Speaking at a panel on systemic risk at the Milken Institute Global Conference, Williams said the biggest systemic financial risk currently is the possibility that "broad sets of assets are going to see big movements downward" as interest rates rise. "That's an area that I think is a potential risk.”

The recent sell-off in global equity markets, along with increases in risk spreads in corporate bond markets, may have made [the risk of asset-price bubbles] less of a concern over the medium term.

If asset prices across the economy -- that is, taking all financial markets into account -- are thought to be excessively high, raising the interest rate may be the appropriate step.

Taken together, the economic data generally point to an economy that is moving in the right direction and has consistently sustained growth over the past five years. This is not to say the economy is issue-free… Unfortunately, although we might wish it so, monetary policy is not the proper tool to address all of these issues. The aggressive monetary actions over the past few years were intended to support economic activity, help labor markets heal and move inflation toward the Fed’s target. I view the considerable progress in labor markets and the relatively steady inflation rate as encouraging. However, keeping interest rates near zero to achieve still further progress toward labor market improvement and higher inflation is risky in my view. In a protracted period of exceptionally low rates, investors seeking out higher returns are willing to take on more risk or seek out more creative financing approaches. When the economy is expanding and rates remain low, adverse events may appear less likely or far into the future, potentially resulting in the mispricing of risk and financial assets. Waiting too long to adjust rates, as we’ve seen in the past, can leave policymakers with few and possibly poor options. … The FOMC has been talking about its exit strategy since 2011. And since March of this year, the Committee has been emphasizing that a decision to raise interest rates would be data dependent. In other words, economic data that confirms further gains in the economy’s performance will drive the timing of the Committee’s actions. So, why hasn’t the FOMC yet raised rates? There are of course different views on the economic data we receive and analyze that lead to legitimate, differing views about what is best for the economy… The continued improvement in the labor market, combined with low and stable inflation, convince me that modestly higher short-term interest rates are appropriate. Current guideposts, or “policy rules,” often used to inform monetary policy decisions also have been signaling that interest rates should be higher. I recognize that a rate increase, however, would be the first one in nearly a decade. So I am not suggesting rates should be normalized quickly or that policy should be tight. Although the economy has improved, economic fundamentals could well mean an accommodative stance of policy is appropriate for some time. I would like to avoid the cost of waiting for more evidence and further postponing liftoff, drawing on a valuable lesson from monetary policy decisions in 2003.

St. Louis Federal Reserve Bank President James Bullard warned Tuesday that low interest rates may be feeding a new asset price bubble.

Bullard said he is open to weighing evidence that conditions are different than in the late 1990s when the stock market went through a high-tech "dot.com bubble," but said it appears to him that stock valuations, particularly in the tech-heavy Nasdaq Composite index are high.

Bullard cited a number of what he considers danger signs of a possible stock bubble and asked "do low interest rates feed this process?"

"The net wealth to disposable income ratio has returned to a high level," he observed in remarks prepared for delivery to an Emerging Venture Leaders Summit. "It has been high and volatile since the mid-1990s."

He also said the Nasdaq is "near a high in real terms" and "the price-earnings ratio is relatively high but still below the 1990s peak."

"Can the U.S. escape the boom-bust cycle this time?"

Answering his own question, Bullard said, "My view is that low interest rates tend to feed bubble processes."

Bullard, who will be a voting member of the Fed's policymaking Federal Open Market Committee next year, said "the Fed should hedge against the possibility of a third major macroeconomic bubble in the coming years by shading interest rates somewhat higher than otherwise.

"The benefit would be a longer, more stable economic expansion," he added.

Ms. Yellen said in May that “equity-market valuations at this point generally are quite high.” Mr. Powell on Tuesday said overall equity values are “certainly higher than normal” but that he doesn’t see evidence of “bubblelike conditions” in valuations or a buildup of risk-taking and leverage in financial markets.

I wouldn’t use the term stretched. I would say PEs are high, I am not particularly troubled at the level of equity values overall. They are certainly higher than normal. But I mean in a world were financial market assets are expected to give low returns PE should be high. So I don’t make predictions, especially about the future, when it comes to the stock market.

HILSENRATH: There are many critics of the FED, some of whom say that the FED is causing another bubble in areas such as stock valuations, what do you say to them?

POWELL: I just don’t see it. I would love to be Paul Revere and be the one who sees the next financial crisis. Everyone would right? I don’t see it. I don’t see the build up of leverage, I don’t see valuations. There are some measures of equity values that will say it is really high, particularly cyclically adjusted PEs, that is the way you see people cite.

But if you look at the range of valuation, and particularly the gap between the risk free rate -- or bond market returns and expected equity returns you don’t see bubble like conditions. What you really don’t see though is the build up of risk taking, the build up of leverage in the financial markets. And the build up in things that really have been crucial to financial crises like housing values. And you don’t see huge aggregate credit growth. You just don’t see the factors that lead to a financial crisis.

