90 Appendix — Reference Information
Price (given yield) with more than one coupon period to redemption:
where:
N =number of coupons payable between settlement date and
redemption date (maturity date, call date, put date, etc.). (If this
number contains a fraction, raise it to the next whole number;
for example, 2.4 = 3)
DSC =number of days from settlement date to next coupon date
K =summation counter
Note: The first term computes present value of the redemption amount,
not including interest. The second term computes the present values for
all future coupon payments. The third term computes the accrued
interest agreed to be paid to the seller.
Yield (given price) with more than one coupon period to redemption:
Yield is found through an iterative search process using the “Price with
more than one coupon period to redemption” formula.
Accrued interest for securities with standard coupons or interest at
maturity:
where:
AI =accrued interest
PA R =par value (principal amount to be paid at maturity)
Modified duration:
2
2. Source for duration: Strong, Robert A., Portfolio Construction, Management, and
Protection, South-Western College Publishing, Cincinnati, Ohio, 2000.
PRI
RV
1
Y
M
-----+
N 1–
DSC
E
------------+
-------------------------------------------
100
R
M
-----
A
E
---
××–
100
R
M
-----
×
1
Y
M
-----+
K 1–
DSC
E
------------+
-------------------------------------------
K 1=
N
∑
+=
AI PAR
R
M
-----
A
E
---
××=
Modified Duration
Duration
1
Y
M
-----+
------------------------=
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