# Do you need multi-period ahead covariance forecast, in order to construct portfolios with weekly/monthly rebalancing?

Suppose I want to rebalance my portfolio each week. Do I then need weekly covariance forecasts, from some multivariate volatility model to do this? Ie. Insert the weekly covariance forecast $$\Sigma_{t+5\vert t}$$ into my model and calculate the weigths for the portfolio $$w_{t+5\vert t}$$ (ie. assume we are working with a global minimum variance portfolio).

I'm a bit confused on whether this is the "correct" way of doing it?

• Generally you get more "bang per buck" trying to improve returns forecasts... – steveo'america Dec 16 '20 at 22:27
• @steveo'america You mean portfolio returns? That might be true, however, I'm just curious on whether you need multi-period ahead covariance forecast, in order to properly rebalance less often? – Pleb Dec 17 '20 at 9:45
• I wonder if I understand the question and its motivation. If the method you are suggesting is a straightforward extension of daily rebalancing, why are you confused / what issues do you suspect? If not, how is it different from a straightforward extension and why not do the latter? – Richard Hardy Jun 16 at 12:26
• Hi @RichardHardy. If the method you are suggesting is a straightforward extension of daily rebalancing: Exactly, it was. At the time, I was confused about whether this was the correct approach of rebalancing each week (asked the question to verify). I didn't suspect any issues, but I was skeptical. In the end, I never used any weekly rebalancing in my academical project paper and just stuck with daily rebalancing. – Pleb Jun 16 at 14:11