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The Modified Dietz calculation can calculate monthly returns for partial periods. This methodology is useful for calculating returns for positions that an entity does not hold for the entire period, such as when a position is completely sold out of or newly bought in during the month. This works at each level of the performance model wherever the position is not in the account for the entire month, from the security level through the total level. The Partial Period Modified Dietz calculation has the ability to weight the cash flows based on the number of days the position exists rather than weighting them using the number of days within the month.
The following table shows how Eagle Performance calculates Modified Dietz inputs for the begin of day, end of day, and middle of day weighting methods. It presents three possible partial period scenarios where there is no beginning market value, no ending market value, and no beginning or ending market value. The Modified Dietz calculation does not change when both begin and ending market values are present for a position.
Weighting Method | Input Type | BMV Only (no EMV) | EMV Only(no BMV) | No BMV and No EMV |
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Begin of Day | begin date | BMV effective date | First cash flow date | First cash flow date |
end date | last cash flow date | EMV effective date | last cash flow date | |
days in period | end date - begin date -1 | end date - begin date +1 | end date - begin date | |
cash flow weight | (days in period - cash flow day) / days in period | (days in period - cash flow day) / days in period | (days in period - cash flow day) / days in period | |
cash flow day | flow date - begin date -1 | flow date - begin date | flow date - begin date | |
Middle of Day | begin date | BMV effective date | First cash flow date | First cash flow date |
end date | last cash flow date | EMV effective date | EMV effective date | |
days in period | end date - begin date -.5 | end date - begin date +.5 | end date - begin date | |
cash flow weight | (days in period - cash flow day) / days in period | (days in period - cash flow day) / days in period | (days in period - cash flow day) / days in period | |
cash flow day | flow date - begin date -.5 | flow date - begin date | flow date - begin date | |
End of Day | begin date | BMV effective date | First cash flow date | First cash flow date |
end date | last cash flow date | EMV effective date | EMV effective date | |
days in period | end date - begin date | end date - begin date | end date - begin date | |
cash flow weight | (days in period - cash flow day) / days in period | (days in period - cash flow day) / days in period | (days in period - cash flow day) / days in period | |
cash flow day | flow date - begin date | flow date - begin date | flow date - begin date |
An example follows. Assume you have the ending market value (EMV) only with no beginning market value (BMV) and use the Begin of Day weighting method. Under this scenario, for a position initiated with a buy on March 10:
Begin Date. The first cash flow on March 10 serves as the begin date for the Modified Dietz calculation for that position.
Days in Period. For weighting purposes, the days in period is the effective date of the end date of the report minus the cash flow effective date plus one day. For a flow on March 15 for the same position, the days in the period is 31 - 10 + 1 = 22 days.
Cash Flow Weight. The weight of the cash flow is 17 / 22 = .7727.
Cash Flow Day. The cash flow day is the effective date of the flow minus the begin date of the period. The cash flow day is equal to 15 - 10 = 5.
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You can create a Modified Dietz field.
To create a Modified Dietz field:
In the Report Rule window, click New Field.
Select Modified Dietz Return from the Custom folder and click New.
The Modified Dietz Field dialog box appears.Complete the fields on the Modified Dietz dialog box and click OK.
In the Fields area, when you click the text box next to a field, a down arrow appears that allows you to select fields from the Custom and Holding folders. The following figure shows an example of the Modified Dietz field.
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The following table describes the calculation in the example above.
Field | Description |
|---|---|
Begin Market Value | This field points to the holding or custom detail calculation field to use for the beginning of period market value. |
End Market Value | This field points to the holding or custom detail calculation field to use for the end of period market value. |
Cash Flow | This field points to the field to use for adjusting the market values for periodic cash flows. The cash adjustment field is the net of the cash flows used to adjust the numerator of the Modified Dietz formula, and the definition of the field to time weight for the denominator of the Modified Dietz formula. It is the field to use for discounting cash flows using the IRR formula. |
Weighting Method | This option specifies the weighting method. Options include:
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Partial Period Option | This option allows you to weight cash flows based on the time a position is held when a position is not held for the entire month. Options include:
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Ignore Significant Cash Flow breaks | This option is identifies the performance impact of significant cash flows. |
for details. | |
Use Absolute Denominator | When looking at single-period returns for securities that are held short, the Modified Dietz formula displays positive performance returns as a negative number and negative performance returns as a positive number. Using this option corrects this issue. Returns generated by the Modified Dietz with Absolute Denominator should not be used for contribution, attribution, or multi-period linking. |
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You can use a Modified Dietz type calculation to calculate the monthly return and run the monthly report using significant cash flow (SCF) processing to prevent distortions caused by large external cash flows. See
for details.
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The Dollar Value Added (DVA) field is related to the Modified Dietz field. It displays the numerator of the Modified Dietz calculation and it is useful for troubleshooting purposes.
The basic calculation follows.
EMV-BMV-Sum of Cash Flows
Where:
EMV is ending market value
BMV is beginning market value
The following figure shows an example of the Dollar Value Added field.
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The Average Invested Balance (ABAL) field is related to the Modified Dietz field. It displays the denominator of the Modified Dietz calculation and is useful for troubleshooting purposes. You can commit the ABAL field to the database for use as the weight field in attribution reporting.
The basic calculation follows.
BMV+Sum of Weighted Cash Flows
Where:
BMV is the beginning market value
The following figure shows an example of the Average Invested Balance field.
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