Morningstar Fixed Income Style Box TM Methodology

Transcription

1 Morningtar Fixed Income Style Box TM Methodology Morningtar Methodology Paper Augut 3, Morningtar, Inc. All right reerved. The information in thi document i the property of Morningtar, Inc. Reproduction or trancription by any mean, in whole or in part, without the prior written conent of Morningtar, Inc., i prohibited.

2 Content Introduction 3 Fixed Income Style Box Horizontal Axi: Interet Rate enitivity Vertical Axi: Credit Quality Source of Data Credit Quality Average Effective Duration Appendix A 9

3 Introduction The Morningtar Style Box wa introduced in 99 to help invetor and advior determine the invetment tyle of a fund. Different invetment tyle often have different level of rik and lead to difference in return. Therefore, it i crucial that invetor undertand tyle and have a tool to meaure their tyle expoure. The updated Morningtar Style Box provide an intuitive viual repreentation of tyle that help invetor build better portfolio and monitor them more accurately. Morningtar claifie bond fund in it tyle box baed on their enitivity to interet rate a limited, moderate and extenive meaured by the average effective duration of the fund holding; and their average credit quality a high, medium, or low baed on letter (or alphanumeric) credit rating of bond holding by third party credit rating agencie. The nine poible combination of thee characteritic correpond to the nine quare of the Morningtar Style Box -- quality i diplayed along the vertical axi and enitivity to interet rate along the horizontal axi. 3

4 Overview The model for the fixed income tyle box i baed on the two pillar of fixed-income performance: interet-rate enitivity and credit quality. A depicted in the image below the three interet enitivity group are limited, moderate and extenive and the three credit quality group are high, medium and low. Thee grouping diplay a portfolio effective duration and third party credit rating to provide an overall repreentation of the fund rik orientation given the enitivity to interet rate and credit rating of bond in the portfolio. Horizontal Axi: Interet-rate Senitivity The horizontal axi focue on interet-rate enitivity a meaured by the bond portfolio effective duration. Prior to October 009, US taxable-bond fund with duration of 3.5 year or le were conidered hort-term (having limited enitivity to interet rate change); more than 3.5 year but le than 6 year; intermediate term (having moderate enitivity to interet rate change); and more than 6 year, longer term (having extenive enitivity to interet rate change). In October 009, Morningtar moved from the aforementioned tatic breakpoint to dynamic breakpoint. 4

5 On a monthly bai Morningtar calculate duration breakpoint baed around the 3 year effective duration of the Morningtar Core Bond Index (MCBI). Limited: Moderate: Extenive: 5% to 75% of MCBI 75% to 5% of MCBI 5% of MCBI (no upper limit on long term duration) By uing the MCBI a the duration benchmark, Morningtar i letting the effective duration band to fluctuate in lock-tep with the market which will minimize market-driven tyle box change Non-US taxable-bond fund ue tatic duration breakpoint. Municipal bond fund with duration of 4.5 year or le qualify a low; more than 4.5 year but le than 7 year, medium; and more than 7 year, high. Non-US domiciled fund ue tatic duration breakpoint. Thee threhold are: Limited: Moderate: Extenive: <= 3.5 year > 3.5 and <= 6 year > 6 year Vertical Axi: Credit Quality Hitorically, Morningtar followed the indutry practice of reporting the average credit rating of a bond portfolio by taking a weighted average of rating baed on data provided by the fund company. However, becaue the default rate increae at an increaing rate between grade (a mathematical property called convexity), thi method ytematically undertated the average default rate of a bond portfolio. For example, for U.S. corporate bond a of the date of thi document, the pread in 5

6 default rate between CCC and BBB rated bond wa over time that of the default rate pread between BBB and AAA bond. Yet, the conventional method aume that thee pread are equal. To ee the impact of thi, conider a portfolio of 90% AAA bond and 0% CCC bond. According to the conventional method, the average credit rating of thi portfolio i AA. However, the average default rate for thi portfolio i that of BB bond. To correct thi bia, Morningtar take the convexity of default rate curve into account when calculating the average credit rating of a portfolio. The firt tep i to map the grade of a portfolio contituent into relative default rate uing a convex curve. Next, average the reulting default rate (rather than the grade) to come up with an average default rate for the portfolio. Finally, uing the ame convex curve Morningtar map the reulting average default rate back into a grade. For example, a portfolio of 90% AAA bond and 0% CCC bond will have an average credit rating of BB under thi new methodology. Independent reearch confirm that the arithmetic average credit rating of a bond portfolio ytematically undertate the credit rik and that a more meaningful meaure would be to average the default probabilitie aociated with each letter grade and then ue the convex curve that relate the numerical repreentation of the letter grade to default probability to aign a letter or alphanumeric rating to the portfolio. Thi procedure i detailed in Appendix A. Baed on following breakpoint Morningtar map the calculated average aet weighted letter credit rating (ee Appendix A) for all portfolio on the vertical axi of the tyle box:. "Low" credit quality where aet weighted average credit rating i le than BBB-.. "Medium" credit quality where aet weighted average credit rating i le than AA-, but greater or equal to BBB-. 3. "High" credit quality where aet weighted average credit rating i AA- and higher. 6

7 Source of Data The data which drive the fixed income tyle box i urveyed from fund companie. Morningtar ak fund companie to end the following information on a monthly or quarterly bai for each of their fixed income or allocation fund. Credit Quality Each fixed income ecurity and cah intrument in a fund are aigned to one of the following eight categorie for the credit quality calculation. The percentage for aet in that letter rating level a a percent of all fixed income and cah aet. AAA AA A BBB BB B Below B Not Rated Total Letter rating data provided to Morningtar in one of the firt even categorie (AAA through below B) only reflect letter rating aigned by one of the Nationally Recognized Statitical Rating Organization (NRSRO). So-called internal or manger-derived, alphanumeric credit rating are not to be included in thoe categorie: rather, bond not rated by an NRSRO are included in the not rated (NR) category. Morningtar i enitive to the reality that ome vendor ue Moody Invetor Service alphanumeric rating rather than or in addition to S&P letter rating claification. Below i a chart howing the equivalent Moody alphanumeric rating cla for each S&P letter rating cla. S&P AAA AA A BBB BB B Below B Moody Aaa Aa A Baa Ba B Below B 7

8 Morningtar prefer that bond be claified according to the Barclay Capital Family of Indice rating rule when rating are available from all three rating agencie (i.e. ue the middle rating of Moody, S&P, and Fitch after dropping the highet and lowet available rating); if only two rating agencie rate a ecurity then the lowet rating hould be ued; if only one agency rate a ecurity then that rating can be ued; if there i a ecurity with no rating that ecurity hould go into Not Rated. Average Effective Duration Morningtar ak fund companie to calculate and end average effective duration (alo known a option adjuted duration ) for each of their fixed income or allocation fund. We ak for effective duration becaue the meaure give better etimation of how the price of bond with embedded option, which are common in many mutual fund, will change a a reult of change in interet rate. Effective duration take into account expected mortgage prepayment or the likelihood that embedded option will be exercied if a fund hold future, other derivative ecuritie, or other fund a aet, the aggregate effective duration hould include the weighted impact of thoe expoure. Standard practice for calculating thi data point require determination of a ecurity option-adjuted pread, including the ue of option model or Monte Carlo imulation, a well a interet-rate cenario teting Morningtar requet that the fund only report data in thi field that ha been pecifically labeled effective or option-adjuted duration, or that fund i certain ha been calculated in the fahion decribed. Morningtar categorize any fixed intrument with le than one year to maturity a cah for the purpoe of calculating a fund aet allocation breakdown. Thee hort-term fixed ecuritie and other cah intrument are included in the calculation of effective duration. 8

9 Morningtar accept urvey returned with modified duration (and no effective duration provided) for fund in the municipal and high yield categorie. Survey for all other US bond categorie that lack a ubmiion for effective duration will not be accepted. Appendix A The firt three column of Table (refer to page ) preent the letter grade and their repective numerical repreentation for at the ecurity level ued in thi methodology. The fourth and fifth column how the mapping from the numerical repreentation to letter grade for a portfolio. Morningtar ha found that a good model of default rate for a number of rated bond univere i a follow: [] d( x) = a + ( d d ) f ( x, Θ) AAA CCC AAA Where x = the numerical repreentation of the bond rating d (x) = the default rate of the bond d AAA = the default rate of AAA bond (Aaa on Moody cale) d CCC = the default rate of CCC bond (Caa on Moody cale) f (.;Θ) = a convex -egment quadratic pline with f ( ;. ) = f ( ;. ) = 0; f ( 9;. ) = ; f ( 0, Θ) = ( Θ) Θ = the convexity parameter; /3 Θ (Thi guarantee that f (.;Θ) i increaing and convex) The value of f (.; Θ) are called the relative default rate. 9

10 The convexity parameter meaure the change in the lope from the AAA-BBB range to the BBB- CCC range, relative to the overall lope of the default rate curve: [] Θ = ( d d ) ( d d ) CCC d BBB CCC d BBB AAA AAA Where d BBB i the default rate for BBB bond (Baa on the Moody cale). Morningtar calculated Θ for a number of bond univere uing equation [] and found that 0.9 i a fair repreentation. Since the methodology require one convex cale for all bond univere, Morningtar et Θ = 0.9 globally. However, ince Morningtar will periodically review the data and could chooe another value in the future; Θ i programmed a a parameter that can be readily changed. The ixth column of Table (refer to page ) how the relative default rate uing Θ = 0.9 and the eventh column how the reulting fitted default rate uing the value of d and d for the corporate bond univere. The eighth column how the empirical default rate for the corporate univere. Figure (refer to page 3) graph thee empirical default rate and the default rate pline, howing that the pline i a good repreentation of the default rate curve. AAA CCC Let y=f(x) denote the value of a quadratic pline at x. Morningtar divide the domain of f(.) into interval of the form [ x, ], reulting interval of the range of the form [ y, y ]. The value of the endpoint are: x x y ½(- Θ ) 9 0

11 If x fall within the interval [ x, x ], the following occur: f x = a 0 + a x + a x [3] ( ) a 0 a a Where, and are parameter to be determined a 0 a a ( ) To determine the 3 parameter, and for egment, 3 equation are needed. Two of the equation follow from the condition that egment connect the point x y and ( x, ). Hence:, y [4] and [5] y = a0 + a x + a x y = a + a y + a y 0 The third condition follow from the condition that the f(.) be differentiable everywhere on the interval [ x, ]. Suppoe for the moment that the value of y f x ) i known. Hence, x = ( [6] y = a + a x a 0 a a Solving equation [4],[5] and [6] for, and, we have: [7] a = y x y + x y x x x + x x a = y y + a x [8] 0 ( )

12 [9] a = y a x We can then calculate + [0] y a a x = Let the numerical repreentation of a letter grade be x and the default probability be y. The interval for x are [, 0] and [0, 9], repreenting AAA-BBB and BBB-CCC repectively. Since the default probability curve i flat near AAA, et [9] to find, and and equation [0] to calculate. Thi proce i then repeated for =. a 0 a a y 0 = 0. With =, ue equation, [7], [8] and y

13 Table : Credit Grade and Default Rate (with Corporate Bond Example) Security Grade Portfolio Grade Relative Fitted Empirical Numerical. Default Default Convexity Moody S&P Repreentation. Moody S&P Rate Rate Breakpoint Aaa AAA Aaa AAA 0.00% Aaa AAA 0.06% 0.35 Aa AA+ 3 Aa AA+ 0.5% 0.80 Aa AA 4 Aa AA 0.56% Aa3 AA- 5 Aa3 AA- 0.99% A A+ 6 A A+.54% A A 7 A A.%.9 95 A3 A- 8 A3 A- 3.0%.69 Baa BBB+ 9 Baa BBB+ 3.95%.0866 Baa BBB 0 Baa BBB 5.00% Baa3 BBB- Baa3 BBB- 7.6% Ba BB+ Ba BB+.4% Ba BB 3 Ba BB 7.78% Ba3 BB- 4 Ba3 BB- 6.3% B B+ 5 B B % B B 6 B B 49.44% B3 B- 7 B3 B- 64.0% Caa CCC+ 8 Caa CCC+ 8.05% Caa CCC 9 Caa CCC 00.00% Caa3 CCC- 0 Caa3 CCC-.05% Caa3 CC CC Caa3 CC 3 Ca CC 4 Ca C Ca C 5 Ca C 57.78% 9.46 NR NR % 4.9 NR Muni NR Muni %

14 Figure : Default Probability Curve Default Rate Spline Empirical AAA AA A BBB BB B CCC C C Aaa Aa A Baa Ba B Caa C Ca Bond Portfolio Given a portfolio of fixed income ecuritie, let x = the i th numerical ecurity credit grade repreentation ( x = x = x = x 0 ) i 7 w i = the portfolio weight of bond with grade w i i= = 3 4 = 4

15 The average default probability of the portfolio i [] y = w f ( x ) p 7 i= i To aign a portfolio letter grade, firt calculate f ( ) i y p. To do thi, firt identify which egment of the pline y p fall into (= for [ y0, y ] or = for [ y, y ]). Then calculate a follow: [] x p a = + a a ( a y ) 4a 0 p Round x p to the nearet integer and ue the third, fourth, and fifth column of Table (refer to page ) to aign letter grade. In term of x p, the vertical axi of the tyle box are: A- "Low" credit quality x > B- "Medium" credit quality 5 x C- "High" credit quality x 5 p p < p 5