DERIVING INFLATION FORECASTS FROM GOVERNMENT BOND PRICES

U finansijskom istraživanju i praksi, široko je prihvaćeno da se nominalne kamatne stope, izvedene iz cena raznih finansijskih proizvoda različitih ročnosti sastoje od odgovarajućih realnih kamatnih stopa i inflacije. Mada se srpovodi ekstenzivno istraživanje o odnosima između ove tri varijable, procena njihovih nivoa i dalje je u velikoj meri zasnovana na pregledima industrije i tržišnim podacima. Pošto ta informacija samo ukazuje na tekuća očekivanja u pogledu kretanja kamatne stope i inflacije tokom vremena, određena upozorenja treba imati u vidu kada se tumače te veličine. U SAD i Velikoj Britaniji, gde su tržišta državnih obveznica najveća i najaktivnija, komparativna analiza između konvencionalnih državnih obveznica i obveznica čiji je prinos vezan za inflaciju pruža meru očekivanja inflacije. Međutim pošto takve analize implicitno uzimaju da je investiranje u državne obveznice praktično bez rizika, pitanje je da li su izvedene procene od bilo kakve vrednosti u tekućim ekonomskim uslovima. Dalje, ovaj pristup ne može da se generalizuje na druge zemlje, gde je broj proizvoda kojima se trguje iz kojih se može utvrditi bilo koji odnos između kamatnih stopa i inflacije ograničen i gde važe drugačiji ekonomski odnosi. Ovaj rad ima za cilj da prikaže pregled metodologija koje se koriste za prognoziranje stopa inflacije iz cena državnih obveznica, usmeravajući pažnju na ključne pretpostavke i ograničenja tih pristupa. Cilj je utvrditi njihovu preciznost i time njihovu vrednost kod utvrđivanja realnih prinosa raznih proizvoda vezanih za kamatne stope.


Summary
In financial research and practice, it is widely accepted that nominal interest rates derived from the prices of various financial products of different maturities comprise of corresponding real interest rates and inflation.While extensive research has been conducted on the relationship between these three variables, estimation of their levels is still largely based on the industry surveys and market data.As this information only indicates the current expectations of interest rate and inflation movements over time, a number of caveats should be noted when interpreting such measures.In the US and the UK, where the government bond markets are the largest and most active, a comparative analysis between conventional government bonds and those whose yield is linked to inflation provides a measure of inflation expectations.However, as such analyses implicitly assume that investment in government bonds is virtually risk free, it is questionable whether the derived estimates are of any value in current economic conditions.Moreover, this approach cannot be generalized to other countries, where number of traded products from which any relationship between interest rates and inflation can be determined is limited and different economic conditions prevail.Thus, this paper aims to present an overview of the methodologies used to forecast inflation rates from government bond prices, drawing attention to the key assumptions and limitations of these approaches.The goal is to ascertain their accuracy, and thus their value in determining the real yields of various interest rate-linked products.

Introduction
Knowledge of inflation expectations is important for several reasons.Firstly, comparison of the government's inflation targets with market forecasts provides a view of the experts' perception of the monetary policy credibility.Secondly, real returns on investment can only be determined once inflation is taken into account.Moreover, comparing different investment options requires estimation of the underlying inflation term structure.Finally, cross-currency transactions implicitly incorporate not only the exchange rate, but also inflation in the two countries.Thus, as inflation affects a broad spectrum of financial decisions, from consumer purchasing behaviours to investments in complex financial products, it is essential to understand the role it plays in pricing financial instruments.Historically, in the US and the UK, inflation forecasts were typically based on a comparison between the prices of the conventional government bonds and those linked to Consumer Price Index (CPI).While consumer purchasing power, determined through a comparison of the cost of the standard basket of goods and average income, is a useful measure of inflation, this information is usually published with a time lag, thus the available data is historical, rather than current.Moreover, products linked to CPI introduce a further delay, as most are linked to the CPI level at the start of the coupon payment, making deriving useful information on inflation rates very difficult.Finally, analyses based on government bonds usually implicitly assume that these are risk-free products, which may not be true at the time of financial crises.Thus, to overcome these inherent flaws of analytical methods, inflation is often forecast based on surveys of economists and market participants.However, this approach is not only subjective and time-consuming, but also dependent on the truthfulness of the respondents, which cannot be guaranteed.Hence, the aim of this paper is to present an overview of the assumptions and limitations of the commonly used inflation forecasting approaches, focusing on their utility when used in economies where government bond markets are not as well developed as in the US and the UK.

