The Morningstar Category Average Methodology

Transcription

1 ? The Morningstar Category Average Methodology Morningstar Research 31 August 2017 Contents 1 Introduction 1 Construction Methodology Calculation Methodology 2 Monthly, Quarterly, and Annual 4 Daily Return Series 8 Active and Passive Averages 8 IA, ABI, AIC, and GIF Averages 12 Non-Return-Based Averages 14 Methodology Changes Morningstar Category averages are designed to represent the average return o unds within their category over time. It will be structurally dierent rom the mean return o the current constituents o the category as it will take into account unds that have changed categories over time and share classes/unds that have subsequently liquidated. This ensures that the category averages are ree o survivorship bias. Morningstar creates a category average daily total return index series, or TRI, as well as monthly, quarterly, and annual returns. The daily category averages are calculated daily and reconstituted monthly. Introduction Morningstar Category averages are designed to represent the average return o unds within their category over time. It will be structurally dierent rom the mean return o the current constituents o the category as it will take into account unds that have changed categories over time and share classes/unds that have subsequently liquidated. This ensures that the category averages are ree o survivorship bias. Morningstar creates a category average daily total return index series, or TRI, as well as monthly, quarterly, and annual returns. The daily category averages are calculated daily and reconstituted monthly. Construction Methodology For the TRI series, only daily pricing share classes will contribute to the Morningstar Category averages. This is to prevent unds with a less-requent pricing basis rom skewing the daily returns o the category average. The monthly/quarterly/annually precalculated returns or all universes will incorporate all share classes that price monthly (or more requently). The category average return is the perormance o a portolio o the unds in the category. The portolio is constructed as ollows. 1. On the last day o each month, the category average is constituted with all share classes o all unds in the category as o that date. 2. Funds that can only be purchased by proessional investors should be excluded rom the average. 3. On the last day o each month, the unds are equally weighted and the share classes within each und are equally weighted. This is called ractional weighting. Consider a very simple category with ive unds, each with ive share classes. Each und has a weight o one, so thereore each share class o each und has a weight o 0.2 (one und divided by ive share classes). The 25 share classes have a combined weight o 25 times 0.2, or ive, the number o unds in the category. By ensuring each und is weighted equally regardless o the number o share classes it has, ractional weighting ensures that unds with multiple share classes do not dominate and skew the returns o the average.

2 Page 2 o The portolio is not rebalanced during the month, unless one or more unds or share classes drop out. I one or more share classes o a und drop out, the weighting o that share class is distributed proportionally among the remaining share classes o the und. I one or more unds drop out entirely, the und's weighting is distributed proportionally among the remaining unds (and then proportionally among each und's share classes). 5. Dividends and other income payouts are reinvested on the reinvestment dates. 6. Rules 3 and 4 are applied daily to create a provisional portolio. I it later turns out that the absences o net asset values or income payouts were due to a lag in reporting, the daily returns are restated once the data become available. 7. Each day, the daily values or the current month and previous month will be recalculated. Hence, the daily category average return is the one-day perormance o a portolio that is reconstituted monthly. Returns o Constituent Share Classes The returns o the individual share classes in each category shall be calculated, ver possible, rom the NAV (or other tradable price) and dividend inormation. The returns shall be calculated on a pretax total return basis. In cases a und does not publish NAVs (or other tradable prices), then the published returns or the und shall be used. Calculation Methodology or the Monthly, Quarterly, and Annual Returns In August 2017, the methodology used to calculate the monthly, quarterly, and annual returns was changed to introduce ractional weighting. For all existing categories, the returns or period-ends ater this date will be calculated using the new methodology, while returns or periods prior to that date will continue to use the old nonractional methodology. Any category launched ater this date will use the new methodology or the entire history. Methodology or All Return Periods Ending Ater August 2017 Each und is represented as one distinct portolio in the category group. Upon reconstitution, a und composed o our share classes receives a ractional weighting o 0.25 on each share class; this is multiplied by the und weighting to determine the share-class weighting. The category return or any given month can be calculated irst by inding each share class' weighting or that period:

3 Page 3 o 14 Exhibit 1 W t (, s) = 1 1 F(t) S(,t) w t (, s) = weighting or share class s o und at t, the end date o the period F(t) = number o unds at time t in the category S(,t) = number o share classes o und at t The category average return is the weighted average return o the constituents. Exhibit 2 R tc = w t(,s) R t(,s) F(t) s S(,t) R tc = average return or category c or period t R t (, s) = return or share class s o und on the inal day o period t w t (, s) = ractional weighting or share class s o und on the inal day o period t F(t) = set o all unds in the category on the inal day o period t S(, t) = set o all share classes o und on the inal day o period t Methodology or All Return Periods Ending Prior to August 2017 The calculation is simply the average o the returns or all share classes (active and obsolete) or that period in the category. For example, Morningstar calculates a calendar-year return or 1997 or the largegrowth category by doing a simple arithmetic average o the 1997 calendar-year returns or all share classes that were assigned to the large-growth category as o Dec. 31, This can include currently obsolete share classes that were active during the 1997 calendar year.

