Too many trades? Mean variance portfolio optimization and rebalancing?

This tool's(http://quicark.com/OptimalPortfolio.aspx) principle is: if prices of securities happened in the past, it will happen in the future in a similar way.

From this point of view, we can value the risk as the value fluctuation diverse from the mean route of the portfolio. The objective of the optimization is

rrr * rate – risk.

Where rrr is the return risk ratio, return is the expected weighted rate of return, and risk is the risk of the portfolio.
 
Quote from zyygsl08:

This tool's(http://quicark.com/OptimalPortfolio.aspx) principle is: if prices of securities happened in the past, it will happen in the future in a similar way.

From this point of view, we can value the risk as the value fluctuation diverse from the mean route of the portfolio. The objective of the optimization is

rrr * rate – risk.

Where rrr is the return risk ratio, return is the expected weighted rate of return, and risk is the risk of the portfolio.

I am not sure if the objective is correct. Regardless, since this is a higly non-linear function, what optimization algorithm is used and how do you know that it does not reach a local optimum point?
 
Quote from mizhael:

Hi all,

How does one handle the too-many-trades problem in mean variance portfolio analysis?

Let's say I have 10 trading strategies, each one is on a basket of instruments(say 100, such as those big ones in SP500).

For each trading strategy, I run a mean-variance weighted portfolio on the 100 instruments. The 10 trading strategies each have a different optimal "rebalance" period.

You handle it by not using mean variance optimization for trading strategies.
 
I agree that the object is non-linear. At least the rate of return part is linear. I cannot expose too much about the detail of the algorithm. You can change the rrr and play with it to see if it is a local optimal point. :)
 
Quote from zyygsl08:

I agree that the object is non-linear. At least the rate of return part is linear. I cannot expose too much about the detail of the algorithm. You can change the rrr and play with it to see if it is a local optimal point. :)

If you add a linear function to a non-linear one you get non-linear. How do you optimize that? What initial feasible point do you use? What type of algorithm do you use? I am not asking you to give details. just the general strategy. Otherwise, what you are doing is just an ad-hoc solution that is far from optimal, maybe even non-optimal.
 
Quote from zyygsl08:

I cannot expose too much about the detail of the algorithm.

To my taste, then it's worth no further discussion. We live in the FOSS era. There are plenty of open-source, fully documented tools available. Life is too short to spend time fiddling with mysterious blackboxes.
 
Quote from Rodney King:

To my taste, then it's worth no further discussion. We live in the FOSS era. There are plenty of open-source, fully documented tools available. Life is too short to spend time fiddling with mysterious blackboxes.

Well said and to the point. No trader should waste one minute discussing black-boxes. They always hide skeletons inside.
 
Quote from intradaybill:

The problem with stocks is those negative correlations that turn positive not with those that remain large and positive.

The correlation of major asset classes may not be stationary but there are other benefits from diversifying there, including minimizing unsystematic risk, credit default risk, foreigh exchange risk, etc. You can still use (Stocks, cash) or (bonds, cash) or (futures, cash) to be safe. Many funds do that, either stocks and cash, or bonds and cash, just to be on the safe side of correlations.

This is why I always say, not too many understand math, very few understand how to apply them and even fewer understand when and where to apply them. Math, and especially complex optimization, is useless and even a dangerous tool in the hands of those who do not have a deeper understanding of finance theory.

What are the assumptions behind mean-variance model?
 
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