CHAPTER INFLATION-INDEXED SWAPS AND OTHER DERIVATIVES
08
By Dariush Mirfendereski, Managing Director, Head of Inflation Linked Trading, UBS Investment Bank
Introduction This chapter focuses on the relevant concepts and ideas as observed in the main inflation derivatives markets of the US, the UK, and the eurozone over recent years and presents the market drivers behind the flows in each market. Central to a full understanding of the market dynamics in inflation derivatives is the recognition that supply and demand flows and/or imbalances in inflation swaps are the key drivers in each market. This has become a crucial issue in the post-credit crunch market. This chapter also focuses on the spreads between the bond- and swap-implied levels for real rates and inflation forwards and provides explanations for these observed differences. To begin with, we explore why the inflation derivative markets developed. The real swap rate curve 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 derivatives markets: the US, the UK, and the eurozone. Supply and demand issues in the inflation swap markets are then considered, as well as the hedging of inflation swaps using inflation-indexed bonds and the use of inflation-indexed bond asset swaps (ASWs) as the inflation swap ‘supply of last resort’. Notation helpful in understanding relative value (RV) analysis between inflation swaps and bonds is then defined, followed by a look at the specifics of this RV analysis via historical data from the three largest global markets. We then outline a ‘unified theory’ that attempts to explain within a consistent framework the historical 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 and especially post-Lehman collapse, when many of the previously accepted market ‘truths’ were challenged and the disruptive market stretched the limits of market participants’ understanding of market dynamics. The chapter then looks at the ‘quirks’ in the inflation derivatives market. A full treatment of these 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 also briefly 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 the government real bond market, e.g. since the early 1990s in the UK and since the late 1990s/early 2000s in the eurozone market. These markets have developed to meet demands from investors and issuers that were not met by investing in existing bond issues or the traditional issuance of inflation-indexed bonds, respectively. The main drivers behind the inflation derivative market’s development have been the need for: 0 0 0 0
Yield enhancement; Diversification of credit exposure; Customised cash flows; and Extending maturity.
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In a world where the majority of corporate issues are fixed or floating, achieving a diversified higher yielding real bond exposure is difficult for fixed income investors. Typically, these investors have been limited to using sovereign inflation-indexed bonds. By investing in a diversified portfolio of fixed and floating credit and overlaying this with inflation swaps, the investor 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, and customised solutions can be tailored for the investor using inflation derivatives. These can be more convenient than a portfolio of inflation-indexed bonds and the associated reinvestment of coupons and principal. Additionally, of course, many pension liabilities also have optionality in their payments, e.g. limited price indexation (LPI) in the UK market. Here too, inflation derivatives 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 want the concentration of exposure risk to this sector. Inflation derivatives have proven useful in separating the inflation component from the issuer exposure through intermediation. A thorough study of the drivers behind the development of the inflation-indexed derivatives markets is beyond the scope of this chapter, but is provided in other publications.1,2
The fourth yield curve The development of inflation-indexed bond markets in the major global markets in recent years have led to the real government yield curve becoming observable in parallel with the much more established nominal government bond yield curve. While the interest rate swap (IRS) market3 has traded liquidly for many years, it is only more recently that an inflation swap curve has become established in the major global markets, typically using the zero coupon inflation swap (ZCIS) as the standard traded instrument across different maturities. The ZCIS curve can be used in conjunction with the nominal IRS curve to infer a real IRS curve – the fourth yield curve – thus completing 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 IRS curve – there were only two useful spreads to consider: that between the pair of real and nominal government bond yields (‘inflation breakeven’) and that between the pair of government and swap nominal yields (‘swap spread’). With the introduction of the fourth yield curve, the real swap curve, two additional useful spreads appear, each an analogue of the familiar ‘inflation breakeven’ and the ‘swap spread’. The quartet of yield curves is presented schematically in Figure 8.14. The two axes cross at the origin where GCBr denotes the real government coupon bond yield. The horizontal axis represents inflation expectations plus risk and liquidity premia, while the vertical axis represents credit spreads to government bonds. Thus the nominal government coupon bond yield, GCBn, is further along the horizontal axis, i.e. with zero credit spread to GCBr, while the nominal IRS rate, IRSn, is located directly above GCBn indicating the swap spread over nominal government yields along the vertical axis.
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 rate swap market developed well before real interest rate swaps, the more commonly used term ‘interest rate swap’ or IRS refers 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.
