# Contribution to Return - from security to portfolio

I have the Contribution to Return (CTR) of all securities in a portfolio for a number of days. I would like to compute the portfolio and securities total return over this period.

The total return of the portfolio for day $$t$$ can be computed as $$Port_{t} = \sum_{i} CTR_{i}$$

The portfolio's total return over a number of days can then be computed as $$Port_{t, t+10} = \prod_{i} (1+Port_{i})$$

How would you compute security $$CTR_{i, t, t+10}$$ (the total contribution to return of security i) over the period in such a way that $$\sum_{i} CTR_{i,t,t+10} = Port_{t, t+10}$$?