Inflation-Indexed Swaps and Other Derivatives

INFLATION-INDEXED SWAPS ANDOTHER DERIVATIVESBy Dariush Mirfendereski, Managing Director, Head of Inflation Linked Trading, UBS Investment Bank

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IntroductionThis chapter focuses on the relevant concepts and ideas as observed in the main inflationderivatives markets of the US, the UK, and the eurozone over recent years and presents themarket drivers behind the flows in each market.

Central to a full understanding of the market dynamics in inflation derivatives is the recognitionthat supply and demand flows and/or imbalances in inflation swaps are the key drivers in eachmarket. This has become a crucial issue in the post-credit crunch market. This chapter alsofocuses on the spreads between the bond- and swap-implied levels for real rates and inflationforwards and provides explanations for these observed differences.

To begin with, we explore why the inflation derivative markets developed. The real swap ratecurve is introduced, and the relevant new spreads that are created with its introduction discussed.This is followed by a description of the standard inflation derivative market instruments.

We move on to an overview of market particulars in the three largest global inflation derivativesmarkets: the US, the UK, and the eurozone.

Supply and demand issues in the inflation swap markets are then considered, as well as thehedging of inflation swaps using inflation-indexed bonds and the use of inflation-indexed bondasset swaps (ASWs) as the inflation swap ‘supply of last resort’.

Notation helpful in understanding relative value (RV) analysis between inflation swaps and bondsis then defined, followed by a look at the specifics of this RV analysis via historical data from thethree largest global markets.

We then outline a ‘unified theory’ that attempts to explain within a consistent framework thehistorical data observed in the various markets , before movoing on to a more detailed analysis of one of the markets, the US. Special focus is given to data points post-credit crunch andespecially post-Lehman collapse, when many of the previously accepted market ‘truths’ werechallenged and the disruptive market stretched the limits of market participants’ understandingof market dynamics.

The chapter then looks at the ‘quirks’ in the inflation derivatives market. A full treatment ofthese topics is beyond the scope of this chapter. Nevertheless, the topics covered are regarded as essential for a good understanding of this area. Seasonality of inflation prints is an example of a difference that distinguishes this market from the nominal market. Fixing risks are alsobriefly covered.

Finally, the chapter concludes with an exploration of the future of the market.

Why inflation derivatives?In most global inflation-indexed markets, a derivative market has developed alongside thegovernment real bond market, e.g. since the early 1990s in the UK and since the late 1990s/early2000s in the eurozone market. These markets have developed to meet demands from investorsand issuers that were not met by investing in existing bond issues or the traditional issuance ofinflation-indexed bonds, respectively.

The main drivers behind the inflation derivative market’s development have been the need for:

0 Yield enhancement;0 Diversification of credit exposure;0 Customised cash flows; and0 Extending maturity.

In a world where the majority of corporate issues are fixed or floating, achieving a diversifiedhigher yielding real bond exposure is difficult for fixed income investors. Typically, theseinvestors have been limited to using sovereign inflation-indexed bonds. By investing in adiversified portfolio of fixed and floating credit and overlaying this with inflation swaps, theinvestor can achieve enhanced real yields and benefit from a diversified credit exposure.

In the case of inflation-indexed pension liabilities, the payments are often bespoke, andcustomised solutions can be tailored for the investor using inflation derivatives. These can bemore convenient than a portfolio of inflation-indexed bonds and the associated reinvestment ofcoupons and principal. Additionally, of course, many pension liabilities also have optionality intheir payments, e.g. limited price indexation (LPI) in the UK market. Here too, inflationderivatives can provide a closer hedge than the available inflation-indexed bonds.

In the case of the UK market, the concentration of payers of inflation in one corporate sector,namely utilities, has meant that there are buyers of the inflation component that would not wantthe concentration of exposure risk to this sector. Inflation derivatives have proven useful inseparating the inflation component from the issuer exposure through intermediation.

A thorough study of the drivers behind the development of the inflation-indexed derivativesmarkets is beyond the scope of this chapter, but is provided in other publications.1,2

The fourth yield curveThe development of inflation-indexed bond markets in the major global markets in recent yearshave led to the real government yield curve becoming observable in parallel with the much moreestablished nominal government bond yield curve. While the interest rate swap (IRS) market3 hastraded liquidly for many years, it is only more recently that an inflation swap curve has becomeestablished in the major global markets, typically using the zero coupon inflation swap (ZCIS) asthe standard traded instrument across different maturities. The ZCIS curve can be used inconjunction with the nominal IRS curve to infer a real IRS curve – the fourth yield curve – thuscompleting the quartet of real and nominal yield curves in both government and swap spaces.

With the three ‘traditional’ yield curves – real and nominal government yield curves and the IRScurve – there were only two useful spreads to consider: that between the pair of real and nominalgovernment bond yields (‘inflation breakeven’) and that between the pair of government andswap nominal yields (‘swap spread’). With the introduction of the fourth yield curve, the realswap curve, two additional useful spreads appear, each an analogue of the familiar ‘inflationbreakeven’ and the ‘swap spread’.

The quartet of yield curves is presented schematically in Figure 8.14. The two axes cross at theorigin where GCBr denotes the real government coupon bond yield. The horizontal axis representsinflation expectations plus risk and liquidity premia, while the vertical axis represents creditspreads to government bonds. Thus the nominal government coupon bond yield, GCBn, is furtheralong the horizontal axis, i.e. with zero credit spread to GCBr, while the nominal IRS rate, IRSn, islocated directly above GCBn indicating the swap spread over nominal government yields along thevertical axis.

CHAPTER08ifrintelligence reports/Investing in inflation: The definitive global guide to inflation-linked securities

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1 Deacon, M., A. Derry, and D. Mirfendereski (2004). “Inflation-Indexed Securities: Bonds, Swaps, and Other Derivatives,2nd Ed.,” Wiley Finance. 2 Goldenberg, S. and D. Mirfendereski (2005). Chapter 5: “Inflation-Linked Derivatives: From Theory to Practice” in“Inflation Linked Products,” B. Benaben (Ed.), Risk Books. 3 A more complete description would be the ‘nominal interest rate swap’, although since the nominal interest rateswap market developed well before real interest rate swaps, the more commonly used term ‘interest rate swap’ or IRSrefers to the nominal market.4 This schematic representation was originally introduced in Deacon, M., A. Derry, and D. Mirfendereski (2004).“Inflation-Indexed Securities: Bonds, Swaps, and Other Derivatives, 2nd Ed.,” Wiley Finance. and further developed in Goldenberg, S. and D. Mirfendereski (2005). Chapter 5: “Inflation-Linked Derivatives: From Theory to Practice” in“Inflation Linked Products,” B. Benaben (Ed.), Risk Books.

Additional spreads definedThe familiar ‘breakeven inflation’ is the spread between real and nominal government yields andis redefined as BEIg to signify government breakevens, while the spread between real and nominalswap yields is defined as BEIl to signify Libor-based breakevens. The spread between nominalgovernment bond yields and the IRS yields is commonly referred to as the ‘swap spread’. Herethis spread is redefined as the SSn standing for nominal swap spread while the spread between realgovernment bond yields and the real IRS level is defined as SSr to signify the ‘real swap spread’.

