A deal in May when Greece agreed to more austerity measures raised hopes of possible debt relief for a country that has endured economic hardship for years, resulting in the longest winning streak for the Athens bourse in more than two decades.
Greek stocks have had at least one false dawn since the country's first EU/IMF bailout in 2010 - the market rose in 2012-14 only to fall back - and on Monday, the creditors failed to reach a deal after eight hours of talks, dashing hopes of an immediate breakthrough.
Nevertheless, expectations are growing that Greece can eventually win additional relief on a debt mountain that is forecast to reach 319 billion euros (£275.3 billion), or 176 percent of its annual economic output, this year.
"With Greece we've learned to be patient... but the direction of travel is clear," said Christopher Colunga, who helps manage an emerging European equities fund for BlackRock.
"With most of the negotiations thus far the agreement is always reached two minutes past midnight. Everybody waits, not just the Greeks," said Colunga, who routinely travels from London to Athens to test the outlook of its Greek investments.
His 1 billion euro Emerging Europe fund has been an early mover into the euro zone country, having built the bulk of its position at the end of 2015. It raised its Greek exposure to 7.1 percent of the fund in April.
In the past decade, the benchmark Athens stock index <.ATG> has dived from well over 5,000 points to around 780 now. The bourse remains cheap because of the risk that the debt talks will collapse, a prospect that would bring economic chaos and raise the spectre of an exit from the euro zone - something that the country only narrowly averted in 2015.
Those risks have kept many investors on the sidelines. Big funds such as BlackRock, Fidelity Investments and Vanguard have already established footholds with stakes in stocks such as National Bank of Greece (>> National Bank of Greece) and gambling firm OPAP (>> Greek Orgnstn of Football Prognostics SA), but Athens remains a frontier market.
"Greece is still considered something difficult to grasp: it's not the bread and butter of the traditional big money managers; it's about special situation hedge funds looking for abnormal returns for their portfolio," said Nick Koskoletos, head of equity research at Eurobank Equities in Athens.
Yet signs are growing that other money managers are starting to count on a deal to make Greek debt sustainable. That could also unlock sorely needed investment and bring back more savings that fled abroad before Athens imposed capital controls at the height of the 2015 crisis.
The controls have since been relaxed and two-thirds of the money that has left Greek stocks since the end of 2007 has returned. Flows into Greek equity funds – a proxy for investor sentiment – topped $20 million in each of the past two weeks, the highest levels since mid-2015, according to fund tracker EPFR Global.
After being ignored for the last seven years Greece has also attracted some foreign direct investment in recent months, with Germany's Fraport (>> Fraport AG Frankfurt Arprt Svcs Wrldwde) taking control of local airports and Italy buying the national railway company.
Local brokers highlight that volumes on the Athens bourse doubled in May from the shallow levels where they have been stuck for nearly two years, with investors targeting banks and blue chips like Hellenic Telecom (>> HELLENIC TELECOM. ORGANIZATION S.A.), refiner Motor Oil (>> Motor Oil (Hellas) Corinth Refineries SA) and toy retailer Jumbo (>> Jumbo S.A.).
"A lot of people are looking at Greece and all wait for a political solution. Money's going to come in for sure if there's one," said Rudolf Bohli, head of Swiss hedge fund RBR Capital.
Bohli invested a sum in the double-digit millions of euros in Greek bank stocks, lured by "ridiculous" low valuations and an economic recovery - private sector forecasters see growth this year at 1.5-1.7 percent after a slight drop in GDP in 2016.
On top of this, Bohli said bad loans are being tackled and the Greek banks - which have undergone three waves of recapitalisation with bailout and private cash since 2012 - looked more efficient, for example, than Italian lenders.
"We like Piraeus and Eurobank," he said.
As hopes first rose earlier in May that a more comprehensive debt deal could be within reach, the Athens stock exchange scored 13 positive sessions in a row and bond yields plummeted.
Yet Greek debt still carries a high premium, with 10-year bonds yielding around 6 percent. Eurobank's Koskoletos estimates that if the country's yields align to those in other peripheral euro zone countries such as Portugal, that would unleash a 20-30 percent upside potential for stocks.
Add to that positive surprises on the macro economic front, with Greece beating budget surplus targets and set to deliver growth this year under Prime Minister Alexis Tsipras, then the Greek investment case gets stronger.
"What we've seen so far are only the early stages of what could happen to the Greek market," said BlackRock's Colunga.
(Reporting by Danilo Masoni; Editing by David Stamp)
By Danilo Masoni