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Figure 8.1: Schematic representation of real & nominal government bond and swap rates and their related spreads Credit Spread
BEIl
IRSr
SSr
GCBr
IRSn
SSn
Inflation expectations + risk & liquidity premia
BEIg GCBn
Notes: IRSi where i∈ {r,n} denoting real (r) & nominal (n) interest rate swaps SSi where i∈ {r,n} i.e. swap spreads in real or nominal spaces between government and LIBOR SSi=IRSi - GCBi GCBi where i∈ {r,n} i.e. real & nominal government coupon bond yields BEIi where i∈ {g,l} denoting breakeven inflation rates for government bonds (g) or swaps (l) Source: UBS
Additional spreads defined The familiar ‘breakeven inflation’ is the spread between real and nominal government yields and is redefined as BEIg to signify government breakevens, while the spread between real and nominal swap yields is defined as BEIl to signify Libor-based breakevens. The spread between nominal government bond yields and the IRS yields is commonly referred to as the ‘swap spread’. Here this spread is redefined as the SSn standing for nominal swap spread while the spread between real government 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 observable in bond space is no longer the only market measure of inflation expectations (plus risk and liquidity premia). So from an economic policy standpoint, the information content in the swap curves will also have some interest to policy makers. Any difference between inflation forwards implied by the swaps and the government bond breakevens should not be mistaken for credit spread differences as in nominal IRS and nominal government bond yields. After all, the swap implied 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 predefine the real swap curve, e.g. if the inflation breakeven is identical to that implied by the real and nominal government bond curves. This is indeed the default starting point for pricing inflation swaps. However, as will be clear from the sections that follow, this is in reality a usually uncommon state of affairs, with few markets exhibiting this feature. The much more common observation across global markets at different maturities is that the inflation breakeven implied by the inflation swaps, BEIl, is typically greater than that shown by BEIg.
Standard market instruments The 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 variations of inflation-indexed swaps exist, such as year-on-year and real rate swaps. However, these are often bespoke in nature and do not trade liquidly in the interbank and broker markets and therefore do not qualify as standard traded market instruments.
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The payout on both legs of a ZCIS occurs at the maturity date, typically an integer number of years 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 to is the index date for the start of the trade. Most markets use a 2- or 3-month lag (or an interpolated 3-month lag) for indexation. Note that the traded rate X% is simply a more convenient 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 user trades 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 broker markets are based on YYISs, namely caps and floors on YYISs. These work similarly to interest rate caps and floor, i.e. they are a series of caplets or floorlets where, except by convention, the payments are on each annual roll date of the underlying YYIS. Although the linear inflation exposure (or delta) from clients facing YYISs can be hedged with ZCISs, the non-linear exposure from caps and floors on YYISs cannot be easily hedged using ZCISs and 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 as an underlying are also featured in the market, their prevalence is still minimal and they therefore cannot yet be considered as standard market traded instruments.
The main global inflation derivative markets The US, UK, and eurozone sovereign inflation-indexed bond markets represent approximately 90–95% of global sovereign outstanding issues by market capitalisation. The respective inflation derivative 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. the Australian and Israeli inflation derivative markets, as well as some of the emerging markets, a wider coverage is beyond the scope of this chapter. Nevertheless, the differences in the three main markets of the US, UK, and the eurozone, cover a wide range of issues and situations that will enable the reader to confidently deal with other inflation derivative markets.
The US CPI derivatives market The US market saw a number of swapped new issues in 1997 when TIPS (Treasury Inflation-Protected Securities) were first introduced by the US Treasury. These swapped new issues necessarily required inflation derivatives to swap out the issuers. However, it was only in 2004 that the US inflation derivatives market started in earnest with flows of any significance and mostly 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’ format of the CPI-linked notes solved this and also paid a steady (typically monthly) income. Typical notes had payouts of year-on-year rate of change of CPI plus a spread and the total coupon was floored at 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-year CPI payout, thus embedding a 0% floor on year-on-year inflation. The main feature of this market was therefore that year-on-year inflation swaps needed to be priced and also floors on year-on-year inflation were necessarily embedded in the notes. The USCPI-linked note market currently has an outstanding notional value of just over US$14bn, with a maturity profile as shown in Table 8.1.
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Table 8.1: Outstanding notionals for CPI-linked notes by maturity date Maturity 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 > 2018 Total
Notional (US$m) 2,682 2,242 1,625 898 2,051 2,471 877 536 263 431 65 14,141
Source: Bloomberg, as of Dec. 28, 2008
Note that over 99% of outstanding issues mature in 10 years or less. Importantly, since in the US market there have been virtually no ‘natural’ payers of inflation swaps to date, market makers and actively trading investors are net short US$14bn of inflation swaps arising from the structured note programme alone.
The eurozone inflation derivatives markets The eurozone also has a large inflation-indexed note market, with a large proportion in the 5- and 10-year maturities targeted at retail investors. However, the size of this market is much larger than in the US; for example, €12bn of these notes were issued in 2003 alone5. Additionally, with both insurance company and pension fund interest for longer maturities (some times out to 40-50 years and longer), the eurozone inflation derivative market is also active in the longer maturities beyond 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 its way into the inflation-indexed swap market directly or via asset swaps. Nevertheless, despite the existence of some ‘natural’ supply in the eurozone market, the demand side is so much larger than the supply volumes that the hedging of inflation-indexed demand flows ultimately has to be balanced 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 eurozone HICP (Harmonized Index of Consumer Prices) ex-tobacco indexed market. Hence, a sizeable basis exists between the supply that exists in inflation swaps versus the demand.
The UK RPI derivatives market The 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 individual investors (who are not taxed on the inflation uplift of the bonds). However, where this demand falls short compared to the eurozone and US markets, it is more than made up for by demand from pension funds and insurance companies hedging inflation-indexed pension liabilities across all maturities. This demand for inflation-indexed derivatives has grown enormously in the past five 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 market challenges, and importantly, due to equity market declines. These challenges reduced inflation swap supply, thereby making hedges more expensive, while the drops in equity markets increased pension fund deficits, which can then impact the ability to ‘de-risk’ via selling equities and switching to real rate hedges, including the use of inflation swaps. 2009 has started with greater promise, despite ongoing financial market challenges. However, 2007 market volumes seem unlikely to be achieved at the current rate for 2009.