With the introduction of the real swap curve or an inflation swap curve, the breakeven observablein bond space is no longer the only market measure of inflation expectations (plus risk andliquidity premia). So from an economic policy standpoint, the information content in the swapcurves will also have some interest to policy makers. Any difference between inflation forwardsimplied by the swaps and the government bond breakevens should not be mistaken for creditspread differences as in nominal IRS and nominal government bond yields. After all, the swapimplied breakeven is the spread between two (real and nominal) swap rates.

At the same time, there is the temptation to believe that the three ‘traditional’ curves predefinethe real swap curve, e.g. if the inflation breakeven is identical to that implied by the real andnominal government bond curves. This is indeed the default starting point for pricing inflationswaps. However, as will be clear from the sections that follow, this is in reality a usuallyuncommon state of affairs, with few markets exhibiting this feature. The much more commonobservation across global markets at different maturities is that the inflation breakeven impliedby the inflation swaps, BEIl, is typically greater than that shown by BEIg.

Standard market instrumentsThe most commonly traded inflation-indexed swap is the zero coupon inflation swap (ZCIS),followed closely in most markets by asset swaps of inflation-indexed bonds. Many other variationsof inflation-indexed swaps exist, such as year-on-year and real rate swaps. However, these areoften bespoke in nature and do not trade liquidly in the interbank and broker markets andtherefore do not qualify as standard traded market instruments.


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Figure 8.1: Schematic representation of real & nominal government bond and swap rates and their related spreads

Notes: IRSi where i∈ {r,n} denoting real (r) & nominal (n) interest rate swapsSSi where i∈ {r,n} i.e. swap spreads in real or nominal spaces between government and LIBOR SSi=IRSi - GCBiGCBi where i∈ {r,n} i.e. real & nominal government coupon bond yieldsBEIi where i∈ {g,l} denoting breakeven inflation rates for government bonds (g) or swaps (l)Source: UBS

Credit Spread

Inflation expectations +risk & liquidity premia

BEIg

SSr

BEIl

SSn

IRSn

GCBn

GCBr

IRSr

The payout on both legs of a ZCIS occurs at the maturity date, typically an integer number ofyears from the spot date. The fixed leg payment is

Notional *[(1+X%)n – 1]

while the inflation-indexed payment is

Notional *[(CPI(tn)/CPI(to) – 1]

where n is the number of years to maturity, tn is the maturity date for the index at maturity, and tois the index date for the start of the trade. Most markets use a 2- or 3-month lag (or aninterpolated 3-month lag) for indexation. Note that the traded rate X% is simply a moreconvenient and familiar way of expressing where the forward inflation index CPI(tn) trades.

Even though over €30bn notional of year-on-year inflation swaps (YYIS) have traded as end usertrades in the eurozone market alone, YYISs typically trade between banks and end users (banks’clients) rather than as a standard market instrument in the interbank or broker markets.Paradoxically, the standard inflation option instruments that trade in the interbank and brokermarkets are based on YYISs, namely caps and floors on YYISs. These work similarly to interest ratecaps and floor, i.e. they are a series of caplets or floorlets where, except by convention, thepayments are on each annual roll date of the underlying YYIS.

Although the linear inflation exposure (or delta) from clients facing YYISs can be hedged withZCISs, the non-linear exposure from caps and floors on YYISs cannot be easily hedged using ZCISsand the market has resorted to hedging the cap and floor exposures between banks.

While caps and floors on ZCISs do get quoted from time to time and swaptions based on ZCISs asan underlying are also featured in the market, their prevalence is still minimal and they thereforecannot yet be considered as standard market traded instruments.

The main global inflation derivative marketsThe US, UK, and eurozone sovereign inflation-indexed bond markets represent approximately90–95% of global sovereign outstanding issues by market capitalisation. The respective inflationderivative markets in these three are the focus of this section.

Although some other national inflation derivative markets are both active and of interest, e.g. theAustralian and Israeli inflation derivative markets, as well as some of the emerging markets, awider coverage is beyond the scope of this chapter.

Nevertheless, the differences in the three main markets of the US, UK, and the eurozone, cover awide range of issues and situations that will enable the reader to confidently deal with otherinflation derivative markets.

The US CPI derivatives marketThe US market saw a number of swapped new issues in 1997 when TIPS (TreasuryInflation-Protected Securities) were first introduced by the US Treasury. These swapped new issuesnecessarily required inflation derivatives to swap out the issuers. However, it was only in 2004that the US inflation derivatives market started in earnest with flows of any significance andmostly in response to retail investor interest in coupon payouts more similar to CDs than to TIPS.

The phantom tax issue with TIPS was always a negative for retail investors. The ‘income’ formatof the CPI-linked notes solved this and also paid a steady (typically monthly) income. Typical noteshad payouts of year-on-year rate of change of CPI plus a spread and the total coupon was flooredat 0%. Thus embedding a floor with strike equal to the negative of the spread, was the norm.Typical floors have been in the -2% to -0.5% range. Other structures had a leveraged year-on-yearCPI payout, thus embedding a 0% floor on year-on-year inflation. The main feature of this marketwas therefore that year-on-year inflation swaps needed to be priced and also floors onyear-on-year inflation were necessarily embedded in the notes.

The USCPI-linked note market currently has an outstanding notional value of just over US$14bn,with a maturity profile as shown in Table 8.1.


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Note that over 99% of outstanding issues mature in 10 years or less. Importantly, since in the USmarket there have been virtually no ‘natural’ payers of inflation swaps to date, market makersand actively trading investors are net short US$14bn of inflation swaps arising from the structurednote programme alone.

The eurozone inflation derivatives marketsThe eurozone also has a large inflation-indexed note market, with a large proportion in the 5- and10-year maturities targeted at retail investors. However, the size of this market is much largerthan in the US; for example, €12bn of these notes were issued in 2003 alone5. Additionally, withboth insurance company and pension fund interest for longer maturities (some times out to 40-50years and longer), the eurozone inflation derivative market is also active in the longer maturitiesbeyond that which typically services retail investor interest. Finally, there is some degree of‘natural’ supply in the eurozone market: examples include securitisation of rents and leases6,inflation-indexed toll road revenues, as well as some corporate and state issuance that can find itsway into the inflation-indexed swap market directly or via asset swaps. Nevertheless, despite theexistence of some ‘natural’ supply in the eurozone market, the demand side is so much largerthan the supply volumes that the hedging of inflation-indexed demand flows ultimately has to bebalanced by sovereign inflation-indexed bonds.

Additionally, many of the ‘natural supply’ routes revolve around hedging of national inflation,whereas much of the demand side has aggregated around the liquidity provided by the eurozoneHICP (Harmonized Index of Consumer Prices) ex-tobacco indexed market. Hence, a sizeable basisexists between the supply that exists in inflation swaps versus the demand.

The UK RPI derivatives marketThe UK market does not have a large demand for inflation-indexed notes for retail investors,largely because government-issued inflation-indexed gilts have a tax advantage for individualinvestors (who are not taxed on the inflation uplift of the bonds). However, where this demandfalls short compared to the eurozone and US markets, it is more than made up for by demandfrom pension funds and insurance companies hedging inflation-indexed pension liabilities acrossall maturities. This demand for inflation-indexed derivatives has grown enormously in the pastfive years, pushing the UK inflation swap market to £25bn a year7.

