Stocks gained broadly on Friday, with the dollar-traded RTS index up 1.3 percent at 1,406.43 points and the rouble-denominated MICEX up 1.0 percent at 1,434.44 points.
Sberbank rose 4.0 percent, reflecting index-trackers' need to reflect a hike of 2.5 percentage points to 14.4 percent in the weight of its shares in the Russia MSCI index, expected to take place today.
Shares in oil company TNK-BP gained 3.6 percent after Rosneft , Russia's biggest oil company, said it should sign a binding agreement next month to buy half of the company from the AAR consortium of Soviet-born tycoons for $28 billion.
Russia's second-largest telecoms operator MegaFon was up 2.7 percent in London and 4.0 percent in Moscow, tracking gains in US telecom futures on Friday and continuing their rebound after a disappointing debut on the London Stock Exchange earlier this week.
Risk aversion towards Russian assets has been subsiding recently. EPFR Global fund tracking data showed outflows of $4 million, the lowest in two months, from Russia-dedicated funds for the week through Wednesday.
"While emerging markets continue to attract new capital, Russia remains on the sidelines until economic growth gathers pace in the second quarter of '13, in our view," analysts at Uralsib wrote in a note.
"Meanwhile, we expect no large outflows until then."
Russia's MICEX index ended the second consecutive month in the red, down 1.2 percent, while the RTS was down 0.2 percent.
Investors favoured Russian debt in November, ahead of the much anticipated liberalisation of the market due early next year, and as weaker economic growth figures played down expectations of the monetary policy tightening.
Russia's 10-year treasury bonds rallied 45 basis points over the month .
"OFZ yields on Thursday declined 10-15 basis points across the curve. The major factor driving this appreciation was international investor demand and a lack of inventories held by local market makers," analysts at VTB Capital wrote in a note.
The yield on Russia's benchmark 2030 Eurobond tightened by 13 basis points in November to 2.78 percent.
At 1402 GMT, the rouble was down 0.3 percent on the day at 30.93 versus the dollar, and was down 0.2 percent against the euro at 40.14 The rouble shed 0.2 percent to 35.07 against the dollar-euro basket the central bank uses to guide the rouble's nominal exchange rate.
The end of the monthly tax period slowed the rouble's recent rally on Friday, but the currency was poised to record weekly gains that have brought it back to levels against the dollar not seen since mid-October.
Companies have finished paying monthly taxes, which has resulted in lower demand for the rouble from exporters who needed to convert their foreign currency earnings into the Russian currency.
Crude prices, a major source of corporate and state revenues in Russia, remained at comfortable levels for Russia, with Brent crude creeping up above $111 a barrel.
Analysts polled by Reuters in November expected the rouble to end 2012 at 31.50 against the dollar and 35.50 against the basket.