Shares on the Nairobi bourse rose for the second session running, extending gains seen in the wake of the central bank action the previous day.
At market close at 1300 GMT, the shilling was quoted at 85.30/50 to the dollar, barely changed from Wednesday's close of 85.25/45.
"We expect the shilling to weaken gradually to about 85.70 on importer demand for dollars," said Julius Kiriinya, a trader at African Banking Corporation.
"Sentiment favours a weak shilling on the fact that its cheaper for importers to access credit."
Citing declining inflation and slowing economic growth, the Central Bank of Kenya (CBK) on Wednesday slashed its key lending rate by 200 basis points to 11 percent. It began easing policy in July but Wednesday's cut was less than the record 350 bps reduction in September.
Analysts say an increase in the import bill due to a hike in government spending ahead of March 2013 elections, coupled with rising oil and global food prices, could lead to an increase in imports and present downside risks to the shilling.
However, Christopher Muiga, a senior trader at Kenya Commercial Bank, said the central bank's frequent liquidity mop-ups using repurchase agreements (repos) would provide some support for the local currency.
At the Nairobi Securities Exchange, the benchmark NSE-20 Share Index rose for the second straight session, up 0.7 percent to 4,148.79 points.
The index has risen 29 percent this year, lifted by a re-allocation of assets after yields fell in the debt market and bets on firms performing better this year as interest rates drop.
"The central bank rate cut was a big boost for equities. It may close the year much higher," said Brenda Kithinji, an analyst at Standard Investment Bank.
Sugarcane grower and miller, Mumias, continued its recovery after it tumbled after going ex-dividend on Monday. It gained 1.8 percent to 5.80 shillings a share.
In the debt market, the weighted average yield on the benchmark 91-day Treasury bills rose to 10.346 percent at the auction, from 10.237 percent last week.