Rule G-33.
(a) Accrued Interest. Accrued interest
shall be computed in accordance with the following formula:
For purposes of this formula, the "number of days"
shall be deemed to be the number of days from the previous interest
payment date (from the dated date, in the case of first coupons)
up to, but not including, the settlement date. The "number
of days" and the "number of days in year" shall
be counted in accordance with the requirements of section (e)
below.
(b) Interest-Bearing Securities
(i) Dollar Price. For transactions in interest-bearing
securities effected on the basis of yield the resulting dollar
price shall be computed in accordance with the following provisions:
(A) Securities Paying Interest Solely at Redemption.
Except as otherwise provided in this section (b), the dollar
price for a transaction in a security paying interest solely
at redemption shall be computed in accordance with the following
formula:
For purposes of this formula the symbols shall be defined
as follows:
"A" is the number of accrued days from the beginning
of the interest payment period to the settlement date (computed
in accordance with the provisions of section (e) below);
"B" is the number of days in the year (computed
in accordance with the provisions of section (e) below);
"DIR" is the number of days from the issue date
to the redemption date (computed in accordance with the provisions
of section (e) below);
"P" is the dollar price of the security for each
$100 par value (divided by 100);
"R" is the annual interest rate (expressed as a
decimal);
"RV" is the redemption value of the security per
$100 par value (divided by 100); and
"Y" is the yield price of the transaction (expressed
as a decimal).
(B) Securities with Periodic Interest Payments. Except as
otherwise provided in this section (b), the dollar price for
a transaction in a security with periodic interest payments
shall be computed as follows:
(1) for securities with six months or less to redemption,
the following formula shall be used:
For purposes of this formula the symbols shall be defined as
follows:
"A" is the number of accrued days from the beginning
of the interest payment period to the settlement date (computed
in accordance with the provisions of section (e) below);
"B" is the number of days in the year (computed in
accordance with the provisions of section (e) below);
"E" is the number of days in the interest payment
period in which the settlement date falls (computed in accordance
with the provisions of section (e) below);
"M" is the number of interest payment periods per
year standard for the security involved in the transaction;
"P" is the dollar price of the security for each
$100 par value (divided by 100);
"R" is the annual interest rate (expressed as a decimal);
"RV" is the redemption value of the security per
$100 par value; and
"Y" is the yield price of the transaction (expressed
as a decimal).
(2) for securities with more than six months to redemption,
the following formula shall be used:
For purposes of this formula the symbols shall be defined as
follows:
"A" is the number of accrued days from beginning
of the interest payment period to the settlement date (computed
in accordance with the provisions of section (e) below);
"B" is the number of days in the year (computed in
accordance with the provisions of section (e) below);
"E" is the number of days in the interest payment
period in which the settlement date falls (computed in accordance
with the provisions of section (e) below);
"N" is the number of interest payments (expressed
as a whole number) occurring between the settlement date and
the redemption date, including the payment on the redemption
date;
"P" is the dollar price of the security for each
$100 par value;
"R" is the annual interest rate (expressed as a decimal);
"RV" is the redemption value of the security per
$100 par value; and
"Y" is the yield price of the transaction (expressed
as a decimal).
For purposes of this formula the symbol "exp" shall
signify that the preceding value shall be raised to the power
indicated by the succeeding value; for purposes of this formula
the symbol "K" shall signify successively each whole
number from "1" to "N" inclusive; for purposes
of this formula the symbol "sigma" shall signify that
the succeeding term shall be computed for each value "K"
and that the results of such computations shall be summed.
(ii) Yield. Yields on interest-bearing securities shall
be computed in accordance with the following provisions:
(A) Securities Paying Interest Solely at Redemption.
The yield of a transaction in a security paying interest solely
at redemption shall be computed in accordance with the following
formula:
For purposes of this formula the symbols shall be defined as
follows:
"A" is the number of accrued days from the beginning
of the interest payment period to the settlement date (computed
in accordance with the provisions of section (e) below);
"B" is the number of days in the year (computed in
accordance with the provisions of section (e) below);
"DIR" is the number of days from the issue date to
the redemption date (computed in accordance with the provisions
of section (e) below);
"P" is the dollar price of the security for each
$100 par value (divided by 100);
"R" is the annual interest rate (expressed as a decimal);
"RV" is the redemption value of the security per
$100 par value (divided by 100); and
"Y" is the yield on the investment if the security
is held to redemption (expressed as a decimal).
