# 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 !

• Considered using the kalman filter? – Kian Feb 8 '16 at 18:57
• hmm... I will to think about it I don't well remember about it ! – glork Feb 8 '16 at 19:13
• You could also consider using a ccc /dcc estimator for the covariance matrix of asset returns – Kian Feb 9 '16 at 18:49
• For the newbies: ccc = constant conditional correlation, dcc = dynamic conditional correlation – noob2 Feb 9 '16 at 19:20
• Many thx , I don't know this techniques but I will see it on Internet ! – glork Feb 9 '16 at 19:30

## 1 Answer

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.

• Yes it's sure than I can 't have a correct estimate of the mean , but only an approximation. I was thinking of accumulating enough datas to have a first mean estimate that will use the trader, and then the trader will take into account the new datas to have new estimates of the mean: it's like a rolling window used for a dynamic portfolio – glork Feb 7 '16 at 17:24
• Yap, as I said, that's how you usually do it. – phdstudent Feb 7 '16 at 17:37
• Ok I will try to implement it but why would it perform poorly ? – glork Feb 7 '16 at 17:40
• As I said, it is almost impossible to feed a Markowitz model out of sample. You might get some improvement using option free implied moments. Check table 2 and 3 of this paper: papers.ssrn.com/sol3/papers.cfm?abstract_id=1474212 – phdstudent Feb 7 '16 at 17:54
• Ahh ok ! Besides it takes a lot of time to calculate at every step ... Many thanks for your answers and reference ! – glork Feb 7 '16 at 18:01