9

There are a few related reasons: The optimization becomes a lot harder when only discrete values are considered. Mean variance has a closed form solution for the continuous case but the case with discrete holdings is quite hard; For small retail investors fixed trading costs will swamp the rounding in your example but also for larger amounts (at least ...


5

The preferred method for calculating the P/E of a stock index depends on how that index is calculated and what you are planning to do with it. Let’s assume the stock index you are looking into is calculated based on free-float market capitalizations (mcaps) of stocks in it, i.e. the index measures changes in total free-float mcaps of the stocks in the index. ...


3

As correctly mentioned in an earlier answer, portfolio optimization is something used for books in hedge funds and other institutions. As a smooth utility function changes slowly near its maximum, perturbation by rounding is inconsequential. If you would like to adopt a utility approach to personal investing, the following algorithm could work: (1) solve ...


3

If the link is insufficient, does this work?


1

In practice, creating a portfolio with (equally) weighted shares is doable as you will invest on "a lot" of shares. Suppose you're an advisor in a private bank and you're creating a portfolio with your client considering your shares example : You will not invest USD 100.00 but USD 100,000.00, thus you would buy : 1333 shares of stock A => USD 33,...


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