4 Page 4 o 14 Exhibit 3 R ct = n i=1 R st n R ct= average return or the category or time period t R st = return or share class s or period t n = number o share classes in the category with returns or period t Calculation Methodology or the Daily Return Index Series In August 2017, the methodology used to calculate the daily return index series was changed to introduce ractional weighting. For all existing categories, the daily returns ater this date will be calculated using the new methodology, while daily returns prior to that date will continue to use the old nonractional methodology. Any category launched ater this date will use the new methodology or the entire history. Methodology or All Daily Returns Ater August 2017 This new methodology is used to calculate the total return index series or Morningstar Categories. The total return index series indicates a category's perormance on a daily basis. Funds are rebalanced to equal weightings upon month-end reconstitution, and during the month their weightings loat dynamically based on their relative perormance in the category. Funds with inceptions or classiication changes during the month are added to the category at the next month-end reconstitution. Funds that exit the category because o termination or classiication change during the month are removed rom the category on the dates they exit, and their weightings in the category average are prorated among surviving unds based on the latter's dynamic weightings. This methodology ensures that the und weightings are dynamically loating and the category returns are ree o survivorship bias. A und is considered terminated when all o its share classes are terminated. In addition, we incorporate ractional weightings into the methodology. This means that each und is represented as one distinct portolio in the category group. Upon reconstitution, a und composed o our share classes receives a ractional weighting o 0.25 on each share class; this is multiplied by the und weighting to determine the share-class weighting. Following the same logic as above, share classes with inceptions or classiication changes during the month are added to the category at the next month-end reconstitution. Share classes that exit the category because o termination or classiication change during the month are removed rom the category on the dates they exit, and their weightings in the category average are prorated among surviving share classes o the same und based on these share classes' dynamic weightings.

5 Page 5 o 14 At month-end reconstitution, the ormula or each und's share-class weighting is: Exhibit w t0 (, s) = F(t0) S(, t0) w t0 (, s)= weighting or share class s o und on day t0, the day o month-end reconstitution F(t0) = number o unds on day t0 S(, t0) = number o all share classes o und on day t0 On a daily basis, the category average TRI is calculated rom the weighted average return (rom the last reconstitution date to the current date) o the surviving constituents. The category average total return index and return are expressed in the ollowing ormulas: Exhibit 5 TRI category t = TRI category e [1 + F(e) s S(,e) w e (,s) R e,t (,s) ] = TRI category e [ w e (, s) TRI t(, s) ] TRI e (, s) F(e) s S(,e) TRI t category = total return index or the category on day t e = date o the most recent und and/or a share class exit, and e < t F(e) = set o all unds in the category on day e S(, e) = set o all share classes o und on day e w e (, s) = weighting or share class s o und on day e. This will equal w t0 (, s) until a share class leaves the category TRI e category = total return index or the category on day e TRI t (, s) = total return index or each, s on day t TRI e (, s) = total return index or, s on day e Note: e will equal t0 rom the date o the month-end until the irst date that a und or share class leaves the category

6 Page 6 o 14 Exhibit 6 R category t 1,t = TRI category t category 1 TRI t 1 R category t 1,t = return or the category in the period rom day t 1 to day t I a category has unds/share classes leaving the category because o liquidation or reclassiication or any other reason, then the weightings o the remaining share classes would need to be recalculated. I an entire und leaves the category--that is, no share classes o that und remain in the category ater that date--then that und's weighting on the day it leaves the category will be distributed across all remaining share classes in the category in proportion to their respective weightings on the day the und leaves. I a share class leaves the category but share classes rom the same und remain in the category, then that share class' weighting on the day it leaves the category will be distributed across the remaining share classes o that und in proportion to their respective weightings on the day the share class leaves. To calculate the new weightings or the remaining unds/share classes on the day the category has a und or share class leave the category, irst calculate: Exhibit 7 w e 1 () = s S(,e 1) w e 1 (, s) w e 1 ()= weighting o und at time period e 1, the day beore any und/share class leaves, e Exhibit 8 v e 1,t (, s) = 1 w e 1 () g F(t) w e 1 (g) q S(,t) w e 1 (,q) w e 1(, s) TRI t (,s) TRI e 1 (,s) v e 1,t (, s)= value at time t o the money invested in und share class s at time e 1 per $1 o the value o the portolio at time e 1 F(t) = the set o unds that are still in the category on day t (g is an element o this set) S(, t) = the set o share classes o und that are still in the category on day t (q is an element o this set)

