NEW YORK (CNN/Money) - In what could be one of his last appearances on Capitol Hill, Federal Reserve Chairman Alan Greenspan admitted even he doesn't know everything.

The chairman, who was asked his opinion on a wide range of economic and policy issues during testimony before the Senate Banking Committee, spent much of his time expressing concerns about the large portfolios of mortgage securities held by Fannie Mae (Research) and Freddie Mac (Research). Greenspan and the White House have called for reductions in those portfolios for more than a year, and Congress is now weighing such limits.

Asked by Sen. Jim Bunning, R-Ky., why Greenspan only raised those concerns relatively recently even though those portfolios grew throughout much of the 1990s, Greenspan conceded it had taken him some time to understand the company's complicated structures, and the risks to the companies and the nation's financial systems posed by the concentration of mortgages in their holdings.

"It's taken me quite a good bit of time to disentangle the complex structure," he said. "I didn't fully understand when I first looked at them.

"It's only fairly recently that it finally became clear to me," he added. "It was a revelation in certain respects."

Shares of both Freddie and Fannie were down more than 1 percent during Greenspan's late-morning testimony.

Greenspan's testimony is the second-half of his two-day appearance on the hill, following Wednesday's testimony before the House Financial Services committee. Thursday he repeated that the economy is generally strong, but warned about the risks posed by of a run-up in housing and fuel prices.

Greenspan disputed claims that Fannie and Freddie's mortgage holdings provide the mortgage finance firms and the overall real estate market with liquidity, as critics of such limits have argued. So Greenspan said such limits on portfolios should not hurt the nation's housing markets.

"The motive for accumulating portfolios is solely, essentially in all respects, profit making," Greenspan said. "I have no objection to that. Indeed they are profit-making organizations. But that is not adding liquidity to the housing market nor, in our judgment, is it assisting the market generally."

He also would not rule out the Fed continuing its course of hiking interest rates even if short-term interest rates become higher than long-term interest rates. That economic condition, known as an inverted yield curve, is generally seen as a indication of a coming recession.

Greenspan argued that an inverted yield curve was not as good an indicator of a recession as it had been in the past. But he said if there was an inverted yield curve, it would be a consideration for the Fed when weighing interest rates.

"Even though its efficacy as predictor is greatly diminished, it's not zero," he said.

Bond prices fell and yields on the 10-year treasury, which moves in the opposite direction, rose, on those comments by Greenspan.

Greenspan gives semi-annual testimony to Congress on the state of the economy. His term as Fed chairman is set to end Jan. 31, so Thursday might have been the last time he made such an appearance.

His statements and answers, while closely watched by investors, are often dense and difficult to dissect, and some senators made reference to that fact during Thursday's committee meeting.

"This is the 35th time you have appeared before a committee that I sit on," said Bunning, among Greenspan's harshest Congressional critics, in his opening remarks. "I think I'm finally beginning to understand your statements and answers, which probably means it's time for one of us to go."

At the end of the session, Sen. Charles Schumer, D-N.Y., was asking Greenspan his opinion on whether the estate tax should be permanently repealed if it meant an increase in the federal deficit.

Greenspan started to qualify his answer and Schumer asked him to give a clear yes or no.

"You mean I'm going to become perfectly clear my last time here?" Greenspan responded with a slight chuckle.

To read more about Greenspan's warnings to the House about housing and fuel prices, click here.