Asset Pricing Anomalies and Macroeconomic Risk

State-varying illiquidity risk in sovereign bond spreads

Paul Docherty and Steve Easton

Newcastle Business School, University of Newcastle, NSW 2308, Australia

Abstract

Illiquidity and default risk are determinants of bond spreads that models suggest vary across market states. But attempts to empiricallyidentify the separate impact of these factors are affected by correlation between them. The Australian sovereign debt market, where the Australian government provided an explicit guarantee over semi-government debt, provides an environment in which to examine these separate factors. We find that illiquidity risk in sovereign spreads is conditional upon market states and is particularly important during periods of market stress, consistent with the notion of flights to liquidity. These flights to liquidity are substantially more prominent at the shorter end of the term structure, whereas volatility predominantly explains longer-maturity sovereign spreads. The term spread of sovereign yields is shown to be negatively related to illiquidity during periods of stress, indicating that theoretical models that incorporate flights to liquidity need to be expanded to include the impact of such flights on both the level and slope of yields.

Keywords: Illiquidity risk,, yield spreads,sovereign debt, volatility.

JEL Codes: E43, G12

Acknowledgements: We wish to thank Doowon Lee and seminar participants at Macquarie University, The University of Melbourne, the 2014 Mid-West Finance Association Conferenceand the 2014 SIRCA Young Researcher Workshop for helpful comments.

Introduction

Two key factors have been shown to be determinants of time-varying bond spreads; namely illiquidity risk and defaultrisk.[1]Theoretical models of the price of illiquidity risk by, for example, Acharya and Pedersen (2005) and Ericsson and Renault (2006), provide three central implications; namely that aversion towards illiquidity is time-varying and positively related to volatility, that cross-asset correlations are positively related to illiquidity, and that illiquid assets demonstrate greater price sensitivity than do liquid assets to aggregate market-wide illiquidity. Consistent with predictions from these models, studies such as those by Acharya et al. (2013) and Dick-Nelson et al. (2012) report that illiquidity premia are significantly larger during periods of crisis than they are in normal states.

However, as demonstrated by Beber et al.(2009),the relative importance of default risk and illiquidity riskin sovereign yield spreads differs depending on the market state, resulting in flights to both quality and liquidity that occur at different times and for different reasons. Specifically, Beber et al. (2009) report that while default risk is the key determinant of bond spreads during normal periods, illiquidity is the key driver of spreads during criseswhen investors increase their aversion towards risky and illiquid assets. Similarly, Acharya, Amihud and Bharath (2013) report that there is a flight-to-liquidity during crisis periods, where investors have a preference for liquid investment grade bonds rather than less liquid sub-investment grade bonds.

However the correlation between default risk and illiquidity risk, and the concomitant correlation between flight-to-quality and flight-to-liquidity,creates empirical challenges when attempting to disentangle their impacts on bond spreads. Where proxies for illiquidity and default risk are positively correlated, regressions may produce unreliable test statistics, overestimating the role of liquidity (Helwege, Huang and Wang, 2014). Crucially, as most extantstudies focus on bonds with different default risks, namely US corporate bonds and European sovereign bonds respectively, they are not able toprovide a clean examination of the differential impact of illiquidity risk across market states.[2] Ericsson and Renault (2006) show that default risk and illiquidity risk are usually positively correlated in the United States corporate bond market, while Beber et al. (2009) report a negative correlation between default risk and illiquidity for European sovereign debt.

This study provides an examination of bond spreads by exploiting an environment that permits the separate identification of default risk and illiquidity risk factors. We examine the spread between Australian government bonds and semi-government bonds. On 25 March 2009, the Australian government announced that they would provide a guarantee on semi-government debt across the period from 24 July 2009 to 31 December 2010 (Australian Government, 2012). For this period the spread between Australian government and semi-government debt will solely reflect illiquidity risk.

Further, vertical fiscal integration between the States and Commonwealth Government minimises the probability of a state defaulting conditional on the Commonwealth Government not defaulting over the period before and after the explicit Australian government guarantee was implemented. Our sample period from 2002 to 2012also includes two periods of significant market stress: the Global Financial Crisis and the subsequent European sovereign debt crisis. By minimising the impact of default risk over this extended period, we are better able to isolate the impacts of illiquidity risk and flight-to-liquidity across market states.

The differential impact of illiquidity premia across the term structure has also garnered recent attention. Ericsson and Renault (2006) provide a theoretical model where illiquidity premia are positively correlated with default risk and the illiquidity premia is a decreasing function of time to maturity. Only two studies have undertaken an empirical examination of this relationship in an environment that controls for default risk (Longstaff, 2004; Kempfet al. 2012). Longstaff (2004) reported a U-shaped liquidity term structure when comparing the yield between Treasuries and so-called Refcorp bonds, that is, bondsissued by a government agency and where their principal is fully collateralisedby Treasury bonds and full payment of coupons is guaranteed by the Treasury. However, his sample was limited as only six Refcorp bonds were available for comparison.Kempf et al. (2012) reported that separate economic factors drive shortand long-term illiquidity premia. They showed that asset market volatility explains the short-term illiquidity premium, while long-term economic risks explain the long-term illiquidity premium.

