Treasury Illiquidity and Funding Liquidity Risk

Transcription

1 Treasury Illiquidity and Funding Liquidity Risk Ruslan Goyenko* McGill University September 23, 2011 Abstract This paper introduces the illiquidity of US Treasuries as a proxy for Brunnermeier and Pedersen (2009) funding liquidity and tests its applications for asset prices. Positive shock to Treasury illiquidity predicts decrease in funding liquidity measured by the Treasury-Eurodollar spread while stock illiquidity has no effect on funding liquidity. Conditioned on the common risk factors in the stock market the risk-adjusted difference between extreme bond illiquidity beta portfolios generates 49 basis point per month. Bond illiquidity risk also generates positive and significant premia in the cross-section of stock returns. Mutual fund portfolios are also exposed to bond illiquidity risk. Funds in the highest bond illiquidity beta decile outperform funds in the lowest decile by about 80 basis points per month. Moreover significant loading on bond illiquidity risk is observed across all fund-size categories. Controlling for the past performance, styles and funds characteristics, mutual fund portfolios with higher exposure to funding liquidity risk earn higher next period risk-adjusted returns. * Ruslan Goyenko, McGill University, 1001 Sherbrooke St. West, Montreal, Quebec H3A 1G5. ruslan.goyenko@mcgill.ca.

2 Treasury Illiquidity and Funding Liquidity Risk Abstract This paper introduces the illiquidity of US Treasuries as a proxy for Brunnermeier and Pedersen (2009) funding liquidity and tests its applications for asset prices. Positive shock to Treasury illiquidity predicts decrease in funding liquidity measured by the Treasury-Eurodollar spread while stock illiquidity has no effect on funding liquidity. Conditioned on the common risk factors in the stock market the risk-adjusted difference between extreme bond illiquidity beta portfolios generates 49 basis point per month. Bond illiquidity risk also generates positive and significant premia in the cross-section of stock returns. Mutual fund portfolios are also exposed to bond illiquidity risk. Funds in the highest bond illiquidity beta decile outperform funds in the lowest decile by about 80 basis points per month. Moreover significant loading on bond illiquidity risk is observed across all fund-size categories. Controlling for the past performance, styles and funds characteristics, mutual fund portfolios with higher exposure to funding liquidity risk earn higher next period risk-adjusted returns.

3 1. Introduction The literature has conclusively established that the level of illiquidity affects stock market returns (Amihud and Mendelson (1986, 1989), Amihud (2002)) and illiquidity is a source of systematic risk not captured by traditional factors (Pastor and Stambaugh (2003), and Acharya and Pedersen (2005)). 1 Most of the literature is focused on the market liquidity or how easily the assets can be traded. This paper extends the exploration of pricing applications of illiquidity and focuses on a different type of illiquidity funding liquidity or availability of trading capital in the economy. Market liquidity and funding liquidity are related and mutually reinforced with a shock to one of them propagating into another and causing the spiral effect (Brunnermeier and Pedersen (2009)). However, they a driven by different fundamentals. Market liquidity, or the easiness to trade, is asset specific and is influenced by firmspecific and market-wide variables (see Chordia, Roll, and Subrahmanyam, 2001), the funding liquidity is agent specific and depends on borrowing constraints of dealers, hedge funds, investment banks and the availability of arbitrage capital overall (Brunnermeier and Pedersen (2009)). Given the fundamental differences between the two types of illiquidity, we can expect that funding liquidity may contain the information about stock prices beyond or extra of what captured by market illiquidity. There are indeed episodes that market crushes are caused by funding liquidity rather than market liquidity (see detailed discussion in Brunnermeier and Pedersen (2009)). The contribution of this paper is twofold. The first contribution is that the paper suggests that Treasury bond illiquidity can capture information about fluctuations in funding liquidity. There are reasons to expect that illiquidity of Treasuries can reflect other information beyond the easiness of trading in the bond market (Goyenko, Subrahmanyam and Ukhov (2011)). Treasury markets are usually characterized by low noise because of their high liquidity and low credit risk and hence any fluctuations in its illiquidity can contain information. Moreover, Treasuries are usually considered a safe haven during market downturns. For example, on August 8, 2011, Wall Street Journal writes: 1 See also Eleswarapu and Reinganum (1993), Brennan and Subrahmanyam (1996), Jones (2002), among others