Fisher Equation
The key assumption underlying most inflation forecasting approaches is that the interest rates quoted in the markets are nominal rates, comprising two components-real rates and inflation (Kozul, 2012a).This premise is based on the Fisher equation, used in finance to derive the relationship between these three variables.Denoting the nominal interest rate as i, real interest rate as r, and inflation as π, the equation can be written as (Fisher, 1977): i ≈ r + π The expression above is derived below.For example, if an investor purchases a bond with annual yield i, in a year's time, it will be redeemed for (1 + i).However, if during that period the bond price has changed to (1 + π), the real value of the bond is: This can be rearranged to solve for i, as follows: 1 1 + i = 1 + r + π +r π Thus, as both inflation and interest rates are small values, their product r π is negligible compared to the other terms, leading to the approximation: i ≈ r + π The same result can be obtained from the following two 1 st order Taylor expansions: (1 + x) (1 + y) ≈1 + x + y Substituting the interest rates and inflation into the above expressions: In economics, this equation is used when attempting to model nominal and real interest rate behaviors (Barro, 1997).In finance, its application is primarily in bond yield to maturity calculations, or in determining the internal rate of return for various investments.In the context of this paper, it simply provides the mathematical justification for the widely teoretski zasnovanih metoda prognoziranja inflacije o kojima se govori u narednoj sekciji.

Theory-based Inflation Forecasting Methods
In the UK, index-linked gilts, i.e., bonds with payments linked to Retail Price Index (RPI), equivalent to CPI in the US, were first introduced in 1981, and since then, their presence in the government bond market had grown considerably (Deacon & Derry, 1994).In essence, their redemption value and coupon payments are linked to the changes in RPI, thus implicitly accounting for inflation.However, as the coupon payments are typically made semiannually, and are based on the RPI value at the beginning of the coupon period, these bonds cannot be seen as true indicators of the current inflation.Moreover, as RPI index is published for the preceding month, this too reflects the historical, rather than actual inflation rate.In short, the coupon payment the investor receives reflects the inflation value seven to eight months prior.Thus, in real terms, gain is realized if inflation declines over the preceding period and vice versa (Arak & Kreichner, 1985).Moreover, when calculating the redemption yield of the index-linked gilt, some assumptions about the future inflation term structure must be known, as shown through the price/yield relationship below.
Recalling the Fisher equation above, bond price can be expressed as follows: where: C is the net coupon value, after the tax deduction (dependent on the investor type) R is the redemption payment i is the known inflation rate, derived from the RPI index published prior to the current coupon period r is the real yield, corresponding to the real interest rate underlying the nominal rate π is the estimated average inflation for the remaining period until bond maturity n is the number of outstanding coupon payment until redemption.
After simplification, the above equation can be written as: This clearly demonstrates that even the products based on known inflation still implicitly assume some inflation value that would apply over their lifetime.
Consequently, most practitioners rely on either industry surveys, simplified inflation models, or a combination of both, when determining the inflation term structure.

