WIXLIB

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Introduction The High Quality Market (HQM) Corporate Bond Yield Curve forthe Pension Protection Act (PPA) uses a methodologygy developedpat Treasury to construct yield curves from extended regressionson maturity ranges. This presentation discusses basic concepts for understanding andusing the HQM yield curve, and presents an overview of thecurve methodology. For links to more detailed documentationand technical descriptionspof the curve,, see the last slide. The methodology for the HQM curve is general. It has beenapplied to Treasury inflation-indexed securities (TIPS) and hasbeen used to construct other corporate bond yield curves; anexample of a AA curve appears at the end of this presentation.2

HQM Yield Curve Summary A yield curve provides information about a sector of the bondmarket at a point in time. The information includes yields ondifferent types of bonds in this sector at various maturities. The HQM yield curve pertains to the high quality corporate bondmarket i.e.,market,i e corporate bonds rated AAAAAA, AAAA, or AA. Theregression methodology of the HQM curve blends AAA, AA, and Abonds into a single yield curve that represents the marketweighted average quality of high quality bondsbonds. The HQM methodology also projects yields beyond 30 yearsmaturity out through 100 years maturity. The methodologyensures that the projections are consistent with yields before 30years maturity and with long-term investment returns availablein the market.3

Spot Rates The yields provided by the HQM Corporate Bond YieldCCurveare spott rates.tThThe HQM curve providesid spott ratestfor each maturity at half-year intervals for maturities of ½year up through 100 years, for a total of 200 spot rates. The spot rate for any maturity is defined as the yield on abond that gives a single payment at that maturity. This iscalled a zero coupon bond. Because high quality zero coupon bonds are not generallyavailable, the HQM methodology computes the spot ratesso as to make them consistent with the yields on other highquality bonds.4

Spot Rates, continued The HQM yield curve is calculated late in the day for eachb ibusinessdday, andd ththe publishedbli h d monthlythl HQM spott ratestare averages of rates for all the business days of the month. Segment rates required by the PPA are derived from themonthly average spot rates. The next chart plots the 200 monthly average spot ratesout through 100 years maturity from the HQM yield curvesfor July and August of this year. The August curve is belowJuly beyond the shortest maturities.5

HQM SPOT YIELD CURVESMonthly Averages, Percent9988776655August 2011July 2011432321041Maturity1020304050607080090 1006

Discounting Liabilities The HQM spot rates are used to discount future pensionli biliti toliabilitiest provideid theth presentt fundingf di levelll neededd d forfthe liabilities. Therefore, regardless of the assets chosen todo the funding, the HQM spot rates give the funding levelatt a market-weightedk ti ht d hihighh creditdit quality.lit A different quality yield curve would give a differentfunding levellevel: the higher the credit quality of the bonds inthe yield curve used for discounting, the higher the fundinglevel and the greater the funding burden on the pensionplan but also the lower the risk that the plan will becomeplan,underfunded.7

Discounting Liabilities, continued Therefore, the choice of the credit quality for the yieldcurve implies a decision about the tradeoff between higherfunding levels and less pension underfunding risk, versuslower funding levels and more risk. Consequently, a different yield curve from the HQM yieldcurve may change funding requirements substantially.E g the use of a Treasury curve would increaseE.g.,significantly the funding burden relative to the HQMcurve.8

Blended High Quality Bonds Although no individual bond has the credit qualityrepresented by the HQM yield curvecurve, the curve can be usedfor an appropriate blended set of high quality bonds. For example, if 5 percent of the high quality market is AAArated, 25 percent is AA rated, and 70 percent is A rated, ablended high quality bond of 10 years maturity consistingof 5 percent 10-year AAA, 25 percent 10-year AA, and 70percent 10-year A can be priced by applying the HQM spotrates to the cash flows from these bonds. ThTherefore,fiin principle,i i l pensioni liliabilitiesbiliti couldld beb fundedf d dby a portfolio of blended high quality bonds, and the valueof this portfolio would track the HQM yield curve.9

Blended High Quality Bonds, continued Of course, this approach is difficult for a variety of reasons,including ratings changes within the portfolio whichrequire rebalancing, and lack of bonds beyond 30 yearsmaturity. Moreover, changes in the relative sizes of the three highquality ratings categories would require changes in theblended bonds to remain consistent with the HQMQ yieldycurve. Therefore, it’s no surprise that typical bond portfolios thatd nott accountt ffor thdothese diffidifficultieslti ddon’t’t ttrackk ththe HQMcurve exactly.10

HQM Risk Aspects Nevertheless, it’s not clear that any other yield curve wouldbe easier to hedge than the HQM yield curve. EvenTreasury coupon issues stop at 30 years maturity, and havespecial inconsistencies such as on-the-run issues. In analyzing hedging, it must also be kept in mind that theHQM yield curve provides a suitable level of pensionfunding that is both accurate and stable over timetime.Therefore, the HQM curve can be relied upon for planning,and in that sense reduces risk.11

HQM Risk Aspects, continued Also, the monthly average feature of the HQM yield curvemay further reduce certain types of risk. This is because no portfolio tracks the HQM curveperfectly and therefore,perfectly,therefore itit’ss important that the curve bestable for planning purposes. The monthly averagereduces the possible volatility in the curve that could comeffromspeciali l behaviorb h i att month-end.th d12

