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The Methodology of Calculation of Indices and Indicators
MICEX calculates indices of Russian government bonds (the Indices) and indicators of the yield of Russian government bonds (the Yield Indicators). The Indices and the Yield Indicators serve as measures of price movements in government bonds (GKO-OFZ) market.
The Indices reflect changes in the market value of government bonds and include:
- the Russian Government Bond Index (RGBI), calculated as clean price index;
- the Russian Government Bond Index - gross (RGBI-g), calculated as gross price index;
- the Russian Government Bond Index - total return (RGBI-tr), calculated as total return index.
The initial values of the Indices are taken as 100 points (31 December 2002).
The Indices are calculated continuously in real-time mode as appropriate deals with bonds, comprising the calculation base of the Indices, are carried out. Only prices which are used to calculate the average weighted prices are taken into account.
The Yield Indicators are government bonds' redemption yields, weighted by market value. The Yield Indicators include:
- the Russian Government Bond Effective Yield (RGBEY); and
- the Russian Government Bond Gross Redemption Yield (RGBY), calculated by the average gross redemption yield methodology.
The Yield Indicators are calculated once a day, at the closing of trades, on the basis of average weighted prices and yields at average weighted price of bond issues comprising the calculation base of the Yield Indicators. Calculation Formulae:
1. The Russian Government Bond Index (RGBI):
2. The Russian Government Bond Index - gross (RGBI-g):
, where
3. The Russian Government Bond Index - total return (RGBI-tr):
4. The Russian Government Bond Effective Yield (RGBEY):
5. The Russian Government Bond Gross Redemption Yield (RGBY):
When index values (points 1-3) are calculated on the first trading day monthly, a new index calculation base is used in the numerator and in the denominator.
Notation:
Pi,t - average weighted price of the i-th bond at time (day) t, in rubles;
Ai,t accrued interest of the i-th bond on day t, in rubles;
Ci,t - coupon yield of the i-th bond on day t, in rubles;
Ni,t-1 - outstanding amount of the i-th bond issue, determined as a result of day t-1, in units of securities;
Yi,t - redemption yield at the average weighted price of the i-th bond on day t, in interest per annum;
Di,t duration of the i-th bond on day t, in days.
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