Can Liquidity Explain the Recent Fall in Breakeven Inflation?

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1 QUANTITATIVE RESEARCH March 2016 Can Liquidity Explain the Recent Fall in Breakeven Inflation? AUTHORS Vasant Naik Executive Vice President Riccardo Rebonato Executive Vice President The recent dynamic in the Treasury Inflation-Protected Securities (TIPS) market has raised many important questions for investors and policymakers. Breakeven inflation (BEI) rates have declined consistently over the last few months, as seen in Figure 1. The zero-coupon breakeven inflation rate for a maturity of 10 years traded roughly in the range of 200 to 250 basis points (bps) from 2010 to 2013 but has declined from about 230 bps in mid-2014 to less than 150 bps at the end of uary Figure 1: History of 10Y U.S. breakeven inflation rate 10Y breakeven inflation rate (%) Source: Federal Reserve Board as of 25 February The figure reports zero-coupon BEI rates for 10 years to maturity.

2 2 March 2016 Quantitative Research Since BEI rates contain information about long-horizon inflation expectations (and inflation risk premium), they are an important input in the assessment by the Federal Reserve Board of how these expectations have changed recently. This in turn is a key question in the formation of monetary policy, which targets medium-term expected inflation as one part of its dual mandate. Therefore, it is important to understand what might be causing the recent decline in BEI rates. We analyze the plausible causes of the recent changes in BEI rates in this note. THE QUESTION The breakeven inflation rate is defined as the difference between yields on same-maturity nominal bonds and TIPS: ( ) ( ) ( ) (1) In this note, we use BEI rates derived from zero-coupon nominal and real yields. The BEI rate should be the sum of inflation expectations and an inflation risk premium. However, the nominal Treasuries and inflation-linked bonds (TIPS) whose yields are used to compute these BEI rates have very different liquidity properties. Nominal Treasuries are much more liquid than TIPS. As a result, it is reasonable to assume that BEI rates also contain a liquidity component: [ ] ( ) (2) As a consequence of this decomposition, the observed fall in BEI may, but need not, imply a decline in expectations. Indeed, recent papers by D Amico, Kim and Wei (2014) and Gospodinov and Wei (2015) 2 use an affine term structure model to conclude that the bulk of the decline mentioned previously has been due to a change (increase) in the compensation for liquidity. The conclusion these studies draw is that, despite the recent weakness in spot inflation measures, long-term expectations have remained well anchored. In this note, we look at statistical evidence to ascertain whether liquidity is indeed likely to be responsible for the observed fall in BEI. A SUMMARY OF OUR RESULTS We identify the liquidity premium in TIPS as the difference between BEI rates and comparable inflation swap rates and relate these to standard proxies of market-wide liquidity. We conclude that: i) variations in BEI-inflation swap rate differentials have a large component uncorrelated with standard proxies for market-wide liquidity (as defined below) in normal market conditions; ii) there was a significant dependence on these proxies during the 2008 crisis and presumably there would be in conditions of similarly severe distress; iii) a large part of the recent decline in BEI rates was shared by a decline in inflation swap rates as well; iv) consequently, in present market conditions, it is unlikely that changes in liquidity explain the dominant part of the observed changes in BEI. We stress that we cannot from this conclude that the observed fall in BEI is for the most part due to a fall in inflation expectations, because empirically we cannot disentangle the expectations from the risk premium components. 3 OUR APPROACH In order to identify the liquidity component, we make use of information from inflation swap rates. This part of our approach is shared by D Amico, Kim and Wei (2014) and Gospodinov and Wei (2015). The observation that underpins both investigations is that there is an important difference in how mid prices for inflation swaps and BEI are affected by liquidity. Since TIPS are funded instruments, and inflation swaps are in zero net supply, the argument is that the mid values of inflation swaps are only modestly affected by liquidity. 4 TIPS prices (and hence the BEI) are instead affected to first order by a change in liquidity. More precisely, given what we argued about the different impact of liquidity on BEI and the inflation swap rate, we can write ( ) [ ] ( ) [ ] ( ) ( ) [ ] ( ) ( ) [ ] ( )

