They're calling it a market melt-up.

Shares on Wall Street's S&P 500 index have roared ahead to the strongest start since 1999 and optimism is back in vogue.

But what is a melt-up? And more importantly, can it last for long in a bull market which is nearing its nine-year anniversary.

"A melt-up is the opposite of a meltdown," says Pie Funds chief executive Mike Taylor.

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"It's when shares go up at a rapid pace and it's unexpected. That's exactly what's happened since late last year and moving into this year - they are literally melting up."

The melt-up concept, while relatively new, is gaining traction with financial commentators around the world as they seek to explain why such a highly valued market has continued to soar.

"Are You Missing Out on the Great Market Melt-Up?," read the Bloomberg headline.

"New year's global stock market 'melt-up' silences bears", said the Financial Times.

"The collapse in global output volatility to 60-year lows is providing a further boost to economic activity and equities," Gabriel Sterne, chief macro strategist at Oxford Economics, told Bloomberg this week. "So we think 2018 is the year of melt-up rather than meltdown."

However, a melt-up typically comes with the built-in implication that it will be followed by a meltdown.

Some argue that this latest market surge is a kind of euphoric last hurrah for the US stock market.

The question of how long the melt-up can last is key.

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One usually bearish investor - Jeremy Grantham, founder of Boston Fund GMO - is tipping it might last for six months to two years.

Grantham is credited as one of the first to acknowledge the melt-up phenomenon in his report of January 3.

The bullish tone surprised many as Grantham is known for dodging the dot.com crash and the worst of the GFC because of his cautious outlook.

"I recognise on one hand that this is one of the highest-priced markets in US History," he wrote. "On the other hand, as a historian of the great equity bubbles, I also recognise that we are currently showing signs of entering the blow-off or melt-up phase of this very long bull market."

The head of the world's largest hedge fund - Ray Dalio of Bridgewater Associates - was quoted at the Davos World Economic Forum this week saying: "If you're holding cash, you're going to feel pretty stupid."

In other words, the caution that was emerging last year about the sustainability of the long bull run appears to be evaporating.

Dalio notes that fears that the bull run was nearing an end prompted many investors to start switching to cash last year. He argues those fears may now prove to be over-played.

"We have had a beautiful deleveraging, inflation isn't a problem, growth is good. Everything is pretty good with a big jolt of stimulus coming from the [US] changes in tax laws."

Dalio's view appears in stark contrast to that of former central banker William White - who made headlines at Davos with a warning that current market conditions looked like those prior to the GFC in 2008.

He warned of an "intoxicating optimism" taking hold.

However, Dalio is also careful to add that melt-up behaviour is classic "late-cycle behaviour".

The big risk was how the US Federal Reserve reacted and whether it put up rates fast enough to spook markets, he said.

The confidence of heavyweight investors like Dalio and Grantham is underpinned by optimism about global economic fundamentals, with markets putting a lot of store in the idea of synchronised growth across the globe.

"It is a Goldilocks scenario," said Pie Funds' Taylor.

From the IMF and World Bank to Goldman Sachs 2018, global economic forecasts are looking rosier than they have for almost a decade.

The US, Europe, China and even Japan are all expected to experience steady growth, driving optimism with equity investors.

That, hopefully, should underpin the high valuations of shares with some positive earnings growth, Taylor said.

It was true that the extremely high value of shares did make it harder for investors to allocate money, he said

The CAPE Shiller Index - which measures the average price to earnings ratio of the S&P across the decades - currently shows shares to be the most expensive they've been since the dot.com bubble in 1999/2000.

While that might look a bit ominous, it is also worth considering the difference between tech stocks now and then, Taylor said.

"Look at big tech around the world and it is not overly expensive, the last time it got expensive was 1999 when all those tech companies had no earnings. Whereas today, they do have earnings. Amazon's growing its revenue, as are the Chinese players."

It was important not to get drawn into becoming either too optimistic or too pessimistic - despite the fact that headlines were often presented that way, he said.

"So you don't fall into the trap of 'fear of missing out' and rushing from sidelines into all equities at a time when shares are expensive," Taylor said.

It was still a time when investors should be thinking about taking profits.

Interestingly, given its strong performance in the past few years, the New Zealand stock exchange had not shown signs of a melt-up this year - although it did rise sharply prior to Christmas.

In fact the NZX-50 is off by more than one per cent since its close on December 29.

That could reflect what has been going on in the US, with the dollar down and US money flowing into the big tech stocks on renewed confidence, Taylor said.

Conversely, that has meant money flowing away from the more conservative yield stocks which dominate the New Zealand market.