Modified Dietz method: Difference between revisions

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{{Short description|Historical performance of an investment portfolio}}

The '''modified Dietz method'''<ref name="Dietz1966">{{cite book

|author=Peter O. Dietz

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|publisher=Institute of Chartered Financial Analysts.

|page=72

|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}} The modified Dietz method is a linear [[Internal_rate_of_return|IRR]].

==Formula==

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:<math>100 \times (1 + 125\%)+ 50 \times (1+125\%)^ \frac{2 - 1}{2} = 225 + 50 \times 150\% = 225 + 75 = 300</math>

so in this case, the modified Dietz return is noticeably less than the unannualized IRR. This divergence between the modified Dietz return and the unannualized internal rate of return is due to a significant flow within the period, andtogether with the fact that the returns are large. If there are no flows, there is no difference between the modified Dietz return, the unannualized IRR, or any other method of calculating the holding period return. If the flows are small, or if the returns themselves are small, then the difference between the modified Dietz return and the unannualized internal rate of return is small.

The IRR is 50% since:

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There are no flows, so the gain or loss is:

:{{nowrap begin}}{{link if exists|end value}} -− {{link if exists|start value}} = 1,125,990 -− 1,128,728 = -2−2,738 {{link if exists| HKD}}{{nowrap end}}

and the average capital equals the start value, so the modified Dietz return is:

:{{nowrap begin}}{{sfrac|{{link if exists|gain or loss}}|{{link if exists|average capital}}}} = {{sfrac|-2−2,738|1,128,728}} = -0−0.24 % 2 d.p.{{nowrap end}}

===Contributions - when not to adjust the holding period===

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:{{nowrap begin}}{{link if exists|average capital}}{{nowrap end}}

::{{nowrap begin}}= {{link if exists|start value}} -− {{link if exists|time weight}} &times; {{link if exists|outflow amount}}{{nowrap end}}

::{{nowrap begin}}= 10,000 -− {{sfrac|1|4}} &times; $8,000{{nowrap end}}

::{{nowrap begin}}= 10,000 -− $2,000{{nowrap end}}

::{{nowrap begin}}= $8,000{{nowrap end}}

The average capital of the shares over the last quarter requires no calculation, because there are no flows after the beginning of the last quarter. It is the $8,000 invested in the shares. However, the average capital in the shares over the whole year is something else. The start value of the shares at the beginning of the year was zero, and there was an inflow of $8,000 at the beginning of the last quarter, so:

:{{nowrap begin}}{{link if exists|average capital}}{{nowrap end}}

::{{nowrap begin}}= {{link if exists|start value}} -− {{link if exists|time weight}} &times; {{link if exists|outflow amount}}{{nowrap end}}

::{{nowrap begin}}= 0 + {{sfrac|1|4}} &times; $8,000{{nowrap end}}

::{{nowrap begin}}= $2,000{{nowrap end}}

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There are sometimes other difficulties when decomposing portfolio returns, if all transactions are treated as occurring at a single point during the day.

For example, consider a fund opening with just $100 of a single stock that is sold for $110 during the day. During the same day, another stock is purchased for $110, closing with a value of $120. The returns on each stock are 10% and 120/110 -− 1 = 9.0909% (4 d.p.) and the portfolio return is 20%. The asset weights ''w_i'' (as opposed to the time weights ''W_i'') required to get the returns for these two assets to roll up to the portfolio return are 1200% for the first stock and a negative 1100% for the second:

:w*10/100 + (1- − w)*10/110 = 20/100 → w = 12.

Such weights are absurd, because the second stock is not held short.

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:At the end of Day 40, the remaining 20 shares are worth 12.50 dollars per share

The gain or loss is end value -− start value + outflow:

:<math>20 \times 12.50 - 100 \times 10 + 80 \times 15</math>

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==Visual Basic==

<syntaxhighlight lang="vbvbnet">

Function georet_MD(myDates, myReturns, FlowMap, scaler)

' This function calculates the modified Dietz return of a time series

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==Java method for modified Dietz return==

<syntaxhighlight lang="java">

private static double modifiedDietz (double emv, double bmv, double cashFlow[], int numCD, int numD[]) {

/* emv: Ending Market Value

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if (numCD <= 0) {

throw new ArithmeticException ("numCD <= 0");

}

for (int i = 0; i < cashFlow.length; i++) {

if (numD[i] < 0) {

throw new ArithmeticException ("numD[i]<0 , " + "i=" + i);

}

weight[i] = (double) (numCD - numD[i]) / numCD;

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double ttwcf = 0; // total time weighted cash flows

for (int i = 0; i < cashFlow.length; i++) {

ttwcf += weight[i] * cashFlow[i];

}

double tncf = 0; // total net cash flows

for (int i = 0; i < cashFlow.length; i++) {

tncf += cashFlow[i];

}

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== Excel VBA function for modified Dietz return ==

<syntaxhighlight lang="VBVBnet">

Public Function MDIETZ(dStartValue As Double, dEndValue As Double, iPeriod As Integer, rCash As Range, rDays As Range) As Double