2008 saw a decline in volumes, partly due to the credit crunch and other financial marketchallenges, and importantly, due to equity market declines. These challenges reduced inflationswap supply, thereby making hedges more expensive, while the drops in equity marketsincreased pension fund deficits, which can then impact the ability to ‘de-risk’ via selling equitiesand switching to real rate hedges, including the use of inflation swaps. 2009 has started withgreater promise, despite ongoing financial market challenges. However, 2007 market volumesseem unlikely to be achieved at the current rate for 2009.


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Table 8.1: Outstanding notionals for CPI-linked notes by maturity date

Maturity Notional (US$m)2009 2,682 2010 2,242 2011 1,625 2012 898 2013 2,051 2014 2,471 2015 877 2016 536 2017 263 2018 431> 2018 65 Total 14,141

Source: Bloomberg, as of Dec. 28, 2008

5 Deacon, M., A. Derry, and D. Mirfendereski (2004). “Inflation-Indexed Securities: Bonds, Swaps, and Other Derivatives,2nd Ed.,” Wiley Finance. 6 Goldenberg, S. and D. Mirfendereski (2005). Chapter 5: “Inflation-Linked Derivatives: From Theory to Practice” in“Inflation Linked Products,” B. Benaben (Ed.), Risk Books. 7 FTfm: Financial Innovation, p. 23, Financial Times, March 3, 2008.

Despite the recent contraction of UK inflation derivative market volumes, the size of liabilitiesand the regulatory regime around UK pensions means that there will be ongoing demand forinflation-indexed derivatives to hedge these pension liabilities for many years to come.

On the supply side, the UK market has been the leading major market. Existing regulations linkutility rates to changes in the retail price index (RPI) while many public-private partnershipprojects have cash flows guaranteed in real terms by the relevant government departments.Additionally, many rental and lease agreements are also linked to the RPI. Helpfully, the indiceson the supply and demand side are predominantly one and the same—the UK RPI. Theseexplicitly inflation-indexed cash-flows make it natural for those receiving these future cash flowsto hedge by paying out inflation-indexed cash flows either using derivatives or throughinflation-indexed issuance, especially when borrowing fixed or floating to finance the project.These examples are all similar to government issuance of inflation-indexed bonds in that they are‘natural’ sources of supply and are not transitory.

Supply and demand for inflation derivativesUnlike the nominal market where corporates, banks, supranational issuers and even somesovereigns pay and receive IRSs, the inflation swap market has been mostly dominated by thereceivers of inflation, i.e. the demand side.

Typically, investors in inflation-indexed bonds are also drivers of demand for inflation-indexedswaps. On the supply side, inflation-indexed issuance is either dominated by sovereign issuers thathave so far not used derivatives to pay inflation, or is the only game in town in the case of the US.In other words, finding payers of inflation in derivatives is typically challenging in most markets.

The UK market had been an exception with large non-government issuers either directly usingthe derivatives market and/or banks indirectly turning non-government-issued inflation-indexedbonds into swap supply through sales to asset swap investors as intermediaries.

What do we mean by ‘natural’ inflation supply?Most demand flows for inflation swaps tend to be good until maturity, i.e. the trade is typicallynever unwound. Swapped issues sold into retail or to insurance companies or pension hedginginflation derivative transactions are typically of this ‘good until maturity’ kind. These are the cashflows that typically dominate the demand side of the major inflation swap markets.

On the supply side, there are, of course, counterparties willing to pay (from time to time) inflationin swap form at a given (usually advantageous) price. However, just because a counterparty ishappy to enter into a swap to pay inflation-indexed cash flows that does not make it a source of‘natural’ supply. The counterparty may be taking a short-term view and would want to get out ofthe short position in a few months or for a fraction of the time to maturity of the swap. Underthese conditions, this should be considered a ‘transient’ supply.

More permanent supply of inflation swaps via asset swaps, e.g. when a buy and hold investor buysan inflation-indexed bond on asset swap, the investor pays out the real coupons plus the back enduplift over par (or proceeds amount) in return for receiving a spread above or below the relevantfloating interest rate (e.g. 6-month GBP Libor in the UK or 6-month Euribor in the eurozone or3-month USD Libor in the US). However, since the investor is effectively recycling theinflation-indexed flows that the sovereign issuer is paying out, this is considered a ‘synthetic’rather than a ‘natural’ supply.

Of course, some ASW positions are only held for a short period and not until maturity (typicallythe case for many leveraged investors) and these will appear as ‘synthetic’ supply but areultimately ‘bridge’ trades, smoothing out market imbalances between ‘natural’ supply anddemand, e.g. in the UK RPI market. In markets where we are still waiting for ‘natural’ supply ofsignificant size, like the US CPI market, any unwinds of ASW positions by leveraged accounts (andothers) will effectively be new demand since, as already noted, most demand flows never unwind.

Hedging inflation swaps using inflation-indexed bonds and IRSsIs there a need for inflation swap supply? Can the market not simply use existing instruments tohedge inflation-indexed swaps, i.e. use inflation-indexed government bonds, IRSs, and nominalgovernment bonds as necessary, to replicate the inflation-indexed swap cash flows?

Figure 8.2 shows a Libor-flat issuer issuing an inflation-indexed bond and swapping out the cash flows with a hedging bank such that the issuer is effectively borrowing at a floating rate ofLibor flat.


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The hedging bank buys the inflation-indexed government bond, sells the nominal governmentbond, and receives fixed with an IRS. For simplicity, if we ignore bid/ask and assume the maturityof the new issue is identical to the hedge instruments and that the government bonds are newlyissued at par, the hedging bank is then left long the nominal swap spread and short the real swapspread as all other cash flows cancel out. The real swap spread exposes the hedging bank to asmall degree of inflation-indexed exposure throughout the curve out to the maturity date, but thisis small compared to the exposures already hedged and, if necessary, can be similarly hedged withshorter-dated instruments.

One item missing from the above is the net funding cost: going long the real government bondwhile going short a similar maturity nominal government bond is not free. Typically, crossing therepo versus reverse-repo spread can cost between 5-10 bps in most major markets. However, thereare also markets in which shorting the nominal government bond (e.g. US Treasuries) can often bemuch costlier relative to the general collateral (GC) level when bonds go ‘special’.

A more subtle missing item is that the hedges shown are not static hedges that can be left untilmaturity. As inflation breakevens (spreads between nominal and real government yields) andnominal swap spreads (spread between the IRS level and the nominal government yield) changelevels, the hedges need to be adjusted. Rehedging, of course, incurs costs simply due to crossingbid/ask. Additionally, depending on the correlation between these moves, the rehedging may alsohave a systematic cost (or benefit) in line with the sign of the correlation. This is analogous to hedginga quanto swap. Typically, historical correlations between government bond breakevens and swapspreads are not stable and it is prudent to be conservative and charge for this ‘quanto’ effect.

Risk limits are another factor that needs to be taken into consideration when contemplating ahedge like the one shown in Figure 8.2. Since inflation-indexed swaps now constitute anindependent market, the basis between where they trade and where government bond impliedlevels indicate can vary considerably over time8. This change in basis would result in large p/lswings if the swapped issue was hedged as shown in Figure 8.2. As a result, banks typically haverisk limits related to how much of this basis can be carried on their books at a given time.

