Yield to Maturity
Debt Instruments and Markets
Professor Carpenter
Yield to Maturity
Outline and Suggested Reading
? Outline
? Suggested reading
¨C Yield to maturity on
¨C Veronesi, Chapter 2
bonds
¨C Tuckman, Chapter 3
¨C Coupon effects
¨C Par rates
? Buzzwords
¨C Internal rate of return,
¨C Yield curve
¨C 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
1
¡Æ (1+ y /2)
s=1
s
=
1
1
(1?
)
y /2
(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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