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.
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Despite the recent contraction of UK inflation derivative market volumes, the size of liabilities and the regulatory regime around UK pensions means that there will be ongoing demand for inflation-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 link utility rates to changes in the retail price index (RPI) while many public-private partnership projects 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 indices on the supply and demand side are predominantly one and the same—the UK RPI. These explicitly inflation-indexed cash-flows make it natural for those receiving these future cash flows to hedge by paying out inflation-indexed cash flows either using derivatives or through inflation-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 derivatives Unlike the nominal market where corporates, banks, supranational issuers and even some sovereigns pay and receive IRSs, the inflation swap market has been mostly dominated by the receivers of inflation, i.e. the demand side. Typically, investors in inflation-indexed bonds are also drivers of demand for inflation-indexed swaps. On the supply side, inflation-indexed issuance is either dominated by sovereign issuers that have 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 using the derivatives market and/or banks indirectly turning non-government-issued inflation-indexed bonds 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 typically never unwound. Swapped issues sold into retail or to insurance companies or pension hedging inflation derivative transactions are typically of this ‘good until maturity’ kind. These are the cash flows 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) inflation in swap form at a given (usually advantageous) price. However, just because a counterparty is happy 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 of the short position in a few months or for a fraction of the time to maturity of the swap. Under these 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 buys an inflation-indexed bond on asset swap, the investor pays out the real coupons plus the back end uplift over par (or proceeds amount) in return for receiving a spread above or below the relevant floating interest rate (e.g. 6-month GBP Libor in the UK or 6-month Euribor in the eurozone or 3-month USD Libor in the US). However, since the investor is effectively recycling the inflation-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 (typically the case for many leveraged investors) and these will appear as ‘synthetic’ supply but are ultimately ‘bridge’ trades, smoothing out market imbalances between ‘natural’ supply and demand, e.g. in the UK RPI market. In markets where we are still waiting for ‘natural’ supply of significant size, like the US CPI market, any unwinds of ASW positions by leveraged accounts (and others) will effectively be new demand since, as already noted, most demand flows never unwind.
Hedging inflation swaps using inflation-indexed bonds and IRSs Is there a need for inflation swap supply? Can the market not simply use existing instruments to hedge inflation-indexed swaps, i.e. use inflation-indexed government bonds, IRSs, and nominal government 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 of Libor flat.
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Figure 8.2: Hedging a swapped new inflation-indexed issue without inflation-Indexed swaps Interest rate swap
GCBn + SSn Libor
Libor Investor
GCBr + SSr
Libor flat issuer
Hedging bank
GCBn
Nominal government bond
GCBr + SSr
Maturity pickup
Maturity pickup
GCBr
Maturity pickup
Real government bond
Notes: IRSi where i∈ {r,n} denoting real (r) & nominal (n) interest rate swaps SSi where i∈ {r,n} i.e. swap spreads in real or nominal spaces between government and Libor SSi=IRSi - GCBi GCBi where i∈ {r,n} i.e. real & nominal government coupon bond yields Source: UBS
The hedging bank buys the inflation-indexed government bond, sells the nominal government bond, and receives fixed with an IRS. For simplicity, if we ignore bid/ask and assume the maturity of the new issue is identical to the hedge instruments and that the government bonds are newly issued at par, the hedging bank is then left long the nominal swap spread and short the real swap spread as all other cash flows cancel out. The real swap spread exposes the hedging bank to a small degree of inflation-indexed exposure throughout the curve out to the maturity date, but this is small compared to the exposures already hedged and, if necessary, can be similarly hedged with shorter-dated instruments. One item missing from the above is the net funding cost: going long the real government bond while going short a similar maturity nominal government bond is not free. Typically, crossing the repo versus reverse-repo spread can cost between 5-10 bps in most major markets. However, there are also markets in which shorting the nominal government bond (e.g. US Treasuries) can often be much 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 until maturity. As inflation breakevens (spreads between nominal and real government yields) and nominal swap spreads (spread between the IRS level and the nominal government yield) change levels, the hedges need to be adjusted. Rehedging, of course, incurs costs simply due to crossing bid/ask. Additionally, depending on the correlation between these moves, the rehedging may also have a systematic cost (or benefit) in line with the sign of the correlation. This is analogous to hedging a quanto swap. Typically, historical correlations between government bond breakevens and swap spreads 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 a hedge like the one shown in Figure 8.2. Since inflation-indexed swaps now constitute an independent market, the basis between where they trade and where government bond implied levels indicate can vary considerably over time8. This change in basis would result in large p/l swings if the swapped issue was hedged as shown in Figure 8.2. As a result, banks typically have risk limits related to how much of this basis can be carried on their books at a given time. 8 Premiums in the 5-year maturity ZCISs in the US CPI market versus the TIPS-implied levels moved from 50 to over 200 bps in a 3-month period in 2008.
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Finally, in a market much more discerning about balance sheet usage, banks may be limited in the amount of balance sheet they can use in order to carry on hedges such as those shown in Figure 8.2. In other words, even if the levels were attractive, they need to be attractive enough over 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 existing instruments (when swap supply was non-existent or limited). The inflation-indexed bond asset swap was the main solution. This is outlined in the next section.
