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.
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.
total return is relatively simple when no cash flow occurs during the month or
formula for simple rate of return (no Cash Flow during the period) is:
= (MVE - MVB) / MVB
: total return
market value of the asset at the end of the period
market value of the asset at the beginning of the period
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.
formula for calculating time-weighted rate of return using Modified Dietz is:
(MVE -MVB -F) / (MVB + FW
sum of the cash flows during the period
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:
(CD -Di +1) / CD
total number of days in the period
number of days since the beginning of the period.
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.