How important is liquidity risk for sovereign bond risk premia? Evidence from the London stock exchange

Journal of International Economics 82 (2010) 219–229

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Journal of International Economics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j i e

How important is liquidity risk for sovereign bond risk premia? Evidence from the London stock exchange Ron Alquist ⁎ International Economic Analysis, Bank of Canada, 234 Wellington Street, Ottawa, ON K1A 0G9, Canada

a r t i c l e

i n f o

Article history: Received 24 November 2008 Received in revised form 23 July 2010 Accepted 23 July 2010 Keywords: Sovereign bond returns Market liquidity Liquidity risk factor Country risk premium

a b s t r a c t Using a unique data set, this paper studies the relationship between market liquidity risk and sovereign bond risk premia. The London Stock Exchange during the late 19th century is an ideal laboratory in which to examine the effect of market liquidity on sovereign bond prices. This period was the last time when the debt of a heterogeneous set of countries was traded in a centralized location and for which sufficiently long time series of observable bond prices are available to conduct asset-pricing tests. Empirical analysis of these data establishes two results. First, illiquid sovereign bonds carry larger factor loadings on market liquidity than liquid bonds. The difference in average excess returns is not only due to the larger transaction costs associated with holding illiquid bonds but also to the greater sensitivity of the returns of illiquid bonds to fluctuations in market liquidity. Second, excess bond returns are linearly related to the returns of a liquiditymimicking portfolio in the cross-section, indicating that market liquidity is a priced common risk factor. At about 2.8% per year, the price for bearing liquidity risk is economically significant. Overall, this evidence underscores the importance of understanding the effect of market liquidity on bond prices, even in an economic environment that seems remote from today's. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved.

1. Introduction Recent events suggest that liquidity risk may be an important component of sovereign bond risk premia. In the fall of 1998, the price of US Treasuries increased sharply relative to less liquid financial instruments in response to the Russian default, the failure of LongTerm Capital Management, and pervasive financial turbulence. More recently, the turmoil associated with the subprime mortgage crisis caused a systemic liquidity crisis in international financial markets and induced a shift into liquid US and European government bonds. For example, in early 2008 investors moved into German government bonds at the expense of less liquid debt instruments (Chung, 2008). To explain these patterns in terms of asset-pricing theory, market liquidity must be a priced common risk factor. That is, there must be a systematic component to variation in liquidity, and, overall, bonds must have low returns when the market becomes illiquid. Some bonds will be more sensitive to fluctuations in market liquidity and carry larger liquidity premia in the cross-section of excess bond returns. Using a unique data set collected from 19th century financial publications, I show that liquidity risk is important for pricing sovereign bonds. The London Stock Exchange before the First World

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War is an ideal laboratory for directly confronting the issue of market liquidity risk and sovereign bond risk premia. A centralized market for trading international debt is a relatively recent development and long time series of transaction data suitable for conducting asset-pricing tests are not widely available. In contrast to today, observable bid-ask spreads for a heterogeneous set of sovereign borrowers are available from the early 1870s until 1907. The data from the Exchange offer an excellent opportunity to study the liquidity premium in the international debt market. The paper reaches two conclusions. First, illiquid sovereign bonds tend to carry larger factor loadings on unexpected changes in market liquidity relative to liquid sovereign bonds, so their returns are more sensitive to these fluctuations. This finding is consistent with the demand for liquidity being sensitive to overall market liquidity; it implies that investors prefer sovereign debt that is easier to trade when market liquidity dries up. Second, market liquidity is a common risk factor important for pricing the cross-section of sovereign bond returns. At about 2.8% per year, the estimated liquidity premium is the largest of all the risk premia. Moreover, this estimate is broadly robust to controlling for the level effect of liquidity on bond prices. Thus, the data validate the predictions of models that postulate market liquidity is a state variable important for pricing international securities and underscore its enduring relevance. Section 2 discusses the features of the 19th century London Stock Exchange that make it an excellent testing ground for studying liquidity risk and sovereign bond risk premia. Section 3 presents the

0022-1996/$ – see front matter. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jinteco.2010.07.007

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theoretical framework and empirical methods. Section 4 describes the data, as well as the market liquidity index and its time-series features. Section 5 presents the evidence and conducts a series of robustness tests. 2. The London Stock Exchange as a Laboratory It may seem surprising that sovereign bond price data for the current era are not more readily available, but a transparent sovereign-debt market is a recent development.1 For example, a study of liquidity risk in the US Treasury market relies on transaction data available since 1992 (Li et al., 2009). Price data for emergingmarket debt span shorter periods. Until the debt crisis in the 1980s, the primary form of sovereign lending to emerging markets was bank loans (Folkerts-Landau, 1985). Although the Brady Plan created a market for emerging-market debt in the early 1990s, the secondary market remained thin for some time, and the available pricing data are considered unreliable (Stone, 1991). To the extent that transaction data for those bonds exist, they are not necessarily publicly available (Boehmer and Megginson, 1990; Cumby and Pastine, 2001). Papers that study the pricing of bonds issued by emerging markets are forced to rely on data from the 1990s onward (for example, González-Rozada and Yeyati, 2008). Transaction data are unavailable because the secondary market for sovereign debt is an over-the-counter market. Pricing is decentralized, so that prices are equalized indirectly, and often imperfectly, by arbitrage.2 The bond price data available from the London Stock Exchange during the late 19th century do not suffer from these limitations. Sovereign bonds were widely traded on the Exchange, so observable bid and ask prices are available from contemporary financial publications. During that era, the breadth and depth of the London capital market made it the center for countries to raise capital. Indeed, the period encompasses three sovereign lending booms — one in the mid-1870s, one in the mid-1880s, and one in the decade before the First World War (Suter, 1990). By current standards, the amount of credit extended to foreign governments was large because sovereign bond issues represented the principal means by which countries imported capital from the rest of the world (Mauro et al., 2002). In 1883, the market value of foreign government bonds traded on the London Stock Exchange was about 76% of British nominal GDP.3 Until the 1890s, foreign government bonds were the largest single asset class traded on the Exchange. Including the market value of British government debt, the size of the government bond market as a percentage of total market value was almost 60% in 1873 and 52% in 1883 (Michie, 1999, Table 3.3). From the 1890s onward, equities issued by foreign railroads surpassed sovereign bonds as a share of total market value.4 Nevertheless, sovereign borrowing remained an important part of the London capital market; its share of London's market value remained above 20% until 1914. 1 Datastream provides sovereign bond price data from the mid-1990s. Bloomberg has price data for some bonds since 1987, but bid and ask prices are available for only a small set of countries and for shorter time periods. 2 The market's opacity makes it difficult to construct transaction-based indicators of liquidity comparable across countries. For example, a Bank for International Settlements study found it problematic to compare measures of liquidity among the G10 (Bank for International Settlements, 1999, pp. 13). Cross-country differences in how transactions are negotiated made it difficult for the authors to compute comparable bid-ask spreads. In the past 10 years, however, technological developments have improved the transparency of bond markets, including the market for sovereign debt, and facilitated the broader dissemination of transaction data (Economist, 2000; Bessembinder and Maxwell, 2008). 3 The market value of foreign government traded on the Exchange in 1883 was £975.1 million and the nominal value of Great Britain's GDP in 1883 was £1,285 million. The foreign government debt data are taken from Michie (1999, Table 3.3) and the GDP data are from Lawrence Officer's webpage http://www. measuringworth.org/ukgdp/. 4 In 1893, foreign railroads comprised about 32% of the Exchange's total market value whereas foreign government bonds made up around 21% (Michie, 1999, Table 3.3).