Inflation-indexed bond asset swaps – the supply of last resort In markets where there is demand for receiving inflation swaps and where there is no natural payer of inflation in swap form, the imbalance between supply and demand can take inflation swap levels forever higher, in theory to infinitely high levels. Of course, a number of market participants, 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 levels reach unattractively high levels for the buyers. Under the above conditions, the high relative value in inflation swaps versus levels implied by the government-issued real and nominal bonds means that on a like-for-like measure, ASWs of inflation-indexed government bonds would price relatively cheaply compared to the nominal bond ASW levels. Figures 8.3 and 8.4 show the cash flows for the two most common forms of inflation-indexed ASWs, the par/par and proceeds types, respectively.
Figure 8.3: Inflation-indexed bond par/par asset swap cash flows Notional = 100
Libor + X
DP = Dirty price C = real coupon
Investor pays
Investor receives
X = Asset Swap Margin Libor + X
Libor + X
Libor + X
= I/L payment 100 DP
100
100 * IR
C * IR
C * IR
Accreting Notional
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= fixed payment = floating payment
C * IR
Source: UBS
IR = Index Ratio
Libor + X
C * IR
C * IR
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Figure 8.4: Inflation-indexed bond proceeds asset swap cash flows Notional = DP
Libor + X DP = Dirty price
Investor receives
C = real coupon Libor + X
Libor + X
Libor + X
Libor + X
X = Asset Swap Margin IR = Index Ratio DP
DP
= I/L payment = fixed payment
Investor pays
= floating payment
100 * IR DP C * IR
C * IR
C * IR
Accreting Notional
C * IR
C * IR
Source: UBS
When selling a government-issued real bond to an ASW investor, the seller receives all the future real 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, while the redemption pickup is a typical ZCIS payment. In the case where these ZCIS flows are valued well above levels implied by the government bond curves, the seller of the ASW is able to compensate the ASW investor with a spread to Libor more attractive to the investor than that available on nominal government bond ASWs of similar maturity. The attraction to the investor is obvious: by buying the inflation-indexed ASW, the investor will own a floater, i.e. a bond that pays Libor (or Euribor, etc.) +/- a spread which is often a substantial pickup in spread relative to the nominal ASW market and, in some cases, a higher interest than the 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 hedge past and future inflation-indexed swap payments. Through selling inflation-indexed government bonds on ASW, market makers are thus converting these bonds into real rate or inflation-indexed swaps, creating swap ‘supply’ when none previously existed. All that is needed therefore is a set of rational investors that would see value in cheap government bond ASWs and take advantage when presented with an opportunity to buy these. These rational investors, however, would be expected to compare like-for-like: due to the back-end pickup, the credit exposure on inflation-linked (IL) ASWs is higher than for nominal ASWs. Additionally, the cash flow profile of an IL bond means that a non-flat term structure of nominal swap spreads may make a fair value price 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 trade increasingly above par on a cash proceeds basis as the trade dates goes several years after issuance, 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 be trading at a real clean price of 100, but would have a proceeds cash price of 100 times 1 plus the cumulative inflation since issuance, say 108.00. Funding this long position on repo means paying interest on a notional of 108, whereas the floating leg of the par/par ASW will pay floating on a par notional. Proceeds ASWs, however, overcome this by using a floating notional equal to the proceeds cash price at the time of the trade. Of course, over time, even a proceeds ASW will start to see mismatches in the funding notional versus the floating leg payments of the ASW. Ultimately, therefore, even the proceeds ASW will face the same deficiencies as a par/par ASW. For investors with relatively short time horizons, the deficiencies of a proceeds ASW will be minor and they would not need to look at alternative solutions. For investors looking to keep the ASW trade on their books for several years, or until maturity, especially if they plan to fund the long bond position via repo, there needs to be a better solution. The market has come up with the so-called ‘accreting’ inflation-indexed ASW, where the
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floating notional of the swap increases in line with the index ratio on the bond, thus closely matching the funding notional (so long as the real clean price is close to 100). The accreting IL ASW also automatically overcomes some of the issues related to the back-end risk exposure.
Formal definitions and notation for relative value analysis Simple bond breakevens (the spread between nominal and real bond yields) and swap spreads are tradable 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 Fisher breakeven, Z-spreads, etc. are better measures. It is even better to map all yields into continuously compounded zero coupon rates, resulting in much easier like-for-like comparisons of the four yield 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 of the leading references covering interest rate modelling. The rates typically referred to in standard texts are the interbank or Libor rates. Here they are considered more generically and additional notation is introduced to distinguish between Libor rates and government rates. The zero coupon bond price and continuously compounded zero rate and their respective notation 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)
lnP(t,T) τ(t,T)
(2)
R(t,T):= –
This generic rates notation is now extended to cover both nominal and real rates, with each associated 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 or nominal rates denoted by subscripts r and n, respectively, and either government or Libor rates denoted by subscripts g and l, respectively, i.e. a total of 4 separate rates defined as Rij(t,T), with i∈ {r,n} and j∈{g,l}
(3)
These are shown in Table 8.2.