7 Page 7 o 14 Exhibit 9 w t (, s) = v e 1,t (,s) g F(t) q S (g,t) v e 1,t(g,q) w t (, s) = weighting o share class s o und at time t This now becomes the new reconstitution date, and the daily TRI is now calculated rom this date and series o weightings. See Exhibit 5. Methodology or Daily Returns Prior to August 2017 The irst step is to calculate the average daily return or each category based on all share classes (active and obsolete) that existed on that day. Exhibit 10 R ct = n i=1 R st n R ct = return or category c on day t R st = return or share class s on day t n = number o share classes in the category on day t Then the total return index value is calculated Exhibit 11 TRI t = TRI 0 * (1 + CR t ) = TRI t 1 (1 + R ct ) TRI t = total return index on day t TRI 0 = total return index at the beginning o the period CR t = total return cumulative rom the beginning to day t, expressed in decimal ormat TRI t 1 = total return index on day (t 1), the day prior to day t R ct = total return on day t, expressed in decimal ormat

8 Page 8 o 14 Methodology or Active and Passive Category Averages In the US Open End and Exchange Traded Product Universe, Morningstar divides the constituents o each Morningstar category into two groups: Active and Passive. Although most exchange-traded products are passively-managed index-based products, not all o them are. Further, a material number o open-end unds are explicitly stated as being index tracking vehicles. Morningstar will group as Passive all open-end unds and exchange-traded products that are marked as 'Index Fund = True', as well as Strategic Beta unds, to create category sub-group averages. The remaining products will be grouped in the Active sub-group. Methodology or IA, GIF, AIC and ABI Daily Returns For the IA, GIF, AIC and ABI sector averages a single share classes within a und (reerred to as the primary share class) is used as a proxy or the und. Funds are rebalanced to equal weights upon monthend reconstitution, and during the month their weights loat dynamically based on their relative perormance in the chosen classiication peer group/sector. For the purpose o this calculation, unds with inceptions or classiication changes during the month are added to the sector at the next monthend reconstitution. Funds that exit the sector because o termination or classiication change during the month are removed rom the sector on the dates they exit, and their weights in the sector average are prorated among surviving unds based on the latter s dynamic weights. These und weights will be reerred to as adjusted weights in order to distinguish them rom equal weighting on that day. This methodology ensures that the und weights are dynamically loating and the sector returns are survivorship-bias ree. On a daily basis, the sector average return is the weighted average return o the surviving constituents. The sector average return and the weight or each und can be expressed in the ollowing ormulas. Exhibit 12 n t sector R t 1,t = w t 1 R t 1,t =1 R Sector t 1,t = return or the sector in the period rom t-1 to t w t 1 = adjusted weight or und on day t - 1 R t 1,t = return or und in the period rom t -1 to t n t = number o unds in the sector at time t

9 Page 9 o 14 Exhibit 13 w t 1 w t 1 w t 1 = 1 n t i t is month-end = w t 1 wi i st t 1 i t is not month-end = pre adjustment weight or und on day t 1 i w t 1 = pre-adjustment weight or und i on day t -1 s t = subset o unds that survived at time t Exhibit 14 w t = w t 1 (1+ R t 1,t) (1 + R Sector t 1,t ) w t = pre-adjustment weight or und on day t w t 1 = pre adjustment weight or und on day t 1 It may not be practical to calculate and store daily weights or a large quantity o unds that are dynamic loating and survivorship-bias ree. Thereore, the rest o the document oers ormulas expressed in total return index ormat that serve as an alternative to ormulas in the section above. The ollowing ormula establishes the relationship between the total return and its total return index. Exhibit 15 R t 1,t = TRI t TRI t 1 1 TRI t = total return index on day t TRI t 1 = total return index on day t 1, the day prior to t R t 1,t = total return or the period t 1to t When perorming a sector average return calculation or a day that does not have a und exit in the month on or beore that day, the sector average return is the equally weighted average o the month-to-