Recalling the tech bubble in the 1990s and the housing bubble of the 2000s, he said: "Zero [interest rates] is too low in that kind of environment. I wouldnt be comfortable with that. A zero rate would feed into an asset price bubble".

"When asset bubbles start, they keep going until they blow up out of control with devastating consequences." [Financial Times]

In addition to our monetary policy responsibilities, the Federal Reserve works to promote financial stability, focusing on identifying and monitoring vulnerabilities in the financial system and taking actions to reduce them. In this regard, the committee recognizes that an extended period of low interest rates has the potential induce investors to reach for yield by taking on increased leverage, duration risk, or credit risk. Some reach for yield behavior may be evident, for example, in the lower-rated corporate debt markets where issuance of syndicated leverage loans and high-yield bonds has continued to expand briskly, spreads have continued to narrow, and underwriting standards have loosened further. While some financial intermediaries have increased their exposure to duration and credit risk recently, these increases appear modest to date, particularly at the largest banks and life insurers. More generally, valuations for the equity market as a whole and other broad categories of assets, such as residential real estate, remain within historical norms. In addition, bank holding companies have improved their liquidity positions and raised capital ratios to levels significantly higher than prior to the financial crisis. For the financial sector more broadly, leverage remains subdued and measures of short-term funding continue to be far below levels seen before the financial crisis. ... So, we can't detect within any certainty whether or not there's an asset bubble. But we can look at a variety of different valuation metrics akin to price-earnings ratios and the stock market; a variety of ways of measuring those. And we can look to see how valuations in that sense moved out of historically normal ranges. And I would say for the equity market as a whole, the answer is that valuations are in historically normal ranges. Now, interest rates, long-term interest rates are low and that is one of the factors that feeds into equity market valuations. So, there is that linkage. So, there are pockets where we could potentially see misvaluations in smaller-cap stocks, but overall those broad metrics don't suggest that we are in obviously bubble territory. But, you know, we don't have targets for equity prices and can't -- can't detect if we're in a bubble with -- with certainty.

I mean, stock prices have risen pretty robustly, but I think that if you look at traditional valuation measures, the kind of things that we monitor, akin to price-equity ratios, you would not see stock prices in territory that suggests bubblelike conditions. When we look at a measure of what's called the equity risk premium, which is the differential between the expected return on stocks and safe assets like bonds, that premium is not -- is somewhat elevated historically, which again suggests valuations that are not in bubble territory.

We do have to take account of what's happening in the markets, what impact market conditions are likely to have on spending and the economic outlook. So it is the case, and we highlighted this in our statement, when we saw a big jump in rates -- a jump that was greater than we would have anticipated from the statements that we made in May and June -- and particularly saw mortgage interest rates rise in the space of a few months by over a hundred basis points, we had to ask ourselves whether or not that tightening of conditions in a sector where we were seeing a recovery and a recovery that could really -- recovery in housing that could drive a broader recovery in the economy -- we did have to ask ourselves whether or not that could potentially threaten what we were trying to achieve.

In short, the recent crisis has underscored the need both to strengthen our monetary policy and financial stability frameworks and to better integrate the two. We have made progress on both counts, but more needs to be done. In particular, the complementarities among regulatory and supervisory policies (including macroprudential policy), lender-of-last-resort policy, and standard monetary policy are increasingly evident. Both research and experience are needed to help the Fed and other central banks develop comprehensive frameworks that incorporate all of these elements. The broader conclusion is what might be described as the overriding lesson of the Federal Reserve's history: that central banking doctrine and practice are never static.

MCKEE: Over the next five years, two of your researchers recently published a paper suggesting investors can expect abnormally high excess returns on the S&P. Do you agree with their conclusion?

DUDLEY: I learned not to follow forecasts of the stock market.

MCKEE: They base that on the current equity risk premium, which was 5.4 percent as of December, a record high. Does that concern you?

DUDLEY: Well, the equity risk premium is as high as it is because, one, PE ratios aren't that high. So if we take the price-earnings ratio of the stock market, it's around 16, 17. So you flip that to get the E-to-P ratio. It's around 6 percent. And you compared that to real interest rates. TIPS yields are negative. So that equity risk premium, that difference between the two is very, very wide. So that would argue that the stock market isn't grossly overvalued, but there are other ways of looking at it.

If you talk to Bob Shiller, who's a very respected academic who's looked at the stock market, you look at the stock market relative to the trailing 10-year earnings, the stock market actually looks quite expensive. So it really depends on what framework you use to evaluate the stock market.

Responding to a question after the speech, Yellen said that the Fed is “We are certainly not targeting equity prices,” yet at the same time, “we would expect any action that we take that’s providing additional accommodation to show up in supporting the stock market.”

“I know that some people are concerned that exuberance is coming back a little too quickly in certain market segments,” though supervisors have a “stronger eye” on some prices, Evans said in response to audience questions.

“I’m hard pressed to second guess the market pricing mechanism” for such assets, he said.