Table 8.2: Notation for real/nominal and government/Libor pairings defining rates Government Interbank or Libor
Real rates Rrg(t,T) Rrl (t,T)
Nominal rates Rng(t,T) Rnl(t,T)
Source: Author
One unit of real currency at time T equals one nominal unit of currency multiplied by the forward inflation index at time T divided by the inflation index at time t = 0. For example, if prices have doubled from t = 0 to t = T then one unit of real currency at time T equals two units of nominal currency. This concept allows the real and nominal zero coupon prices to be linked using the ratio of 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, Euromoney Derivatives and Risk Management Handbook 2007, Euromoney Publishers, when this was first introduced in the context of the inflation markets.
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Pr(0,T) =
I(T) P (0,T) I(0) n
(4)
where Pr(0,T) and Pn(0,T) are the generic real and nominal zero coupon prices (i.e. ignoring the credit 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 to define the forward inflation index implied by those pairings’ prices. In other words, the forward inflation index is not unique, since the real and nominal curves associated with government and Libor 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 or Libor space, the forward inflation index is henceforth defined with two subscripts such that the pairing 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, the subscripts 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 Pri(0,T) Iij(T): = I0 for i,j ∈{g,l} (6) Pnj(0,T) It is also useful to define the zero inflation rate, Zij(t,T), where Iij(T) eZij(0,T)τ(0,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 single credits, i.e. taken from the same credit class. This then results in implied forward inflation indices for 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) Png(0,T)
(9)
and the corresponding inflation zero rate would follow as before Zgg(0,T) = Rng(t,T)–Rrg(t,T)
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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 Prl(0,T) Ill(t): = I0 (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 traded liquid instrument in the market for inflation derivatives – the zero coupon inflation-indexed swap – and the continuously compounded zero inflation swap rate, Zll(0,T), is closely related to the zero 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 for continuously compounded zero rates and related spreads.
Figure 8.5: Schematic representation of continuously compounded zero rates and their related spreads r: real rates
n: nominal rates
Zll
Rrl
ζr,lg
l: Libor
ζn,lg
Zgg
Rrg
Rnl
Rng
g: Government
Notes: Rij where i ∈ {r,n} and j ∈ {g,l} i.e. real or nominal zero rates for government and Libor ζi,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-Rik Zii where i ∈ {g,l} i.e. zero inflation rates for govenment bonds or inflation swaps Zii=Rni-Rri Source: UBS
The term ‘rich/cheap’ can have various meanings in different contexts. For example, IRSs can be cheap to nominal government bonds when the IRS rates are higher than the nominal bond yields of the same maturity. In the context of inflation bond and swap relative value analysis, rich/cheap refers to how rich or cheap the inflation swaps are trading relative to comparables derived from the 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 the levels and evolution of rich/cheap in each market.
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Historical data Comparing rich/cheap with nominal zero swap spreads reveals some fundamental relative value (RV) behaviour in the different global inflation markets. Markets with a reliance on inflation-indexed bond ASWs as a supply of last resort will typically display rich/cheap levels with a certain degree of correlation with nominal swap spreads. Markets with ‘natural’ inflation swap supply and balanced supply/demand dynamics, however, are more likely to: (a) show little correlation between rich/cheap and nominal swap spreads; and (b) exhibit rich/cheap levels close to fair value, i.e. where bond-implied inflation zeros are very similar to traded inflation swap levels.
The US market Figure 8.6 shows nominal zero spreads versus rich/cheap for 5-, 10-, and 20-year maturities covering the period January 2006 through May 2008.
Figure 8.6: US market zero nominal spreads vs. inflation rich/cheap for 5-, 10-, and 20-year maturities Zero nom. spread 1 0.9 0.8
20y 10y 5y
0.7 0.6 0.5 0.4 0.3 0.2 0.1 -0.3
-0.2
-0.1
0
0
0.1 0.2 0.3 Zll -Z gg (rich/cheap)
0.4
0.5
0.6
Source: UBS
What is clear from the data is that regardless of maturity, there appears to be the same approximate relationship between zero spreads and inflation swap rich/cheap across all the maturities and at all times for the time sample. The relationship is one of rich/cheap being proportional to zero nominal spreads—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. Inflation swaps therefore trade at levels where ‘synthetic’ supply can be brought in. With increasingly expensive inflation swap levels, at some price TIPS ASWs would look cheap to enough ASW investors. During the pre-credit crunch period, this was at the flat carry level, i.e. where TIPS would 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%, but 10-year Treasuries traded at Libor minus 0.50%, TIPS would be approximately 25 bps cheaper than nominal 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 of 10-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 swaps over fair value. Conversely, the narrowing of 10-year nominal swap spreads would result in less cheapness in TIPS ASWs (e.g. Libor - 0.40% versus Libor-GC spread of 20bps) and therefore a reduced richness in inflation swaps over fair value.
10 “The fair value of swap spreads is theoretically related to expectations of the future spread between the Libor rate and the general collateral (GC) repo rate. Evidence, however, suggests that there seems to be no clear relationship between the current Libor-GC repo spread and actual swap spreads.” Cortes, F. (2003). “Understanding and modelling swap spreads,” Bank of England Quarterly Bulletin, Winter 2003.
