The modified Dietz method 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 investments in the portfolio, such as interest, coupons or dividends.) To calculate the modified Dietz return, divide the gain or loss in value, net of external flows, by the average capital over the period of measurement. The average capital weights individual cash flows by the length of time between those cash flows until the end of the period. Flows which occur towards the beginning of the period have a higher weight than flows occurring towards the end. The result of the calculation is expressed as a percentage return over the holding period.
GIPS This method for return calculation is used in modern portfolio management. It is one of the methodologies of calculating returns recommended by the Investment Performance Council (IPC) as part of their Global Investment Performance Standards (GIPS). The GIPS are intended to provide consistency to the way portfolio returns are calculated internationally.
Origin The method is named after Peter O. Dietz. The original idea behind the work of Peter Dietz was to find a quicker, less computer-intensive way of calculating an IRR as the iterative approach using the then-quite-slow computers that were available was taking a significant amount of time; the research was produced for BAI, Bank Administration institute. The modified Dietz method is a linear IRR.
Formula The formula for the modified Dietz method is as follows:
gain or loss average capital = B − A − F A + ∑ i = 1 n W i × F i {\displaystyle {\cfrac {\text{gain or loss}}{\text{average capital}}}={\cfrac {B-A-F}{A+\sum _{i=1}^{n}W_{i}\times F_{i}}}}
where
A {\displaystyle A} is the starting market value
B {\displaystyle B} is the ending market value
F = ∑ i = 1 n F i {\displaystyle F=\sum _{i=1}^{n}F_{i}} is the net external inflow for the period (so contributions to a portfolio are treated as positive flows while withdrawals are negative flows) and
∑ i = 1 n W i × F i = {\displaystyle \sum _{i=1}^{n}W_{i}\times {F_{i}}=} the sum of each flow F i {\displaystyle F_{i}} multiplied by its weight W i {\displaystyle W_{i}}
The weight W i {\displaystyle W_{i}} is the proportion of the time period between the point in time when the flow F i {\displaystyle F_{i}} occurs and the end of the period. Assuming that the flow happens at the end of the day, W i {\displaystyle W_{i}} can be calculated as
W i = C − D i C {\displaystyle W_{i}={\frac {C-D_{i}}{C}}}
where
C {\displaystyle C} is the number of calendar days during the return period being calculated, which equals end date minus start date (plus 1, unless you adopt the convention that the start date is the same as the end date of the previous period)
D i {\displaystyle D_{i}} is the number of days from the start of the return period until the day on which the flow F i {\displaystyle F_{i}} occurred. This assumes that the flow happens at the end of the day. If the flow happens at the beginning of the day, the flow is in the portfolio for an additional day, so use the following formula for calculating the weight:
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