The importance of the London debt market offers a unique opportunity to study liquidity as a common risk factor in sovereign risk premia. The fact that the bonds were traded in a single, centralized market permits the identification of the relationship between market liquidity and sovereign risk premia without conducting the test across markets that may be not be fully integrated (see Bekaert et al., 2007). In addition, the diverse cross-section of issuers ensures dispersion in the liquidity factor loadings, which aids in the identification of the asset-pricing model. Finally, the time series of bond prices are long enough to conduct asset-pricing tests with statistical power. Thus, the London sovereign bond market during the late 19th century is a rich laboratory for studying the link between market liquidity risk and the price of sovereign debt. 3. Theoretical framework and empirical methods The empirical analysis is guided by asset-pricing models that predict investors demand compensation for bearing the risk associated with fluctuations in market liquidity. Two asset-pricing models that formalize the relationship between expected returns and liquidity risk are Acharya and Pedersen (2005) and Bekaert et al. (2007).5 Acharya and Pedersen propose a liquidity-adjusted capital asset pricing model in which liquidity varies randomly and exogenously and a security's required rate of return reflects compensation for bearing market risk as well as the risk associated with fluctuations in market liquidity. In a similar vein, Bekaert et al. introduce exogenous fluctuations in market liquidity directly into the stochastic discount factor, so that it affects the required rate of return on risky assets. The empirical implication of both models is that expected excess returns reflect a premium associated with fluctuations in market liquidity. Furthermore, several papers study the empirical importance of liquidity risk in the equity market (Pástor and Stambaugh, 2003; Liu, 2006; Goyenko and Sarkissian, 2008; Korajczyk and Sadka, 2008), while Li et al. (2009) examines the pricing of liquidity risk in the returns of US Treasury securities. From this perspective, arbitrage-pricing theory is a natural framework for evaluating the effect of liquidity as a pervasive risk factor on sovereign risk premia. It predicts that a security's risk premium is proportional to its sensitivity to unexpected changes in a set of pervasive risks (Ross, 1976; Connor, 1984). Security returns are driven by K common risk factors K

ri = E½ri  + ∑K

= 1 βki fk

+ εi

ð1Þ

where E[ri] is the expected return on security i = 1,...; N; fk = Fk − E[Fk] is the unexpected change in the common risk factor Fk that drives security returns; βki is the sensitivity of security i's returns to unexpected changes in risk factor k; and εi is the idiosyncratic component in the returns of security i. The expected risk premium E[ri − rf] of a security i can be expressed as a linear function of its K factor betas h i K E ri −rf = ∑K

= 1 βki λk

ð2Þ

where rf is the risk-free rate of interest; λk = E[rk − rf] is the expected risk premium associated with the kth pervasive risk factor; and E[rk] is the return on the factor-mimicking portfolio pk that has a unit loading on the kth common risk factor βpk = 1. The factor-mimicking portfolio captures the marginal returns associated with unit exposure to the common risk factor and provides a way to estimate the risk premium associated with that factor. 5 Developing a structural model in which market liquidity varies endogenously remains a major outstanding research challenge, but some progress has been made in this area. For instance, Eisfeldt (2004) proposes a model in which real-sector liquidity varies over time because of productivity shocks.

R. Alquist / Journal of International Economics 82 (2010) 219–229

221

Fig. 1. The cross-section of sovereign bonds, 1871.1–1907.12.

4. Data The data set consists of closing bid and ask prices, as well as the coupon payments for all regularly traded sovereign bonds listed on the London Stock Exchange between 1871 and 1907. It contains 213 bonds issued by 38 countries and 110 bonds issued by 11 British colonial possessions.6 In light of London's role as banker to the world, these data comprise almost the entire population of sovereign bonds traded during that era. This sample is larger than those used in other papers to study the behavior of bond returns during the same period (for example, Mauro et al., 2002; Bordo and Murshid, 2006). Fig. 1 depicts the evolution of the cross-section of sovereign bonds with observable bid-ask spreads. The number of bonds ranges from a minimum of 15 (January 1871) to a maximum of 164 (January 1903), as the cross-section of bonds traded on the Exchange expanded. The figure shows that even as the number of bonds grows over time, the size of the cross-section changes as bonds enter, exit, and mature out of the data set. In addition, there are time periods when the prices of some bonds were simply not reported, possibly because the editors of the periodicals faced space constraints (see Chabot and Kurz, 2010). As long as the probability that the price data are missing is uncorrelated with security returns, the missing observations will not bias the sample. Accordingly, I test the null hypothesis that the periods with missing data are missing completely at random (MCAR) for each individual bond (Little, 1988). After removing the bonds in default, 272 bonds remain in the data set. A sequential test of the MCAR null using a modified Bonferroni bound does not uncover any systematic evidence that the missing periods are correlated with returns (see Holm, 1979; Simes, 1986).7

4.1. Measuring market liquidity Different indicators capture different dimensions of liquidity. For example, indicators based on the volume of transactions capture how broad the market is — that is, the extent to which the market is able to

6 7

Further details on the data set are contained in the Data Appendix. The results are available upon request.

absorb numerous orders without large changes in the transaction price. This paper uses bid-ask spreads to measure liquidity. The bid-ask spread measures the costs of providing investors with the opportunity to exchange a security immediately. It reflects the costs of holding inventory, of doing business with better-informed traders, and of dealing in securities that trade only infrequently, among other costs (see Hasbrouck, 2007). It is thus a good indicator of an individual bond's liquidity. Aggregating a security-specific measure of liquidity into an indicator of market liquidity is an accepted procedure (see, among others, Chordia et al., 2001), so I construct an indicator of market-liquidity fluctuations based on the cross-sectional average of bid-ask spreads. Although any empirical measure of liquidity is imperfect, the bidask spread provides a direct estimate of the round-trip cost of trading a security. Indeed, Fleming (2003) concludes that the bid-ask spread dominates a wide class of competing indicators in the US Treasury market. Some alternative indicators of liquidity are used to overcome the lack of consistent transaction cost data (like bid-ask spreads) and implicitly measure it by imputing a transaction cost threshold that demarcates when a trade will occur (Lesmond et al., 1999; Chen et al., 2007). The availability of directly observable bid and ask prices avoids the need to resort to such imputations. Moreover, several studies that compare alternative indicators of liquidity show that (1) price-based measures are highly correlated with bid-ask spreads where the data overlap sufficiently to conduct a comparison (Fleming, 2003; Lesmond, 2005; Liu, 2006; Bekaert et al., 2007); and (2) there is a common component among different measures of liquidity, suggesting that the alternative indicators are approximations to a common underlying liquidity factor (Korajczyk and Sadka, 2008). Although the data span the period from 1870.1 to 1907.12, I focus on the period starting from January 1871 because the cross-section of bonds was narrow until 1871.8 The bid-ask spread for bond i is Sit =

P a −P b  ita it b  0:5 Pit + Pit

ð3Þ

8 The price data are sampled every 28 days resulting in 13 “monthly” observations each year. There are 482 rather than 481 observations because there were 14 “months” in 1897.

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R. Alquist / Journal of International Economics 82 (2010) 219–229

Fig. 2. Market-wide bid-ask spread and selected events, 1871.1–1907.12. Notes: The market-wide bid-ask spread is the cross-sectional average of the individual bond bid-ask spreads defined in Eq. (4). An increase in the index indicates a decrease in market liquidity.

where Pita is the ask price of the bond; and Pitb is the bid price of the bond. The equally weighted bid-ask spread index for the entire market at a point in time is an indicator of market liquidity −1

N

St = Nt ∑i t= 1 Sit

ð4Þ

where Nt is the number of bonds trading in period t.9 Pervasive liquidity risk is measured with respect to unexpected changes in market liquidity. I estimate the time series model selected by the Schwarz Information Criterion (SIC) using a maximum lag length of 1 calendar year (13 observations). The SIC selects an AR (2) model, so I use the residual from the regression St = ρ0 + ρ1 St−1 + ρ2 St−2 + ηt

ð5Þ

estimated over the sample period 1870.1 to 1907.12 to construct the liquidity shock series (see also Amihud, 2002; Acharya and Pedersen, 2005; Li et al., 2009). Unexpected changes in market liquidity are defined as Lt = −

^ η t ^η σ

ð6Þ

where σ̂η is the standard deviation of η̂t, so that a one-unit change in Lt corresponds to a one standard deviation shock to market liquidity. It is

9 It is also possible to construct a value-weighted index of bid-ask spreads. A valueweighted portfolio would assign weights to each bid-ask spread based upon the market value of the shares outstanding. For example, if the market value of Argentine bonds was ten times the value of Danish bonds, Argentina would receive ten times the weight of Denmark in the market liquidity index. The advantage of using the equally weighted bid-ask spread as a measure of market liquidity is that it ensures the index is not skewed toward bonds with large market capitalizations. The equally weighted index is a broader measure of market liquidity than one that assigns larger bonds a greater weight.

multiplied by negative one so that an increase in the indicator corresponds to an unexpected increase in market liquidity.

