Hi, I do, actually, consider it relevant, for several reasons.

With my empirical scientist hat on, it just seems to possess the right kind of properties for a metric of use in this context. i.e. That performance be proportional to information content and the number of bets made, with the power of that quantity being consistent with the law of large numbers and the way independent random outcomes accumulate. Perhaps another Hurst exponent is needed, but 1/2 seems like a good ballpark number for a "mostly random" market.

In my latest book, Essays on Trading Strategy, I go through several strategy optimizations analytically and the optimum Sharpe Ratio comes back, at the end of a ton of maths, as something like Z=f(X)*R*sqrt(P) where Z is the Sharpe Ratio, f(X) is strategy specific, R is the IC (sqrt of R^2), and P is the number of trades per annum. For me, this kind of indicates that the FLAM is supported analytically.

However, I would throw a lot of shade at the idea that the Sharpe Ratio, as a statistic for the measurement of strategy performance, is any good at all over the time-scales it is typically used for. The sampling distribution of the SR is very wide unless the SR is unrealistically high, and I believe many reported SR measurements by fund managers are essentially worthless. I have been a victim of this myself, I confess. (This is covered in Chapter 1 of Essays...)

So in all, I would regard it as a "rule of thumb" indicator, rather than a truth. I expect performance to increase with information content, I expect performance to increase with the cadence of independent bets less than linearly in some way. I expect people to report SR's that are wholly meaningless for their investment strategies too.

GG