3 March 2016 Quantitative Research 3 (where real and infl signify real rates and inflation, respectively) and therefore the difference between the BEI rate for a given maturity and the inflation swap rate for that maturity should be a reasonable proxy of the liquidity premium embedded in TIPS, i.e., ( ) ( ) ( ) ( ) Note that the liquidity premium in (3) is expected to be negative. Of course, liquidity is not directly observed. We therefore use three variables that have been used by researchers as proxies of market-wide liquidity conditions. These variables are: (i) the Chicago Board Options Exchange volatility index (VIX), which shows the implied volatility of near-term options on the S&P 500 Index. It is highly sensitive to short-term risk perceptions in financial markets (and to the consequent changes in demand for liquid assets); (ii) the spread between the 10-year, on-the-run U.S. Treasuries and off-the-run Treasuries. The most recently issued 10-year notes are more liquid than older issues. Hence this spread, much like the VIX index, responds quickly to changes in demand-supply imbalances in market-wide liquidity, and (iii) the J.P. Morgan Index of All High-grade, Credit-Default Swaps - Cash Spreads. This is a variable from credit markets and measures the difference between the credit spreads on a portfolio of CDS of investment grade issuers and the credit spreads in the cash bonds of these issuers. CDS are considered more liquid instruments in credit markets than cash bonds and like inflation swaps are in zero net supply. As such, an index of these spread differentials is a good proxy for changing liquidity conditions in financial markets, particularly in credit markets. We regress the difference between the BEI and the inflation swap rate on these liquidity proxies to identify the component of this difference that is linked to market-wide liquidity conditions. Our approach thus makes use of the different responsiveness of inflation swap rates and BEI to liquidity shocks to isolate the liquidity component of BEI. RESULTS Figure 2 presents summary statistics of the data series on the 10-year zero-coupon BEI rates and inflation swap rates (which are quoted on a zero-coupon basis). It can be seen that the time series of inflation swap rates are less volatile than that of BEI rates. For Figure 2: Summary statistics (sample period: March 2005 uary 2016) Data BEI Rate from TIPS (10y) Inflation Swap Rate (10y) BEI-Inflation Swap Differential Average level (bps) Std dev (level) (bps) Std dev (changes) (bps pa) Change between Feb 2016 (bps) Change between Feb 2016 (bps) Post Crisis ( ) Average level (bps) Std dev (level) (bps) Std dev (changes) (bps pa) Change between Feb 2016 (bps) Change between Feb 2016 (bps) Source: Federal Reserve Board, Bloomberg and PIMCO as of February Notes: The average level, the standard deviations of the level and the (annualized) standard deviation of the changes of the BEI rate and of the inflation swap rate (10Y) in basis points are shown for the full sample (top panel), and the post crisis period (bottom panels).the last two rows in both panels shows the fall (basis points) in the BEI and inflation swap rates between the start of the year and the 1 February The right- most column shows the averages and standard deviations for the differences.

4 4 March 2016 Quantitative Research example, over the period March 2005 to uary 2016, the 10-year BEI rate had a standard deviation of 68 bps while the comparable inflation swap rate had a standard deviation of 55 bps. In the period after the financial crisis (uary 2010 to uary 2016), the volatility of both rates has declined modestly. However, inflation swap rates continue to be less volatile. Also, a comparison of the standard deviations of the changes in these variables shows that there is an additional source of volatility affecting the BEI, over and above the volatility of the inflation swap rate. To identify whether this source of additional volatility is indeed significantly related to market-wide liquidity, we regress the difference between 10y BEI rates and 10y inflation swap rates against the previously mentioned proxies of liquidity. We estimate three specifications, introducing one additional variable in each specification: Model 1: Model 2: ( ) ( ) ( ) ( ) ( ) where ( ) ( ) ( ) ( ) ( ) ( ) ( ) Treasury liquidity spread (t)= 10y benchmark Treasury yield - 10y off-the-run fitted Treasury par rate and Model 3: where ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) The regressions are carried out on monthly data for the full sample (March 2005 to uary 2016), as well as a pre-crisis period (March 2005 to December 2007) and a post-crisis period (uary 2010 to uary 2016). The regression results are shown in Figure 3. The units of measurement of these variables are basis points for the BEI-inflation swap rate differentials, Treasury liquidity spreads and high grade all CDS-bond basis while the VIX index is measured in percentage points. Consequently, all variables are roughly of the same order of magnitude. Figure 3: Regressions of BEI-inflation swap differentials on proxies of liquidity (monthly data) All variables are measured in basis points except for VIX which is measured in percentage points. Sample Period Beta (VIX) Beta (on-the-run/off-the-run spread) Beta (CDS bond basis) R 2 Mar Model * 41% Model * 0.51* 47% Model * 56% Mar 2005 Dec 2007 Model * 12% Model * -1.02* 26% Model * -1.29* 0.28* 36% Model * 9% Model * % Model * -0.46* 0.12* 18% *Significant at 95% confidence level Source: Federal Reserve Board, Bloomberg, JPMorgan and PIMCO as of 25 February 3 March Notes: Regression results for the full period (top panel), the pre-crisis period (middle panel), and the post crisis period (bottom panel). The columns headed beta(.) display the slope in the univariate (Model 1), bivariate (Model 2) or trivariate (Model 3) regressions. Model 1 uses the VIX index only, Model 2 uses the VIX index and the actual on-the-run/ off-the-run spread as regressors and Model 3 uses the VIX index, the actual on-the-run/off-the-run spread and the CDS bond basis as regressors. The last column shows the R 2 for the various regressions. Regression coefficients which are significant at the 95% confidence level are market with an asterisk (*).

