Are markets at risk of 1999-style Fed bubble?

Watch out, US market correction coming: Pro

As the continued rise in U.S. stocks to record highs has led to some speculation about the formation of a market bubble, analysts told CNBC that investors are not appreciating the full risk of another 1999-style bubble.

This week the S&P 500 and the both surged to record highs of 1,775.22 and 15,721 respectively. The two global benchmarks closed slightly lower on Wednesday, however, following slightly less dovish than expected comments from the Federal Reserve.

According to Michael Gayed, chief investment strategist at investment advisers Pension Partners, the healthy performance seen this year has been purely driven by the Fed's expansive quantitative easing (QE) program, rather than valuations, a sure sign of the potential for a correction.

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"You are seeing fairly sizable inflows into equities – the most since 2000, yet inflation expectations are still not trending up... [It] now appears to be the start of a potential bubble given how far U.S. equities have diverged from the underlying economy, inflation expectations and the overall reality of where we are in the economic cycle," he said.

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"This is really a big, big problem that is being under-appreciated," he added.

Gayed drew parallels with the market environment seen in the late 1990s, when huge appetite for internet-based stocks led to massive gains for U.S. indices and their eventual crash in 2000, broadly known as the bubble.

A similar trend is emerging in U.S. stock markets today, he said, due to the Fed's huge monetary stimulus program, which has pumped $2.8 trillion into the U.S. economy since late 2008. But rather than stimulate the economy, the flow of easy money has instead stimulated the stock market.

"[As a result] they are risking the embarrassment of another 1999 Fed induced/liquidity induced bubble," he added.

(Read more: Taper tease? Market worries Fed will end easing)

The Pension Partners' chief investment strategist highlighted a number of warning signs that a bubble could be forming in the U.S. stock market, including the recent poor performance of U.S. small caps, strong appetite for defensive sectors and the fact that bond yields were not rising in a way "that suggests the stock market is right about the future."

"Big [corrections] in stock market... are preceded by complacency, the illusion of stability, leverage and a sense of entitlement," he added.

However, Gayed also told CNBC that the Fed's "power of words" which has been demonstrated by the huge impact its use of the word 'taper' has had on markets could give the central bank the ability to prevent a severe correction.

"Just by introducing the word 'taper' yields spike. Maybe they can use a few words here and there to just calm the stock market down," he said.

Gayed's concerns echo a number of industry commentators who have recently started to warn of a bubble forming in U.S. stocks.

(Read more: For the Fed, 'bubble' talk may top 'taper' talk)

Larry Fink, CEO of Blackrock, the world's largest money manager, warned this week that the Fed's quantitative easing policy was leading to the formation of market bubbles and advised the central bank to start tapering immediately.

Meanwhile Robert Heller, former Governor at the Fed from 1986 to 1989, told CNBC on Thursday that markets were "perilously close" to the formation of a bubble.

The S&P 500 and the Dow Jones have risen 24.5 percent and nearly 20 percent, respectively, year to date.

—By CNBC's Katie Holliday; Follow her on twitter @hollidaykatie