Inflation Surveys
Driven by the assumption that the investors and market practitioners act in a rational manner, the late columnist Joseph Livingston started the Livingston Survey in 1946, which was taken over by The Federal Reserve Bank of Philadelphia in 1990.This survey of economists' expectations summarizes the forecasts of economists from government, banking, industry, and academia with the aim to provide some information of their views of the future economic and market developments (Deacon & Derry, 1994).Similarly, in the UK, Gallup Poll (started in 1935) and UK CBI Industrial Trends Survey (commenced in 1958) aim to provide industry views on a wide range of issues, including optimism regarding the general and export business conditions, domestic and export production and order capacity, employment rates, investment, capacity, output, deliveries, stocks, prices, constraints to output, constraints on investment, competitiveness, innovation and training.While these polls (and others of this type) offer a wealth of information, this data is not easily translated into mathematical models.Moreover, they were criticized for their veracity, as they assume that the survey participants would respond truthfully and rationally.On the other hand, in a view of many economists, even irrational decisions are of value, if they result in market movements that can be measured and analyzed.For this reason, when forecasting inflation, many market practitioners anketa i prikupljanje i objavljivanje rezultata zahteva vreme, tako da čak i ova mera uvodi kašnjenje u procene inflacije.

The "Simple" Approach to Inflation Estimation
The simplest way to obtain an inflation estimate relies on the Fisher equation, thus assuming that inflation for a specific time horizon is equal to the difference between nominal and real interest rates.Inflation rates are commonly derived by comparing the yields of index-linked gilts with those of conventional government bonds of the same or similar maturity.This approach is characterized by all the shortcomings discussed above, and the process is further complicated by the difficulty in finding matching bond pairs that can be used in the comparison.Moreover, as was shown above, index-linked gilt prices implicitly incorporate an estimate of future inflation; hence, the inflation estimate derived from this simple comparison is based on its previously made estimate.Finally, as the bond pricing methodology, as well as the inflation estimate, provide the average inflation rate over the analyzed period, rather than the inflation expectation for the end of that period, when building the inflation term structure, this value must be decomposed using one of the approaches employed when building the interest rate yield curve.Thus, this approach lacks internal consistency and is rarely used alone, without any references to survey data or other methods.

Estimating "Break-even" Inflation Levels
In order to address the issue of internal consistency, the average inflation for a specific future time period is obtained by comparing the index-linked government bond yield with that of a conventional bond of similar maturity, using a more complex form of Fisher equation.This results in break-even inflation forecasts, whereby investors should be indifferent as to whether to invest in conventional or index-link bond, which should yield the same nominal return.In this methodology, a compound form of Fisher identity is used, i.e.: ) Implicit in this approach is the risk neutrality assumption, which implies that investors should not require any compensation for inflation-related risk premium, irrespective of holding conventional or index-linked bond.Under this assumption, the compound form of Fisher identity and the index-linked bond pricing equation are sufficient to derive the inflation rate estimate.While this approach is widely used, its main criticism derives from the attempts to match bonds on their maturity.Given that bond duration is typically used when comparing investments of this type, it seemed logical to extend this to inflation forecasting.

Estimating Break-even Inflation using Duration-matched Government Bonds
Bond duration is a measure of bond's sensitivity to the fluctuations in interest rates.In simplest terms, duration can be understood as the time it would take for the bond price to be redeemed.Thus, given that two bonds can be compared in terms of their duration when deciding on an investment, it is reasonable to use this approach when matching index-linked and government bonds for the purpose of deriving inflation estimates.More specifically, duration indicates the relationship between the bond price and nominal rates, and thus implicitly real rates and inflation.Therefore, it is more likely that two duration-matched bonds would have the same real yield than those matched by maturity.However, as bonds of equal duration may have significantly different maturities (as, for example, higher yield results in shorter duration, while zero-coupon bonds have duration equal to their maturity), it is very difficult to interpret results of such comparisons.If, for example, one bond has maturity of seven and other of ten years, should the derived inflation rate correspond to the seven-or tenyear period, or some intermediate term?