4.2. Time-series features of bond market liquidity Fig. 2 depicts the behavior of the market-wide bid-ask spread between 1871 and 1907. Its average is 2.4%, and it ranges between about 1.5% and 4.5%. The London bid-ask spreads are much wider than those in the US Treasury bill market during the second half of the 1990s, which are typically only a couple of basis points (Fleming, 2002; see also Takagi, 1987). The London spreads are closer in size to those associated with the non-Brady sovereign debt issued by emerging markets. In the late 1990s, the bid-ask spreads on those types of bonds ranged between about 0.67% for Argentina and 1.8% for Venezuela (Dittmar and Yuan, 2008). The market-wide bid-ask spread is persistent. The autoregressive parameter for the index is 0.90, which is consistent with the magnitude documented by studies of the equity market using current data (Korajczyk and Sadka, 2008). Fig. 3 depicts the innovations in market liquidity. Diagnostic tests indicate that the liquidity innovation series exhibits only small, statistically insignificant autocorrelation and that it appears stationary around a zero mean.10 Fig. 2 also provides visual evidence that the market-wide bid-ask spread identifies periods that coincide with periods of market stress. The sharpest increase in this index of market illiquidity occurred during 1875–76 and is associated with Egypt's default in April 1876. At the time, Egypt was one of the largest borrowers in London. The market-wide bid-ask spread also increased in anticipation of the Baring crisis in November 1890 and the Brazilian default in 1897–98. There was little response to the October 1907 panic that affected US markets. Moreover, the market-wide bid-ask spread was relatively low during 1870–75, 1880–85, and 1905 onward, periods that correspond to foreign lending booms (Suter, 1990). Although one

10

The results are available upon request.

R. Alquist / Journal of International Economics 82 (2010) 219–229

223

Fig. 3. Innovations in sovereign bond market liquidity, 1871.1–1907.12. Notes: The innovation series is defined in Eq. (6) of the text. The series is standardized so that a unit change corresponds to a one-standard deviation market-liquidity shock.

cannot push this anecdotal evidence too far, the indicator's behavior seems to capture movements in market liquidity.11 5. Empirical evidence This section reports the results of the empirical tests. Sections 5.1 and 5.2 present time-series evidence on the relationship between bond risk premia and fluctuations in market liquidity for portfolios sorted by the ex-ante bid-spread (Section 5.1) and the size of the issue (Section 5.2). Section 5.3 tests if market liquidity is a priced common risk factor in the cross-section of bond returns. Section 5.4 subjects the results to sensitivity analysis. 5.1. Time-series evidence: are illiquid bonds more sensitive to liquidity innovations? I consider a factor model that controls for pervasive fluctuations in market liquidity, as well as other common risk factors. The benchmark model is     rit −rft = γi0 + γi1 rMt −rft + γi2 rCt −rft + γi3 Lt +

DEF γi4 HMLt

+

EXP γi5 HMLt

ð7Þ

+ εit

for each of the i = 1,...,10 test portfolios. The first factor (rMt − rft) is the excess return of the value-weighted portfolio of all British and foreign equities traded on the Exchange. This market factor captures the timeseries variation of the business-cycle component common to foreign bond returns (Ilmanen, 1995; Barr and Priestley, 2004). The second factor (rct − rft) is the term premium equal to the difference between the returns of the British consol and the 28-day banker's bill rate, a proxy for the risk-free interest rate. The rationale for including the 11 During this period, there was a broadening of the Exchange's customer base, as well as substantial technological and financial innovation, that could have led to a secular narrowing of individual bonds' bid-ask spreads (Neal and Davis, 2006). Although data limitations prevent me from constructing contiguous time series of individual bonds' bid-ask spreads, I formed ten liquidity-sorted portfolios to get at the finer details of the data. The ten series show no obvious secular narrowing of the bidask spreads over the sample period. The results are available upon request.

term premium is the evidence that it is a common risk factor explaining bond risk premia (Ammer and Campbell, 1993; Fama and French, 1993). The third factor Lt is the unexpected change in market liquidity defined in Eq. (6). I include two factors to capture the risk premia associated with fluctuations in the common, default-related factor. The two factors are ) and the mimicking portfolios based on the deficit-GDP ratio (HMLDEF t export-GDP ratio (HMLEXP t ). The returns of these portfolios capture the premium associated with buying the bonds of countries less likely to default (countries with strong macroeconomic fundamentals) and selling short the bonds of countries more likely to default (countries with weak macroeconomic fundamentals). The deficit-GDP ratio and export-GDP ratio are obvious candidates for measuring a country's ability to repay its foreign debt (Edwards, 1986; Eichengreen and Mody, 2000). Not only are such indicators used by sovereign credit analysts today, but they are also good predictors of sovereign default in the late 19th century (Flandreau and Zumer, 2004).12 To construct the mimicking portfolios, I first sort countries into three mutually exclusive categories (high, medium, and low) based on the value of the characteristic at the beginning of each year. Next, I sort the bonds issued by countries into the high and low categories to form value-weighted portfolios. Finally, I compute the returns of the factor-mimicking portfolio by forming leveraged high minus low (HML) portfolios for each macroeconomic variable. For example, the deficit HML portfolio is formed by buying the bonds in the top third of the deficit-GDP category and selling short the bonds in the bottom third.13

12 Another indicator of sovereign default risk is the debt-GDP ratio. Although debtGDP data are available for some countries during the late 19th century, data constraints prevent me from constructing a mimicking portfolio based on such data. The intersection of the set of countries for which both this indicator and returns are available is not large enough to construct a mimicking portfolio without substantial gaps in the time series. 13 The macroeconomic data used to construct the portfolios are available for up to 17 countries in the sample and were obtained from Obstfeld and Taylor (2003). A list of the countries for which macroeconomic data are available is contained in the Data Appendix.

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R. Alquist / Journal of International Economics 82 (2010) 219–229

Table 1 Bid-ask spread sorted sovereign bond portfolios. Dependent variable: rit − rft Annualized -ri − -rf Annualized γ0 γ1 γ2 γ3 γ4 γ5 R 2̅

Illiquid

2

3

4

5

6

7

8

9

Liquid

IML

4.61 4.27*** (1.32) 0.22*** (0.08) 0.17 (0.13) 0.95*** (0.28) −0.15** (0.06) −0.11** (0.05) 0.19

3.23 2.81*** (0.91) 0.21*** (0.06) 0.28*** (0.10) 0.67*** (0.15) −0.11* (0.06) −0.13*** (0.04) 0.22

3.60 3.36*** (0.85) 0.27*** (0.05) 0.14* (0.08) 0.69*** (0.13) − 0.19*** (0.04) − 0.04 (0.05) 0.24

2.65 2.37*** (0.70) 0.20*** (0.04) 0.29*** (0.09) 0.46*** (0.08) − 0.11*** (0.03) − 0.05** (0.02) 0.28

1.84 1.49*** (0.45) 0.14*** (0.03) 0.19*** (0.05) 0.30*** (0.07) −0.02 (0.03) −0.03 (0.02) 0.22

