Yield to Maturity Lecture

# Yield to Maturity Lecture - Debt Instruments and Markets...

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Debt Instruments and Markets Professor Carpenter Yield to Maturity 1 Yield to Maturity Outline and Suggested Reading • Outline – Yield to maturity on bonds – Coupon effects – Par rates • Buzzwords Internal rate of return, Yield curve Term structure of interest rates Suggested reading – Veronesi, Chapter 2 – Tuckman, Chapter 3

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Debt Instruments and Markets Professor Carpenter Yield to Maturity 2 Definition of Yield Suppose a bond (or portfolio of bonds) has price P and positive fixed cash flows K 1 , K 2 ,..., K n at times t 1 , t 2 ,..., t n . Its yield to maturity is the single rate y that solves: Note that the higher the price, the lower the yield. Example • Recall the 1.5-year, 8.5%-coupon bond. • Using the zero rates 5.54%, 5.45%, and 5.47%, the bond price is 1.043066 per dollar par value. • That implies a yield of 5.4704%:
Debt Instruments and Markets Professor Carpenter Yield to Maturity 3 Yield of a Bond on a Coupon Date For an ordinary semi-annual coupon bond on a coupon date, the yield formula is where c is the coupon rate and T is the maturity of the bond in years. Annuity Formula Math result: Finance application: This formula gives the present value of an annuity of \$1 to be received every period for n periods at a simply compounded rate of r per period. 1 (1 + y /2) s s = 1 2 T = 1 y /2 (1 1 (1 + y /2) 2 T )

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Debt Instruments and Markets Professor Carpenter Yield to Maturity 4 Yield-to-Price Formula for a Coupon Bond Value the coupon stream using the annuity formula: The closed-form expression simplifies computation. Note that if c=y , P= 1 (the bond is priced at par). If c>y , P> 1 (the bond is priced at a premium to par). If c<y , P< 1 (the bond is priced at a discount ). The yield on a zero is the zero rate: c= 0 ; y=r T Class Problem: Suppose the 1.5-year 8.5%-coupon bond is priced to yield 9%. What is its price per \$1 par? Bond Yields and Zero Rates Recall that we can construct coupon bonds from zeroes, and we can construct zeroes from coupon bonds.
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