5 March 2016 Quantitative Research 5 When we look at the full sample, we find a strong dependence (R 2 of 56% for Model 3) of the BEI-inflation swap rate difference on the market-wide liquidity proxies. However, this dependence is reduced in the pre- and post-crisis periods. The R 2 of the regression in the post-crisis sample is 18% (for Model 3) indicating that a large part of the variation in the BEI-inflation swap rate differential in the post-crisis period is orthogonal to movements in the liquidity proxies. The effect of VIX is negative; a higher VIX implies worsening liquidity conditions and hence a declining BEI-inflation swap rate differential. The CDS-cash basis variable has a positive sign indicating that liquidity in both credit and TIPS markets might be driven by common factors. The beta on on-the-run/off-therun spreads has the correct sign in full sample but not so in the sub-samples. This seems to be driven by a negative correlation between VIX and this spread. The index of CDS-cash basis has declined considerably in recent months (from a value of -17 bps on 1 uary 2014 to -73 bps on 1 February 2016). A positive sign of the beta on this variable suggests that a part of the movement in BEI-inflation swap differentials is common to this movement in the CDS-cash basis. However, as Figure 1 shows, between the start of 2014 and the end of February 2016, the fall in the BEI was 99 bps and the corresponding drop in the 10-year inflation swap rate was 86 bps. If the assumption about the difference in liquidity of TIPS and inflation swaps is correct, it is difficult to attribute the fall in BEI to liquidity. When we use the regression coefficients either for full-sample or for the second-half to attribute changes in BEI rates to changes in our liquidity proxies, we find a small contribution (of the order of 8 bps to 10 bps). A supporting piece of evidence that the decline in BEI rates may not be just liquidity driven is seen in the projections in the Survey of Professional Forecasters. Figure 4 shows a decline in the projections for the 10-year-ahead inflation starting at least in the second quarter of From the first quarter of 2014 to the first quarter of 2016, these projections have declined from 2.30% to 2.12%. (The volatility of quarterly changes in the 10-year inflation projections is about 8 bps, estimated on data since uary 2005.) Figure 4: Median of the inflation projections from the Survey of Professional Forecasters Inflation projection % (pa) Y Inflation Y Inflation Source: Federal Reserve Bank of Philadelphia as of 9 March The median of the predictions available is shown in the Survey of Professional Forecasters (SPF) for the 5- and 10-year-ahead inflation. There are four predictions per year, one each quarter. COMPARISON OF OUR EMPIRICAL FINDINGS WITH THE MODEL-BASED ESTIMATES It is clear from the above that our empirical analysis reaches different conclusions than those arrived at by the models used by D Amico, Kim and Wei (2014) and Gospodinov and Wei (2015). These authors derive a no-arbitrage affine term structure model with four latent variables to express nominal yields, real yields, breakeven rates, inflation swap rates and expected inflation as a linear function of the latent variables. The innovation in these papers is to explicitly model a liquidity factor in the valuation of TIPS and then use a comprehensive dataset including nominal yields, real yields, inflation swap rates and realized inflation to estimate the model. With estimated parameters of the model at hand, the authors can decompose breakeven rates into expected inflation, inflation risk premium and a liquidity premium.

