences, advantages to roundaboutnessIrving Fisher 1867-1947, wrote Theory of Interest 1930Irving Fisher Yale ‘88Irving Fisher Diary at YaleJuly 31, 1885 “it is neither politic nor right to study at the expense of one’s health.” Rowing.“When I fall in love she must be a girl of pure morality, broad culture and fine tastes.”“I have an earnest desire to be good and useful”April 4, 1886, roommate dies of a “cold.”May 29, 1887, “I take great satisfaction in my election to Bones for I felt it to be my first little conquest among men. As a freshman I was afraid of my own voice.”Irving Fisher Diagram TodayForward RatesForward rates are interest rates that can be taken in advance using term structureJ. R. Hicks Value and Capital 1939Example of Forward RatesSuppose I in 1925 expect to have £100 to invest in 1926, but want the money back by 1927. How can I guarantee the interest rate on the £100 investment today (1925)?Buy in 1925 (1+r2 )2/(1+r1) 2-period discount bonds maturing at £100 in 1927. Cost: £1/(1+r1)Short in 1925 one 1-period discount bond maturing at £100 in 1926. Receive: £1/(1+r1)I have now locked in the interest rate 1+f=(1+r2)2/ (1+r1) between 1926 and 1927.Expectations TheoryForward rates equal expected spot ratesSlope of term structure indicates expected future change in interest rates.Liquidity Preference HypothesisForward rates equal expected future spot rates plus a “risk premium.” (J. R. Hicks, 1939)Modigliani and Sutch: Risk premium could be either positive or negative. Preferred habitat hypothesisInflation and Interest RatesNominal rate quoted in dollars, real rate quoted market basketsNominal rate usually greater than real rate.Indexed BondsPaul Revere, Massachusetts, 1780U. S. Treasury, 1997TIPS Treasury Inflation Protection Securities, $115 billion outstanding 2000, 2% of US national debtUK Index-Linked Gilts 20% of debtFrance recently issued Euro Index bonds