2.38 1.98*** (0.48) 0.11*** (0.02) 0.21*** (0.05) 0.27*** (0.05) 0.04 (0.03) 0.02 (0.01) 0.20

1.78 1.24* (0.75) 0.21*** (0.06) 0.08 (0.09) 0.32*** (0.07) − 0.01 (0.03) − 0.02 (0.02) 0.13

2.41 2.14*** (0.66) 0.21*** (0.04) 0.17* (0.10) 0.16 (0.15) − 0.11 (0.10) − 0.05 (0.03) 0.09

2.75 2.07*** (0.68) 0.32*** (0.05) 0.20*** (0.05) 0.30*** (0.08) − 0.08* (0.04) − 0.08** (0.03) 0.30

2.40 1.26 (0.78) 0.32*** (0.05) 0.21*** (0.07) 0.44*** (0.09) 0.06* (0.03) − 0.12*** (0.02) 0.34

2.21 3.02** (1.44) − 0.10 (0.10) − 0.03 (0.17) 0.51* (0.30) − 0.22*** (0.08) 0.01 (0.04) 0.04

Notes: The regression is based on Eq. (7). The estimation period is 1871.1–1907.12 (482 observations). IML denotes the leveraged portfolio that is long the most illiquid bonds and short the most liquid bonds. The parameter estimate associated with the liquidity factor γ3 is multiplied by 100. Newey and West (1987a) standard errors are reported in parentheses. *** (**) (*) denotes statistical significance at the 1% (5%) (10%) level for a two-sided hypothesis test.

primarily attributable to the portfolio's sensitivity to fluctuations in market liquidity rather than exposure to the other common risk factors. The difference in the factor loadings between the illiquid and liquid portfolios associated with unexpected changes in market liquidity is statistically significant at the 10% level. In the IML portfolio, the loading on the liquidity factor is the largest in absolute terms. Overall, the results suggest an independent role for market liquidity in the factor model explaining the time-series variation in bond risk premia. These results are consistent with the demand for less liquid bonds being sensitive to overall market liquidity conditions (see Li et al., 2009). For example, if an investor faces a margin constraint, he avoids holding bonds that are difficult to sell when market liquidity becomes scarce because holding those bonds prevents him from meeting a margin call. The demand for less liquid bonds will therefore be more sensitive to fluctuations in market liquidity than that for more liquid bonds.

Table 1 reports the estimated coefficients using equally weighted bond portfolios as test assets.14 The first row shows that, unconditionally, the portfolio with the least liquid sovereign bonds earns, on average, an annualized excess return of about 4.6% whereas the portfolio with the most liquid bonds earns, on average, an annualized excess return of 2.4%. Conditional on the common risk factors, the difference in excess returns between the least liquid bonds and the most liquid bond persists, with the least liquid bonds earning about 4.3% per year and the most liquid bonds about 1.3% per year. With the exception of two portfolios, all of the adjusted R-squareds are 19% or higher, which is respectable for monthly return data. The factor model thus does a good job of capturing the time series variation in sovereign bond returns. An unexpected increase in market liquidity increases contemporaneous returns, consistent with economic theory (Acharya and Pedersen, 2005; Bekaert et al., 2007). The illiquid bond portfolio is more than twice as sensitive to increases in market liquidity as the liquid bond portfolio. On average, a one standard deviation increase in the market liquidity increases the contemporaneous return of the least liquid bond portfolio by 0.95% per month, whereas a similar change in market liquidity increases the return of the most liquid bond by 0.44% per month.15 In comparison with the estimated loadings of the other factors, the loading on the liquidity factor is the largest, indicating that the effect of market liquidity on sovereign bond returns is economically important. For example, the next largest factor loading for the illiquid and liquid portfolios is that associated with market risk. The loading for the least liquid portfolio indicates that a 1% change in the London market index implies a 0.22% change in the returns of the least liquid portfolio and a 0.32% change in the returns of the most liquid portfolio. This difference in the size of the factor loadings is sensible insofar as large changes in market liquidity are associated with periods of market stress and, hence, large changes in returns. With one exception, the estimated liquidity factor loading for each of the portfolios is statistically significant at the 1% level. The last column in Table 1 shows the excess returns and factor loadings of the illiquid minus liquid (IML) portfolio. This portfolio reflects the returns of a position that is long £1 of the least liquid sovereign bond portfolio and short £1 of the most liquid sovereign bond portfolio. The IML portfolio would have generated an average annual excess return of about 3.0% per year. This excess return seems

for each of the i = 1,...,10 test portfolios. Table 2 reports the results for the equally weighted test portfolios.17 The last column shows that the small minus large portfolio (SML) long £1 of the smallest bonds and short £1 of the largest bonds would have earned 0.31% annual premium, after controlling for the other common risk factors. This difference in mean returns is not statistically different from zero. The difference in the liquidity factor loadings between small and large bonds is positive and statistically different from zero at the 5% level, indicating that

14 The results using value-weighted portfolios as test assets are similar. They are available upon request. 15 The estimated coefficient associated with the market liquidity factor is scaled by 100 to facilitate comparison with the other coefficient estimates.

16 Every month each bond is assigned to one of ten portfolios based on the bond's bid-ask spread lagged by two months to avoid bid-ask bounce. 17 The results for the value-weighted portfolios are similar. They are available upon request.

5.2. Time-series evidence: are smaller bonds more sensitive to liquidity innovations? The evidence that sorting bonds by bid-ask spreads introduces dispersion in the market-liquidity factor loadings suggests examining if the liquidity-mimicking portfolio IML prices sovereign bonds.16 Hence, I estimate Eq. (7) but replace Lt with IMLt and sort the bonds by size. That is, I estimate     rit −rft = γi0 + γi1 rMt −rft + γi2 rCt −rft + γi3 IMLt DEF

+ γi4 HMLt

EXP

+ γi5 HMLt

ð8Þ

+ εit

R. Alquist / Journal of International Economics 82 (2010) 219–229

225

Table 2 Size-sorted sovereign bond portfolios. Dependent variable: rit − rft Annualized -ri − -rf Annualized γ0 γ1 γ2 γ3 γ4 γ5 R ̅2

Small

2

3

4

5

6

7

8

9

Large

SML

3.73 2.75*** (0.55) 0.10*** (0.03) 0.18*** (0.05) 0.25*** (0.09) 0.05 (0.04) − 0.02 (0.02) 0.29

2.50 1.47** (0.66) 0.17*** (0.04) 0.18** (0.07) 0.24*** (0.09) 0.01 (0.04) − 0.05** (0.02) 0.23

3.21 1.53* (0.79) 0.23*** (0.04) 0.18*** (0.06) 0.39*** (0.09) 0.08** (0.04) −0.02 (0.02) 0.43

3.31 2.29*** (0.61) 0.29*** (0.04) 0.12** (0.05) 0.16*** (0.04) −0.02 (0.03) −0.04** (0.02) 0.24

4.01 2.30* (1.33) 0.42*** (0.06) 0.05 (0.10) 0.29*** (0.10) 0.00 (0.04) − 0.07*** (0.03) 0.25

2.53 1.59** (0.70) 0.32*** (0.04) 0.23*** (0.06) 0.18** (0.08) − 0.10** (0.04) − 0.04 (0.02) 0.30

3.00 2.46** (0.99) 0.38*** (0.05) 0.17* (0.10) 0.08 (0.07) − 0.26** (0.11) − 0.14*** (0.05) 0.20

1.82 1.01 (0.67) 0.24*** (0.04) 0.33*** (0.08) 0.12** (0.05) − 0.04 (0.04) − 0.05** (0.03) 0.26

2.98 1.74** (0.80) 0.35*** (0.05) 0.30*** (0.07) 0.10* (0.05) 0.03 (0.04) − 0.08** (0.03) 0.26

