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Lecture 9: Debt Markets and Term Structure

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. Term T, Yield to Maturity (YTM) r. Compound Interest.

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Lecture 9: Debt Markets and Term Structure

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  1. Lecture 9: Debt Markets and Term Structure

  2. 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

  3. Compound Interest • If annual rate is r, compounding once per year, balance = (1+r)tafter t years. • If compounded twice per year, balance is (1+r/2)2tafter t years. • If compounded n times per year, balance is (1+r/n)ntafter t years. • Continuous compounding, balance is ert.

  4. 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.)

  5. 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%

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

  7. Bond Yield Tables

  8. 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

  9. Term Structure of Interest Rates, 1999 and 2004

  10. 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

  11. Irving Fisher Yale ‘88

  12. 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.”

  13. Irving Fisher Diagram Today

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

  15. 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+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.

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

  17. 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

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

  19. 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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