The market has given a mixed response to banks’ half-year results this week. Virgin Money was applauded with an 8.7% rise on Tuesday. Fellow UK ‘challenger’ banks Metro and Shawbrook had their shares pushed up 7.8% and 5.1%, respectively on Wednesday, while international player Santander gained a more modest 2.5% on the same day. Then, yesterday, Lloyds was given a big thumbs down, its shares tumbling 5.8%.

Barclays (LSE: BARC) stepped up to the plate this morning, and the market likes what it sees, driving the shares up over 5.8% in early trading.

Core and non-core

Group pre-tax profit for the first half of the year fell 21% to £2.06bn from £2.6bn. Performance was held back by the Non-Core unit, the run-down of which has been accelerated since the arrival of chief executive Jes Staley in December. So, while pre-tax profit in the Core business advanced 19% to £3.97bn from £3.35bn, Non-Core losses widened to £1.9bn from £0.75bn.

Core return on tangible equity (RoTE) was a healthy 12.5%, with Barclays UK delivering 19.4% and Corporate & International 10.7%. Group RoTE was dragged down to 4.8% by Non-Core.

As Staley said, the Core performance demonstrates “the already high quality franchises at the centre of the future of this Group. Non-Core rundown — the key to unlocking the full earnings power of that Core — has good momentum, and we remain committed to closing the unit in 2017.” He added that he sees no reason to “adjust [the bank’s strategy], or the pace of delivery, in light of the vote by the UK last month to exit the EU.”

Improving outlook

I believe the outlook for Barclays is improving under the new chief executive. Taking the short-term pain of the accelerated run-down of Non-Core is a no-nonsense move that bodes well for the longer-term future. Fines and compensation for past misconduct have also yet to work through — for example, the bank announced a further £400m provision for Payment Protection Insurance redress — but again this should now be a relatively short-term drag.

Staley has made some bold decisions during his short time at the helm, and some unpopular ones — notably slashing the dividend in half earlier this year — but I see a man intent on getting Barclays back to full health in the shortest time possible. There were plenty of encouraging indicators in today’s results, including the common equity tier 1 ratio a little ahead of consensus expectations at 11.6% and the cost-to-income ratio in the Core business improving to 58% from 65%.

The chief executive has shown his confidence in his own abilities and in the future of Barclays by making multi-million-pound share purchases since joining — and at higher prices than today’s 155p. I share his confidence, and reckon market sentiment is set to turn.

Take off

Barclays’ shares are at a depressed level and valuation, providing a low base from which to take off. Improving performance and sentiment could lead to a significant rerating in the next few years.

As things stand, the shares are trading at a huge 46% discount to the tangible net asset value of 289p announced today. A forward P/E of 16 may not appear cheap, but Barclays could rapidly ‘grow into’ that rating. Similarly, a current prospective dividend yield of 1.9% has potential to rise strongly further down the line. As such, I rate the shares a buy.

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G A Chester has no position in any shares mentioned. The Motley Fool UK has recommended Barclays. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.