Yield Curve Methodology The following slides contain an overview of the HQM yieldcurve methodology.th d l Different yield curve methodologies can produce verydifferent results, which affect pension liabilities andeverything else for which the curve is used. Therefore, it’sessential to develop the methodology that accuratelycaptures market behavior.behavior Moreover, an understanding of the HQM methodology aidsgreatly in the appropriate use of the HQM curve.13

HQM Methodology FeaturesThe HQM yield curve methodology contains features andcapabilities that do not appear in other yield curveapproaches: This methodology combines regression variables with theyield curve. The methodology projects yields beyond 30 years. The methodology makes use of established bond marketcharacteristics to help generate a stable curve thatcaptures market movements.movements14

HQM Methodology: Regression Variables The HQM methodology has the special capability of combiningregression variables with the yield curve. The regressionterms adjust for the particular attributes of individual bonds. The HQM yield curve contains two regression terms. Thesettermsare adjustmentdj tt ffactorstththatt blblendd AAAAAA, AAAA, anddAbonds into a single HQM yield curve that pertains to themarket-weighted average quality of high quality bonds. Other yield curve approaches were typically developed forTreasury securities, and they do not take into account thedistinctive characteristics of corporatepbonds. Otherapproaches do not have regression variables and cannot blendbonds of different qualities.15

HQM Methodology: Projections The HQM methodology projects yields beyond 30 yearsmaturity out to 100 years maturity to get discount rates forlong-dated pension liabilities.gy ensures that the pprojectionsjare The methodologyconsistent with yields before 30 years maturity and withlong-term investment returns available in the market. OthOther yieldi ld curve approachesh generallyll stopt att 30 yearsmaturity and contain no provision for projection.16

HQM Methodology: Established Market Views The HQM methodology is derived from basic hypothesesabout corporate bond markets. The hypotheses inform thesetting of the parameters that underpin the HQM yieldcurve. Other yield curve approaches typically use mathematicalfunctions that don’t have any foundation in markethypotheses.hypotheses Consequently, differences among yield curves given byppwith different mathematics are arbitrary,y,other approachesin that there is no way to choose among them.17

Estimation of HQM Spot Rates Estimation of the spot rates in the HQM yield curve startsb choosingbyh i an appropriatei t sett off bbondsd (d(describedib d llater).t ) The regression terms are computed so that the price ofeach bond adjusted by the regression terms equals what itwould have been if the bond were of market average highquality. (Technical discussion of the regression terms isfound in the references.)references ) The spot rates are chosen to be the rates that give the beststatistical fit to all the prices in the bond set. This meansthat the estimated prices of the bonds, given as their cashflows discounted by the spot rates, come closest on averageto their actual prices.18

Estimation of HQM Spot Rates, continued Note that the HQM yield curve estimation employs a modelof bond pricesprices. The estimation does not directly use bondyields or averages of yields. However, the description so far of the estimation is toogeneral actually to get spot rates statistically. To carry outthe estimation, the spot rates must be assumed to follow amathematical pattern or functional form. The main source of differences among yield curveapproaches is their different choices of functional forms,and as noted,noted functional forms in other approachestypically are not grounded in market hypotheses. TheHQM methodology bases the functional form on hypothesesaboutb t maturityt it ranges iin ththe market.k t19

The Forward Rate The concept of the forward rate is useful for picking afunctional form for estimating the spot rates. The forward rate is straightforward: for each maturity,consider entering into a contract to invest an amount atthe time of that maturity for a small amount of timebeyond that maturity. The forward rate at that maturity isthe future interest rate on this investment.20

The Forward Rate, continued In ggeneral,, analogousgto spotp rates,, the market does notprovide explicit forward rates, and they must be inferredfrom other prices in the market. ThThe fforwardd ratet iis hihigherh att a givenimaturityt it whenhinvestors who are trading at that maturity are less eager tolend based on their views of uncertainty and theirexpectationsiaboutbtheh market,k whilehil borrowersbare moreeager to borrow based on their perceptions. The forwardrate summarizes market views at each maturity in a singlenumber.21

Maturity Ranges Trading in bonds tends to divide into maturity ranges. Thetrades that take place in each maturity range on averagereflect similar preferences and expectations of traders inthat range. As a consequence, the forward rates in each maturity rangeare related, because they reflect the views of traders. Therefore, the HQM methodology models the forward ratesin each maturity range as a smooth (cubic) function, andjjoins the functions togethergsmoothlyy ((as a cubic spline).p)22

Maturity Ranges, continued The HQM methodology uses five maturity rangesranges,delineated by the maturity points 0, 1.5, 3, 7, 15, and 30years maturity. The choice of fixed maturity ranges increases significantlythe stability of the HQM yield curve estimates over time.23

The Long-Term Forward Rate Assumptionspmust be made in order to pprojectjforwardrates beyond 30 years maturity so as to obtain spot ratesout through 100 years maturity. FiFirstt off all,ll ththe llong-termtfforwardd ratet bbeyondd 30 yearsmaturity is set to a constant, because there are usually notenough data to estimate accurately movements in thefforwardd ratet bbeyondd 30 years maturity.t it24