# How to adjust a portfolio's rate of return for contributions and withdrawals?

Suppose we have a portfolio with many assets.

Since this portfolio receives monthly contributions and withdrawals, what is the best method to evaluate its global rate of return and avoid computing these contributions as a "profit" and withdrawals as "losses"?

I've already seen some people using abstract entities (e.g.: we may define that we start with 100 entities, and, for a \$100 portfolio, each entity would cost \$1), but I don't know the name of this method in English.

• I think you are probably referring to the "NAV per unit" method of computing Time Weighted Returns. ("units" = what you call "entities"). It is the method used by US Mutual Funds, but is difficult to find clear explanations. I made an attempt here quant.stackexchange.com/questions/44594/… – noob2 Aug 12 '20 at 21:50
• Another even better article is here quant.stackexchange.com/questions/55466/… where the same method is dicussed for partnership accounting – noob2 Aug 12 '20 at 21:55
• That's exactly what I was looking for! Thank you @noob2 – Vinícius Lopes Simões Aug 13 '20 at 0:24
• vote if you found anyone's comments or answers useful – develarist Aug 13 '20 at 23:16

Usually this would be evaluated using an internal rate of return, the rate $$r$$ which makes the PV of inflows and outflows equal -- assuming a starting inflow of portfolio value at the start date and an outflow as though the portfolio were liquidated at the end date.