3.15 2.44*** (0.73) 0.32*** (0.05) 0.26*** (0.07) − 0.09 (0.07) − 0.01 (0.05) − 0.12*** (0.03) 0.21

0.59 0.31 (0.93) − 0.22*** (0.05) − 0.08 (0.09) 0.34** (0.14) 0.06 (0.06) 0.09** (0.04) 0.22

Notes: The regression is based on Eq. (8). The estimation period is 1871.1–1907.12 (482 observations). SML denotes the leveraged portfolio that is long the smallest bonds and short the largest bonds. Newey and West (1987a) standard errors are reported in parentheses. *** (**) (*) denotes statistical significance at the 1% (5%) (10%) level for a two-sided hypothesis test.

small sovereign bonds are more exposed to changes in the liquidity factor. A 1% increase in the returns of the IML portfolio implies a 0.34% per month increase in the excess returns of the SML portfolio. The size of the loading on the IML portfolio is the largest (in absolute terms), indicating that the premium associated with a position exposed to liquidity risk is economically important for explaining excess bond returns. In addition, the returns of large bond issues tend to be more sensitive to the market portfolio and term premium than those of small bonds. In the leveraged portfolio, the loading on the market portfolio is larger than that for the term premium and is statistically significant at conventional levels. The last column also shows that the returns of small bond issues are more sensitive to the default-related common risk factors than the returns of large bond issues. This difference is statistically significant at the 5% level only for the exportGDP mimicking portfolio. These results indicate that IML portfolio helps to account for differences in the variation of sovereign risk premia. Its ability to capture the time-series variation in bond returns is not solely related to variation in a common default factor, suggesting an independent role for fluctuations in market liquidity in explaining the pattern of bond returns. 5.3. Cross-sectional evidence: is market liquidity a priced common risk factor? Using generalized method of moments (GMM), I estimate h i E ri −rf = βMi λM + βCi λC + βIMLi λIML + βDEFi λDEF + βEXPi λEXP

ð9Þ

to obtain estimates of the λs. Here ri is the return of the i = 1,...,10 test portfolios; the subscripts are defined as before; βji denotes the factor loading of portfolio i with respect to the common risk factor j; and λj = E[rj − rf] is the expected premium associated with exposure to risk factor j. I tie down the mean discount factor by assuming it is one. Table 3 reports the estimates of the risk premia for the equally weighted portfolios.18 Column (1) contains the full model. A portfolio with unit loading on the liquidity-mimicking portfolio and zero loadings on the other factors would have earned about 8.3% per year. The next largest risk premia are those associated with the two defaultrelated factors. A portfolio with a unit beta on the deficit-GDP factor 18 The results for the value-weighted portfolios are similar. They are available upon request.

would have earned 6.8% per year, and one with a unit beta on the export-GDP factor would have earned −26.6% per year. Yet these values are somewhat misleading. What is important is the contribution of each factor to the sovereign risk premium, which is given by the product of the estimated risk premia in Table 3 and the factor loading on the SML portfolio in Table 2. For the liquidity premium, it is about 2.8% per year (0.0828 × 0.34). In absolute terms, it is the largest premium associated with any of the risk factors and is comparable in size to the premium associated with the export-GDP factor, which is about −2.4% per year (− 0.2658 × 0.09). It is instructive to compare this estimate of the liquidity premium to estimates from modern equity markets. Pástor and Stambaugh (2003) report liquidity premia in the US equity market of about 7.5% per year. Acharya and Pedersen (2005) find a smaller effect of liquidity risk on equity premia in the US (1.1% per year). For a set of emerging equity markets, Bekaert et al. (2007) find the price of liquidity risk to be about 3.2% per year. Goyenko and Sarkissian (2008) conclude that US Treasury market liquidity is priced in global equity markets and estimate it to be about 1% per year. Column (2) shows the estimated risk premia for the specification excluding the market portfolio. Again, the evidence indicates the importance of the liquidity premium in explaining sovereign risk premia. The estimated liquidity premium in this specification (about 8.4%) is comparable in size to the one estimated in the full model. The D-test statistic does not reject the null that the restriction implied by excluding the market portfolio is satisfied, suggesting that the other factors by themselves are able to characterize the cross-section of sovereign risk premia. Column (3) shows that the D-test also fails to reject the restriction implied by excluding the British term premium. Column (4) reports the estimates from the specification excluding the liquidity-mimicking factor. Importantly, the D-test rejects the null that the restricted model is valid. Thus, the data indicate that including the liquidity-mimicking factor is necessary to characterize the cross-section excess sovereign bond returns. The results of the Dtest reported in column (5), which shows the estimates from the specification that excludes the default risk factors, suggest that it is necessary to include them in the specification. This evidence supports the view that market liquidity is a priced common risk factor. 5.4. Sensitivity analysis 5.4.1. Does including the level of liquidity affect the estimate of the liquidity premium? Although the factor model used to identify the effect of liquidity risk makes a minimal set of assumptions, it does not necessarily

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R. Alquist / Journal of International Economics 82 (2010) 219–229

Table 3 Estimated risk premia for size-sorted sovereign bond portfolios.

Table 5 Bid-ask spread-sorted British colonial bond portfolios.

Dependent variable: E[rit − rft] (1) λM λc λIML λDEF λEXP J-stat. (p-value) D-test stat. (p-value) Reject H0?

Dependent variable: rit − rft (2)

5.12 (2.86) −0.58 (2.32) 8.28* (3.33) 6.82* (3.16) −26.58** (9.95) 13.24 (0.02)

0.05 (2.12) 8.37* (3.51) 7.03* (3.32) −30.65*** (7.56) 12.73 (0.05) 0.39 (0.53) No

(3)

(4)

(5)

4.14 (2.52)

7.07** (2.54) 1.82 (2.20)

7.91*** (1.85) 1.22 (2.03) 10.51*** (2.47)

8.78** (3.39) 6.64* (3.11) − 27.70** (9.75) 13.97 (0.03) 0.44 (0.51) No

8.04** (3.01) − 10.00 (8.87) 20.11 (0.00) 10.24 (0.00) Yes

h i E rit −rft −κE½cit 

ð10Þ

Table 4 Estimated risk premia for size-sorted sovereign bond portfolios. Dependent variable: E[rit − rft] − κ E[cit]

λM λc λIML λDEF λEXP J-stat. (p-value) D-test stat. (p-value) Reject H0?

κ = 1/65

(1)

(2)

(3)

(4)

(5)

(6)

4.90 (2.56) −2.04 (2.13) 4.85* (2.26) 6.82* (2.72) −21.54* (9.61) 9.96 (0.08)

5.81** (2.37) − 1.08 (2.06)

5.01 (2.61) − 1.71 (2.15) 5.63* (2.45) 6.83* (2.79) − 22.74* (9.66) 10.86 (0.05)

6.07** (2.39) − 0.53 (2.08)

5.12 (2.70) − 1.21 (2.20) 6.76* (2.78) 6.84* (2.93) − 24.45* (9.75) 12.10 (0.03)

6.47** (2.44) 0.38** (2.11)

7.75** (2.70) − 10.75 (8.47) 11.73 (0.07) 9.29 (0.00) Yes

7.81** (2.74) − 10.40 (8.48) 13.21 (0.04) 10.05 (0.00) Yes

γ2

γ4 21.11 (0.00) 8.33 (0.02) Yes

permit the statistical identification of the level effect of liquidity. An individual bond's level of liquidity can have a direct effect on its price because transaction costs reduce its cash flow (see Amihud and Mendelson, 1986; Amihud and Mendelson, 1991; Strebulaev, 2002; Hund and Lesmond, 2006; Chen et al., 2007). Thus, the estimated liquidity premium in the benchmark specification should be interpreted as the total effect of the level of liquidity and covariance of bond returns with the liquidity-mimicking factor. To examine if omitting the level affects the estimate of the liquidity premium, I estimate Eq. (9) using the size-sorted portfolios after adjusting each portfolio by its expected transaction costs (see Acharya and Pedersen, 2005). The net excess returns of the test portfolios are calculated as

κ = 1/39

γ1

γ3

Notes: The model is Eq. (9). The risk premia are reported as percent per year. J-stat. is the overidentification test statistic (Hansen, 1982). D-test stat. is the Newey and West (1987b) specification test statistic. “Reject H0?” refers to the null hypothesis that the restrictions are valid. The estimates in the restricted model are based on the optimal weighting matrix from the unrestricted model. Newey and West (1987a) standard errors are reported in parentheses. *** (**) (*) denotes statistical significance at the 1% (5%) (10%) level for a two-sided hypothesis test.

