# Return Contribution for Annual Returns

I have a portfolio $p$ made up of a bunch of assets $i$ where the weights change slowly over time. The returns over each period $j$ composed of the weighted returns of the asset $r^j_p$

$$r^j_p = \sum_i w^j_i r^j_i$$

The annualized return $\bar{r}_p$ given $n_y$ periods per year and $n$ total periods is:

$$\bar{r}_p = \prod_j (1+r^j_p)^{(n_y/n)} -1$$

Is there a financially reasonable way to understand return contribution on this portfolio. I.E. find a $\bar{r}_i$ such that

$$\bar{r}_p = \sum_i \bar{r}_i$$

If I annualize the weighted return series of each asset the sum of those of course do not at to the portfolio annualized returns.