Annualize Returns

Various components of Eagle Performance annualize performance for cumulative performance greater than one year. In addition to Performance Link Analysis fields, these components include the Performance Risk Analysis fields, Composite Performance Analysis fields, Performance Query Tool Operation Definition, Multi-Period Calculator (MPC) fields, Internal Rate of Return fields, Global Attribution, and Dynamic Mutual Fund Returns fields.

The system wide annualization methods for annualizing returns include the following:

A description of each method follows.

A performance system parameter, Sys Item 8, (SYS_ITEM) stores the value that determines the annualization option to use across the system. The SYS_ITEM has a default value of Months. See Numerator for Annualization Based on Days for examples.

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Default Annualization Method

For the Default annualization method, the Performance Link Analysis returns are annualized using the following formula:

(([Linked Growth Rates] raised to [Annualization Factor]) -1) * 100

The formula for the annualization factor is:

[Numerator] / [Day or Month Count]

Only periods greater than one year are annualized:

One Year for non-leap years equals 365 days.
One Year for leap years equals 366 days. Leap years are any period that includes February 29th.

The following table lists the rules used to determine the Numerator and Day Count.

Use Business Calendar Option	Single-Period Return Frequency	Numerator	Field Type	Day Count
Off	D, M, Q, Y	365	Inception-to-date	Actual number of days since inception
			NOT Inception-to-date	Actual number of days in period
On	D	365	Inception-to-date	Actual number of days since inception +1
			NOT Inception-to-date	Number of days since the first PERF_SUMMARY record of the period
On	M	12	Inception-to-date	Number of monthly records in PERF_SUMMARY up to and including the end date
On	M	12	NOT Inception-to-date	Number of monthly records in PERF_SUMMARY for the custom period
On	Q	4	Inception-to-date	Number of quarterly records in PERF_SUMMARY up to and including the end date
On	Q	4	NOT Inception-to-date	Number of quarterly records in PERF_SUMMARY for the custom period

Several examples showing the calculation of the day count and numerator follow:

Example 1. Daily Frequency (Inception Date 12/31/1999, first return on 1/3/2000)
Business Calendar Off

ITD as of 12/31/2002 = 365 / (366 + 365 + 365) = 365 / 1096
3YR as of 12/31/2002 = 365 / (366 + 365 + 365) =365 / 1094
2YR as of 12/31/2002 = 365 / (365 + 365) = 365 / 730

Business Calendar On

ITD as of 12/31/2002 = 365 / (366 + 365 + 365 + 1) = 365 / 1097
3YR as of 12/31/2002 = 365 / (364 + 365 + 365) =365 / 1094
2YR as of 12/31/2002 = 365 / (365 + 365) = 365 / 730

Example 2. Monthly Frequency (Inception Date 12/31/1999, first return on 1/31/2000)
Business Calendar Off

ITD as of 6/30/2002 = 365 / (366 + 365 + 181) = 365 / 912
2YR as of 6/30/2002 = 365 / (365 + 365) = 365 / 730
18MO as of 6/30/2002 = 365 / (365 + 184) = 365 / 549

Business Calendar On

ITD as of 6/30/2002 = 12 / (12 + 12 + 6) = 12 / 30
2YR as of 6/30/2002 = 12 / (12 + 12) = 12 / 24
18MO as of 6/30/2002 = 12 / (12 + 6) = 12 / 18

Days Annualization Method

The Days annualization method uses an actual day count regardless of the business calendar option, data frequency, or period type. The numerator to the annualization factor is variable by changing the performance system parameter setting, Sys Item 9, called "Numerator for annualization based on days." In addition, the return is only annualized if there are more than 365 days in a given period, unless that period has February 29th. In that case, more than 366 days are required. This is the same logic the default option uses.

Months Annualization Method

The Months annualization method uses a month count regardless of the business calendar option, data frequency, or period type. The numerator to the annualization factor would be hard coded to 12. The month count in the denominator is determined by counting all the months in a period, unless the period includes inception or termination dates. If the period contains an inception or termination date, a fractional representation of the inception or termination month is used instead of a count of 1. This fractional representation is calculated using the number of days in the month minus the inception day then divided by the number of days in the month.

For termination dates, the fraction is calculated by taking the termination day number divided by the number of days in the given month. A number is only annualized if there are more than 12 months in a given period.

Numerator for Annualization Based on Days

When annualizing based on days, instead of hard coding the numerator of the annualization factor to 365, the performance system parameter, Sys Item 9, (SYS_ITEM) stores a number to use instead of 365. This setting applies to the Days method only.

To configure the numerator, the SYS_ITEM stores the value that determines the numerator for annualization based on days to use across the system. To support backwards compatibility, the SYS_ITEM is scripted to 365 in upgrade and installation scripts.

Examples of each annualization method are shown in the following three figures.

Annualization Method