Despite being one of the most important concepts in investment management, performance measurement is often manipulated or at best not well understood in terms of its calculation, presentation and use. 

There are different approaches to performance measurement and reporting.  The difficulty originates when when there are cash flows (inflows and outflows) throughout a period.  This is especially a problem when there are large inflows or outflows of funds.

Calculating total return is relatively simple when no cash flow occurs during the month or the period.  

The formula for simple rate of return  (no Cash Flow during the period) is:

RTR = (MVE - MVB) / MVB

Where:

RTR :   total return

MVE:  market value of the asset at the end of the period

MVB:  market value of the asset at the beginning of the period

Modified Dietz Calculation

The modified Dietz Calculation is used when there are cash flows during the month or during the period. 

A time-weighted rate of return takes into consideration the cash flows that occur and the market value of the asset on the cash flow date.  This method does not require daily valuations.  Instead, it uses beginning and ending asset values for the period and weights each cash flow by the amount of time it is invested.

The formula for calculating time-weighted rate of return using Modified Dietz is:

RDietz= (MVE -MVB -F) / (MVB + FW

Where:

F:     sum of the cash flows during the period

FW:  the sum of each cash flow Fi, multiplied by its weights Wi.  Weight Wi is the proportion of the total number of days in the period that the cash flow Fi has been in (or out of) the asset.  THe formula for Wi is:

Wi = (CD -Di +1) / CD

where:

CD:   total number of days in the period 

Di:    number of days since the beginning of the period.

Daily flows are assumed to occur at the beginning of the day, so the +1 is added to the numerator to force beginning-of-day weighting.

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