Two years ago, CS Venkatakrishnan was unexpectedly thrust into the top job at British banking giant Barclays. A year later, he felt a lump on his neck and was diagnosed with cancer.

Now, after successfully undergoing treatment, Venkatakrishnan faces a career-defining test. The Indian-born risk specialist is trying to succeed where his predecessors failed, to persuade investors that Barclays’s eclectic mix of Main Street finance and Wall Street heft makes sense.