Modified Dietz method: Difference between revisions

Revision as of 03:13, 14 November 2020

Revision as of 03:32, 14 November 2020

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|quote=A slightly improved version of this method is the day-weighted, or modified Dietz, method. This method adjusts the cash flow by a factor that corresponds to the amount of time between the cash flow and the beginning of the period.}}</ref> 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.{{Citation needed|date=October 2017}}

Dietz or Modified Dietz being MWRR (money weighted rates of return) methodologies<ref>Paolo Antonio Cucurachi, Ph.D. & Ugo Pomante, Ph.D. [https://spauldinggrp.com/product/modification-modified-dietz-approach/ "A Modification of the Modified Dietz Approach"], The Journal of Performance Measurement, Summer 2013</ref>, his approximation was therefore to generate a money weighted rate of return for the period (IRR is also a MWRR). Because there is a GIPS requirement to produce a valuation on a monthly basis at least, using modified Dietz with monthly valuations provides a series of individual monthly money-weighted rates with which can be compounded together to produce a good quality approximation for the longer time period time weighted rate of return.<ref>{{Cite journal|last=Dietz|first=Peter|date=May 1968|title=Measurement of Performance of Security Portfolios COMPONENTS OF A MEASUREMENT MODEL: RATE OF RETURN, RISK, AND TIMING|journal=The Journal of Finance|volume=Volume 23, Issue 2|issue=2|pages=267–275|doi=10.1111/j.1540-6261.1968.tb00802.x}}</ref>

==Formula==

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The modified Dietz method has the practical advantage over the [[true time-weighted rate of return]] method, in that the calculation of a modified Dietz return does not require portfolio valuations at each point in time whenever an external flow occurs. The [[internal rate of return]] method shares this practical advantage with the modified Dietz method.

With the advance of technology, most systems can calculate a true time-weighted return by calculating a daily return and geometrically linking in order to get a monthly, quarterly, annual or any other period return. However, the modified Dietz method remains useful for performance attribution, because it still has the advantage of allowing modified Dietz returns on assets to be combined with weights in a portfolio, calculated according to average invested capital, and the weighted average gives the modified Dietz return on the portfolio. Time weighted returns do not allow this.

The modified Dietz method also has the practical advantage over [[internal rate of return]] (IRR) method that it does not require repeated trial and error to get a result.<ref name="Feibel2003">{{cite book

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The modified Dietz method is different from the [[simple Dietz method]], in which the cash flows are weighted equally regardless of when they occurred during the measurement period. The [[simple Dietz method]] is a special case of the Modified Dietz method, in which external flows are assumed to occur at the midpoint of the period, or equivalently, spread evenly throughout the period, whereas no such assumption is made when using the Modified Dietz method, and the timing of any external flows is taken into account.

Note that in the example above, the flow occurs midway through the overall period, which matches the assumption underlying the simple Dietz method. This means the simple Dietz return and modified Dietz return are the same in this particular example.

==Money-weighted return==

The Modified Dietz return is money-weighted, as opposed to [time weighted return|time-weighted]. If the Modified Dietz return earned on a portfolio with average capital <math>A_1</math> over a holding period is <math>R_1</math>, the average capital over the same holding period on second portfolio is <math>A_2</math>, and the Modified Dietz return earned on the second portfolio is <math>R_2</math>, then the Modified Dietz return earned on the combined portfolio, including both these portfolios, is the weighted average Modified Dietz return:

:<math>W_1 R_1 + W_2 R_2</math>

where

:<math>W_1 = \cfrac {A_1}{A_1 + A_2}</math>

and

:<math>W_2 = \cfrac {A_2}{A_1 + A_2}</math>

==Adjustments==