κ = 1/31

Annualized r̄i − r̄f Annualized γ0

7.91** (2.84) −10.05 (8.58) 15.73 (0.02) 10.51 (0.00) Yes

Notes: The model is Eq. (9). The risk premia are reported as percent per year. J-stat. is the overidentification test statistic (Hansen, 1982). D-test stat. is the Newey and West (1987b) specification test statistic. “Reject H0?” refers to the null hypothesis that the restrictions are valid. The estimates in the restricted model are based on the optimal weighting matrix from the unrestricted model. Newey and West (1987a) standard errors are reported in parentheses. *** (**) (*) denotes statistical significance at the 1% (5%) (10%) level for a two-sided hypothesis test.

γ5 R2 No. obs.

Illiquid

2

3

4

Liquid

IML

1.88 1.82*** (0.43) 0.04* (0.02) 0.05* (0.03) 0.02 (0.05) − 0.02 (0.02) − 0.02 (0.02) 0.03 390

1.06 1.11*** (0.41) 0.05** (0.02) 0.17*** (0.03) 0.07* (0.04) − 0.03 (0.02) 0.01 (0.02) 0.14 406

2.58 2.46*** (0.40) 0.08*** (0.02) 0.17*** (0.03) 0.02 (0.04) − 0.02 (0.02) 0.01 (0.01) 0.17 437

1.78 1.71*** (0.35) 0.07*** (0.02) 0.10*** (0.02) 0.03 (0.03) − 0.05*** (0.02) − 0.01 (0.01) 0.13 440

1.30 1.08** (0.43) 0.11*** (0.02) 0.14*** (0.03) 0.09*** (0.03) − 0.06*** (0.02) 0.02 (0.02) 0.18 435

0.84 0.95 (0.59) − 0.07** (0.03) − 0.13*** (0.04) − 0.08 (0.06) 0.04 (0.03) − 0.04** (0.02) 0.08 360

Notes: The regression is based on Eq. (7) using the available case estimator. The estimation period is 1871.1–1907.12. IML denotes the leveraged portfolio that is long the most illiquid bonds and short the most liquid bonds. The parameter estimate associated with the liquidity factor γ3 is multiplied by 100. Newey and West (1987a) standard errors are reported in parentheses. *** (**) (*) denotes statistical significance at the 1% (5%) (10%) level for a two-sided hypothesis test.

where κ is the parameter that measures the per-period cost of illiquidity; and E[cit] is the equally weighted average of the bid-ask spread for portfolio i. The lack of average monthly turnover data prevents me from calibrating κ to my data set, so I use the estimate from Acharya and Pedersen (κ = 1/31) as a benchmark.19 Table 4 reports the estimates of the liquidity premia for holding periods of up to 5 years. They range between 1.6%–2.3% per year, depending on the choice of κ.20 Even though these estimates are somewhat smaller than the original estimate of 2.8% per year, they remain sizable. Furthermore, conditional on the effect due to the level of liquidity the data reject the restriction implied by omitting the liquidity-mimicking portfolio for each κ, which is consistent with liquidity risk being priced. Shutting down the level effect of liquidity has a modest effect on the economic importance of liquidity risk. 5.4.2. Are British colonial bonds sensitive to fluctuations in market liquidity? During the late 19th century, many observers perceived that the debt issued by British colonies was implicitly guaranteed by Great Britain (see, among others, Ferguson and Schularick, 2006). To examine if this guarantee biases the estimates of the liquidity factor loading, I estimate the benchmark model (7) using the debt issued by British colonies and possessions. Focusing on the colonial bonds gives rise to gaps in the time series of returns and forces me to estimate the model using five test portfolios and the available case estimator.21 Table 5 shows that the colonial bond returns are, in general, insensitive to changes in market liquidity. Although two of the estimated loadings on the liquidity factor are statistically significant at conventional levels, they are much smaller than those obtained in the full sample of bonds. Moreover, the estimated loading of the liquidity factor for the illiquid minus liquid portfolio is economically small and statistically insignificant from zero. This evidence suggests that the 19 Acharya and Pedersen identify the level effect of liquidity by calibrating the perperiod cost of illiquidity to average monthly turnover on the New York Stock Exchange. They estimate it to be 29 months. Since Acharya and Pedersen use monthly returns and I use 28-day returns, their calibration corresponds to 31 “months” in my data set. 20 For all of the calibrations, the estimated liquidity factor loading on the SML portfolio is 0.334 in the time series regression. The results are available upon request. 21 The available case estimator is only valid if the data are MCAR. The Little (1988) test does not reject this assumption for the subsample of British colonial bonds. The results are available upon request.

R. Alquist / Journal of International Economics 82 (2010) 219–229 Table 6 Estimated risk premia for size-sorted sovereign bond portfolios.

Table 7 Estimated risk premia for size-sorted equity portfolios.

Dependent variable: E [rit − rft]

λM λc λIML λDEF λEXP λf1 J-stat. (p-value) D-test stat. (p-value) Reject H0?

227

Dependent variable: E [rit − rft]

(1)

(2)

(3)

4.24 (4.56) − 0.24 (2.34) 10.02* (4.45) 5.73 (3.78) − 23.53* (9.71) 5.21 (19.15) 12.34 (0.02)

5.12 (2.86) −0.58 (2.32) 8.28* (3.33) 6.82* (3.16) −26.58** (9.95)

9.12* (3.79) − 1.79 (2.61)

13.24 (0.02) 0.07 (0.80) No

8.59* (3.68) − 16.91 (9.72) − 17.74 (17.16) 9.77 (0.08) 9.68 (0.00) Yes

Notes: The model is based on Eq. (9), including the first statistical factor extracted from the cross-section bond returns. The risk premia are reported as percent per year. J-stat. is the overidentification test statistic (Hansen, 1982). D-test stat. is the Newey and West (1987b) specification test statistic. “Reject H0?” refers to the null hypothesis that the restrictions are valid. The estimates in the restricted model are based on the optimal weighting matrix from the unrestricted model. Newey and West (1987a) standard errors are reported in parentheses. *** (**) (*) denotes statistical significance at the 1% (5%) (10%) level for a two-sided hypothesis test.

implicit guarantee, if any, immunized colonial bond returns against fluctuations in market liquidity. Mixing the debt of colonies and noncolonies biases the estimates of the liquidity factor loading against detecting a market-liquidity effect on bond risk premia. 5.4.3. Testing for an unobserved common risk factor It is important to guard against the possibility that the factor model omits a relevant common risk factor. Using the Connor and Korajczyk procedure (1987, 1988), I compute the first statistical factor extracted from the component of each bond's excess returns that is orthogonal to a constant and the five factors. By construction, this factor contains the most information about excess bond returns that is uncorrelated with the other factors. Table 6 reveals two things. First, column (2) shows that the data fail to reject the restrictions implied by excluding the first statistical factor from the full specification. Second, the results in column (3) indicate that the data reject the restriction implied by excluding the liquidity-mimicking factor but including the first statistical factor. The five factor model does a good job of accounting for the common variation in excess bond returns. 5.4.4. Is liquidity risk priced in the cross-section of equity returns? If market liquidity is a valid common risk factor, then the liquiditymimicking portfolio should account for the cross-sectional variation in equity risk premia.22 Table 7 reports the results for ten equally weighted equity portfolios sorted by size. The specification is estimated without the default risk factors for 3 samples — the full set of equities, British equities, and foreign equities. Overall, liquidity risk appears to be priced. The restrictions implied by excluding the liquidity-mimicking portfolio are rejected in the full 22 Since price data for all of the equities traded on the Exchange are available (see Chabot and Kurz, forthcoming), it would be natural to consider a liquidity-mimicking portfolio constructed from the cross-section of equities. However, this strategy is inadvisable. The share of foreign equities traded on the Exchange grew rapidly during this period as entirely new industries appeared and expanded. A consequence of London's role in financing these industries is that a number of very different stocks were simultaneously listed on the Exchange at periodic intervals. Thus, bid-ask spreads in the Exchange's equity market move around due to composition effects rather than actual changes in market liquidity.

