Recently I've been learning about the markowitz algorithm. It's pretty interesting, but I'm curious how we apply this in practice. Lets say I have some optimal portfolio:
$R_p = x_aR_a + x_bR_b$
Which for simplicity's sake, we will say is just a simple two asset portfolio. This question will apply to a portfolio with a riskless asset and a tangency portfolio as well, and the n-asset case.
Let's suppose the markowitz algorithm says
$$ x_a = 0.34938 $$ $$ x_b = 0.65062 $$
This is fine in theory, but now how do we buy the stock? If I have $10,000 to invest then my dollar value given to asset A is
$10,000 * 0.34938$
and my dollar value in asset B is
$10,000 * 0.65062$
So if I go to my broker and say "buy me $3493.8 dollars worth of asset A", I will most likely be buying some fraction of a share of a company to get this exact value. I'm not aware of a case where you can buy fractional shares of a company via a broker.
Is there a rule to go by here to use these weights, or am I not understanding how to apply them correctly?