Barclays boss Antony Jenkins faces one of the biggest tests of his leadership this month when he decides whether the bank, Britain’s third largest, should fight accusations it deceived and defrauded customers in the US.

If Jenkins accepts the allegations, made in a lawsuit filed by New York’s Attorney General, he will face a dilemma arising from his pledge to jettison any business that does not fit into the bank’s new, squeaky-clean image.

But the US trading desk at the centre of the allegations is part of Barclays’ equities business, an area it had planned to keep largely intact while shrinking its investment bank.

It comes at a time of mounting discontent among investors. Some say that after almost two years in the CEO hot seat Jenkins is failing to turn around both culture and performance.

Barclays’ shares are down around 9 per cent, close to two-year lows, since the lawsuit was filed, compared with a 3.5 per cent fall in European bank stocks in the same period. They have also underperformed their European peers since Jenkins was appointed in 2012.

“We are concerned about some of the revenue and cost trends and the pace of management implementation,” said Colin McLean, managing director of SVM Asset Management, which owns Barclays stock. “There’s a gap between the promises and the actual delivery, particularly on costs and bonuses,” he said.

Fighting the allegations from the New York attorney general would be a high-risk gamble, as other banks have found when they have taken on the authorities. If the allegations are proven to be even partially true, Jenkins’s credibility as the man to lead Barclays out of its scandal-scarred past would be in tatters.

Investment banks’ in-house platforms for buying and selling shares, known as dark pools, are under investigation by authorities in the US and Europe amid allegations they have been used to rip off some investors.

New York Attorney General Eric Schneiderman said in his lawsuit he had evidence that Barclays staff falsified marketing material and misled big institutional clients in an effort to grow its dark pool to increase revenues and bonuses.

He said that occurred from 2011 to as recently as April, some 20 months after Jenkins took the helm, unlike other conduct issues the bank has faced, which occurred before he became CEO.

Barclays has hired external lawyers to help it investigate the allegations, including Matthew Martens, formerly the chief litigator at the US Securities and Exchange Commission. The bank has until around July 25 to decide whether or not to fight the charges.

Dark pools let institutional investors trade shares anonymously and only make trading data available afterwards, reducing the chance of information leaking about their trade orders. Trading at the venues, rather than on formal stock exchanges, has swelled since 2007, and it is estimated that more than 40 per cent of all US equities trades are executed in one of the several dozen dark pools in operation.

Barclays’ dark pool, known as LX, is the second most active alternative trading system in the US after Credit Suisse’s, according to regulatory data. Other banks with big dark pools include UBS, Bank of America, Morgan Stanley, Deutsche Bank and Goldman Sachs.

Potentially most damaging in Schneiderman’s complaint is that Barclays lied to core institutional clients, such as pension funds and insurance companies.

US asset manager Alliance Bernstein said it suspended activity with the LX dark pool after the lawsuit was filed, and more clients have pulled out, industry sources said.

Barclays has said it is conducting a full internal investigation into the allegations and had brought in outside help, but declined further comment.

Barclays grew its dark pool business aggressively from 2011, helped by a service called Liquidity Profiling.

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