Yield to Maturity - New York University
Debt Instruments and Markets
Professor Carpenter
Yield to Maturity
Outline and Suggested Reading
? Outline
? Suggested reading
? Yield to maturity on ? Veronesi, Chapter 2
bonds ? Coupon effects
? Tuckman, Chapter 3
? Par rates
? Buzzwords ? Internal rate of return,
? Yield curve
? Term structure of
interest rates
Yield to Maturity
1
Debt Instruments and Markets
Professor Carpenter
Definition of Yield
Suppose a bond (or portfolio of bonds) has price P and positive fixed cash flows K1, K2,..., Kn at times t1, t2,..., tn. 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%:
Yield to Maturity
2
Debt Instruments and Markets
Professor Carpenter
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:
2T s=1
(1 +
1 y /2)s
=
1 (1- y /2
(1 +
1 y /2)2T
)
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.
Yield to Maturity
3
Debt Instruments and Markets
Professor Carpenter
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 ................
................
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