** Australia's banking sub-index .AXFJ gains 1.3% after two consecutive sessions of losses

** Morningstar says ANZ's ANZ.AX stock offers best value among "Big Four" banks

** Adds ANZ working to lower costs, settle regulatory hangs, but execution, governance risks loom

** Notes major Australian banks mostly expensive; Commonwealth Bank of Australia CBA.AX underperformed in Q3 as investors turned towards less expensive alternatives

** Says ANZ offers upside from improving operating efficiency, successful integration of Suncorp Bank

** Adds Valuation divergence between CBA, its peers narrowed, but "in our view, is still too wide and unjustified"

** Notes credit growth healthy among financials and bank margins relatively steady; adds financials hold surplus capital, which supports modest dividend growth

** AXFJ gains 12.1% YTD

(Reporting by Rishav Chatterjee in Bengaluru)

((Rishav.Chatterjee@thomsonreuters.com;))