ACI and Yield Calculation Methods
Determining the Number of Days between Two Dates
All formulas for calculating ACI and the yield imply the necessity for the number of calendar days from one date to another or the duration of the period determined by two dates be calculated.
365 (366)-day basis
This is the main basis used in the Trading System. The number of calendar days (and the duration of the period) from date T1 to date T2 is determined as the difference in the dates: T2 – T1. For example, there lies one day from the 5th of January 2001 to the 6th of January 2001 (the duration of the period – one day), and ten days lie from the 10th of March 2002 to the 20th of March 2002 (the duration of the period – ten days).
30/360-day bases
The difference in the dates N between the two dates T1 and T2 is calculated by the following formula:
N = D2 — D1 + 30 (M2 — M1) + 360 (Y2 — Y1), where
D1/M1/Y1 is the date T1 (the first date)
D2/M2/Y2 is the date T2 (the second date)
There are three versions of 30/360-day basis.
30/360
If D1 falls on the 31st day of the month, D1 shall be taken equal to 30.
If D2 falls on the 31st day of the month, D2 shall be only taken equal to 30, if D1 falls on the 30th or the 31st day of the month.
30E/360
If D1 falls on the 31st day of the month, D1 shall be taken equal to 30.
If D2 falls on the 31st day of the month, D2 shall be taken equal to 30.
30E+/360
If D1 falls on the 31st day of the month, D1 shall be taken equal to 30.
If D2 falls on the 31st day of the month, D2 shall be taken equal to 1, and М2 shall be increased by 1.
The Formula for Calculating Yield on Non-Coupon Bonds
Y — yield to redemption, % per annum
P — price of the bond, % of the nominal value
t — the number of days from the current date to the date of maturity
The Formulas for Calculating the ACI and Yield to Redemption for Coupon Bonds
Formula for Calculating ACI (Version 1)
Formula for Calculating ACI (Version 2)
Formula for Calculating Yield
P — bond price in rubles
A — accumulated coupon income
m — current coupon period
n — the number of coupon periods
С i — amount of the i-th coupon in rubles
t i — the number of days before the payment of the i-th coupon
t — the number of days before redemption of the bond
N — nominal value of the bond in rubles
Y — effective yield to redemption
YearBasis — year basis (the number of days in the year)
C — coupon rate for the coupon period in rubles
t С — the number of days before the date of the coupon payment
T С — date of the coupon payment
T 0 — starting date of the coupon period
The Formula for Calculating the Yield on Bonds for which the ACI is Calculated Using a Currency Coefficient
P C — foreign currency equivalent of the bond price
P — bond price in rubles as of the date of purchase
N — nominal value of the bond in rubles
C i — annual interest rate of the i-th coupon
A — accumulated coupon income in rubles
a — foreign currency equivalent of the accumulated coupon income
T i — ending date of the coupon period
T i-1 — starting date of the coupon period
T C — date of purchase \ sale transaction
T n — redemption date of the bond
n — the number of coupons
m — current coupon period
R 0, R С — RUB \ USD exchange rates calculated in accordance with the rules established for the security
YearBasis — year basis (the number of days in the year)
The Formula for Calculating the Yield on Bonds for which the ACI is Calculated Taking into Account the Refinance Rate
S n — refinance rate effective at the time of concluding the transaction, % per annum
x — coefficient established by the issuer, for example, 0.85
m — divisor, usually equal to the annual number of coupons
P — bond price in rubles
N — nominal value of the bond in rubles
T — the number of days before redemption
A — ACI in rubles
S 1 — the first of the refinance rates having been effective during the current coupon period, %
T 1 — the number of days that the first refinance rate in the current coupon period is effective
S i — the i-th refinance rate effective during the current coupon period, %
T i — the number of days of the i-th refinance rate in the current coupon period
S n — current refinance rate
T n — the number of days that the current refinance rate is effective
YearBasis — year basis (the number of days in the year)
The Formula for Calculating the ACI and the Yield for Coupon Bonds
(Version 1)
P — bond price in rubles
A — ACI in rubles
R — price of the nearest offer in rubles
C — nearest coupon payment in rubles
t — the number of days before the date of the nearest offer
YearBasis — year basis (the number of days in the year)
t С — the number of days before the date of the coupon payment
T С — date of the coupon payment
T 0 — starting date of the coupon period
(Version 2)
P — bond price in rubles
A — ACI in rubles
R — price of the nearest offer in rubles
C — nearest coupon payment in rubles
t — the number of days before the date of the nearest offer
T O — the number of days from the beginning of the current coupon period until the date of the nearest offer
YearBasis — year basis (the number of days in the year)
t С — the number of days to the date of the coupon payment
T С — date of the coupon payment
T 0 — starting date of the coupon period
Note: this formula is only valid where the date of the offer comes after the date of the end of the current coupon period and the value of the coupon payment for the coupon period on which the date of the offer falls agrees with the current one.
(Version 3)
P — bond price in rubles
P O — price of the offer in rubles
A — accumulated coupon income
m — current coupon period
n — the number of coupon periods before the date of the offer inclusive
С i — value of the i-th coupon in rubles
t i — the number of days before the payment of the i-th coupon
t — the number of days before the date of the offer
Y — effective yield at maturity
YearBasis — year basis (the number of days in the year)
C — coupon rate in rubles for the coupon period
t С — the number of days before the date of the coupon payment
T С — date of the coupon payment
T O — starting date of the coupon period
