Absolute Ranks, Percentile Ranks, and Fractional Ranks Morningstar Methodology Paper February 28, 2011 2011 Morningstar, Inc. All rights reserved. The information in this document is the property of Morningstar, Inc. Reproduction or transcription by any means, in whole or in part, without the prior written consent of Morningstar, Inc., is prohibited.
Absolute Ranks In order to assign percentile ranks to funds Morningstar first assigns an absolute rank. The following procedure is used for assigning absolute ranks to funds: 1. Pull in the returns for the time period being ranked for all funds in a category. 2. Sort the returns in descending order. 3. Assigned a value of 1 to the highest return value. 4. When two share classes or two distinct portfolios share the same return assign the same absolute rank to the share class or distinct portfolio. Name Tot Ret Annlzd 3 Yr Absolute Rank AXP Global Technology A 1.8386 36 AXP Global Technology Y 1.8386 36 5. For the next return that has a different value assign a rank equally to the absolute rank of the previous fund plus the number of share classes or distinct portfolios that shared the same return. In the example below two share classes shared the same return 1.8386. Name Tot Ret Annlzd 3 Yr Absolute Rank AXP Global Technology A 1.8386 36 AXP Global Technology Y 1.8386 36 Fidelity Select Software & Comp 1.7194 38 6. Continuing counting until the last absolute rank is assigned. The last absolute rank value should be equal to the number of share classes in the category (n). This value will be used in the formula for calculating the percentile rank. Please note that Morningstar freezes absolute ranks and counts at the end of each month. If a discrepancy is found in a fund return Morningstar may recalculate the fund s percentile rank by using breakpoints. By using breakpoints Morningstar does not have to recalculate the percentile ranking for the entire peer group. Recalculation is not possible with absolute ranks therefore instances may occur where absolute rank and percentile rank do not match. We expect these instances to occur very seldom. in whole or part, without the prior written consent of Morningstar, Inc., is prohibited. 2
Percentile Ranks Morningstar uses the following formula to determine the percentile rank of an item in a series. It is commonly used for calculating an investment s total return percentile rank against others in its Morningstar Category. With this method, percentile ranks always range from 1 (best) to 100 (worst) with all intermediate values spread evenly over that range. All observations are ranked in the desired order (usually descending). Percentile ranks are assigned as follows: PctRank = i for i = 1 FLOOR[99*(i-1)/(n-1)+1] for i > 1 where: n = Total number of observations i = Absolute Rank of each observation Floor = A function that rounds down to the next integer (e.g., 89.83 rounds down to 89) Morningstar does not require a minimum number of items in order to percentile rank a set of data. For example, if there are only three funds in a category for a certain time period, we will percentile rank those three (1, 50, 100). Percentile ranks can be mapped into deciles and quartiles in the following manner. Range Decile Range Quartile 0 < Percentile Rank <= 10 1 0 < Percentile Rank <= 25 1 10 < Percentile Rank <= 20 2 25 < Percentile Rank <= 50 2 20 < Percentile Rank <= 30 3 50 < Percentile Rank <= 75 3 30 < Percentile Rank <= 40 4 75 < Percentile Rank <= 100 4 40 < Percentile Rank <= 50 5 50 < Percentile Rank <= 60 6 60 < Percentile Rank <= 70 7 70 < Percentile Rank <= 80 8 80 < Percentile Rank <= 90 9 90 < Percentile Rank <= 100 10 in whole or part, without the prior written consent of Morningstar, Inc., is prohibited. 3
