If you have seen any of my views of Markowitz for portfolio optimization for improved expected return. You see them here:
You can always search for more with this
Here are some corrections on both Sortino and Markowitz from some an expert on my Telegram PRIVATE group:
Corrected view
I just wanted to mention a couple of things related to your recent posts.
The first is that Markowitz optimisations assume the returns are normally distributed (which is never the case in finance), so don’t expect to achieve the ‘expected’ return. Also bear in mind that such portfolio optimisation is intended to be done over much longer periods of time; doing it over a week or month is likely an exercise in futility because you’ll constantly be fitting your weights to very recent data which is almost guaranteed to change in the subsequent period due to the nature of financial markets.
In fact, many practioners have come up with improvements to Modern Portfolio Theory (which is certainly not modern these days), and many have also found equally-weighted portfolios to be preferable (e.g. https://www.diva-portal.org/smash/get/diva2:694576/FULLTEXT01.pdf). In any case, minimum variance optimizations should be preferred to mean-variance (aka Markowitz); the ‘expected’ return will likely be lower, but it will also be much more realistic than that of the Markowitz portfolio due to the greater out-of-sample persistence of risk-related measures such as variance when compared to those that contain information about absolute returns (e.g. mean of the return distribution).
The second is in relation to the Sortino ratio. You mentioned that the difference between it and the Sharpe is that the Sortino accounts for volatility. This is not the case; the Sortino is identical to the Sharpe except that it does not penalise positive deviation. For me personally, I prefer Sharpe because the objective function that I’m maximising is stability of returns. If you’re more interested in absolute returns, then Sortino is still preferable. But again, measuring over 7 or 30 days is essentially a random exercise.
Combining best performing forex pair should hugely increase your expected return and Sharpe Ratio
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