Figure 8.2: Hedging a swapped new inflation-indexed issue without inflation-Indexed swaps

Notes: IRSi where i∈ {r,n} denoting real (r) & nominal (n) interest rate swapsSSi where i∈ {r,n} i.e. swap spreads in real or nominal spaces between government and Libor SSi=IRSi - GCBiGCBi where i∈ {r,n} i.e. real & nominal government coupon bond yieldsSource: UBS

Investor Libor flatissuer

Hedging bank

Interest rateswap

Real government

bond

Nominal government

bond

Maturitypickup

Maturitypickup

Maturitypickup

Libor

Libor

GCBr + SSr

GCBr + SSr

GCBn + SSn

GCBn

GCBr

8 Premiums in the 5-year maturity ZCISs in the US CPI market versus the TIPS-implied levels moved from 50 to over200 bps in a 3-month period in 2008.

Finally, in a market much more discerning about balance sheet usage, banks may be limited inthe amount of balance sheet they can use in order to carry on hedges such as those shown inFigure 8.2. In other words, even if the levels were attractive, they need to be attractive enoughover and above that which can be justified for using up a bank’s balance sheet.

All the above led banks to seek solutions other than hedging inflation swaps with existinginstruments (when swap supply was non-existent or limited). The inflation-indexed bond assetswap was the main solution. This is outlined in the next section.

Inflation-indexed bond asset swaps – the supply of last resortIn markets where there is demand for receiving inflation swaps and where there is no naturalpayer of inflation in swap form, the imbalance between supply and demand can take inflationswap levels forever higher, in theory to infinitely high levels. Of course, a number of marketparticipants, usually market makers, proprietary trading desks, or hedge funds will step in and‘take the other side’ at some high price and/or the demand will abate once inflation swap levelsreach unattractively high levels for the buyers.

Under the above conditions, the high relative value in inflation swaps versus levels implied by thegovernment-issued real and nominal bonds means that on a like-for-like measure, ASWs ofinflation-indexed government bonds would price relatively cheaply compared to the nominalbond ASW levels.

Figures 8.3 and 8.4 show the cash flows for the two most common forms of inflation-indexedASWs, the par/par and proceeds types, respectively.


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DP = Dirty price

= I/L payment

C = real coupon

= fixed payment

X = Asset Swap Margin

= floating payment

IR = Index Ratio

Accreting Notional

C * IRC * IRC * IRC * IR

Libor + X

Libor + X Libor + X Libor + X Libor + X

C * IR

100 * IR

100

Notional = 100

Inve

stor

pay

sIn

vest

or r

ecei

ves

100

DP

Figure 8.3: Inflation-indexed bond par/par asset swap cash flows

Source: UBS

When selling a government-issued real bond to an ASW investor, the seller receives all the futurereal coupons plus a redemption ‘pickup’ at maturity equal to the pickup over par (in the case of‘par/par’ ASWs) or the pickup over the dirty price at the time of the ASW trade (in the case of the‘proceeds’ ASW). The real coupon payments are a strip of ZCISs, albeit of small magnitude, whilethe redemption pickup is a typical ZCIS payment. In the case where these ZCIS flows are valuedwell above levels implied by the government bond curves, the seller of the ASW is able tocompensate the ASW investor with a spread to Libor more attractive to the investor than thatavailable on nominal government bond ASWs of similar maturity.

The attraction to the investor is obvious: by buying the inflation-indexed ASW, the investor willown a floater, i.e. a bond that pays Libor (or Euribor, etc.) +/- a spread which is often a substantialpickup in spread relative to the nominal ASW market and, in some cases, a higher interest thanthe funding cost of borrowing the issue on repo, resulting in a positive carry trade.

The attraction to the seller is that he receives inflation swap flows that can then be used to hedgepast and future inflation-indexed swap payments. Through selling inflation-indexed governmentbonds on ASW, market makers are thus converting these bonds into real rate or inflation-indexedswaps, creating swap ‘supply’ when none previously existed. All that is needed therefore is a set ofrational investors that would see value in cheap government bond ASWs and take advantagewhen presented with an opportunity to buy these. These rational investors, however, would beexpected to compare like-for-like: due to the back-end pickup, the credit exposure oninflation-linked (IL) ASWs is higher than for nominal ASWs. Additionally, the cash flow profile ofan IL bond means that a non-flat term structure of nominal swap spreads may make a fair valueprice for IL ASWs look ‘cheap’, i.e. have a more favourable spread to LIBOR.

Since it is in the nature of inflation-indexed bonds (at least when inflation is positive) to tradeincreasingly above par on a cash proceeds basis as the trade dates goes several years afterissuance, par/par asset swaps mean mismatched cash flows on the floating side versus funding.For example, a bond trading after three years of positive year-on-year inflation prints may betrading at a real clean price of 100, but would have a proceeds cash price of 100 times 1 plus thecumulative inflation since issuance, say 108.00. Funding this long position on repo means payinginterest on a notional of 108, whereas the floating leg of the par/par ASW will pay floating on apar notional. Proceeds ASWs, however, overcome this by using a floating notional equal to theproceeds cash price at the time of the trade.

Of course, over time, even a proceeds ASW will start to see mismatches in the funding notionalversus the floating leg payments of the ASW. Ultimately, therefore, even the proceeds ASW willface the same deficiencies as a par/par ASW. For investors with relatively short time horizons, thedeficiencies of a proceeds ASW will be minor and they would not need to look at alternativesolutions. For investors looking to keep the ASW trade on their books for several years, or untilmaturity, especially if they plan to fund the long bond position via repo, there needs to be a bettersolution. The market has come up with the so-called ‘accreting’ inflation-indexed ASW, where the


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DP = Dirty price

= I/L payment

C = real coupon

= fixed payment

X = Asset Swap Margin

= floating payment

IR = Index Ratio

Accreting Notional

C * IRC * IRC * IRC * IR

DP

Libor + X

Libor + X Libor + X Libor + X Libor + X

C * IR

100 * IR

DPDP

Notional = DP

Inve

stor

pay

sIn

vest

or r

ecei

ves

Figure 8.4: Inflation-indexed bond proceeds asset swap cash flows

Source: UBS


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floating notional of the swap increases in line with the index ratio on the bond, thus closelymatching the funding notional (so long as the real clean price is close to 100). The accreting ILASW also automatically overcomes some of the issues related to the back-end risk exposure.

Formal definitions and notation for relative value analysisSimple bond breakevens (the spread between nominal and real bond yields) and swap spreads aretradable spreads and have a valid use in quoting markets when trading pairs of instruments.However, they do not represent the ideal parameters for relative value (RV) analysis. The Fisherbreakeven, Z-spreads, etc. are better measures. It is even better to map all yields into continuouslycompounded zero coupon rates, resulting in much easier like-for-like comparisons of the fouryield curves of real and nominal yields in government and swap space9.

The following is based on the standard interest rate (or simply ‘rates’) notation used in many ofthe leading references covering interest rate modelling. The rates typically referred to in standardtexts are the interbank or Libor rates. Here they are considered more generically and additionalnotation is introduced to distinguish between Libor rates and government rates.

The zero coupon bond price and continuously compounded zero rate and their respectivenotation are classically defined as:

P(t,T) : time t price of a zero-coupon bond maturing at time T, in other words the value at time t of $1 (or one unit of currency) at time T

R(t,T) : time t continuously compounded, zero spot rate of maturity T

τ(t,T) : year fraction associated between time t and time T

P(t,T):= e–R(t,T)τ(t,T) (1)

R(t,T):= –lnP(t,T)

(2)τ(t,T)

This generic rates notation is now extended to cover both nominal and real rates, with eachassociated in turn with Libor and government rates.