10 Page 10 o 14 date cumulative returns o the constituent unds. Following is the ormula expressed in return and total return index ormats. Exhibit 16 TRI Sector t = TRI Sector 0 [1 + 1 n 0 Sector R n 0 =1 0,t ] = TRI 0 [1 + 1 n 0 ( TRI t n 1) 0 =1 ] TRI 0 TRI t Sector = total return index or sector on day t TRI 0 Sector = total return index or sector on day 0, the time o last reconstitution n 0 = number o unds in the sector on day 0, the time o last reconstitution R 0,t = return or und in the period rom day 0, the time o the last reconstitution, to day TRI t = total return index or und on day t TRI 0 = total return index or und on day 0 When perorming sector average return calculation or a day that has a und exit in the month on or beore that day, the sector average return is the weighted average o the cumulative returns o the constituent unds rom the last und exit date to the calculation date. Below is the ormula. Exhibit 17 TRI t Sector = TRI e Sector [ 1 + n e =1 w e TRI t Sector = total return index or sector on day t n e R e,t ] = TRISector e [1 + w e =1 TRI e Sector = total return index or sector on day e, last und exit date n e = number o unds in the sector on day e, last und exit date w e = adjusted weight or und on day e, last und exit date R e,t = return or und in the period rom day e, the last und date, to day t TRI t = total return index or und on day t TRI e = total return index or und on day e, the last und exit date ] ( TRI t TRI 1) e The adjusted weight o each surviving und can be obtained by using the recursive ormulas in Exhibits 13 and 14 in the section above; however, it is more eiciently deined in the ollowing ormula.

11 Page 11 o 14 Exhibit 18 w e w e 1 (1+Re 1,e ) = = w e 1 (TRI e /TRIe 1 ) i i Se w e 1 (1 + R i e 1,e ) i i Se w e 1 (TRI i e /TRIi e 1 ) note w e 1 = 1 when e is the irst und exit or the month n 0 w e = adjusted weight or und on day e, the last und exit date w e 1 = adjusted weight or und on day e 1, the prior und exit date R e 1,e = return or und in the period rom day e 1, the prior und exit date, to day e, the last und exit date i R e 1,e = return or und i in the period rom day e 1, the prior und exit date, to day e, the last und exit date TRI e = total return index or und on day e, the last und exit date TRI e 1 = total return index or und on day e 1, the prior und exit date TRI e i = total return index or und i on day e, the last und exit date i TRI e 1 = total return index or und i on day e 1, the prior und exit date Only unds that price daily are included in the sector average calculation. This is done to prevent the averages rom skewing. I the current price is unavailable the previous day s closing price is used. I the und is ound to have changed pricing availability the und may be removed rom the sector average. In addition, the index is rerun every month-end and, in order to capture all distributions that are collected near the end o the calendar year, the index is rerun in January and February.

12 Page 12 o 14 Calculation o Non-Return-Based Averages or the Category For data points such as ees or share class sizes, share classes within a und would normally have dierent values, the calculation o a category average or those data points is a simple mean average basis o the values o all the share classes in the category. Exhibit 19 V tc = n i=1 x tci n V tc = value or category c during time period t x tci = value or share class i in category c during time period t n = total number o share classes in the category For data points share classes within a und can be expected to have the same or very similar values (such as yields or risk statistics such as alpha, beta, correlation, and so on), then the average is calculated ractionally by inding out each share class weight at the time o calculation. Exhibit 20 w t (, s) = 1 1 F(t) S(,t) w t (, s) = weighting or share class s o und at t F(t) = number o unds at time t in the category S(,t) = number o share classes o und at time t The category average is the weighted average value o the constituents.

13 Page 13 o 14 Exhibit 21 v tc = w t (, s) v t (, s) F(t) s S(,t) v tc = average value or category c or month t v t (, s) = value or share class s o und on the inal day o month t w t (, s) = ractional weighting or share class s o und on the inal day o month t F(t) = set o all unds in the category on the inal day o month t S(, t) = set o all share classes o und on the inal day o month t

14 Page 14 o 14 Methodology Changes The ollowing is a timeline o signiicant methodology changes to the Morningstar ranking methodologies. Date August 2017 Description Introduction o ractional weighting changes to category averages. New methodology paper replacing: Morningstar Calendar Year Category Averages Methodology November 2010 The category averages and sector averages sections o the Morningstar Total Return Index Methodology 2013