6 6 March 2016 Quantitative Research A detailed examination and extension of this work is the subject of ongoing research at PIMCO and is beyond the scope of this note. However, a few observations are in order about the parameter estimates that drive the result in D Amico, Kim and Wei (2014) that inflation expectations have not changed much in the last few years and that the decline in breakeven inflation rates seen in the last couple of years being attributable to increasing liquidity premium in the TIPS market. In the affine framework of these authors, expected inflation for any horizon is an affine function of the underlying state variables. So for example, expected inflation over a 10-year horizon, (denoted EI(t,10) below) is given by: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (4) where x 1 (t), x 2 (t), and x 3 (t) are the (first three) latent variables of the model. The coefficients a(10), b 1 (10), b 2 (10), and b 3 (10) are functions of the estimated parameters. Given the parameters estimated by D Amico (parameter estimates given in Table IA.1 of the paper for Model L-II), it turns out that ( ) ( ) ( ) ( ) Also, as per the authors estimates, the instantaneous volatility of changes in x 1 (t) is 100 bps p.a., that of changes in x 2 (t) is 126 bps p.a. and of changes in x 3 (t) is 414 bps p.a. As such (holding everything else constant) a one standard deviation move in x 1 (t) will lead to a 5 bps move in EI(t,10). Similarly, a one standard deviation move in x 2 (t) will lead to a 13 bps move in EI(t,10). The effect of changes in x 3 (t) would be negligible. Thus it appears that inflation expectations in the model are not very sensitive to movements in the state variables. This is caused by the low values of b 1 (10), b 2 (10), b 3 (10). Thus, for all dates the model would predict an expected inflation that stays around the constant value of 3%, (because a(10)=.03), in Equation (4). This would happen no matter what the shocks to the state variables happened to be (within a reasonable range). In other words, the calibration of the model makes it difficult for inflation expectations to move substantially, regardless of what happens (within reasonable bounds) to the state variables. 5 CONCLUSIONS Starting from the observed fall in BEI, we have tried to answer the question of whether this fall can be mainly attributed to deterioration in liquidity. We have made use of the same assumptions about differences in liquidity of TIPS and inflation swaps as have been made in recent papers by the Federal Reserve Board and the Federal Reserve Bank of Atlanta, but we have approached the problem from an empirical, rather than theoretical, point of view. By running regressions against plausible proxies of liquidity, we found a marked dependence of the BEI on liquidity during periods of severe market distress; however, this dependence moderates in less extreme market conditions. Moreover, a large part of the decline in BEI rates in the last two years has also been shared by inflation swap rates. Hence, if BEI-inflation swap rate differentials are good measures of the liquidity premium in TIPS, it is difficult to attribute the observed fall in BEI rates predominantly to deterioration in liquidity. We cannot disentangle from our empirical analysis whether the observed fall in BEI is due to a change in expectations or in risk premium. We stress, however, that the only additional source of information for this decomposition via an affine term-structure model are cross-sectional information (fit to bond prices) and the imposition of the conditions of no arbitrage. Recent work in affine term structure modeling 6 has raised strong doubts as to how informative the conditions of no arbitrage are. And as for the fitting to the yield curve, a heavy predictive burden is placed on the shoulders of the quality of the fit, because, as is well known, with the current multi-variable affine models, very different combinations of parameters can give rise to similarly good (and all high-quality) fits. We therefore caution at this stage against relying too much on its results to draw conclusions about whether inflation expectations have remained well anchored or have substantially changed. More empirical and theoretical work is needed, and, indeed, is underway.

7 March 2016 Quantitative Research 7 1 We thank David Pottinton and Wendong Qu for their substantial contributions to this research. 2 D Amico S., D. Kim, and M. Wei, 2014, Tips from Tips: the Information Content of Treasury Inflation-Protected Security Prices, Finance and Economics Discussion Series, Federal Reserve Board. Gospodinov, N., and B. Wei, 2015, A Note on Extracting Inflation Expectations from Market Prices of TIPS and Inflation Derivatives, Federal Reserve Bank of Atlanta Working Paper. 3 In the articles mentioned previously, the decomposition is possible because of the added constraints imposed by the condition of no arbitrage and the cross-sectional information from the recovery of the yield curve. 4 Of course, the bid-offer spread of an inflation swap is strongly affected by liquidity, but the mid only mildly so. 5 It is true that, since the state variables are latent, we cannot easily interpret them; however, from the calibration we can find their volatilities, and therefore their plausible ranges of variation. 6 See, e.g., Joslin S, Anh Le, Singleton K J, (2013), Why Gaussian Macro-Finance Models Are (Nearly) Unconstrained Factor-VARs, Journal of Financial Economics, Vol 109, Issue 3, Also: Joslin, Singleton and Zhu (2011) show that within any canonical [Gaussian dynamic term structure model] and for any sample of bond yields, imposing no-arbitrage does not affect the conditional P expectation of [the underlying factors] emphasis in the original, page 927, A New Perspective on Gaussian Dynamic Term Structure Models, Review of Financial Studies, 24.3,

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