The continuously compounded zero spot rate, R(t,T), can be defined for any pairings of the real ornominal rates denoted by subscripts r and n, respectively, and either government or Libor ratesdenoted by subscripts g and l, respectively, i.e. a total of 4 separate rates defined as

Rij(t,T), wit h i∈ {r,n} and j∈{g,l} (3)

These are shown in Table 8.2.

One unit of real currency at time T equals one nominal unit of currency multiplied by the forwardinflation index at time T divided by the inflation index at time t = 0. For example, if prices havedoubled from t = 0 to t = T then one unit of real currency at time T equals two units of nominalcurrency. This concept allows the real and nominal zero coupon prices to be linked using the ratioof the inflation index I(t) at t = T and t = 0

9 See Mirfendereski, D. (2007). “Relative Value Analysis in the Global Inflation Markets,” Chapter 2, EuromoneyDerivatives and Risk Management Handbook 2007, Euromoney Publishers, when this was first introduced in thecontext of the inflation markets.

Table 8.2: Notation for real/nominal and government/Libor pairings defining rates

Real rates Nominal ratesGovernment Rrg(t,T) Rng(t,T)Interbank or Libor Rrl(t,T) Rnl(t,T)

Source: Author

Pr(0,T) = I(T)

Pn(0,T) (4)I(0)

where Pr(0,T) and Pn(0,T) are the generic real and nominal zero coupon prices (i.e. ignoring thecredit element) at time t = 0 for the real and nominal economies, respectively.

Pairings of real and nominal zero coupon bonds in government and Libor space can be combined todefine the forward inflation index implied by those pairings’ prices. In other words, the forwardinflation index is not unique, since the real and nominal curves associated with government andLibor rates result in potentially different implied values for the forward inflation index.

Since each of the real and nominal zero coupon bonds can in theory be in either government orLibor space, the forward inflation index is henceforth defined with two subscripts such that thepairing is uniquely defined:

Iij(t): the forward inflation index at time t associated with real and nominal curve pairings associated with different spaces – government or Libor – where i refers to the real rate space while j refers to the nominal rate space.

However, since the inflation index at time zero is already known and therefore unique, thesubscripts can be dropped and, in this case, a new symbol defined as

Io:= Iij(0)=I(0) for i,j ∈{g,l} (5)

Therefore (4) is now rewritten as

Iij(T): = I0

Pri(0,T)for i,j ∈{g,l} (6)

Pnj(0,T)

It is also useful to define the zero inflation rate, Zij(t,T), where

eZij(0,T)τ(0,T) =Iij(T)

for i,j ∈{g,l} (7)I0

and since

Iij(T)=

Pri(0,T) for i,j ∈{g,l}I0 Pnj(0,T)

eZij(0,T)τ(0,T) =e-Rri(0,T)τ(0,T)

for i,j ∈{g,l}e-Rnj(0,T)τ(0,T)

It follows therefore that

Zij(0,T): = Rnj(0,T)–Rri(0,T) for i,j ∈{g,l} (8)

thus the zero inflation rate equals the difference between the relevant nominal and real zero rates.

The combinations of the real and nominal zero coupon prices can be restricted to be for singlecredits, i.e. taken from the same credit class. This then results in implied forward inflation indicesfor a particular credit, i.e. Iii(t) for i∈{g,l} .

For the government rates, the relevant forward inflation index is Igg(t)

Igg(t): the forward inflation index associated with government real and government nominal curves, or simply the government-based forward inflation index

Igg(T): = I0

Prg(0,T)(9)

Png(0,T)

and the corresponding inflation zero rate would follow as before

Zgg(0,T) = Rng(t,T)–Rrg(t,T) (10)


109

Similarly, for Libor-based credit, the forward inflation index is Ill(t)

Ill(t): the forward inflation index at time t associated with Libor real and Libor nominal curves, or simply the Libor-based forward inflation index

Ill(t): = I0

Prl(0,T) (11)

Pnl(0,T)

and the corresponding inflation zero rate would follow as before

Zll(0,T) = Rnl(t,T)–Rrl(t,T) (12)

These are important expressions as Ill(t) is the index derived from the most commonly tradedliquid instrument in the market for inflation derivatives – the zero coupon inflation-indexedswap – and the continuously compounded zero inflation swap rate, Zll(0,T), is closely related to thezero coupon inflation-indexed swap rates traded in the market.

Figure 8.5 replicates the concepts shown in Figure 8.1, but using the notation derived above forcontinuously compounded zero rates and related spreads.

The term ‘rich/cheap’ can have various meanings in different contexts. For example, IRSs can becheap to nominal government bonds when the IRS rates are higher than the nominal bond yieldsof the same maturity. In the context of inflation bond and swap relative value analysis, rich/cheaprefers to how rich or cheap the inflation swaps are trading relative to comparables derived fromthe bond market.

Using the notation derived above, inflation swap ‘rich/cheap’ is thus defined as:

Rich/Cheap: = Zll(0,T)-Zgg(0,T) (13)

The next section looks at historical data in the main global markets and seeks to explain thelevels and evolution of rich/cheap in each market.


110

Figure 8.5: Schematic representation of continuously compounded zero rates and their related spreads

Notes: Rij where i ∈ {r,n} and j ∈ {g,l} i.e. real or nominal zero rates for government and Liborζ

i,jk where i ∈ {r,n} and j and k ∈ {g,l} i.e. zero swap spreads in real or nominal space between government & Libor ζi,jk=Rij-RikZii where i ∈ {g,l} i.e. zero inflation rates for govenment bonds or inflation swaps Zii=Rni-RriSource: UBS

Rnl

RngRrg

Rrl

r: real rates n: nominal rates

l: Libor

g: Government

Zll

ζn,lg

Zgg

ζr,lg

Historical dataComparing rich/cheap with nominal zero swap spreads reveals some fundamental relative value(RV) behaviour in the different global inflation markets. Markets with a reliance oninflation-indexed bond ASWs as a supply of last resort will typically display rich/cheap levels with acertain degree of correlation with nominal swap spreads. Markets with ‘natural’ inflation swapsupply and balanced supply/demand dynamics, however, are more likely to: (a) show littlecorrelation between rich/cheap and nominal swap spreads; and (b) exhibit rich/cheap levels close tofair value, i.e. where bond-implied inflation zeros are very similar to traded inflation swap levels.

The US marketFigure 8.6 shows nominal zero spreads versus rich/cheap for 5-, 10-, and 20-year maturitiescovering the period January 2006 through May 2008.

What is clear from the data is that regardless of maturity, there appears to be the same approximaterelationship between zero spreads and inflation swap rich/cheap across all the maturities and at alltimes for the time sample. The relationship is one of rich/cheap being proportional to zero nominalspreads—wider spreads being matched by higher levels of rich/cheap.

The USCPI swap market is one where there is no ‘natural’ supply to offset demand. Inflationswaps therefore trade at levels where ‘synthetic’ supply can be brought in. With increasinglyexpensive inflation swap levels, at some price TIPS ASWs would look cheap to enough ASWinvestors. During the pre-credit crunch period, this was at the flat carry level, i.e. where TIPSwould trade at an ASW spread equal to the Libor-GC spread.

