what is the money weighted rate of return 
the money weighted rate of return mwrr is a measure of the performance of an investment the mwrr is calculated by finding the rate of return that will set the present values pv of all cash flows equal to the value of the initial investment the mwrr is equivalent to the internal rate of return irr mwrr can be compared with the time weighted return twr which removes the effects of cash in and outflows understanding the money weighted rate of returnthere are many ways to measure asset returns so it is important to know which method is used when reviewing asset performance the mwrr incorporates the size and timing of cash flows so it effectively measures portfolio returns the mwrr sets the initial value of an investment to equal future cash flows such as dividends added withdrawals deposits and sale proceeds in other words the mwrr helps to determine the rate of return needed to start with the initial investment amount factoring all of the changes to cash flows during the investment period including the sale proceeds the formula for the mwrr is as follows pvo pvi cf0 cf1 1 irr cf2 1 irr 2 cf3 1 irr 3 cfn 1 irr nwhere pvo pv outflowspvi pv inflowscf0 initial cash outlay or investmentcf1 cf2 cf3 cfn cash flowsn each periodirr initial rate of return begin aligned pvo pvi cf 0 frac cf 1 1 irr frac cf 2 1 irr 2 qquad quad frac cf 3 1 irr 3 frac cf n 1 irr n textbf where pvo text pv outflows pvi text pv inflows cf 0 text initial cash outlay or investment cf 1 cf 2 cf 3 cf n text cash flows n text each period irr text initial rate of return end aligned pvo pvi cf0 1 irr cf1 1 irr 2cf2 1 irr 3cf3 1 irr ncfn where pvo pv outflowspvi pv inflowscf0 initial cash outlay or investmentcf1 cf2 cf3 cfn cash flowsn each periodirr initial rate of return because the formula for mwrr is complex and requires guesswork and trial and error you d want to use a spreadsheet or calculator to help you estimate returns so we ll use a spreadsheet to explain how to calculate it let s say you buy one share of a stock for 50 that pays an annual 2 dividend and sell it after three years for 65 you received two dividends before selling the stock the initial outlay of 50 in year one is negative because it is money you ve spent each year after the purchase you gain 2 until you sell it for 65 in year three after receiving the dividend the irr function used in most spreadsheet applications will calculate the mwrr for you as shown in the following table the irr function in the spreadsheet asks for values and a rate guess which is optional to use the function highlight the cells that contain your cashflow values so that the column and cell numbers are entered into the field between the parenthesis skip the rate guess and press enter cash flows and the money weighted rate of returnas stated above the mwrr for an investment is identical in concept to the irr in other words it is the discount rate on which the net present value npv 0 or the present value of inflows the present value of outflows with that in mind it s critical to know how to identify the cash flows in and out of a portfolio including the sale of the asset or investment some of the cash flows that an investor might have in a portfolio include the difference between money weighted rate of return and time weighted rate of returnthe mwrr is often compared to the time weighted rate of return twrr but the two calculations have distinct differences the twrr is a measure of the compound rate of growth in a portfolio the twrr measure is often used to compare the returns of investment managers because it eliminates the distorting effects on growth rates created by inflows and outflows of money it can be difficult to determine how much money was earned on a portfolio because deposits and withdrawals distort the value of the return on the portfolio investors can t simply subtract the beginning balance after the initial deposit from the ending balance since the ending balance reflects both the rate of return on the investments and any deposits or withdrawals during the time invested in the fund the twrr breaks up the return on an investment portfolio into separate intervals based on whether money was added to or withdrawn from the fund the mwrr differs in that it takes into account investor behavior via the impact of fund inflows and outflows on performance but doesn t separate the intervals where cash flows occurred as the twrr does therefore cash outflows or inflows can impact the mwrr if there are no cash flows then both methods should deliver the same or similar results limitations of using money weighted rate of returnthe mwrr considers all the cash flows from the fund or contribution including withdrawals should an investment extend over several quarters for example the mwrr lends more weight to the fund s performance when it is at its largest hence the description money weighted the weighting can penalize fund managers because of cash flows over which they have no control in other words if an investor adds a large sum of money to a portfolio just before its performance rises it equates to positive action this is because the larger portfolio benefits more in dollar terms from the portfolio s growth than if the contribution had not been made on the other hand if an investor withdraws funds from a portfolio just before a performance surge it equates to a negative action the now smaller fund sees less benefit in dollar terms from the portfolio growth than if the withdrawal had not occurred 