"In the short term there is probably further to run particularly with a weaker yen and slightly improving numbers on the inflation front, but beyond that we are going to need to see a real adjustment in terms of inflation expectations which we haven't seen yet," said Konyn.
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Japan's financial markets have seen a turnaround this year, ever since Prime Minister Shinzo Abe launched his ambitious late last year to haul the economy out of an over a decade long period of deflation. His plan, which involves aggressive easing, fiscal stimulus and structural reform has helped power stocks over 51 percent higher year-to-date, while the yen has weakened around 19 percent against the dollar.
But Konyn added that investors needed to remember that the Bank of Japan did not have limitless means to prop up the economy.
"We're going to need to see wage inflation over the next six months, because if you look at the Bank of Japan and its ability to keep on expanding its balance sheet, it's going to run out of powder within the next six to seven months before it reaches limits where it isn't able to go any further, so we really need to see those expectations change," he added.
Meanwhile David Roche, global strategist at Independent Strategy, also told CNBC he was also concerned about Abenomics working out in the long term.
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"It [Abenomics] will run out of steam by next May because it won't deliver on supply side reforms," he said.
"Without the market reforms, there is no miracle in Japan and the market will wake up to this when the consumer has finished spending ahead of the consumer tax price increase in May and then the whole thing will fall back," he added, referring to the upcoming hike in sales tax to 8 percent from 5 percent scheduled for April.
— By CNBC's Katie Holliday: Follow her on Twitter