optimal asset allocation - MTCR and Sharpe

Excess Return over MTCR’s formula is equivalent to a Sharpe Ratio.
The calculation is: (Rp -Rf) / MCTR
The Sharpe ratio adjusts for risk, and can help you determine the investment choice that will deliver the highest returns
while considering risk.

However, I still cannot understand why an optimal asset allocation involves the fact that ALL assets have MCTR and hence equal Sharpe ratios? Why is not an optimal asset allocation involving assets with highest Sharpe ratios? (but not necessarily equal?)

Thanks!!

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It is a mathematical expression. Let us say between a rectangular and a square of equal perimeter, which one will have greater area ? The square.

Similarly, for an optimal portfolio the same Sharpe ratio

back against the wall. no retreat no surrender.

The way I understand it is: In an optimal asset allocation, you will have the same Sharpe (slope)

Even if you change the risk-return combination (higher risk-higher return, lwoer risk-lower return), with rf as a constant, Sharpe stays the same.

Now the connection to the MCTR is: as you gradually increase the amount of risk taken (relative to overall risk), MCTR will stay the same as Sharpe, following the same idea as above: add a certain amount of risk, you add a certain amount of return as well.

Hence Sharpe and MCTR are the same. Is this correct?

Thank you!