I think that P/B does not tell much for financial companies and whatever it tells can be misleading. I am borrowing from my earlier post in CanFin Homes discussion board. Please correct me where you feel that I am wrong and feel free to give your inputs.
Let me explain:
RoE = Earning / BV of Equity
PE = Price / Earning
PB = Price / BV of Equity
So, PB = PE * RoE
Even at the same RoE, Price to Book can rise to a much higher value if PE ratio goes up. I find much easier to interpret PE ratio, because it tells how much is the market paying for 1 rupee of current earnings. PE ratio depends on the growth in future earnings and their discount rate/risk and hence I can form my opinion about justified PE looking at the expected growth and risk of future earnings. PB tells at how many rupees is the market valuing each rupee of equity investment (book value). But, PB does not yield itself to an interpretation like PE where I can form an opinion about its justified levels looking at firm performance.
So, I use PE as the cause and PB as the effect and interpret all this as: if Market revises its assumptions of future earnings upward or lowers the associated risk then P/B will go up at the same RoE. So, the question that I ask myself is whether the company is doing something to improve its earnings and/or reduce the risks and try to judge the combined effect of these two factors.
Also Market Cap to AUM is Price/Asset, or P/A. Now, P/A = (P/E) * (E/A). In other words, Market Cap to AUM = PE * RoA. Here also, RoA is an accounting variable denoting past business performance. At the same RoA, if the PE ratio of the stock changes (due to change in expectations of growth and/or risk in future earnings) then it will cause Market Cap to AUM to change proportionally.
I think PE is a good metric for understanding stock valuation levels and RoA is good for understanding overall business performance of the company.
~Pranav