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Lecture 9: Debt Markets and Term Structure

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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. Term T, Yield to Maturity (YTM) r

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Compound Interest If 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 e rt.

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Price & Yield on T-Bills For buyer, Price = 100-Discount Discount = 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.)

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Example Dec 18, 2000 T-Bill maturing March 15, Asked=5.83%, 87 days to maturity. Discount = 5.83*87/360=1.40891 Price=100-1.40891=98.59108 Yield=(1.40891/98.59108)(365/87)=5.995%

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Conventional Bonds Carry Coupons Conventional Bond Issued at par (100), coupons every six months. Term is time to maturity.

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Bond Yield Tables

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Term Structure of Interest Rates Yield to maturity plotted against term Also called “The Yield curve” Usually upward sloping Inverted yield curve Hump shaped yield curve

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Term Structure of Interest Rates, 1999 and 2004

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Causes of Interest Rates Eugen von Böhm-Bawerk: Capital and Interest, 1884: technological progress, time preferences, advantages to roundaboutness Irving Fisher 1867-1947, wrote Theory of Interest 1930

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Irving Fisher Yale ‘88

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Irving Fisher Diary at Yale July 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.”

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Irving Fisher Diagram Today

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Forward Rates Forward rates are interest rates that can be taken in advance using term structure J. R. Hicks Value and Capital 1939

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Example of Forward Rates Suppose 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+r 2 ) 2/( 1+r 1 ) 2-period discount bonds maturing at £100 in 1927. Cost: £1/(1+r 1 ) Short in 1925 one 1-period discount bond maturing at £100 in 1926. Receive: £1/(1+r 1 ) I have now locked in the interest rate 1+f=(1+r 2 )2 / (1+r 1 ) between 1926 and 1927.

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Expectations Theory Forward rates equal expected spot rates Slope of term structure indicates expected future change in interest rates.

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Liquidity Preference Hypothesis Forward 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 hypothesis

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Inflation and Interest Rates Nominal rate quoted in dollars, real rate quoted market baskets Nominal rate usually greater than real rate.

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Indexed Bonds Paul Revere, Massachusetts, 1780 U. S. Treasury, 1997 TIPS Treasury Inflation Protection Securities, $115 billion outstanding 2000, 2% of US national debt UK Index-Linked Gilts 20% of debt France recently issued Euro Index bonds

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