4 Treasury bonds proved again Monday that they are still a haven for global investors despite the first credit-rating downgrade on the U.S. in modern history from one of the big three firms. Bond prices rallied broadly as investors fled risky assets including U.S. stocks, with the benchmark 10-year note's yield falling toward the lowest level since October. The two-year note's yield earlier hit a fresh record low of 0.232%, falling below the top end of zero-0.25% range for the Federal Reserve's key policy rate. WSJ, August 8, 2011, Treasuries Rally as U.S. Debt Remains Go-To Haven Funds inflows into Treasuries suggest lower capital availability in the stock market. The scarcity of trading capital in the stock market decreases the ability of arbitragers to provide liquidity in the stock market and therefore increases stock market illiquidity. Brunnermeier and Pedersen (2009) for example suggest that under this scenario, the positions of arbitragers are negatively correlated with the investors demand causing market liquidity to dry up. Indeed, the results of Goyenko and Ukhov (2009) provide an empirical support to above argument. Positive shocks to bond illiquidity which occur during times of flight-to-liquidity (Longstaff (2004)) lead to the next period increase in the stock market illiquidity. The empirical results show that increase in Treasury bond illiquidity predicts decrease in the Treasury-Eurodollar (TED) spread. TED spread is commonly used as a measure of interbank borrowing-lending abilities and also characterizes the availability of speculative capital in the economy (see Teo (2011), Gupta and Subrahmanyam (2000), Boyson, Stahel, and Stulz (2010) among others). Stock illiquidity which in the context of Brunnermeier and Pedersen (2009) reflects the easiness to trade has no significant impact on TED spread. The second contribution of the paper is to explore the pricing implications of funding liquidity for stock and mutual fund returns. Since funding liquidity amplifies market liquidity (Brunnermeier and Pedersen (2009)) stocks/portfolios with higher funding liquidity risk should have higher returns. The main findings can be summarized as follows. Controlling for Fama-French and Carhart factors, stock portfolios sorted on bond illiquidity betas generate economically and statistically significant premium. A simple strategy of taking a short position in low bond illiquidity beta portfolio and long position in high bond illiquidity beta portfolio

5 results in risk adjusted profits of 49 basis points per month. This number increases to 78 basis points in the last half of the sample. To disentangle market illiquidity effect (the easiness to trade) from funding illiquidity effect (the availability of trading capital), bond illiquidity betas are confronted with common proxies for stock market illiquidity such as size and Amihud (2002) illiquidity (ILLIQ) measure. In particular, all stocks are first sorted into size (or ILLIQ) quintile portfolios and then each size (ILLIQ) quintile is sorted into bond illiquidity beta quintiles. Bond illiquidity beta portfolios generate significant risk-adjusted spread for small and medium size quintiles and for the most illiquid ILLIQ quintile. Therefore bond illiquidity risk contains information beyond stock market illiquidity which is proxied by size or ILLIQ. The paper also estimates the significance of Treasury bond illiquidity premia on the cross-section of individual stocks. Controlling for factor loadings on Fama-French and Carhart factors, bond illiquidity beta generates positive and statistically significant risk premium on the cross-section of NYSE/AMEX common stocks for the period of January 1971 to December Among other factors, consistent with the previous literature, only Fama-French value factor (HML) has positive and significant premium. However, value premium becomes insignificant after controlling for firm characteristics size, ILLIQ and book-to-market while bond illiquidity premium remains positive and significant. The next hypothesis tested in this paper is whether the above results hold on the portfolio level. In particular are mutual fund portfolios exposed to funding liquidity risk? It is not obvious at least why asset managers should load on high funding liquidity risk stocks. If, for example, a fund is forced to liquidate in a fire sale (Coval and Stafford (2007)) it will have higher losses in stocks with high funding liquidity risk which will further destroy fund s value. In contrast, if a financially stable fund holds high funding liquidity risk stocks and their liquidation is avoided, the fund should earn abnormal returns in excess of fund s benchmark as a reward to taking an extra risk. The paper finds that funds with high bond illiquidity beta portfolios outperform funds with low beta portfolios by about 80 basis points per month in excess returns. The sample is 2,587 active open-ended US equity mutual funds between January 1990 and

