Could you invert the ROE to get "equity per return" and then look for the lowest value, a bit like using earnings yield instead of p/e?

That would certainly be the right way to express it.

I don't calculate the ROE (or its inverse, which I guess is assets-to-profit ratio) myself because I have seen so many screens produce seemingly excellent results with the ROE field from VL, which doesn't seem to match last fiscal (or TTM) net income / shareholders' equity. I'm not sure what other adjustments they do. Eliminating extraordinary items? Year to year smoothing? Dunno.

But sure, you could easily do that inversion for the negative book crowd.

For any firms in that category, I like to try to make sure that they really are good, not bad firms with a data quirk. I'd check for firms where stated ROE is negative, net income is positive, book value per share is negative, "Current EPS" positive, and maybe even projected EPS growth rate positive. The goal is to eliminate any duds that had an anomalously profitable period, for example selling off their only factory at a profit.

The more interesting question you raise is whether (say) $1 of earnings on mildly negative book is better than $1 earnings on extremely negative book. I have always used the simplifying assumption that they're all equally good. There are basically two types of firm in the negative book category: those that have such sustainable earnings with low assets needed that they eventually pay out all their equity as dividends, sometimes getting cheap debt from bond buyers who know their earnings are sustainable. Coke, say. The other category is firms that had a big whopping loss in the past which wiped out equity. Some of them might be good, but certainly not what you desire in an investment.

Another way to sort among these would be to look at ROCTE, return on tangible capital employed. Sometimes calculated as EBIT/(Net Plant + Working Capital - Excess Cash). I define excess cash as max(0, Cash - 3*(Total Current Liabilities)), on the theory that cash far beyond the working capital scale is probably not needed to produce the earnings. However this sort wouldn't mix in with the firms a meaningful traditional ROE. You'd have to do two sorts, and not be sure how to mix them.

Jim