Fractional Ranks For some calculations, such as those related to the Morningstar Rating, Morningstar ranks investments based on the number of distinct portfolios in a category, rather than giving equal weight to each share class. This ensures that funds with multiple share classes do not have a disproportionate weight compared to single-share funds. When several funds are merely different share classes of the same underlying portfolio, each share class is counted as a fraction of a fund. For example, if a fund has five share classes with three years of returns available, each share class will get a weight of 0.20 for ranking three-year returns. The first step in assigning ranks is to assign a fractional weight to each fund in the category. The fractional weight is assigned based on the number of share classes and whether each share class has a return available. In this example, Convertible Income Growth is assigned a fractional weight based on four share classes because the fifth share class, the Adv share class, does not have a three year return. Oldest Share Class Fractional Convertible A -7.113 0.2 Convertible A Load Waived -5.594 0.2 Convertible B -7.158 0.2 Convertible C -5.35 0.2 Convertible I -5.35 0.2 Convertible Income Growth A -12.749 0.25 Convertible Income Growth A Load Waived -11.009 0.25 Convertible Income Growth Adv Convertible Income Growth B -12.522 0.25 Convertible Income Growth M -12.522 0.25 Convertible Securities A -6.871 0.2 Convertible Securities Adv -8.799 0.2 Convertible Securities A Load Waived -7.145 0.2 Convertible Securities B -8.7 0.2 Convertible Securities C -7.822 0.2 Investment Grade Convertible A -10.976 0.5 Investment Grade Convertible A Load Waived -10.374 0.5 US Convertible I -4.913 0.5 US Convertible II -4.804 0.5 in whole or part, without the prior written consent of Morningstar, Inc., is prohibited. 4
There are five distinct portfolios in the example above: Convertible, Convertible Income Growth, Convertible Securities, Investment Grade Convertible and US Convertible. The next step is to sort all the funds in the category with the highest value first and the lowest value last. Oldest Share Class Fractional US Convertible II -4.804 0.5 US Convertible I -4.913 0.5 Convertible C -5.35 0.2 Convertible I -5.35 0.2 Convertible A Load Waived -5.594 0.2 Convertible Securities A -6.871 0.2 Convertible A -7.113 0.2 Convertible Securities A Load Waived -7.145 0.2 Convertible B -7.158 0.2 Convertible Securities C -7.822 0.2 Convertible Securities B -8.7 0.2 Convertible Securities Adv -8.799 0.2 Investment Grade Convertible A Load Waived -10.374 0.5 Investment Grade Convertible A -10.976 0.5 Convertible Income Growth A Load Waived -11.009 0.25 Convertible Income Growth B -12.522 0.25 Convertible Income Growth M -12.522 0.25 Convertible Income Growth A -12.749 0.25 You then calculate the cumulative weight for each fund. There are two steps to assigning the cumulative weight. For step 1, the cumulative weight for the first fund is equal to the fractional weight. The cumulative weight for the second fund is equal to the fractional weight of the second fund plus the cumulative weight of the first fund and so forth. in whole or part, without the prior written consent of Morningstar, Inc., is prohibited. 5
US Convertible II US Convertible I Convertible C Convertible I Convertible A Load Waived Convertible Securities A Convertible A Convertible Securities A Load Waived Convertible B Convertible Securities C Convertible Securities B Convertible Securities Adv Investment Grade Convertible A Load Waived Investment Grade Convertible A Convertible Income Growth A Load Waived Convertible Income Growth B Convertible Income Growth M Convertible Income Growth A Oldest Share Class Fractional Cumulative Step 1-4.804 0.5 0.5-4.913 0.5 1-5.35 0.2 1.2-5.35 0.2 1.4-5.594 0.2 1.6-6.871 0.2 1.8-7.113 0.2 2-7.145 0.2 2.2-7.158 0.2 2.4-7.822 0.2 2.6-8.7 0.2 2.8-8.799 0.2 3-10.374 0.5 3.5-10.976 0.5 4-11.009 0.25 4.25-12.522 0.25 4.5-12.522 0.25 4.75-12.749 0.25 5 In step 2 you need to compare the returns of the funds. In the example above if we went from step 1 directly to assigning the percentile rank Convertible C and Convertible I would receive different rankings even though they have the exact same return. To get the final cumulative weight assign the first funds final cumulative weight equal to the cumulative weight step 1. Next, if the return of the second fund is not equal to the return of the first fund then the final cumulative weight is equal to the cumulative weight step 1. If the return of the second fund is equal to the return of the first fund then the final cumulative weight is equal to the cumulative weight step 1 of the first fund. in whole or part, without the prior written consent of Morningstar, Inc., is prohibited. 6
