Williamson said the bottom might not have been reached.
"Until there's a medium to long-term solution to those [sovereign debt] issues then the market is likely to remain volatile," he said.
Williamson said "bargain hunters" had come into the NZX this morning, buying stocks that have seen big devaluations since late last week.
"There is certainly a fair amount of retail investors coming back into the market place," he said.
Williamson said the local market would focus on the performance of the Australian stock market after it opened at 12pm (NZ time).
"Initially [the ASX] will rally, but because it already forecast [yesterday] what was going to happen in the states [the Fed's announcement] it's not going to be as significant as our market's rally," he said.
The ASX rallied late in the day yesterday, closing up 1.22 per cent after falling by as much as 5.66 per cent during morning trading.
Williamson said some selling could take place on the NZX this afternoon if the ASX sees a fall.
In the US, the Standard & Poor's 500 Index posted its best day in more than two years, following a drop of nearly 17 per cent over the past weeks.
The Fed's guaranteed of super-low interest rates for two more was an unprecedented step to arrest the alarming decline of the stock market and the economy. Wall Street roared its approval.
The rally was remarkably fast and enough to erase two-thirds of the decline the day before.
The central bank also left open the possibility of a third round of bond purchases designed to hold interest rates down and push stock prices up.
The yield on the 10-year Treasury bond briefly hit a record low, 2.03 per cent, and low interest rates for two more years could make the stock market a better bet because bonds will return less money. That appeared to be at least part of the reason stocks rallied so much after investors had a chance to digest the Fed's statement.
The Dow Jones industrial average gained 4 per cent to end at 11,239.77, the Standard & Poor's 500 Index rose 4.7 per cent to 1172.53, and the Nasdaq Composite Index added 5.3 per cent to 2482.52.
with NZPA