(B) Securities with Periodic Interest Payments. The
yield of a transaction in a security with periodic interest
payments shall be computed as follows:
(1) for securities with six months or less to redemption,
the following formula shall be used:
For purposes of this formula the symbols shall be defined as
follows:
"A" is the number of accrued days from the beginning
of the interest payment period to the settlement date (computed
in accordance with the provisions of section (e) below);
"E" is the number of days in the interest payment
period in which the settlement date falls (computed in accordance
with the provisions of section (e) below);
"M" is the number of interest payment periods per
year standard for the security involved in the transaction;
"P" is the dollar price of the security for each
$100 par value (divided by 100);
"R" is the annual interest rate (expressed as decimal);
"RV" is the redemption value of the security per
$100 par value; and
"Y" is the yield on the investment if the security
is held to redemption (expressed as a decimal).
(2) for securities with more than six months to redemption
the formula set forth in item (2) of subparagraph (b)(i)(B)
shall be used.
(c) Discounted Securities.
(i) Dollar Price. For transactions in discounted securities,
the dollar price shall be computed in accordance with the following
provisions:
(A) The dollar price of a discounted security, other than
a discounted security traded on a yield-equivalent basis,
shall be computed in accordance with the following formula:
For purposes of this formula the symbols shall be defined as
follows:
"B" is the number of days in the year (computed in
accordance with the provisions of section (e) below);
"DR" is the discount rate (expressed as a decimal);
"DSM" is the number of days from the settlement date
of the transaction to the maturity date (computed in accordance
with the provisions of section (e) below);
"P" is the dollar price of the security for each
$100 par value; and "RV" is the redemption value of
the security per $100 par value.
(B) The dollar price of a discounted security traded on a yield-equivalent
basis shall be computed in accordance with the formula set forth
in subparagraph (b)(i)(A).
(ii) Return on Investment. The return on investment
for a discounted security shall be computed in accordance with
the following provisions:
(A) The return on investment for a discounted security, other
than a discounted security traded on a yield-equivalent basis,
shall be computed in accordance with the following formula:
For purposes of this formula the symbols shall be defined as
follows:
"B" is the number of days in the year (computed in
accordance with the provisions of section (e) below);
"DSM" is the number of days from the settlement date
of the transaction to the maturity date (computed in accordance
with the provisions of section (e) below);
"IR" is the annual return on investment if the security
is held to maturity (expressed as a decimal);
"P" is the dollar price of the security for each
$100 par value; and
"RV" is the redemption value of the security per
$100 par value.
(B) The yield of a discounted security traded on a yield-equivalent
basis shall be computed in accordance with the formula set forth
in subparagraph (b)(ii)(A).
(d) Standards of Accuracy; Truncation.
(i) Intermediate Values. All values used in computations
of accrued interest, yield, and dollar price shall be computed
to not less than ten decimal places.
(ii) Results of Computations. Results of computations
shall be presented in accordance with the following:
(A) Accrued interest shall be truncated to three decimal
places, and rounded to two decimal places immediately prior
to presentation of total accrued interest amount on the confirmation;
(B) Dollar prices shall be truncated to three decimal places
immediately prior to presentation of dollar price on the confirmation
and computation of extended principal; and
(C) Yields shall be truncated to four decimal places, and
rounded to three decimal places, provided, however,
that for purposes of confirmation display as required under
rule G-15(a) yields accurate to the nearest .05 percentage
points shall be deemed satisfactory.
Numbers shall be rounded, where required, in the following manner:
if the last digit after truncation is five or above, the preceding
digit shall be increased to the next highest number, and the last
digit shall be discarded.
(e) Day Counting.
(i) Day Count Basis. Computations under the requirements
of this rule shall be made on the basis of a thirty-day month
and a three-hundred-sixty-day year, or, in the case of computations
on securities paying interest solely at redemption, on the day
count basis selected by the issuer of the securities.
(ii) Day Count Formula. For purposes of this rule,
computations of day counts on the basis of a thirty-day month
and a three-hundred-sixty-day year shall be made in accordance
with the following formula.
Number of Days = (Y2 - Y1) 360 + (M2 -
M1) 30 + (D2 - D1)
For purposes of this formula the symbols shall be defined as
follows:
"M1" is the month of the date on which the computation
period begins;
"D1" is the day of the date on which the computation
period begins;
"Y1" is the year of the date on which the computation
period begins;
"M2" is the month of the date on which the computation
period ends;
"D2" is the day of the date on which the computation
period ends; and
"Y2" is the year of the date on which the computation
period ends.
For purposes of this formula, if the symbol "D2"
has a value of "31," and the symbol "D1"
has a value of "30" or "31," the value of
the symbol "D2" shall be changed to "30."
If the symbol "D1" has a value of "31,"
the value of the symbol "D1" shall be changed to "30."
For purposes of this rule time periods shall be computed to
include the day specified in the rule for the beginning of the
period but not to include the day specified for the end of the
period.
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