If 10-year TIPS traded at an ASW spread equal to the Libor-GC spread, say Libor minus 0.25%, but10-year Treasuries traded at Libor minus 0.50%, TIPS would be approximately 25 bps cheaper thannominal Treasuries simply because the inflation swaps were approximately 25 bps expensive to‘fair value’ levels implied by TIPS and nominal Treasuries.

As the 10-year swap spread typically moves in a wider range than Libor-GC spreads10, widening of10-year nominal swap spreads would result in an additional cheapness in TIPS ASWs (e.g. Libor -0.60% versus Libor-GC spread of 30bps) and therefore an additional richness in inflation swapsover fair value. Conversely, the narrowing of 10-year nominal swap spreads would result in lesscheapness in TIPS ASWs (e.g. Libor - 0.40% versus Libor-GC spread of 20bps) and therefore areduced richness in inflation swaps over fair value.


111

Zero nom. spread

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0-0.3 -0.2 0 0.1 0.5 0.6-0.1 0.40.30.2

Z -Z (rich/cheap)

20y10y5y

Figure 8.6: US market zero nominal spreads vs. inflation rich/cheap for 5-, 10-, and 20-year maturities

Source: UBS

10 “The fair value of swap spreads is theoretically related to expectations of the future spread between the Libor rateand the general collateral (GC) repo rate. Evidence, however, suggests that there seems to be no clear relationshipbetween the current Libor-GC repo spread and actual swap spreads.” Cortes, F. (2003). “Understanding and modellingswap spreads,” Bank of England Quarterly Bulletin, Winter 2003.

ll gg

The above would result in the relationship between nominal spreads and rich/cheap shown inFigure 8.6. Of course, as 10-year nominal swap spreads narrow to reach Libor-GC spreads, thedifferential between TIPS and nominal Treasury ASW spreads would diminish to zero, i.e. a zerorich/cheap. This effect is seen by extrapolating the data points in Figure 8.6 to see where a straightline fit would hit the origin. Levels close to historical Libor-GC spreads for the y-axis intercept areencouraging (see below and Figure 8.10).

Of course, if TIPS ASW investors change their views on the level at which they are prepared tobuy and/or if the type of investors involved changes and the new aggregate set of investors has adifferent threshold at which they would be willing to buy the bonds on ASW, the diagonal linewill shift up or down and the intersect at the vertical axis will move to be in line with the level atwhich TIPS ASWs tend to trade.

The UK marketHistorically, the UK market has exhibited a natural two-way flow dynamic. At times supply hasexceeded demand, while at other times the reverse has been the case. This has generally resultedin rich/cheap for inflation swaps trading close to ‘fair value’ or zero levels.

The above is confirmed in Figure 8.7 which shows nominal zero spreads versus rich/cheap for 5-, 10-, 15-, 20-, 25-, and 30-year maturities covering the period January 2006 through May 2008.

The impact of the credit crunch on monoline insurers by implication resulted in a lack ofAAA-wrapped utility and/or PFI bond issues. These were two of the main routes for generating RPIswap supply through the sale of these bonds to ASW investors (who needed high-rated paper). The credit crunch similarly put an end to the securitisation of rents and leases that had been thethird main source of RPI swap supply. The combination of these effects gradually changed thedynamics of the UK market, making it less balanced and moving more towards a one-way,demand-driven market relying more and more on ASWs of sovereign bonds to generate RPI swapsupply, i.e. similar to the dynamics observed in the US market.

Eurozone marketsSimilarly to Figures 8.6 and 8.7, Figure 8.8 shows nominal zero spreads versus rich/cheap for 5-, 10-, 15-, 20-, 25-, and 30-year maturities covering the period January 2006 through May 2008.Note that the reference government curve for this data is the French government OAT curve11.Note that a similar chart can be generated using the Italian government BTP curve as thereference curve.


112

Zero nom. spread

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 -0.3 -0.2 0 0.1 0.5 0.6-0.1 0.40.30.2

Z -Z (rich/cheap)

15y10y5y20y25y30y

Figure 8.7: UK market zero nominal spreads vs. inflation rich/cheap for 5-, 10-, 15-, 20-, 25-, and 30-year maturities

Source: UBS

11 This was chosen as the French OAT curve has a longer history and more of the bonds on the curve tend to trade onASW.

ll gg

The eurozone data shows certain characteristics similar to the US market, i.e. a linear relationshipbetween zero nominal spreads and inflation swap rich/cheap. This reflects the reliance on ASWflows as a major source of inflation swap supply. The data in Figure 8.8 also shows certaincharacteristics that are similar to the UK market, i.e. with rich/cheap close to fair value and notdependent on zero swap spreads. This reflects some degree of ‘natural’ inflation swap supply inthis market as noted earlier in this chapter.

The eurozone market has yet another feature which is likely related to the different sovereignissuers involved across the curve. France, Italy, Greece, and Germany all issue inflation-indexedsovereign bonds linked to the HICP ex-tobacco index, yet they each have different swap spreadsacross different maturities. This translates into a ‘fatter’ distribution of the proportional line seenin Figure 8.8 as compared to the US market in Figure 8.6.

Unified theory for inflation bond and swap relative valueIn this section, an attempt is made to explain the data observed above through a unified view ofthe market – a ‘unified theory’ of inflation bond and swap RV.

Markets with little or no natural inflation swap supply will have a proportional linear relationshipbetween zero swap spreads and inflation swap rich/cheap. The level at which this trend line sitsdepends largely on the level at which ASW investors are prepared to buy the sovereign’sinflation-indexed bonds on ASW.

Markets with a balanced, two-way, inflation swap market, will tend to have little relation betweenzero swap spreads and inflation swap rich/cheap and rich/cheap would tend to trade close to zero(or ‘fair value’). During transitions, if demand flows dominate, rich/cheap can diverge from fairvalue until balance returns. This divergence can take rich/cheap up to levels where the ASW flowcan bring the ‘supply’ back.

These concepts are illustrated schematically in Figure 8.9:


113

Zero nom. spread0.50

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0-0.10 -0.05 0 0.05 0.15 0.200.10

Z -Z (rich/cheap)

15y10y5y20y25y30y

Figure 8.8: Eurozone market zero nominal spreads vs. inflation rich/cheap for 5-, 10-, 15-, 20-, 25-, and 30-year maturities

Source: UBS

ll gg

The angle of the transition path relative to the horizontal would be zero if market flows werepurely inflation flows and when nominal spreads are not changing. If the flows were real rate swapflows, the angle would be between zero and 45 degrees depending on what proportion of the total(real and nominal) swap market was made up of real rate swaps. In the US market, since theinflation-indexed or real rate swaps are such a small proportion of the overall swap market, theangle will be close to zero, while in the UK market, where in the long-end of the curve pension LDItrades and utility real rate swaps can dominate, the angle is perceptibly greater than zero.

Of course the above applies during conditions of stable nominal spreads, or more precisely,conditions of balanced nominal IRS paying/receiving versus nominal government bondissuance/investment.

It should be underlined again that where the ASW-implied boundary lies depends largely on theaggregate level at which investors are prepared to buy and hold the inflation-indexed sovereignbonds on ASW.

Detailed US CPI market data analysisLibor-GC historical spreadsThe Libor-GC spread can serve as a good barometer of changing market conditions since the startof the credit crunch in the summer of 2007, through the Bear Stearns sale, the Lehman Brothersbankruptcy on 15 September 2008, and beyond. Figure 8.10 shows the 3-month USD Libor-GCspread over the past three years, from well before the start of the credit crunch until late 2008.


