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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 $\sum_{i} CTR_{i,t,t+10} = Port_{t, t+10}$?

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