All

λM λc λIML J-stat. (p-value) D-test stat. (p-value) Reject H0?

British

Foreign

(1)

(2)

(3)

(4)

(5)

(6)

2.00 (2.91) − 11.50 (10.76) 57.43** (22.76) 5.45 (0.60)

2.86** (1.15) − 1.63 (4.31)

1.21 (3.65) 1.18 (9.15) 57.83 (32.88) 3.51 (0.83)

1.66** (1.48) 5.39 (3.46)

2.50 (3.69) − 20.98 (13.20) 32.33 (22.96) 3.60 (0.82)

2.95* (1.30) − 15.60** (5.39)

50.82 (0.00) 6.33 (0.01) Yes

31.41 (0.00) 3.11 (0.08) Yes

34.15 (0.00) 1.94 (0.16) No

Notes: The model is Eq. (9), excluding the two default-related factors. The risk premia are reported as percent per year. J-stat. is the over identification test statistic (Hansen, 1982). D-test stat. is the Newey and West (1987b) specification test statistic. “Reject H0?” refers to the null hypothesis that the restrictions are valid. The estimates in the restricted model are based on the optimal weighting matrix from the unrestricted model. Newey and West (1987a) standard errors are reported in parentheses. *** (**) (*) denotes statistical significance at the 1% (5%) (10%) level for a two-sided hypothesis test.

sample at the 5% significance level and in the British subsample at the 10% significance level. The estimates of the liquidity premia seem large, but they represent the excess return of an equity portfolio with unit loading on the liquidity factor and zero loading on the other two risk factors. For the full sample, the premium implied by the liquidity factor loading of the SML portfolio long £1 of the smallest equities and short £1 of the largest equities is about 7.4% per year.23 This evidence lends further credibility to the interpretation of market liquidity as a common risk factor. 6. Conclusion Despite the importance of uncovering the economic significance of market liquidity risk in sovereign bond prices, contemporary data are ill-suited to answering this question. By contrast, a new data set containing all of the sovereign bonds regularly quoted on the London Stock Exchange during the late 19th century provides the best available case for studying this relationship. Empirical analysis of these data establishes two results. First, illiquid sovereign bonds carry larger factor loadings on fluctuations in market liquidity relative to more liquid sovereign bonds. This evidence indicates that investors value a bond's liquidity and avoid holding illiquid bonds during periods when market liquidity dries up. It independently validates findings from the US Treasury security market (Li et al., 2009) and highlights the importance of finding a theoretical mechanism that ties investor demand for illiquid assets to market liquidity shocks. Second, liquidity risk is important for pricing sovereign debt. Cross-sectional differences in sovereign risk premia are linearly related to the covariance of bond returns with fluctuations in market liquidity, indicating that market liquidity is a priced common risk factor. At about 2.8% per year, the liquidity premium's contribution to the sovereign risk premium is economically important. Taken together, this evidence underscores the generality of liquidity risk's first-order effect on sovereign bond risk premia. Acknowledgments I thank Laura Beny, Ben Chabot, Sharon Kozicki, Peter Morrow, Sergei Sarkissian, Linda Tesar, Garima Vasishtha, Marc Weidenmier, 23 The estimated factor loading on the equity SML portfolio for equities is 0.128. The results are available upon request.

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R. Alquist / Journal of International Economics 82 (2010) 219–229

Jun Yang, Kathy Yuan, and seminar participants at the Bank of Canada, the IEER Conference, Fordham, and Rutgers for helpful comments. The editor, Charles Engel, and two anonymous referees also provided suggestions that improved the paper. Amberly Jane Coates, Brian DePratto, Maggie Jim, and Golbahar Kazemian provided first-rate research assistance. The views expressed in the paper represent those of the author and do not reflect the position of the Bank of Canada or its Governing Council.

Appendix A. Data appendix The sovereign bond prices in the data set are sampled every 28 days from the quotation list published in the Money Market Review between 1866 and 1907, when such detailed price quotations ceased to be available. The price quotations from the Review were supplemented with price data from the Times and the Economist. The Review is a financial weekly that was published every Saturday and reported the previous Friday's closing prices. All three sources recorded the prices from the official quotation list of the London Stock Exchange, so the prices reflect actual spot transactions between members of the Exchange, unless explicitly noted. The transactions had to meet a minimum size requirement, which for sovereign bonds was usually £1000. All of the bonds traded on the Exchange are what would be considered long-term instruments today. Virtually all of the bonds had maturities longer than 10 years, and most had maturities of 20 years or more (see Mauro et al., 2002). Trading among non-members occurred off the Exchange as well. Although I am unaware of data on price differentials between trading on and off the Exchange, the available evidence indicates that barriers preventing arbitrage between the on- and off-Exchange markets were low. It was relatively straightforward to become a member of the Exchange (Michie, 1999), and the period between 1870 and 1914 was one of rapid growth in the Exchange's membership (Davis and Neal, 1998). Working with sovereign debt data raises the question of how to treat bonds in default. Depending on the outcome of negotiations between the borrower and its creditors, these bonds could remain on the underwriters' books for many years, and the prices of these bonds were reported in the Exchange's official quotation list. Bonds in default had very wide bid-ask spreads and low or zero returns (because their prices did not change), and including them in the sorts would thus bias the IML portfolio's returns downward. I identified bonds in default in the following way. The default event itself is often directly observable in returns as the market repriced the bonds. In addition, the publications themselves reported the suspension of coupon payments due to default. I also consulted Suter (1990). Based on the evidence from these sources, I removed bonds whose prices were less than 40% of par.

A.1. Full sample Argentina; Australia; Austria–Hungary; Belgium; Brazil; British Guiana; Bulgaria; Canada; Ceylon; Chile; China; Colombia; Costa Rica; Denmark; Ecuador; Egypt; France; Germany; Greece; Guatemala; Hawaii; Honduras; Hong Kong; Italy; Jamaica; Japan; Liberia; Mauritius; Mexico; Netherlands; New Zealand; Nicaragua; Norway; Orange Free State; Paraguay; Peru; Portugal; Russia; Saint Lucia; Santo Domingo; South Africa; Spain; Straits Settlements; Sweden; Trinidad; Turkey; the United States; Uruguay; and Venezuela. A.2. British colonies and possessions Australia; British Guiana; Canada; Ceylon; Hong Kong; Jamaica; Mauritius; New Zealand; Saint Lucia; South Africa; and Trinidad.