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The above would result in the relationship between nominal spreads and rich/cheap shown in Figure 8.6. Of course, as 10-year nominal swap spreads narrow to reach Libor-GC spreads, the differential between TIPS and nominal Treasury ASW spreads would diminish to zero, i.e. a zero rich/cheap. This effect is seen by extrapolating the data points in Figure 8.6 to see where a straight line fit would hit the origin. Levels close to historical Libor-GC spreads for the y-axis intercept are encouraging (see below and Figure 8.10). Of course, if TIPS ASW investors change their views on the level at which they are prepared to buy and/or if the type of investors involved changes and the new aggregate set of investors has a different threshold at which they would be willing to buy the bonds on ASW, the diagonal line will shift up or down and the intersect at the vertical axis will move to be in line with the level at which TIPS ASWs tend to trade.
The UK market Historically, the UK market has exhibited a natural two-way flow dynamic. At times supply has exceeded demand, while at other times the reverse has been the case. This has generally resulted in 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.
Figure 8.7: UK market zero nominal spreads vs. inflation rich/cheap for 5-, 10-, 15-, 20-, 25-, and 30-year maturities
Zero nom. spread 1
15y 10y 5y 20y 25y 30y
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.3
-0.2
-0.1
0
0.1 0.2 0.3 Zll -Z gg (rich/cheap)
0.4
0.5
0.6
Source: UBS
The impact of the credit crunch on monoline insurers by implication resulted in a lack of AAA-wrapped utility and/or PFI bond issues. These were two of the main routes for generating RPI swap 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 the third main source of RPI swap supply. The combination of these effects gradually changed the dynamics 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 swap supply, i.e. similar to the dynamics observed in the US market.
Eurozone markets Similarly 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 the reference curve.
11 This was chosen as the French OAT curve has a longer history and more of the bonds on the curve tend to trade on ASW.
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Figure 8.8: Eurozone market zero nominal spreads vs. inflation rich/cheap for 5-, 10-, 15-, 20-, 25-, and 30-year maturities Zero nom. spread 0.50
15y 10y 5y 20y 25y 30y
0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 -0.10
-0.05
0
0
0.05 0.10 Zll -Zgg (rich/cheap)
0.15
0.20
Source: UBS
The eurozone data shows certain characteristics similar to the US market, i.e. a linear relationship between zero nominal spreads and inflation swap rich/cheap. This reflects the reliance on ASW flows as a major source of inflation swap supply. The data in Figure 8.8 also shows certain characteristics that are similar to the UK market, i.e. with rich/cheap close to fair value and not dependent on zero swap spreads. This reflects some degree of ‘natural’ inflation swap supply in this market as noted earlier in this chapter. The eurozone market has yet another feature which is likely related to the different sovereign issuers involved across the curve. France, Italy, Greece, and Germany all issue inflation-indexed sovereign bonds linked to the HICP ex-tobacco index, yet they each have different swap spreads across different maturities. This translates into a ‘fatter’ distribution of the proportional line seen in Figure 8.8 as compared to the US market in Figure 8.6.
Unified theory for inflation bond and swap relative value In this section, an attempt is made to explain the data observed above through a unified view of the market – a ‘unified theory’ of inflation bond and swap RV. Markets with little or no natural inflation swap supply will have a proportional linear relationship between zero swap spreads and inflation swap rich/cheap. The level at which this trend line sits depends largely on the level at which ASW investors are prepared to buy the sovereign’s inflation-indexed bonds on ASW. Markets with a balanced, two-way, inflation swap market, will tend to have little relation between zero 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 fair value until balance returns. This divergence can take rich/cheap up to levels where the ASW flow can bring the ‘supply’ back. These concepts are illustrated schematically in Figure 8.9:
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Figure 8.9: Eurozone market zero nominal spreads vs. inflation rich/cheap for 5-, 10-, 15-, 20-, 25-, and 30-year maturities Balanced Market One-way Market Îśn, lg
Transition Paths
Zll-Zgg Source: UBS
The angle of the transition path relative to the horizontal would be zero if market flows were purely inflation flows and when nominal spreads are not changing. If the flows were real rate swap flows, 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 the inflation-indexed or real rate swaps are such a small proportion of the overall swap market, the angle will be close to zero, while in the UK market, where in the long-end of the curve pension LDI trades 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 bond issuance/investment. It should be underlined again that where the ASW-implied boundary lies depends largely on the aggregate level at which investors are prepared to buy and hold the inflation-indexed sovereign bonds on ASW.
Detailed US CPI market data analysis Libor-GC historical spreads The Libor-GC spread can serve as a good barometer of changing market conditions since the start of the credit crunch in the summer of 2007, through the Bear Stearns sale, the Lehman Brothers bankruptcy on 15 September 2008, and beyond. Figure 8.10 shows the 3-month USD Libor-GC spread over the past three years, from well before the start of the credit crunch until late 2008.
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Figure 8.10: 3 month Libor-GC USD spreads Jan 2006 through Jan 2009
Libor-GC spread
Pre-credit crunch
Intermediate
Post-15-Sep-08
4.53 4.00 3m Libor - 3m Repo
3.50 3.00 2.50 2.00 1.50 1.00 0.50 0
Jan ‘06
Jul ’06
Jan ‘07
Jul ’07
Jan ‘08
Jul ’08
Jan ‘09
Source: UBS
Three distinct time periods In 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 12 September 2008. Here, this is called the ‘intermediate’ period. From 15 September 2008, 3-month Libor-GC spreads moved to as high as 400 bps, averaging around 200 bps, although in the last three weeks of December, levels came back down sharply to close the year below 120 bps, still much higher than the average for the intermediate period, but well below the 200 average in the post-Lehman period.
