3
$\begingroup$

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 !

$\endgroup$
  • 1
    $\begingroup$ Considered using the kalman filter? $\endgroup$ – Kian Feb 8 '16 at 18:57
  • $\begingroup$ hmm... I will to think about it I don't well remember about it ! $\endgroup$ – glork Feb 8 '16 at 19:13
  • 1
    $\begingroup$ You could also consider using a ccc /dcc estimator for the covariance matrix of asset returns $\endgroup$ – Kian Feb 9 '16 at 18:49
  • 1
    $\begingroup$ For the newbies: ccc = constant conditional correlation, dcc = dynamic conditional correlation $\endgroup$ – noob2 Feb 9 '16 at 19:20
  • $\begingroup$ Many thx , I don't know this techniques but I will see it on Internet ! $\endgroup$ – glork Feb 9 '16 at 19:30
3
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ 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 $\endgroup$ – glork Feb 7 '16 at 17:24
  • $\begingroup$ Yap, as I said, that's how you usually do it. $\endgroup$ – phdstudent Feb 7 '16 at 17:37
  • $\begingroup$ Ok I will try to implement it but why would it perform poorly ? $\endgroup$ – glork Feb 7 '16 at 17:40
  • $\begingroup$ 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 $\endgroup$ – phdstudent Feb 7 '16 at 17:54
  • $\begingroup$ Ahh ok ! Besides it takes a lot of time to calculate at every step ... Many thanks for your answers and reference ! $\endgroup$ – glork Feb 7 '16 at 18:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.