* The CEO of Europe's fourth largest pension fund steps down
* He was criticised for tax schemes at Nordea from 2005-2008
* Several politicians said Hyldahl was not right CEO for ATP (Adds quotes, details, background)
COPENHAGEN, Nov 26 (Reuters) - The chief executive of Danish pension fund ATP has decided to step down following criticism of the tax policies at a banking business when he was at the helm around a decade ago.
ATP is Europe's fourth largest pension fund with around $120 billion of assets under management and handles mandatory pensions for more than 5 million Danes.
Christian Hyldahl said he had decided to resign because he had lost the confidence of stakeholders in ATP and "I must draw the conclusion that this will not change."
"At the same time, there is an increasing risk that the reputation of ATP will suffer which should be avoided on any account," he added in a statement issued by ATP. He declined to comment further.
The focus on tax treatment has intensified in Denmark after a money laundering scandal involving its largest lender Danske Bank and a wider European dividend stripping scandal.
Five political parties, representing 43 percent of the seats in parliament and including two of the coalition government's three parties, had prior to Monday's announcement said they did not think Hyldahl was the right CEO.
A division of Nordea bank has been criticised in the Danish media for trading schemes from 2005-2008 that included buying shares in Swiss francs from Swiss investors shortly before the annual dividend was paid out, and selling them back shortly after.
Under a tax agreement between Denmark and Switzerland the division, Nordea Markets, was able to get the divided tax it had paid refunded, unlike the Swiss nationals who held the shares for the rest of the time.
Hyldahl was managing director, co-head of markets, at Nordea Markets from 2005 to 2007, and chief investment officer, head of investments, at Nordea Asset Management from 2007 to 2011.
Hyldahl and Nordea Markets have not been accused of any unlawful activity.
Hyldahl had previously defended the trades as "decent", but last week told online media Finans: "Today, I think it was wrong that we entered that kind of trades".
As CEO of ATP, Hyldahl has mostly been known for pushing companies for better corporate governance and for introducing random checks on business partners to avoid being entangled in tax avoidance.
A temporary CEO will be named as soon as possible, ATP said.
"I certainly hope that ATP's board have learned from this. My confidence in the Danish financial sector and in ATP is very small now, and I think a lot of Danes feel that way," left-wing lawmaker Finn Sorensen told Reuters.
As a self-owned entity, ATP is not under direct political control, but not immune to political pressure either as its board members, who are nominated by employers' associations and labour unions, are appointed by the employment minister.
ATP's board has been "highly satisfied" with Hyldahl, chairman professor Torben M. Andersen said in the announcement.
"But at the same time, I have great understanding and respect for the decision Christian has made," Andersen said. He was not immediately available for further comment. (Reporting by Teis Jensen, Editing by Edmund Blair and Mark Potter)