Implications for the inflation-indexed bond ASW market Due 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 relationship between zero nominal spreads and rich/cheap. This data is split and shown for the pre-credit crunch period and the intermediate period separately for 5-year and 10-year maturities in Figures 8.11 and 8.12, respectively.
Figure 8.11: 5y zero nominal spreads vs rich/cheap
Zero nominal spread 1.2
03-Jan-06 to 12-Jul-07 13-Jul-07 to 12-Sep-08
1.0 0.8 0.6 0.4 0.2 0 0
0.25
0.50 Rich/cheap
Source: UBS
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Figure 8.12: 10y zero nominal spreads vs rich/cheap Zero nominal spread 0.8
03-Jan-06 to 12-Jul-07 13-Jul-07 to 12-Sep-08
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.25 Rich/cheap
0.50
Source: UBS
It is clear from the data that this relationship did not significantly change from the pre-credit crunch period into the intermediate period. The 3-month Libor-GC spread can be viewed as a good proxy for the reduced willingness of banks to lend and therefore also reflects pressures on banks and other market players to reduce balance sheet usage. The rise in Libor-GC spreads for the intermediate period, however, did not appear to impact upon the market dynamics previously established. This is possibly due to the extra implicit positive carry. For example, TIPS ASW at 3-month Libor – 0.35% has a positive carry of 40 bps if 3-month Libor-GC spreads are at 75 bps, as compared to previously being close to flat carry when 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 September 2008 data, it is worthwhile looking at the impact of the credit crunch on inflation forwards.
5y5y inflation forwards 5y5y TIPS inflation forwards have been a topic of special interest to many, including the Federal Reserve. 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 premium over levels implied by TIPS, 5y5y forward inflation swaps displayed a steady premium over 5y5y implied by the Treasury market in the pre-credit crunch world as shown in Figure 8.13.
Figure 8.13: Treasury- and swap-implied 5y5y inflation forwards 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
5y5y Zgg Source: UBS
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Jan ‘08
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However, shortly after the start of the credit crunch, 5y5y inflation swap forwards converged towards levels implied by TIPS. There had been some speculation by some market participants that 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 linear function of nominal swap spreads. Post-credit crunch, 5-year spreads widened much more than 10-year spreads, which in turn took 5-year rich/cheap wider than 10-year rich/cheap, thus lowering the level of 5y5y forwards in swap space. In other words, the move in 5y5y inflation swaps converging with TIPS 5y5y levels had everything to do with what the nominal swap spreads were 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 while Figure 8.15 shows how 5-year rich/cheap outperformed 10-year rich/cheap.
Figure 8.14: 5y and 10y zero nominal spread vs time
Zero Nominal Spread 1.20 5y
10y 1.00 0.80 0.60 0.40 0.20 0 Jan ‘06
Jul ’06
Jan ‘07
Jul ’07
Jan ‘08
Jul ’08
Source: UBS
Figure 8.15: 5y and 10y rich/cheap vs time
Rich/Cheap 0.80 10y rich/cheap 0.70
5y rich/cheap
0.60 0.50 0.40 0.30 0.20 0.10 0 Jan ‘06
Source: UBS
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Jul ’07
Jan ‘08
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The market post-Lehman With 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 put new money to work in buying ultra cheap TIPS on ASW. This in effect took away inflation supply at a time when a large numbers of Lehman counterparties were scrambling to replace swap flows that Lehman had provided (e.g. for swapped inflation-indexed notes), i.e. when inflation swap demand spiked dramatically. The above led to an unprecedented and sharp move up in rich/cheap levels across all traded ZCIS maturities as shown in Figure 8.16. Figure 8.17 shows nominal spread levels during the same period.
Figure 8.16: Rich/Cheap in 5- and 10-year maturities: Jan 2006 - Jan 2009 Rich/Cheap 3.00 2.50
10y rich/cheap
5y rich/cheap
2.00 1.50 1.00 0.50 0 Jan ‘06
Jul ’06
Jan ‘07
Jul ’07
Jan ‘08
Jul ’08
Jan ‘09
Source: UBS
Figure 8.17: 5y and 10y zero nom spread vs time
Zero Nominal Spread 1.40 5y
10y 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
Source: UBS
Each of the 5- and 10-year maturity data sets are now plotted separately in Figures 8.18 and 8.19 in order to observe the nominal spread versus rich/cheap relationship, both pre- and post-Lehman.
