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The internal rate of return (IRR) (which is a variety of money-weighted rate of return) is the rate of return which makes the net present value of cash flows zero. It is a solution r {\displaystyle r} satisfying the following equation:
Return and rate of return are sometimes treated as interchangeable terms, but the return calculated by a method such as the time-weighted method is the holding period return per dollar (or per some other unit of currency), not per year (or other unit of time), unless the holding period happens to be one year. Annualization, which means ...
Time-weighted return (TWR) calculates an investment portfolio or fund’s performance while accounting for external cash flows. Investment funds usually have money flowing in or out at various times.
The modified Dietz method [1] [2] [3] is a measure of the ex post (i.e. historical) performance of an investment portfolio in the presence of external flows. (External flows are movements of value such as transfers of cash, securities or other instruments in or out of the portfolio, with no equal simultaneous movement of value in the opposite direction, and which are not income from the ...
The rate of return on a portfolio can be calculated indirectly as the weighted average rate of return on the various assets within the portfolio. [3] The weights are proportional to the value of the assets within the portfolio, to take into account what portion of the portfolio each individual return represents in calculating the contribution of that asset to the return on the portfolio.
Thus, internal rate(s) of return follow from the NPV as a function of the rate of return. This function is continuous. Towards a rate of return of −100% the NPV approaches infinity with the sign of the last cash flow, and towards a rate of return of positive infinity the NPV approaches the first cash flow (the one at the present).