Oldest Share Class Fractional Cumulative Step 1 Final Cumulative US Convertible II -4.804 0.5 0.5 0.5 US Convertible I -4.913 0.5 1 1 Convertible C -5.35 0.2 1.2 1.2 Convertible I -5.35 0.2 1.4 1.2 Convertible A Load Waived -5.594 0.2 1.6 1.6 Convertible Securities A -6.871 0.2 1.8 1.8 Convertible A -7.113 0.2 2 2 Convertible Securities A Load Waived -7.145 0.2 2.2 2.2 Convertible B -7.158 0.2 2.4 2.4 Convertible Securities C -7.822 0.2 2.6 2.6 Convertible Securities B -8.7 0.2 2.8 2.8 Convertible Securities Adv -8.799 0.2 3 3 Investment Grade Convertible A Load Waived -10.374 0.5 3.5 3.5 Investment Grade Convertible A -10.976 0.5 4 4 Convertible Income Growth A Load Waived -11.009 0.25 4.25 4.25 Convertible Income Growth B -12.522 0.25 4.5 4.5 Convertible Income Growth M -12.522 0.25 4.75 4.5 Convertible Income Growth A -12.749 0.25 5 5 The last fund in the peer group receives a cumulative weight equal to the number of distinct portfolios. The final step is to assign a percentile rank to each fund. The ranks are simply the fund s raw rank in peer group (the cumulative weight of all funds up to and above it) divided by the total number of distinct portfolios adjusted for the number of distinct observations in that group. in whole or part, without the prior written consent of Morningstar, Inc., is prohibited. 7
Final Cumulative Percentile Rank US Convertible II -4.804 0.5 10.00% US Convertible I -4.913 1 20.00% Convertible C -5.35 1.2 24.00% Convertible I -5.35 1.2 24.00% Convertible A Load Waived -5.594 1.6 32.00% Convertible Securities A -6.871 1.8 36.00% Convertible A -7.113 2 40.00% Convertible Securities A Load Waived -7.145 2.2 44.00% Convertible B -7.158 2.4 48.00% Convertible Securities C -7.822 2.6 52.00% Convertible Securities B -8.7 2.8 56.00% Convertible Securities Adv -8.799 3 60.00% Investment Grade Convertible A Load Waived -10.374 3.5 70.00% Investment Grade Convertible A -10.976 4 80.00% Convertible Income Growth A Load Waived -11.009 4.25 85.00% Convertible Income Growth B -12.522 4.5 90.00% Convertible Income Growth M -12.522 4.5 90.00% Convertible Income Growth A -12.749 5 100.00% This technique allows Morningstar to rank each fund share class individually, while ensuring that any single portfolio with many versions does not crowd out others within a range. Morningstar does not require a minimum number of items in order to percentile rank a set of data. in whole or part, without the prior written consent of Morningstar, Inc., is prohibited. 8
Many funds are offering hedged share classes as part of their funds line up. These share classes are for investors who want to hold across border assets but not have the foreign exchange risk. To accommodate these funds Morningstar will put the hedged currency share class in a different category which reflects the funds investing style as well as the currency hedge strategy. For rating purposes a portfolio with a hedged share class and a non-hedged share class will be represented as distinct portfolios in different categories for rating purposes. For example: Portfolio: Investment A Name Category Fractional Dollar Bond A1 USD USD Category 0.5 Dollar Bond A2 EUR USD Category 0.5 Represents one distinct non-hedged portfolio in the USD Category. te the base currency of a class does not impact its classification absent hedging. Name Category Fractional Dollar Bond A1 EUR Hedged EUR Category 0.5 Dollar Bond A2 EUR Hedged EUR Category 0.5 Represents one distinct hedged portfolio in the EUR Category. These classes are placed in a different category as they are hedged to EUR. in whole or part, without the prior written consent of Morningstar, Inc., is prohibited. 9