Bubbles occur when investors drive prices above where a company's value should be, based on a multiple of its earnings.
During the dotcom bubble shares in technology companies soared but then crashed with some businesses collapsing altogether.
Stubbs said the low interest rate environment was driving a change in investor behaviour pushing people to invest in the sharemarket.
"People made money last year so they feel very positive, bringing over-confidence into the markets. We are starting to see the first signs of irrational exuberance."
Stubbs said they were also seeing the herd effect where investors piled into companies which already had high share prices.
"That is very common when you start to see bubbles."
Stubbs said the effect was driven by emotion.
"People think because a stock has a high price it equals high quality."
Tower equities manager Stephen Bennie said about half of the NZX50 was trading on a multiple of 15 times earnings.
He said that level of multiple usually indicated a company was high quality but that was simply not the case for all the companies.
"We have an imbalance."
Bennie warned that when reality hit, the share price of those companies could come back down giving investors a poor return.
But Mark Lister, head of research at Craigs Investment Partners, did not believe the market was headed for a bubble.
"The market has had a great run. Does it look pricey? A little. But not in a major way."
Lister said companies were upbeat about growth in their earnings and had low levels of debt.
The housing market was also starting to pick up.
"All of these fundamental indicators suggest a rally. We are not seeing a bubble."
He said the current price to earnings ratio for the NZX50 was 15.4 times but that was only 10 per cent higher than New Zealand's long-term average of 14 times.
He said he did not believe the sharemarket would be up by as much this year but he did not believe it would start falling.
Since the start of the year the NZX-50 has continued to rise and was up 2.9 per cent as of yesterday's market close.
Hamilton Hindin Green client adviser James Smalley said the market had continued its strong run so far this year and he did not see any signs of a bubble.
Smalley said three factors typically pointed to a bubble - price to earnings ratios well above the historic average, dividend yields that were similar to what savers could get in the bank and a raft of new public listings of poor quality.
"I certainly don't see that happening in this market. What I see is a reflection of the low interest rate environment."
He said investors should look to the earnings season next month where some companies would be asked to justify their strong share price growth and there should be more guidance on where company earnings were going.