114

Figure 8.9: Eurozone market zero nominal spreads vs. inflation rich/cheap for 5-, 10-, 15-, 20-, 25-, and 30-year maturities

Source: UBS

Transition Paths

One-way Market

Zll-Zgg

Balanced Market

ζn, lg

Three distinct time periodsIn the pre-credit crunch period, 3-month Libor-GC spreads averaged 22 bps with two-thirds of the spread fixings in the 20-24 bp range. From around mid-July 2007, spreads quickly widened out to 50 bps within a month and averaged 88 bps in the period 13 July 2007 through 12September 2008. Here, this is called the ‘intermediate’ period. From 15 September 2008, 3-monthLibor-GC spreads moved to as high as 400 bps, averaging around 200 bps, although in the lastthree weeks of December, levels came back down sharply to close the year below 120 bps, stillmuch higher than the average for the intermediate period, but well below the 200 average in thepost-Lehman period.

Implications for the inflation-indexed bond ASW marketDue to the lack of ‘natural’ supply of inflation swaps, the traded values for ZCISs in the US market are derived from where ASW investors buy TIPS, thus establishing the relationshipbetween zero nominal spreads and rich/cheap. This data is split and shown for the pre-creditcrunch period and the intermediate period separately for 5-year and 10-year maturities in Figures8.11 and 8.12, respectively.


115

Libor-GC spread

4.53

4.00

3.50

3.00

2.50

2.00

1.50

1.00

0.50

0Jan ‘06 Jul ’06 Jan ‘07 Jul ’07 Jan ‘08 Jul ’08 Jan ‘09

Pre-credit crunch Intermediate Post-15-Sep-08

3m Libor - 3m Repo

Figure 8.10: 3 month Libor-GC USD spreads Jan 2006 through Jan 2009

Source: UBS

Zero nominal spread

1.2

1.0

0.8

0.6

0.4

0.2

00 0.500.25 0.75

Rich/cheap

03-Jan-06 to 12-Jul-07

13-Jul-07 to 12-Sep-08

Figure 8.11: 5y zero nominal spreads vs rich/cheap

Source: UBS

It is clear from the data that this relationship did not significantly change from the pre-creditcrunch period into the intermediate period.

The 3-month Libor-GC spread can be viewed as a good proxy for the reduced willingness of banksto lend and therefore also reflects pressures on banks and other market players to reduce balancesheet usage. The rise in Libor-GC spreads for the intermediate period, however, did not appear toimpact upon the market dynamics previously established. This is possibly due to the extraimplicit positive carry. For example, TIPS ASW at 3-month Libor – 0.35% has a positive carry of 40bps if 3-month Libor-GC spreads are at 75 bps, as compared to previously being close to flat carrywhen trading at Libor – 0.25% and with Libor-GC spreads at 25 bps.

The above, however, all changed post-Lehman. Prior to looking in detail at the post-15 September2008 data, it is worthwhile looking at the impact of the credit crunch on inflation forwards.

5y5y inflation forwards5y5y TIPS inflation forwards have been a topic of special interest to many, including the FederalReserve. It is therefore logical to also observe 5y5y forward inflation from inflation swap data.

Not surprisingly, just as each of the spot starting 5-year and 10-year swaps traded at a premiumover levels implied by TIPS, 5y5y forward inflation swaps displayed a steady premium over 5y5yimplied by the Treasury market in the pre-credit crunch world as shown in Figure 8.13.


116

Zero nominal spread

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 0.500.25

Rich/cheap

03-Jan-06 to 12-Jul-07

13-Jul-07 to 12-Sep-08

Figure 8.12: 10y zero nominal spreads vs rich/cheap

Source: UBS

Inflation Forward Rate

3.50

3.30

3.10

2.90

2.70

2.50

2.30

2.10

1.90

1.70

1.50 Jan ‘06 Jul ’06 Jan ‘07 Jul ’07 Jan ‘08 Jul ’08

Figure 8.13: Treasury- and swap-implied 5y5y inflation forwards

Source: UBS

5y5y Zgg 5y5y Zll

However, shortly after the start of the credit crunch, 5y5y inflation swap forwards convergedtowards levels implied by TIPS. There had been some speculation by some market participantsthat this carried some meaning regarding lower inflation expectations in the swap market.However, an alternative explanation is available which is more valid.

Essentially, as has been demonstrated in previous sections, rich/cheap levels have been a linearfunction of nominal swap spreads. Post-credit crunch, 5-year spreads widened much more than10-year spreads, which in turn took 5-year rich/cheap wider than 10-year rich/cheap, thuslowering the level of 5y5y forwards in swap space. In other words, the move in 5y5y inflationswaps converging with TIPS 5y5y levels had everything to do with what the nominal swap spreadswere doing and nothing to do with the inflation swap market’s views on inflation forwards.

Figure 8.14 shows how 5-year nominal spreads widened much more than 10-year spreads whileFigure 8.15 shows how 5-year rich/cheap outperformed 10-year rich/cheap.


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Zero Nominal Spread

1.20

1.00

0.80

0.60

0.40

0.20

0

Jan ‘06 Jul ’06 Jan ‘07 Jul ’07 Jan ‘08 Jul ’08

10y 5y

Figure 8.14: 5y and 10y zero nominal spread vs time

Source: UBS

Rich/Cheap

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

0Jan ‘06 Jul ’06 Jan ‘07 Jul ’07 Jan ‘08 Jul ’08

10y rich/cheap 5y rich/cheap

Figure 8.15: 5y and 10y rich/cheap vs time

Source: UBS

The market post-LehmanWith the post-Lehman market came nominal government bond ASW levels at Libor plus,unwinds of existing TIPS ASW positions, and the unwillingness and/or inability of investors to putnew money to work in buying ultra cheap TIPS on ASW. This in effect took away inflation supplyat a time when a large numbers of Lehman counterparties were scrambling to replace swap flowsthat Lehman had provided (e.g. for swapped inflation-indexed notes), i.e. when inflation swapdemand spiked dramatically. The above led to an unprecedented and sharp move up in rich/cheaplevels across all traded ZCIS maturities as shown in Figure 8.16. Figure 8.17 shows nominal spreadlevels during the same period.

Each of the 5- and 10-year maturity data sets are now plotted separately in Figures 8.18 and 8.19 inorder to observe the nominal spread versus rich/cheap relationship, both pre- and post-Lehman.


118

Rich/Cheap

0

0.50

1.00

1.50

2.00

2.50

3.00

Jan ‘06 Jul ’06 Jan ‘07 Jul ’07 Jan ‘08 Jul ’08 Jan ‘09

10y rich/cheap 5y rich/cheap

Figure 8.16: Rich/Cheap in 5- and 10-year maturities: Jan 2006 - Jan 2009

Source: UBS

Zero Nominal Spread

1.40

1.20

1.00

0.80

0.60

0.40

0.20

0.0

-0.20

Jan ‘06 Jul ’06 Jan ‘07 Jul ’07 Jan ‘08 Jul ’08 Jan ‘09

10y 5y

Figure 8.17: 5y and 10y zero nom spread vs time

Source: UBS

Clearly, the long-established relationship between nominal spreads and rich/cheap that hadwithstood the onset of the credit crunch and the market dislocations in the aftermath of the BearStearns sale broke down in mid-September 2008. As seen in Figures 8.18 and 8.19, there is nolonger a discernable relationship between nominal spreads and rich/cheap.