Discussion
As shown above, measuring even the current inflation levels is difficult without making assumptions.Thus, when attempting to forecast inflation trends, industry practitioners have to resort to a combination of various theory-based and survey methods, each carrying its own drawbacks.In their recent work, Seifried and Zunft (2011) analyzed US index-linked debt market in order to ascertain whether the breakeven inflation rates derived from the market data are a reliable measure of true inflation.Moreover, the authors have compared the survey-based inflation forecasts with their findings, concluding that, while there is little correlation between market-derived and survey-based inflation, the former is still the best currently available measure of future inflation.Research on the link between index-linked products and inflation is extensive, dating back to the 1980s, when these financial instruments first started to be offered (Hamilton, 1985;Arak & Kreichner, 1985).Since then, many practitioners have analyzed and modelled inflation, mostly focusing on the US and UK markets, as the largest and most active ones.For example, Jordan, Jorgensen, and Kuipers (2000) analyzed the US STRIPS (Separate Trading of Registered Interest and Principal of Securities) market, while Sack (2000) provided similar, and related, analysis of the TIPS (Treasury Inflation-Protected Securities) products.As STRIPS allow the investors hold and trade the individual interest and principal components of eligible Treasury notes and bonds as separate securities, these are directly linked to TIPS as a sub-class of Treasury bonds.Thus, these analyses provide useful information of the value of these instruments as a measure of future inflation.As Sack (2000) argued, for the Treasury, the main motivation behind issuing index-linked bonds is its protection against unforeseen inflation fluctuations, which would be reflected in the investor demand for higher yields on conventional bonds.Moreover, as these securities are not as liquid as other forms of government debt, their prices may not fully reflect the inflation compensation.As Seifried and Zunft (2011) pointed out, in addition to the expected inflation, break-even inflation rates derived from market data include risk premium, dependent on how risk-averse the investors are; liquidity risk premium, due to the disparity between available contracts in conventional and index-linked debt markets; counterparty default risk, which used to be negligible before the economic downturn, but is now a real issue; currency risk; interest rate risk; as well as other components associated with pricing methodologies, such as convexity and compounding issues.These risks and their effects on bond prices are best exemplified through a discussion of changes in bond prices under different market conditions.
As with any market product, bond price is driven by supply and demand, among other factors.
As the bond price increases, its yield to maturity and the expected return decline, resulting in lower demand.As bond prices and interest rates are inversely related, higher bond prices imply lower interest rates, which typically encourage borrowing, i.e., increase the demand for bonds.Thus, shift in bond prices results in the shift in the equilibrium rate, under which supply and demand are equal.Some of the factors influencing the bond demand are:  3. Changes in business conditions -improved economic conditions and tax incentives make business expansion attractive, thus increasing the need for borrowing.For larger firms, this may result in bond issuance, thus increasing the bond supply.
In sum, when considering methodologies to be used for estimating inflation, one must be mindful of the two-sided nature of all products, and thus government bonds.This, combined with other factors discussed above, makes deriving inflation estimates difficult.The summary below can serve as a useful guideline, for determining the direction of bond supply and demand, as well as interest rate changes, when various variables increase:

Conclusion
Despite extensive body of literature devoted to inflation and inflation forecasts, this crucial economic variable remains difficult to predict.Notable theoretical work in this filed resulted in the well-known Phillips curve that aimed to link low inflation to high unemployment and vice versa, which was later replaced by Keynesian and New Keynesian economic models that distinguish between demand-related and cost-driven inflation (Kozul, 2012b).Many practitioners preferred to draw information from the market data, which resulted in many attempts to derive the term structure of inflation expectations (Remolona, + i -pokazuju povećanje i smanjenje.
Ang & Bekaert, 2003;Hördahl, 2008;Adrian, & Wu 2010)008;Adrian, & Wu 2010).However, when historical inflation estimates are compared the actual inflation for the corresponding time periods, it is evident that these cannot be viewed as reliable a measure of inflation term structure.In particular, in economies where government bond markets are not well developed and available contracts scarce, even such estimates cannot be made without introducing significant errors due to lack of data and numerous assumptions.Recent economic downturn has challenged even the fundamental premise of government bonds being risk-free securities.Thus, new inflation measures are clearly needed, ideally combining sound theory with more current market data.
Note: the + and -sings indicate increase and decrease, respectively.