A.3. Factor-mimicking portfolios The deficit-GDP mimicking portfolios are based on data from Australia; Austria–Hungary; Brazil; Canada; Chile; Egypt; India; Italy; Japan; New Zealand; Portugal; Spain; Sweden; and the United States. The export-GDP mimicking portfolios are based on data from Australia; Austria–Hungary; Canada; Chile; Egypt; India; Italy; Japan; New Zealand; Portugal; Spain; Sweden; the United States; and Uruguay. References Acharya, V., Pedersen, L., 2005. Asset pricing with liquidity risk. Journal of Financial Economics 77, 375–410. Amihud, Y., 2002. Illiquidity and stock returns: cross-section and time-series effects. Journal of Financial Markets 5, 31–56. Amihud, Y., Mendelson, H., 1986. Asset pricing and the bid-ask spread. Journal of Financial Economics 17, 223–249. Amihud, Y., Mendelson, H., 1991. Liquidity, maturity, and the yields on US treasury securities. Journal of Finance 46, 1411–1425. Ammer, J., Campbell, J., 1993. What moves stock and bond markets? A variance decomposition for long-term asset returns. Journal of Finance 48, 3–37. Bank for International Settlements, 1999. Market Liquidity: Research Findings and Selected Policy Implications. BIS, Basel. Barr, D., Priestley, R., 2004. Expected returns, risk, and the integration of international bond markets. Journal of International Money and Finance 23, 71–97. Bekaert, G., Harvey, C., Lundblad, C., 2007. Liquidity and expected returns: lessons from emerging markets. Review of Financial Studies 20, 1–49. Bessembinder, H., Maxwell, W., 2008. Transparency and the corporate bond market. The Journal of Economic Perspectives 22, 217–234. Boehmer, E., Megginson, W., 1990. Determinants of secondary market prices for developing country syndicated loans. Journal of Finance 45, 1517–1540. Bordo, M., Murshid, A., 2006. Globalization and changing patterns in the international transmission of shocks in financial markets. Journal of International Money and Finance 25, 655–674. Chabot, B., Kurz, C., 2010. That's where the money was: foreign bias and English investment abroad, 1866–1907. Economic Journal 120, 1056–1079. Chen, L., Lesmond, D., Wei, J., 2007. Corporate yield spreads and bond liquidity. Journal of Finance 62, 119–149. Chordia, T., Roll, R., Subrahmanyam, A., 2001. Market liquidity and trading activity. Journal of Finance 56, 501–530. Chung, J., 2008. Flight to liquidity pushes Eurozone bond yields apart. Financial Times 27 February 27. Connor, G., 1984. A unified beta pricing theory. Journal of Economic Theory 34, 13–31. Connor, G., Korajczyk, R., 1987. Estimating pervasive economic factors with missing observations. Unpublished. Available at http://papers.ssrn.com/sol3/papers.cfm? abstract_id=1268954. Connor, G., Korajczyk, R., 1988. Risk and return in an equilibrium APT: application of a new test methodology. Journal of Financial Economics 21, 255–289. Cumby, R., Pastine, T., 2001. Emerging market debt: measuring credit quality and examining relative pricing. Journal of International Money and Finance 20, 591–609. Davis, L., Neal, L., 1998. Micro rules and macro outcomes: the impact of microstructure on the efficiency of security exchanges: London, New York, and Paris, 1800–1914. The American Economic Review 88, 40–45. Dittmar, R., Yuan, K., 2008. Do sovereign bonds benefit corporate bonds in emerging markets? Review of Financial Studies 21, 1983–2014. Economist, 2000. E-bonds, licensed to kill, January 15, p. 73. Edwards, S., 1986. The pricing of bonds and bank loans in international markets: an empirical analysis of developing countries' foreign borrowing. European Economic Review 30, 565–589. Eichengreen, B., Mody, A., 2000. Lending booms, reserves, and the sustainability of short-term debt: inferences from the pricing of syndicated bank loans. Journal of Development Economics 63, 5–44. Eisfeldt, A., 2004. Endogenous liquidity in asset markets. Journal of Finance 59, 1–30. Fama, E., French, K., 1993. Common risk factors in the returns of stocks and bonds. Journal of Financial Economics 33, 3–56. Ferguson, N., Schularick, M., 2006. The empire effect: the determinants of country risk in the first age of globalization, 1880–1913. Journal of Economic History 66, 283–312. Flandreau, M., Zumer, F., 2004. The Making of Global Finance, 1880–1913. Organization for Economic Cooperation and Development, Paris. Fleming, M., 2002. Are larger treasury issues more liquid? Evidence from bill reopenings. Journal of Money, Credit, and Banking 34, 707–735. Fleming, M., 2003. Measuring treasury market liquidity. Federal Reserve Bank of New York Economic Policy Review 9, 83–108. Folkerts-Landau, D., 1985. The changing role of bank lending in development finance. International Monetary Fund Staff Papers 32, 317–363. González-Rozada, M., Yeyati, E.L., 2008. Global factors and emerging market spreads. The Economic Journal 118, 1917–1936. Goyenko, R., Sarkissian, S., 2008. Flight-to-liquidity and global equity returns. Under review. Available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1100174. Hansen, L., 1982. Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.

R. Alquist / Journal of International Economics 82 (2010) 219–229 Hasbrouck, J., 2007. Empirical Market Microstructure: The Institutions, Economics, and Econometrics of Securities Trading. Oxford University Press, New York. Holm, S., 1979. A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6, 65–70. Hund, J., Lesmond, D., 2006. Liquidity and credit risk in emerging markets. Unpublished. Available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1107586. Ilmanen, A., 1995. Time-varying expected returns in international bonds. Journal of Finance 50, 481–506. Korajczyk, R., Sadka, R., 2008. Pricing the commonality across alternative measures of liquidity. Journal of Financial Economics 87, 45–72. Lesmond, D., 2005. Liquidity of emerging markets. Journal of Financial Economics 77, 411–452. Lesmond, D., Ogden, J., Trzcinka, C., 1999. A new estimate of transaction costs. Review of Financial Studies 12, 1113–1141. Li, H., Wang, J., Wu, C., He, Y., 2009. Are liquidity and information risks priced in the Treasury bond market? Journal of Finance 64, 467–503. Little, R., 1988. A test of missing completely at random for multivariate data with missing values. Journal of the American Statistical Association 83, 1198–1202. Liu, W., 2006. A liquidity-augmented capital asset pricing model. Journal of Financial Economics 82, 631–671. Mauro, P., Sussman, N., Yafeh, Y., 2002. Emerging market spreads: then versus now. Quarterly Journal of Economics 117, 695–733. Michie, R., 1999. The London Stock Exchange: a history. Oxford University Press, New York. Neal, L., Davis, L., 2006. The evolution of the structure and performance of the London Stock Exchange in the first global financial market, 1812–1914. European Review of Economic History 10, 279–300.

229

Newey, W., West, K., 1987a. A simple, positive definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708. Newey, W., West, K., 1987b. Hypothesis testing with efficient method of moments estimation. International Economic Review 28, 777–787. Obstfeld, M., Taylor, A., 2003. Sovereign risk, credibility, and the gold standard: 1870– 1913 versus 1925–31. The Economic Journal 113, 241–275. Pástor, L., Stambaugh, R., 2003. Liquidity risk and expected stock returns. Journal of Political Economy 111, 642–685. Ross, S., 1976. The arbitrage pricing theory of capital asset pricing. Journal of Economic Theory 13, 341–360. Simes, R., 1986. An improved Bonferroni procedure for multiple tests of significance. Biometrika 73, 751–754. Stone, M., 1991. Are sovereign debt secondary market returns sensitive to macroeconomic fundamentals? Evidence from the contemporary and interwar markets. Journal of International Money and Finance 10, 100–122. Strebulaev, I., 2002. Many Faces of Liquidity and Asset Pricing: Evidence from the US Treasury Securities Market. Unpublished. Available at http://papers.ssrn.com/sol3/ papers.cfm?abstract_id=275843. Suter, C., 1990. Schuldenzyklen in der dritten Welt: kreditaufnahme, zahlungskrisen und schuldenregelungen peripherer länder im weltsystem von 1820 bis 1986. Anton Hain, Frankfurt. Takagi, S., 1987. Transaction costs and the term structure of interest rates in the OTC bond market in Japan. Journal of Money, Credit, and Banking 19, 515–527.