Both extant studies of the term structure of the illiquidity premia focus on the period prior to the Global Financial Crisis and do not examine the differential impact of illiquidity and default risk on the term structure across different market states.Our sample period from 2002 to 2012permits us to examine the differential impact of the term structure of illiquidity across different market states and to extend upon Beber et al. (2009) to determine whether the flights to liquidity observed in sovereign yields is more pronounced at either the short or long end of the term structure.

The paper proceeds as follows. Section 2 provides a discussion of the institutional features of the Australian sovereign debt market. The data are described in Section 3 with the results presented in Sections 4. A summary is provided in Section 5.

Institutional Features of the Australian Sovereign Debt Market

Semi-government bonds have traditionally been considered to be an extension of the Australian government bond asset class (Lancaster and Dowling, 2011). This belief may have been derived from the explicit guarantee provided by the respective state governments and their semi-government debt, along with the close fiscal relationship between the Commonwealth and states of Australia. As detailed in Twomey and Withers (2007, p. 37), the level of vertical fiscal integrationresulting from the Australian Constitution is ‘the most extreme of any federation in the industrial world’. As they document, across the 1990s for the five major federations that they examined (Australia, Canada, Germany, Switzerland and the United States), Australia had the highest share of federal government spending, the highest share of federal taxation, and the largest relative gap between these two measures. The effect of strong vertical fiscal integration in Australia is that, while there is no explicit Commonwealth guarantee of State and Territory debts, the system of revenue sharing results in cash flows to State and Territory governmentsthat are relatively uncorrelated with economic conditions within those jurisdictions.

In addition to the extreme vertical fiscal integration that exists in Australia, there is also a widely held perception that the Commonwealth provides an implicit guarantee over the debt of its states. This perception may be influenced by the fact that on two occasions during the Great Depression, the New South Wales government defaulted on its debt by failing to make a coupon payment. On both occasions, the Commonwealth government sought and was granted an extension of its constitutional power over state debt and took authority to pay these coupons and avoid default (National Archives of Australia, 2012). The Commonwealth government now has constitutional authority to take over the debt of any state, and to indemnify itself in the event that it does elect to do so; a right that was exercised in 2009 when the Commonwealth government offered an explicit guarantee over semi-government debt. The states of New South Wales and Queensland, the largest bond issuing states in Australia, paid a fee and elected to take up this guarantee, while the other Australian states did not.

With respect to the state of New South Wales, there are reasons in addition to that of vertical fiscal integration between the States and Commonwealth Government to expect the probability of that state defaulting conditional on the Commonwealth Government not defaultingto be minimal. Both NSW and Commonwealth debt held a AAA credit rating with Standard and Poor’s across the study period. Further, these debts are both risk-weighted at 0% under the Basel regulations and are both eligible securities for repurchase agreements.[3] Further, in 2012 New South Wales represented 32% of the Australian population (Australian Bureau of Statistics (2013)) and 30% of Australian Gross Domestic Product (Australian Bureau of Statistics (2012)).

Despite the similarities between Commonwealth government and semi-government bonds, there is also a strong case to suggest that investors should consider these securities as belonging to different asset classes. Most notably, semi-government bonds tend to trade with a significantly higher yield compared with Commonwealth government bonds, particularly during periods of financial crisis. Figure 1 reports innovations in the 3-, 5- and 10-year spreads and the term structure of the spread across our sample period. The average spreads across the entire sample are 25 basis points, 28 basis points and 31 basis points respectively. All three spreads increased substantially from mid-2007 onwards and then again from early 2011. These periods correspond with periods associated with the Global Financial Crisis and the European sovereign debt crisis. The grey shaded areas in Figure 2 represent periods when the Australian economy is contracting according to the Melbourne Institute’s ‘phase of the business cycle’ dating of the business cycle. It is clear that, on average, the spreads increase during periods of contraction and decrease during periods of expansion. The average 3-, 5- and 10-year spreads are 21 basis points, 26 basis points and 27 basis points respectively during of ‘expansion’ and 46 basis points, 54 basis points and 58 basis points respectively during periods of ‘contraction’.

