Fiera Capital s CIA Accounting Discount Rate Curve Implementation Note. Fiera Capital Corporation

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1 Fera aptal s IA Accountng Dscount Rate urve Implementaton Note Fera aptal orporaton November 2016 Ths document s provded for your prvate use and for nformaton purposes only as of the date ndcated heren and s subject to change wthout notce. It has been prepared and s based on nformaton beleved to be relable. However, Fera aptal orporaton ( Fera aptal ) makes no representaton or warranty, express or mpled, n respect thereof, takes no responsblty for any errors and omssons whch may be contaned theren or accepts any lablty whatsoever for any loss arsng from any use of or relance on ths document whether reled upon by the recpent or user or any other thrd party (ncludng, wthout lmtaton, any customer of the recpent or user). The nformaton, opnons, estmates, projectons and other materals contaned heren are not to be construed as an offer to sell, a solctaton for or an offer to buy, any products or servces referenced heren (ncludng, wthout lmtaton, any commodtes, securtes or other fnancal nstruments), nor shall such nformaton, opnons, estmates, projectons and other materals be consdered as nvestment advce or as a recommendaton to enter nto any transacton. No part of ths document or any related materal and nformaton may be reproduced n any manner wthout the pror wrtten permsson of Fera aptal. The Fera aptal s IA Accountng Dscount Rate urve and certan content of the related Implementaton Note have been created usng data from, unless otherwse specfed, the Bank of Amerca Merrll Lynch anada Broad Bond Market Index whch s used wth permsson from Bank of Amerca Merrll Lynch. The Bank of Amerca Merrll Lynch anada Broad Bond Market Index s compled usng bond valuatons provded by Statpro. Bank of Amerca Merrll Lynch s lcensng the Bank of Amerca Merrll Lynch ndces "as s," makes no warrantes regardng same, does not guarantee the sutablty, qualty, accuracy, tmelness, and/or completeness of the Bank of Amerca Merrll Lynch ndces or any data ncluded n, related to, or derved therefrom, assumes no lablty n connecton wth ther use, and does not sponsor, endorse, or recommend Fera aptal, or any of ts products or servces.

2 Table of ontent 1 Background Securtes Selecton Yeld to Maturty Observatons for the Spot urve Extracton alculaton of the rovncal Spread Adjustments reparaton of the Generc anada Yeld urve alculaton of the Average orporate Spread alculaton of the Average rovncal Spread alculaton of the Spread Rato R alculaton of the rovncal Spread Adjustments Fera aptal Spot urve Extracton Methodology Reference

3 1 Background In September 2011, the anadan Insttute of Actuares ( IA ) retaned the servces of Fera aptal orporaton ( Fera aptal ) to produce, on a monthly bass, the Fera aptal s IA Accountng Dscount Rate urve that can be used by sponsors to select the approprate accountng dscount rate to value penson and other post-employment benefts plans labltes. In ts orgnal verson, ths yeld curve was derved from the approach suggested by the IA and descrbed n the offcal document Educatonal Note, Accountng Dscount Rate Assumpton for enson and ost-employment Beneft lans ( Educatonal Note ), publshed n September At that tme, three approaches were consdered by the IA for the accountng dscount rate curve constructon and Approach from the Educatonal Note was retaned: For purposes of developng the yeld curve, AA-rated corporate bonds are used for maturtes up to 10 years snce the market s suffcently deep at these maturtes. For maturtes greater than 10 years, the yeld curve s extrapolated usng AA-rated anadan provncal bonds. In order to reflect the dfference n credt rsk between AA-rated corporate bonds and AA-rated provncal bonds, a spread adjustment s added to the provncal bond yelds. As part of the curve constructon process, an approach was developed by the IA to calculate the spread adjustment to be added to the provncal bonds yelds wth maturtes greater than 10 years. That approach, whch s descrbed n detal n the 2011 Educatonal Note as well as n Fera aptal s Implementaton Note from 2011, heavly reled on nformaton from AA-rated corporate bonds wth maturtes greater than 10 years. Followng changes n the anadan bond market envronment over the last few years, partcularly wth regards to the sgnfcant reducton n the number of AA-rated corporate bonds wth maturtes greater than 10 years, the IA decded to revst the yeld curve constructon process n order to further mprove the extrapolaton approach and the spread adjustment calculaton for bonds wth maturtes greater than 10 years. Ths document descrbes the revsed approach developed by the IA, after consderng a number of possble approaches, and used by Fera aptal n developng the Fera aptal s IA Accountng Dscount Rate urve startng from November Informaton on the prevous approach used to prepare the Fera aptal s IA Accountng Dscount Rate urve before November 2016 can be found n the Fera aptal s Implementaton Note from For the purpose of calculatng penson and other post-employment benefts plans labltes, yelds used to dscount a projected stream of penson beneft payments should be based on zero coupon bond yelds. Hence, the term spot curve s used n reference to Fera aptal s IA Accountng Dscount Rate urve. 2

4 2 Securtes Selecton The frst step n the spot curve constructon s securtes selecton. For ths purpose, three subsets are defned: a anada Bond subset, a rovncal Bond subset and a orporate Bond subset. The Bank of Amerca Merrll Lynch anada Broad Bond Market Index 1, whch s consdered to be representatve of the anadan bond market, s used as the startng pont to determne these three subsets. The prcng methodology used n Bank of Amerca Merrll Lynch anada Broad Bond Market Index s consdered to approprately reflect market valuaton. The Bank of Amerca Merrll Lynch anada Broad Bond Market Index s compled usng bond valuatons provded by Statpro. In lght of the 2011 Educatonal Note s recommendaton to nclude several representatve crtera of the anadan fxed ncome market, a flter s appled to the Bank of Amerca Merrll Lynch anada Broad Bond Market Index to remove all bonds: wth non-standard cash flow structures such as amortzers and/or snkers ; wth explct callable optons (the anada call provson as an explctly callable bond s not consdered for the purpose of ths flter); and whch have less than $100,000,000 of outstandng nomnal amount n the ndex. In addton, n order to be ncluded n the subsets, the followng crtera must be met: for the anada Bond subset, ssuers must not be anadan federal agences; for the rovncal Bond subset, ssuers must have a credt ratng greater or equal to AA by at least one major ratng agency 2 and must be drect provncal ssuers (e.g. Ontaro, Brtsh-olumba, Alberta, etc.); for the orporate Bond subset, ssuers must have a credt ratng equal to AA by at least one major ratng agency 2 and must not be quas-governmental enttes (e.g. ort and Arport Authortes, Hosptals, Unverstes, etc.). The flterng characterstcs of each ssue n the ndex are drawn from Bank of Amerca Merrll Lynch anadan Broad Market Index characterstcs. It s mportant to note that the flters may change over tme to reflect market condtons. Any change to these flters wll be dscussed and agreed upon by the IA and Fera aptal. 3 Yeld to Maturty Observatons for the Spot urve Extracton As descrbed n the 2011 Educatonal Note under Approach, the yeld to maturty observatons for the spot curve extracton are derved from two groups of bonds: 1. The yeld to maturty subset, where Y for each corporate bond from the orporate Bond Y s the quoted yeld to maturty of the bond (md-market) expressed as a sem-annually compounded rate; and 1 Source: Bank of Amerca Merrll Lynch (used wth permsson). Bank of Amerca Merrll Lynch s lcensng the Bank of Amerca Merrll Lynch ndces "as s," makes no warrantes regardng same, does not guarantee the sutablty, qualty, accuracy, tmelness, and/or completeness of the Bank of Amerca Merrll Lynch ndces or any data ncluded n, related to, or derved there from, assumes no lablty n connecton wth ther use, and does not sponsor, endorse, or recommend Fera aptal, or any of ts products or servces. 2 The credt ratngs agences used to determne the credt ratng qualty crtera are: Standard & oor s (S&), Moody s, Ftch Group and Domnon Bond Ratng Servce (DBRS). 3

5 2. The adjusted yeld to maturty * Y for each provncal bond from the rovncal Bond subset wth a maturty greater than 10.5 years at constructon date, defned as Y * Y, where Y s the quoted yeld to maturty of the bond (md-market) expressed as a sem-annually compounded rate and s the provncal spread adjustment of the provncal bond, as descrbed n secton 4. 4 alculaton of the rovncal Spread Adjustments Ths secton descrbes the approach used to derve the provncal spread adjustments to add to the observed yeld to maturty of provncal bonds wth maturtes greater than 10.5 years to account for credt rsk of AA-rated corporate bonds. 4.1 reparaton of the Generc anada Yeld urve The frst step n the calculaton of the provncal spread adjustments s to derve a generc anada yeld curve, whch wll subsequently be used to calculate the spreads of ndvdual provncal and corporate bonds over ths curve. The methodology Fera aptal uses to derve ths generc anada yeld curve s based on a kernel smoothng method. Ths results n a smoothed yeld curve as a functon of term to maturty usng the anada Bond subset, as shown n Fgure 1. The smoothng method ensures that the yeld curve s approxmately defned at each term to maturty. Fgure 1: anada Bond Subset and anada Yeld urve as at October 31,

6 4.2 alculaton of the Average orporate Spread In order to compute the average corporate spread over the anada yeld curve, bonds wth maturtes between 4.5 and 10.5 years from the orporate Bond subset are used. For each corporate bond wth a maturty between 4.5 and 10.5 years, ts spread computed relatve to the generc anada yeld curve descrbed n secton 4.1 as S Y ( T ), S s where Y s the quoted yeld to maturty of the bond (md-market) expressed as a semannually compounded rate and ( ) s the sem-annually compounded yeld to maturty T at maturty of the corporate bond T obtaned from the generc anada yeld curve methodology descrbed n secton 4.1. The average corporate spread over the anada yeld curve where 1 N N S s computed as S S, 1 N s the number of corporate bonds wth maturtes between 4.5 and 10.5 years. 4.3 alculaton of the Average rovncal Spread In order to compute the average provncal spread over the anada yeld curve, bonds wth maturtes between 4.5 and 10.5 years from the rovncal Bond subset are used. For each provncal bond wth a maturty between 4.5 and 10.5 years, ts spread computed relatve to the generc anada yeld curve descrbed n secton 4.1 as S Y ( T ), S s where Y s the quoted yeld to maturty of the bond (md-market) expressed as a semannually compounded rate and ( ) s the sem-annually compounded yeld to maturty T at maturty of the provncal bond T obtaned from the generc anada yeld curve methodology descrbed n secton 4.1. The average provncal spread over the anada yeld curve where 1 N N S s computed as S S, 1 N s the number of provncal bonds wth maturtes between 4.5 and 10.5 years. 4.4 alculaton of the Spread Rato R The spread rato R s defned as the rato of the average corporate spread to the average provncal spread, as defned respectvely n sectons 4.2 and 4.3 and as shown below: R S S 5

7 4.5 alculaton of the rovncal Spread Adjustments For each provncal bond from the rovncal Bond subset wth a maturty greater than 10.5 years at constructon date, the provncal spread adjustment s calculated as: Y ( T ) *( R 1), where Y s the quoted yeld to maturty of the bond (md-market) expressed as a semannually compounded rate, ( ) s the sem-annually compounded yeld to maturty T at maturty of the provncal bond T obtaned from the generc anada yeld curve methodology descrbed n secton 4.1, and R s the spread rato defned above. 5 Fera aptal Spot urve Extracton Methodology The objectve of the spot curve extracton methodology s to derve the most representatve spot curve from IA s yeld to maturty adjusted observaton set, as defned n secton 3. Fera aptal s analyss tested varous parametrc and non-parametrc models to acheve the best balance between the dfferent crtera descrbed below. As a result, a parametrc approach for dervng the spot curve was adopted. The followng crtera wll govern the curve extracton methodology: The spot curve should avod havng negatve forward rates; The spot curve should produce a good ft to the IA s yeld to maturty adjusted observatons. The mathematcal crtera used n Fera aptal s methodology s to mnmze the overall prcng error (.e. the dfference between the adjusted observed prce and ts prce obtaned through the dscountng of ts future cash flows wth the spot curve); The chosen methodology should exhbt enough flexblty to enable varous curve shapes; The spot curve should be smooth (e.g. mathematcally the second order fnte dfference approxmaton); The model mpled short term rate and ultmate long term rate must be reasonable; and The spot curve model must be stable over tme. Fera aptal s spot curve extracton methodology can qualtatvely be descrbed by the followng optmzaton program: An optmal parametrc specfcaton by mnmzng the sum of squared prcng dfferences (.e., the norm) between the adjusted observed prces and the theoretcal prces obtaned by dscountng the future cash flows wth the adopted parametrc spot curve model; The prce dfference norm uses a dfferent weghtng scheme than the usual 1/N weghts n order to obtan a better ft to the adjusted observed market prces that s based on the duraton of each bond; and The parametrc specfcaton s constraned through constrants on the short and long term spot rates obtaned by the adopted parametrc spot curve model. The quanttatve procedure requred to ft the adopted parametrc yeld curve model s based on non-lnear least squares regresson technques nvolvng non-lnear optmzaton routnes. All the quanttatve models and tools nvolved n the spot curve extracton methodology are developed by Fera aptal. 6

8 The followng fgure shows, as at October 31, 2016, the yelds to maturty orporate Bond subset and the adjusted yelds to maturty * Y Y from the from the rovncal Bond subset wth maturtes greater than 10.5 years, as defned n secton 3. The fgure also shows the ftted sem-annual yeld-to-maturty curve and the ftted spot curve as at October 31, 2016 based on the approach descrbed above. Fgure 2: Fera aptal Spot urve Extracton Approach as at October 31, Reference anadan Insttute of Actuares (2011), Accountng Dscount Rate Assumpton for enson and ost-employment lans, Educatonal Note by the Task Force on enson and ost-retrement Beneft Accountng Dscount Rates, anadan Insttute of Actuares (2016), Accountng Dscount Rate Assumpton for enson and ost-employment Beneft lans, Webcast by the Task Force on enson and ost-retrement Beneft Accountng Dscount Rates, 7