Determining the number of days from one date to the other date:
When calculating the accrued coupon yield and the profitability, it is necessary to calculate the number of calendar days from one date to the other date or the duration of the period determined by two dates.

Basis 365 (366)
The main basis used in the Trading System. The number of calendar days (and the period duration) from date T1 to date T2 is determined as the difference between dates: T2 - T1. For instance, from 5 January 2001 to 6 January 2001: one day (period duration - one day), while from 10 March 2002 to 20 March 2002: ten days (period duration - ten days)

Bases 30/360
The difference in days N between two dates T1 and T2 is calculated as:
N = D2 - D1 + 30 (M2 - M1) + 360 (Y2 - Y1), where
D1/M1/Y1 - date T1 (the first date)
D2/M2/Y2 - date T2 (the second date)
There are three versions of basis 30/360.

30/360
If D1 falls on the 31st, D1 changes to 30.
If D2 falls on the 31st, D2 changes to 30 only if D1 falls on the 30th or the 31st.

30E/360
If D1 falls on the 31st, D1 changes to 30.
If D2 falls on the 31st, D2 changes to 30.

30E+/360
If D1 falls on the 31st, D1 changes to 30.
If D2 falls on the 31st, D2 changes to 1 and М2 increases by one.

Calculation of profitability for noncoupon bonds

Y - yield to maturity as percentage of yearly interest
P - bond price as percentage of the face value
t - number of days from the current date to the redemption date

Calculation of the accrued coupon yield and yield to maturity for coupon bonds

P - bond price in rubles
A - accrued coupon yield
m - current coupon period
n - number of coupon periods
Сi - size of the i-th coupon in rubles
ti - number of days before payment of the i-th coupon
t - number of days before the redemption of the bond
N - ruble-denominated face value of the bond
Y - effective yield to maturity
YearBasis - year basis (number of days in the year)
C - ruble-denominated coupon rate for the coupon period
tС - number of days before the date of the coupon payment
TС - date of the coupon payment
T0 - date of the beginning of the coupon period

Profitability formula for bonds whose accrued coupon yield is calculated taking into account the foreign exchange ratio

Pc - foreign exchange equivalent of the bond price
P - ruble-denominated bond price on the day of purchase
N - ruble-denominated face value of the bond
Ci - rate of the i-th coupon as percentage of yearly interest
A - ruble-denominated accrued coupon yield
a - foreign exchange equivalent of the accrued coupon yield
Ti - date of the end of the coupon period
Ti-1 - date of the beginning of the coupon period
Tc - date of purchase/sale
Tn - date of the bonds redemption
n - number of coupons
m - current coupon period
R0, RС - exchange rates of the ruble against the US dollar, calculated by the rules determined for the security
YearBasis - year basis (number of days in the year)

Profitability formula for bonds whose accrued coupon yield is calculated taking into account the rate of refinancing

Sn - refinancing rate on the moment of transaction as percentage of yearly interest
x - coefficient set by the issuer, e.g., 0.85
m - divisor, usually the number of coupons a year
P - ruble-denominated price
N - ruble-denominated face value of the bond
T - days to maturity
A - ruble-denominated accrued coupon yield
S1 - the first of the refinancing rates which were effective during the current coupon period, as percentage
T1 - the number of days of the first refinancing rate of the current coupon period
Si - the i-th refinancing rate which was effective during the current coupon period, as percentage
Ti - the number of days of the i-th refinancing rate of the current coupon period
Sn - current refinancing rate
Tn - the number of days of the current refinancing rate
YearBasis - year basis (number of days in the year)

Calculation of the accrued coupon yield and yield to offer for coupon bonds

(1st version)

P - ruble-denominated bond price
A - ruble-denominated accrued coupon yield
R - ruble-denominated price of the nearest offer
C - ruble-denominated nearest coupon payment
t - number of days to the date of the nearest offer
YearBasis - year basis (number of days in the year)
tС - number of days to the date of the coupon payment
TС - date of the coupon payment
T0 - date of the beginning of coupon period

(2nd version)

P - ruble-denominated bond price
A - ruble-denominated accrued coupon yield
R - ruble-denominated price of the nearest offer
C - ruble-denominated size of the nearest coupon payment
t - number of days to the date of the nearest offer
TO - number of days from the beginning of the current coupon period to the date of the nearest offer
YearBasis - year basis (number of days in the year)
tС - number of days to the date of the coupon payment
TС - date of the coupon payment
T0 - date of the beginning of coupon period

Comment: this function is valid only when the date of the offer comes some time 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.

(3rd version)

P - ruble-denominated bond price
PO - ruble-denominated price of the offer
A - accrued coupon yield
m - current coupon period
n - number of coupon periods before the date of the offer inclusive
Сi - ruble-denominated size of the i-th coupon
ti - number of days before the payment of the i-th coupon
t - number of days before the date of the offer
Y - effective yield to maturity
YearBasis - year basis (number of days in the year)
C - ruble-denominated coupon rate for the coupon period
tС - number of days before the date of the coupon payment
TС - date of coupon payment
T0 - date of the beginning of the coupon period

Comment: this function is valid only when the date of the offer agrees with the date of the coupon payment.