While the large and time-varying yield spreads reported in Figure 1 are of interest to investors as they conflict with the view that Commonwealth government and semi-government bonds can be considered to be the same asset class, these spreads also have implications for existing theoretical models. Most notably, given the probability of New South Wales defaulting conditional on the Commonwealth Government not defaulting is expected to be minimal, the spreads shown in Figure 1 appear to be too large to be explained by default risk, which is consistent with previous studies that find that credit spreads tend to be higher than those predicted by Merton’s (1974) structural model.[4]

Data

Our analysis is based on bond yield data provided by the Thomson Reuters Tick History database that is maintained by Sirca. The market yield for 3-, 5- and 10-year maturities is provided for both Australian government bonds and NSW semi-government bonds on a daily basis. Our analysis comprises the ten-year period from January 2003 to December 2012. This sample period provides two key benefits. First, it includes two periods of market stress: the Global Financial Crisis and the European sovereign debt crisis. The inclusion of periods of market stress within our sample is important, as recent studies have argued that a flight-to-liquidity takes place during periods of market stress, increasing illiquidity premia during these periods (Brunnermeier and Pedersen (2009), Acharya et al. (2013)). Second, our sample includes an 18-month period where NSW semi-government bonds were covered by the Commonwealth Government guarantee, allowing for illiquidity premia to be examined across this period without the confounding impact of default risk.[5]

We calculate the implied yield at monthly frequency for maturities between three and ten years by interpolating the market yields for both Australian government bonds and NSW semi-government bonds. To estimate the term structure, we apply Svensson’s (1994) extension of the Nelson and Siegel (1987) model. This model uses a flexible, smooth parametric function that allows for two humps in the term structure; which is important to capture convexity effects at longer horizons. The use of the Nelson-Siegel-Svensson model is appealing given this family of models has been show to accurately construct term structure forecasts (Diebold and Li, 2006; Fabozziet al. 2005) and is widely applied by central banks (Bank for International Settlements, 2005). Applying the Nelson-Siegel-Svensson model, the yield for each term to maturity is calculated as:

where i(n,t) is the yield of the curve at maturity m at time t, β0, β1, β2, β3, τ1 and τ2 are parameters to be fitted via a least-squares estimation. To validate our results, our calculated yields for the three, five and ten year maturities are compared with the equivalent yields for Australian government and semi-government bonds reported by the Reserve Bank of Australia.[6]

The spread between semi-government and government bonds is then calculated as:

Ψn,t = iNSW,n,t – iAustralia,n,t (1)

where Ψn,tis the spread for bonds with n years to maturity at time t, iNSW,n,t is the market yield on NSW semi-government bonds with n years to maturity at time t and iAustralia,n,tis the market yield on Australian government bonds with n years to maturity at time t.[7]

We also examine the term structure of the spread to perform an empirical test of Ericsson and Renault’s (2006) theoretical model, where the illiquidity premia is a decreasing function of time to maturity. To calculate the term structure of the spread, we estimate a cross-sectional regression each month, where the spread for each pair of bonds is regressed against the time to maturity (m):

Ψm,t = β0,t + β1,t(m) + εt(3)

where β1,tis used as our estimate of the term structure of the spread (TERM) at time t.[8]

The term structure of the spread across time is reported in Figure 2. While the term structure of the spread is generally positive, there are three instances across our sample in which it becomes negative, and all three instances are during periods of ‘contraction’ as defined by the Melbourne Institute. These negative values of the term structure during periods of contraction provide formative evidence to suggest that flights to liquidity are more prominent at the shorter end of the term structure in times of market stress.

The implementation of the Australian government guarantee provides us with a unique environment that we can exploit to undertake an examination of the relative importance of the default and illiquidity premia during normal times and times of market stress.Figure 3provides the daily 3-, 5- and 10-year spreads at the announcement on 25 March 2009 and cessation on 31 December 2010 of the Australian government guarantee. As shown in Panel A, the spreads declined by 29, 30 and 27 basis points respectively on the announcement day. The magnitude of the decline in each spread represents the size of the conditional default premia that was priced into the market yields of each of the bonds examined in this study. Furthermore, the magnitude of the remaining spread represents the residual risk, which includes illiquidity risk. Immediately prior to the announcement of the government guarantee, the spreads were 111, 122 and 138 basis points respectively across the term structure. Therefore, we can determine that default risk attributes 26% (19%) of the total spread at the shorter (longer) end of the term structure.

Panel B of Figure 13shows the spreads at the time the Australian government guarantee ceased to apply to new issuances of debt. The 3-, 5- and 10-year spreads increased by 12, 18 and 18 basis points respectively on the day that the government guarantee was removed. The magnitude of the liquidity premium for these three spreads on the day after cessation was 29, 45 and 54 basis points respectively. Therefore, default risk can be seen to account for 42% (33%) of the total spread at the shorter (longer) end of the term structure at a period when relatively calm had returned to financial markets. This result suggests that default risk is a more important determinant of sovereign yield spreads during normal periods.

We examine the economic drivers behind the bond spread and the term structure of the spreadby incorporating into our models a number of proxies for default risk and illiquidity risk, together with control variables that capture the state of the economy and international flows of funds.

In the spirit of Pastor and Stambaugh (2003) we measure illiquidity risk as the covariance between the yield spreads at each maturity and a market-wide measure of illiquidity. To calculate our bond illiquidity measure, we collected bid and ask orders for Australian government and NSW semi-government bonds from SIRCA. Only the best bid and ask price quoted at any point in time are included in the sample. We calculate an adjusted spread as the bid-ask spread divided by the midpoint of the quote. The daily adjusted spread is then calculated as the average of all spreads quoted across all maturities throughout the day. It is given by: