Investors should not get too optimistic over the formation of the next German government, according to analysts, who believe the policies of the country's lawmakers still remain very vague and there is still a chance that fresh elections will be needed. The Social Democratic Party (SPD) narrowly approved the start of formal coalition talks with Angela Merkel's Christian Democrats on Sunday. This follows months of uncertainty after elections in September failed to produce an overall majority for any party. This caused a rise in stock markets on Monday morning, most notably on the German DAX, but Leopold Traugott, a policy analyst at Open Europe, told CNBC that the intentions of the next government are still far from being concrete. "In many European capitals, in particular Paris and also Brussels, people were very happy about yesterday's (Sunday) results," he said. "We have to be careful not to exaggerate in what this new government wants to achieve and can achieve. Yes, the coalition agreement as it stands so far is very pro-European, they want to reform the euro zone, a more social Europe, but it's all very vague still," Traugott warned.

A new German government is being warmly welcomed in Europe, mainly in France, due to plans to reform the euro area, which would likely not happen without German backing. The SPD agreed to work with Chancellor Merkel's party to form a new government on Sunday, but with the support of only 56.4 percent of its members. Though the majority vote allows the Socialist leader Martin Schulz to work with Merkel, it also puts him in a tricky position to convince the entire political party that he is the right leader. Schulz left the presidency of the European Parliament last year in order to battle for the German chancellery. At the time, he denied he would join another coalition with the conservatives, given that in the past this has damaged the position of the party. However, after the conservatives failed to reach an agreement with other smaller parties, Schulz found himself in a complicated situation. Also, German President Frank-Walter Steinmeier, a socialist party member, asked Schulz to reach an agreement with Merkel and avoid the need for another election.

German Chancellor and head of the German Christian Democrats (CDU) Angela Merkel during statements following all-night preliminary coalition talks on January 12, 2018 in Berlin, Germany. Steffi Loos | Getty Images

"Martin Schulz is under a lot of pressure right now," Traugott said, but "the problem is that there is not much room anymore to negotiate because most is already written down in the accord after the exploratory talks, so they will try to get a bit more on social security for example or ease up migration rules. But it will be difficult to actually get a grand bargain in the next two, three weeks of negotiations." Schulz, the SPD leader, is said to be relieved after the vote to kick off formal talks. "The coalition talks are going to be just as hard as the exploratory talks," he said on Sunday. "We will talk to the conservatives in the coming days and agree on a time frame. Then I hope that we will start negotiations soon."