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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?

Thank you!

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That's the way you apply. Usually you get the closest number of shares possible. However, if you use that strategy you are very likely to underperform the market. Check table 3 on this paper for the Out of sample performance of the Markowitz strategy. Over their sample the Sharpe Ratio is 0.07 whereas a simple naive strategy 1/N yielded 0.18.

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  • $\begingroup$ I would guess an additional concern is depending on how you massage the numbers you also alter your risk and return together, so you would need to re-solve for volatility after you find out how close you can get. $\endgroup$ – Steve Jul 28 '15 at 17:00

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