The maximum diversification portfolio takes no account of the risk-free rate of return. I understand that it isn't trying to. But from the point of view of an investor making decisions in the real world, does it really make sense that you would ignore it? I personally remember back in 2007, I was doing some kind of rebalancing, I don't remember what, and I'd sold a largish bond mutual fund holding, so I'd just reduced my bond allocation (and thus increased my stock/bond ratio) and remembered thinking, casually, "hey, wait--if the money market settlement fund is earning 5%, why am I bothering with bonds at all?"
That is to say, when risk-free interest rates are competitive with bond returns, it seems reasonable just to take the sure thing, rather than gambling that the low-correlation independent movements of bonds against stocks are going to help more than they are going to hurt.
In the MPT/CAPM framework, if you can get higher risk-free return, the tangent point moves toward stocks. That is to say, if we wish to hold portfolio risk constant, and we look at all three traditional assets (stocks/bond/cash), if cash has a higher return, we shift out of bonds and into cash. In the extreme case, if cash is doing well enough, you don't use bonds at all--you use a stocks/cash portfolio instead of stocks/bonds. This seems like common sense. (See the three diagrams below, representing a highly exaggerated example).
In the "maximum diversification" framework, if I understand it, we continue to invest the same way, making no changes, regardless of the risk-free rate. Is that actually what advocates of the approach are advocating?
Actual data for Total Stock/Total Bond; over 1987-2017 inclusive, the actual risk-free rate was 3.2% and the tangent portfolio was 18/82.
However, if we had been able to get a risk-free return of 5.2%, the tangent portfolio changes to 44/56 (i.e. we allocate relatively more to stocks than bonds... while, of course, allocating more to cash if we wish to maintain the same risk level)
And if we had been able to get a risk-free return of 6%, it changes to 100/0. (That is, including cash as an asset and maintaining the same level, we shift entirely into cash in place of stocks).
I'm not saying that's sensible, or that I necessarily think it's better than sticking with the "most diversified portfolio" and ignoring times when the money market settlement account doing really well. A huge problem with MPT/CAPM is precisely that the tangent portfolio is very, very sensitive to small changes in the characteristics of the assets and the risk-free return.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.