Dynamic Markowitz Portfolios and the Difficulty of Estimating Returns

Summary

This exchange considers how to update expected asset returns when rebalancing a Markowitz portfolio day by day. The question proposes incorporating each new observation into the historical sample and recalculating the expected returns and portfolio weights. The response cautions that this procedure may be theoretically consistent with time-varying means, but that estimating expected returns out of sample is difficult. It contrasts mean estimation with second-moment estimation, describing the latter as easier.

The answer argues that an accurate estimate of the mean would require an effectively infinite sample, so a dynamically re-estimated Markowitz strategy may perform poorly out of sample. It points to further discussion of mean estimation but provides no empirical results, forecasting method, or alternative portfolio construction procedure. The main takeaway is a limitation of historical mean estimates, not a complete daily rebalancing algorithm. The stated concern is especially relevant because Markowitz weights depend on expected returns, though performance will also depend on the data, estimation choices, constraints, and evaluation design, which the exchange does not examine.

Key ideas

• The question proposes updating historical expected returns as new daily observations arrive.
• The answer emphasizes that expected returns are difficult to estimate out of sample.
• Estimating second moments is presented as easier than estimating means.
• The response warns that a dynamically re-estimated Markowitz strategy may perform poorly, without offering an alternative method.

Tags

# dynamic Markowitz portfolio


# dynamic Markowitz portfolio












Let's take 4 assets, whose values are known during a period of time of 2 years. Then I calculate the expected returns for each of these 4 assets thanks to these 2 years - historical data. I deduce the optimal weights that maximizes the expected return of the entire portfolio under a given risk (so I calculated the Makowitz's portfolio).

Now I want to test my algorithm dynamically. I want that the algorithm readjusts the optimal weights for each trading day (because until now I calculated my Markowitz's portfolio for a single period of time)

So my question is : if I am a trader who wants to calculate these optimal weights day after day, how to calculate the expected returns for each of these assets dynamically, day after day ?

Suppose I know their expected returns for the period [1:n], if I take into account the new datas at time n+1 to calculate the new expected return, is is the good procedure ?

Many thanks !

## Answer by phdstudent (score 2, accepted)

https://quant.stackexchange.com/a/23148

Out-of-sample is basically impossible to predict means. Second moments are much easier. You can take a look at this post: Estimating $\mu$ - only increasing $T$ improves estimate?

Only with infinite $T$ you would be able to correctly estimate $\mu$. So theoretically your procedure could be correct if means are time-varying, but out of sample I bet your Markowitz strategy will perform poorly.

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