In the data that follows the above charts, there are signs that a new linear relationship betweennominal spreads and rich/cheap is being established, corresponding to a much cheaper level inTIPS ASWs – basically a line parallel to the previous relationship, but intersecting the horizontalaxis at a level in line with the new equilibrium level in TIPS ASWs (6-month Libor plus 90-100 atthe time of writing12 for most 5-10 year TIPS maturities).


119

Zero nominal spread

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

0

0.25

0.50

0.75

1.00

1.20

1.50

1.75

2.00

2.25

2.50

03-Jan-06 to 12-Jul-07

13-Jul-07 to 12-Sep-08

15-Sep-08 to 23-Dec-08

Rich/cheap

Figure 8.18: Nominal spread vs rich/cheap in the 5y maturity: Jan 2006 - Jan 2009

Source: UBS

Zero nominal spread

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

-0.1

-0.2

0

0.25

0.50

0.75

1.00

1.20

1.50

Rich/cheap

03-Jan-06 to 12-Jul-07

13-Jul-07 to 12-Sep-08

15-Sep-08 to 23-Dec-08

Figure 8.19: Nominal spread vs rich/cheap in the 10y maturity: Jan 2006 - Jan 2009

Source: UBS

12 April 2009.

Market quirks: seasonality and fixing risksSeasonalityReal rates can be inferred from nominal rates and inflation rates. Inflation rates are typicallyyear-on-year rates, i.e. the year-on-year rate of change of the underlying inflation index. Theinflation index, typically a number normalised to 100 (and rebased back to 100 every few years),normally comes out each month in most countries/economic areas13. With positive inflationrates, the index will display a rising trend. However, this does not mean that the index goeshigher every month. Typically, in most markets, the index actually drops in certain months due tosales or other seasonal factors. This means that month-on-month rates for inflation exhibitunusual and non-smooth variations. This of course translates into real rates, since nominalforward rates tend to be smooth through the year. How the market deals with this seasonal effectfor inflation is a dynamic that requires careful consideration when pricing, investing, and tradingin inflation-indexed markets.

Other references14 cover the topic of inflation seasonality in greater detail and it is beyond thescope of this chapter to discuss this to the same extent. Nevertheless, a few examples are citedhere to alert the reader to the issues that need attention.

The most liquid inflation derivative market traded instruments are ZCISs and inflation-indexedbond ASWs. Starting with the ZCISs, one can infer forward inflation indices by decomposing theZCIS payout and mid-market traded rate. Assuming that ZCISs trade for all annual maturities, onecan infer all fixings for a particular date for each forward year. The problem comes when one hasto price an inflation-indexed payout that uses a fixing that is on another date. Inflation-indexedASWs have the fixing of the redemption of the bond as their main inflation risk, and this typicallydoes not correspond to the on-the-run ZCIS maturity that is trading at a particular date. To pricethe ASW one therefore needs to make an assumption about the seasonal variation of inflationindices in between the annual points inferred from the ZCIS curve.

The converse is also true: in some markets where ASWs are more liquid than ZCISs, it may bemore valid to start with the ASWs and use seasonal assumptions to then infer the ZCIS levels.Either way, market participants require an assumption about the seasonal variation of theinflation index through a 12-month cycle.

Seasonal assumptions have typically used historical data averaging as a starting point. However,since the crude oil market has exhibited a very large variation in prices in the past three to fouryears and most energy prices exhibit a strong correlation with the price of crude oil, historicalaveraging can be misleading. A recent trend in the market has been the stripping of the energycomponent from price indices prior to historical averaging. The rationale for this is that the largevariations in energy prices are not seasonally repeatable and should not therefore influenceprojections for future seasonal variations.

Fixing risksFor a typical IRS book, Libor fixing risks are a standard issue that needs attention. The existence ofliquid Libor and Euribor futures contracts means that the market has a way to deal with theserisks. Furthermore, the smooth nature of nominal rates means that having futures contracts withfixed dates for 3-month contracts is typically sufficient to provide a good hedge, even thoughthere are as many Libor fixings per year as there are trading days in each year. The inflationmarkets have the simplicity of only having 12 fixings per year. However, the complication is eachyear’s fixings cannot be approximated with less than 12 different instruments.

Futures contracts for US CPI and the Euro HICP ex-tobacco index have both been introduced bythe exchanges. However, these have met with mixed success at best. Further, without an efficienthedging mechanism in place, fixing risks represent an unresolved issue in the inflationderivatives markets. If a fixing risk matches that of an existing inflation-indexed bond, then thereis a ready-made hedging instrument for that fixing risk. Otherwise, the investor or market makerwill have a large unhedgeable uncertainty for that fixing risk.

The success of futures contracts depends to a great extent on a two-way interest and theparticipation of arbitrage players, who ‘take the other side’ when prices reach unreasonablelevels. Arbitrage players, however, require liquidity which the inflation futures markets currentlylack. It is therefore a classic ‘Catch-22’ situation. The history of interest rate futures markets


120

13 Australia is an exception amongst the main traded markets where inflation data comes out on a quarterly basis.14 For example, Goldenberg, S. and D. Mirfendereski (2005). Chapter 5: “Inflation-Linked Derivatives: From Theory toPractice” in “Inflation Linked Products,” B. Benaben (Ed.), Risk Books.

which are now extremely liquid suggests that the process of establishing volume and liquidity isone which may take many years and the market needs to persevere and consider variations tocurrent contract designs and trading practices in order to expedite their development.

Future of the marketThe quest for a ‘natural’ two-way market for inflation derivatives continues and in the long termthis is the only viable basis for the healthy growth of the inflation derivatives market.

Using ASWs of inflation-indexed sovereign bonds as the source of inflation swap supply isultimately unsustainable when the demand side for inflation swaps is growing every year. In theshort term, real money interest in these ASW can help the market as it has in the immediatepost-Lehman period. Corporate issuance and associated alternatives to issuance such as the use ofswaps will be a more sustainable long-term solution. This particular angle, however, is stillhampered by various regulatory and accounting hurdles which may take many years to resolve.Another alternative solution, and one that is unlikely to need to cross many hurdles, is the use ofinflation swaps by sovereign issuers. Many currently use IRSs for their debt managementsolutions and in theory can extend this to use inflation swaps, both taking advantage offavourable inflation swap levels and helping the derivatives market find a more sustainablesource of swap supply.

AcknowledgementsMany thanks to numerous UBS colleagues past and present who have over the past five yearshelped to provide a rich environment for exposure to the breadth of issues in theinflation-indexed markets globally. I would especially like to thank Chris Lupoli for stimulatingdiscussions on the global inflation-indexed markets generally and Pierre Lalanne for convertingraw market data (nominal and real government bond prices, IRS levels, and ZCIS levels) into acomprehensive database of continuously compounded zero real and nominal rates in governmentand swap space. Most of the relative value analysis in this chapter is based on this database.

Finally, many thanks to clients of UBS too numerous to mention who have over the past five yearsdeepened my understanding of this topic through challenging questions and suggestions raisedduring calls, meetings, and conference presentations.

DisclaimerThe views expressed in this chapter are those of the author and do not necessarily reflect those of UBS.


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Inflation-Indexed Swaps and Other Derivatives