# Ledoit-Wolf, expected order of optimal shrinkage intensity

I have a question regarding the optimal shrinkage intensity derived in the Ledoit-Wolf method. Specifically, I'm referring to their version concerned with the target defined as the single index factor model. I comprehend the bulk of the derivations, I think I do anyway, but it isn't entirely apparent to me why the optimal alpha value is inherently equal to K/T. From my understanding, this is related to the fact that the sample CoVar matrix is consistent while the target is not and the fact that the derived optimal alpha value vanishes as N tends towards infinity. I've researched this a bit and it might be that I don't have a good enough understanding of what is meant by optimal alpha being of the "expected order O(1/T)". In summary - How does dividing the asymptotically optimal shrinkage (K) by T result in an optimal finite-sample alpha? Thanks