IRR (Internal Rate of Return)

IRR is also known as Realized Return or Dollar-Weighted Return.

IRR is the annualized implied discount rate calculated from a series of cash flows. It is the return that equates the present value of all invested capital in an investment to the present value of all returns, or the discount rate that will provide a net present value of all cash flows equal to zero.

Said differently, IRR is the discount rate that equates the cost of an investment with the present value of the cash generated by that investment.



Internal Rate of Return (IRR) provides a measure of the growth of a portfolio in absolute terms; it is the single rate of return that makes everything you put into the investment equal to everything you took out.

To calculate the internal rate of return, we can use either the trial and error method of calculation or estimation using average capital base.

The trial and error method requires the following data for the time period under consideration:

We assume that all deposits and withdrawals occur at the beginning of the day. Therefore, the portfolio value before a capital flow is the closing value of the portfolio on the day before the capital flow. The internal rate of return for the time period can be calculated as following:

PV = Sum of (FVi/(1+r)ni) + FVe/(1+r)N


PV is Begin Value

FVi is future value for cash flow i

ni is number of period for i

r is IRR

FVe is End Value

N is number of period at the end

Note: For holding periods shorter than 3 months, we will use The Average Capital Base method and for all others we will use the Trial and Error method.

The Average Capital Base Method uses this formula to calculate IRR:

IRR = (End Value – Begin Value – Total Contributions + Total Withdrawals) /      (Begin Value + Total Weighted Contributions – Total Weighted Withdrawals)


Total Weighted Contributions – Total Weighted Withdrawals = Sum of (Each Change in Capital Xi (Days Left in Period for Xi / Total Days in Period))

Multiple solutions might exist for Trial and Error method. We will use the one that is closest to 0 as our solution.

Cash flows for different transaction types

Basic assumptions: