Method for Calculating Bond Yield and Duration

1. Government short-term zero-coupon bonds (GKO) and Bank of Russia bonds (BBR)
Annual yield until maturity at auction and secondary trading for each specific GKO or BBR is determined by the following formula:

where:
N — the nominal value of the bond;
P — the price at auction or secondary bond trading (% of the nominal value);
T — the number of days before redemption of the bond.

The average weighted period before payment (duration) of each GKO or BBR is equal to the period before the redemption of the respective issue.

2. Federal loan bonds (OFZ)
Effective annual yield until maturity for redemption at auction or secondary trading of each specific OFZ is determined by the following formula:

where:
P — the price of the bond;
A — accrued interest;
Y — effective yield until maturity;
t _i — the number of days before the payment of the i-th coupon;
C _i — the amount of the i-th coupon;
n — the number of coupons;
t _j — the period before the j-th payment of the nominal value;
N _j — the amount of the j-th payment of the nominal value;
m — the number of payments required to repay the principal.

where:
C ₁ — the amount of the closest coupon;
T ₁ — the duration of the closest coupon period (the number of days);
t ₁ — the number of days before payment of the closest coupon.

where:
N — the nominal value of the bond / the outstanding portion of the nominal value of the bond;
r _i — the coupon interest rate;
T _i — the duration of the coupon period (the number of days).

For calculating yield on federal loan bonds with variable coupon yield (OFZ-PK), the rates for unspecified coupons are equal to the last known rate for that respective issue.

The average weighted period before payment (duration) for OFZ is calculated with the following formula:

where:
Y — effective yield until maturity;
t _i — the number of days before payment of the i-th coupon;
C _i — the amount of the i-th coupon;
n — the number of coupons;
t _j — the period before the j-th payment of the nominal value;
N _j — the amount of the j-th payment of the nominal value of the bond;
m — the number of payments required to repay the principal.

The price, yield, and duration of any outstanding government federal bond may be calculated with the help of the financial calculator