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Figure 8.18: Nominal spread vs rich/cheap in the 5y maturity: Jan 2006 - Jan 2009 Zero nominal spread 1.4 1.2 1.0 0.8 0.6 03-Jan-06 to 12-Jul-07 0.4
13-Jul-07 to 12-Sep-08 15-Sep-08 to 23-Dec-08
0.2
2.50
2.25
2.00
1.75
1.50
1.20
1.00
0.75
0.50
0
0.25
0
Rich/cheap
Source: UBS
Figure 8.19: Nominal spread vs rich/cheap in the 10y maturity: Jan 2006 - Jan 2009
Zero nominal spread 0.8
03-Jan-06 to 12-Jul-07 13-Jul-07 to 12-Sep-08
0.7
15-Sep-08 to 23-Dec-08
0.6 0.5 0.4 0.3 0.2 0.1 0
1.50
1.20
1.00
0.75
0.50
0.25
-0.2
0
-0.1
Rich/cheap Source: UBS
Clearly, the long-established relationship between nominal spreads and rich/cheap that had withstood the onset of the credit crunch and the market dislocations in the aftermath of the Bear Stearns sale broke down in mid-September 2008. As seen in Figures 8.18 and 8.19, there is no longer 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 between nominal spreads and rich/cheap is being established, corresponding to a much cheaper level in TIPS ASWs – basically a line parallel to the previous relationship, but intersecting the horizontal axis at a level in line with the new equilibrium level in TIPS ASWs (6-month Libor plus 90-100 at the time of writing12 for most 5-10 year TIPS maturities).
12 April 2009.
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Market quirks: seasonality and fixing risks Seasonality Real rates can be inferred from nominal rates and inflation rates. Inflation rates are typically year-on-year rates, i.e. the year-on-year rate of change of the underlying inflation index. The inflation 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 inflation rates, the index will display a rising trend. However, this does not mean that the index goes higher every month. Typically, in most markets, the index actually drops in certain months due to sales or other seasonal factors. This means that month-on-month rates for inflation exhibit unusual and non-smooth variations. This of course translates into real rates, since nominal forward rates tend to be smooth through the year. How the market deals with this seasonal effect for inflation is a dynamic that requires careful consideration when pricing, investing, and trading in inflation-indexed markets. Other references14 cover the topic of inflation seasonality in greater detail and it is beyond the scope of this chapter to discuss this to the same extent. Nevertheless, a few examples are cited here to alert the reader to the issues that need attention. The most liquid inflation derivative market traded instruments are ZCISs and inflation-indexed bond ASWs. Starting with the ZCISs, one can infer forward inflation indices by decomposing the ZCIS payout and mid-market traded rate. Assuming that ZCISs trade for all annual maturities, one can infer all fixings for a particular date for each forward year. The problem comes when one has to price an inflation-indexed payout that uses a fixing that is on another date. Inflation-indexed ASWs have the fixing of the redemption of the bond as their main inflation risk, and this typically does not correspond to the on-the-run ZCIS maturity that is trading at a particular date. To price the ASW one therefore needs to make an assumption about the seasonal variation of inflation indices 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 be more 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 the inflation 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 four years and most energy prices exhibit a strong correlation with the price of crude oil, historical averaging can be misleading. A recent trend in the market has been the stripping of the energy component from price indices prior to historical averaging. The rationale for this is that the large variations in energy prices are not seasonally repeatable and should not therefore influence projections for future seasonal variations.
Fixing risks For a typical IRS book, Libor fixing risks are a standard issue that needs attention. The existence of liquid Libor and Euribor futures contracts means that the market has a way to deal with these risks. Furthermore, the smooth nature of nominal rates means that having futures contracts with fixed dates for 3-month contracts is typically sufficient to provide a good hedge, even though there are as many Libor fixings per year as there are trading days in each year. The inflation markets have the simplicity of only having 12 fixings per year. However, the complication is each year’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 by the exchanges. However, these have met with mixed success at best. Further, without an efficient hedging mechanism in place, fixing risks represent an unresolved issue in the inflation derivatives markets. If a fixing risk matches that of an existing inflation-indexed bond, then there is a ready-made hedging instrument for that fixing risk. Otherwise, the investor or market maker will 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 the participation of arbitrage players, who ‘take the other side’ when prices reach unreasonable levels. Arbitrage players, however, require liquidity which the inflation futures markets currently lack. It is therefore a classic ‘Catch-22’ situation. The history of interest rate futures markets 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 to Practice” in “Inflation Linked Products,” B. Benaben (Ed.), Risk Books.
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which are now extremely liquid suggests that the process of establishing volume and liquidity is one which may take many years and the market needs to persevere and consider variations to current contract designs and trading practices in order to expedite their development.
Future of the market The quest for a ‘natural’ two-way market for inflation derivatives continues and in the long term this 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 is ultimately unsustainable when the demand side for inflation swaps is growing every year. In the short term, real money interest in these ASW can help the market as it has in the immediate post-Lehman period. Corporate issuance and associated alternatives to issuance such as the use of swaps will be a more sustainable long-term solution. This particular angle, however, is still hampered 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 of inflation swaps by sovereign issuers. Many currently use IRSs for their debt management solutions and in theory can extend this to use inflation swaps, both taking advantage of favourable inflation swap levels and helping the derivatives market find a more sustainable source of swap supply.
Acknowledgements Many thanks to numerous UBS colleagues past and present who have over the past five years helped to provide a rich environment for exposure to the breadth of issues in the inflation-indexed markets globally. I would especially like to thank Chris Lupoli for stimulating discussions on the global inflation-indexed markets generally and Pierre Lalanne for converting raw market data (nominal and real government bond prices, IRS levels, and ZCIS levels) into a comprehensive database of continuously compounded zero real and nominal rates in government and 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 years deepened my understanding of this topic through challenging questions and suggestions raised during calls, meetings, and conference presentations.
Disclaimer The views expressed in this chapter are those of the author and do not necessarily reflect those of UBS.
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