6 December Thus, there is evidence that mutual funds take an advantage of funding liquidity risk. Further tests reveal that this strategy is as common among small-size funds as among large-size funds. In particular, the abnormal risk-adjusted return of low size quintile and high bond illiquidity beta quintile (low size/high beta) of fund sorted portfolios is 43 basis points per month which is insignificantly different from big size/high beta portfolio return. Moreover, bond illiquidity beta generates statistically significant spread for each fund size quintile portfolio with higher beta portfolios having higher abnormal returns. Further, consistent with the intuition that holding higher funding liquidity risk stocks involves frequent rebalancing and results in higher expenses and portfolio turnover, the paper shows that high expenses (high turnover)/high beta portfolios outperform all other mutual fund portfolios by significant amount. Specifically, the abnormal return of high expenses (turnover) quintile/high bond-illiquidity beta quintile is 52 (54) basis points per month. These are after-fees abnormal returns. Therefore, the subset of mutual fund industry which actively manages funding liquidity risk is able to outperform the benchmarks. Further evidence is provided in the panel regression analysis. After controlling for fund characteristics, past performance, style and time effects, funds with the portfolios with higher bond illiquidity betas have higher next period Alpha. Thus funds with higher exposure to funding liquidity risk earn higher abnormal returns. The paper also investigates the determinant of bond illiquidity betas on fund level. Funds with higher current period alphas tend to have higher next period bond illiquidity betas. Older funds also have higher betas. This suggests that funds with lower financial constraints (higher alphas) and lower hazard of investors running out of the fund which comes with higher age and established reputation can afford to have higher funding liquidity risk. The paper proceeds as follows. Section 2 describes the data and liquidity measures. Section 3 links bond illiquidity and funding liquidity. Section 4 presents cross-sectional results for stock returns. Section 5 describes similar funding for the cross-section of mutual fund portfolios. Section 6 concludes.

7 2. Data The majority of the analysis is done for NYSE/AMEX common stocks from CRSP for the period January 1967 to December The starting point coincides with the availability of bond data described below. Stocks with prices below $5 in a month of portfolio formation are excluded from the sample. Changes in Fed fund rates (FED) are used as an indicator of monetary stance following Bernanke and Blinder (1992). FED data are obtained from the Federal Reserve Bank of St. Louis. The Treasury Eurodollar (TED) spread is the difference between 3- month Eurodollar LIBOR rate and 3-month Treasury bill rate where the data are obtained from Federal Reserve Board s website. A. Bond Illiquidity Illiquidity in the US Treasury market is measured with relative quoted spreads. This is a standard measure for the Treasury market. The simple bid-ask spread, based on widely available data, is highly correlated with price impact, which otherwise is difficult to estimate on a timely basis due to data limitations (Fleming (2003)). Goyenko, Subrahmanyam, and Ukhov (2011) analyze the illiquidity of U.S. Treasuries across all maturities and on-the-run/off-the-run status and find that the illiquidity of off-the-run T- bills with maturities of up to one year best captures the illiquidity of the Treasury market overall. Accordingly, the paper uses the illiquidity of off-the-run T-bills as a proxy for the illiquidity of the U.S. Treasury bond market. More specifically, the average percentage bid-ask spread of off-the-run U.S. T-bills with maturities of up to one year is used to proxy for U.S. Treasury bond market illiquidity. The quoted bid and ask prices come from CRSP s daily Treasury Quotes file. This file includes Treasury fixed income securities of three and six months, as well as 1, 2, 3, 5, 7, 10, 20, and 30 years, to maturity. Under the standard definition, when a new security is issued it is considered to be on-the-run and the older issues are treated as off-the-run. The paper uses quotes for three-, six-, and 12-month securities. For each month the monthly average spread is first computed for each security as the average proportional daily spread for the month and then equally weighted across short-term assets. 2 These data have also been used by 2 The results are similar when non-scaled (raw) quoted spreads are used as an alternative to proportional quoted spreads. This is consistent with Chordia, Sarkar, and Subrahmanyam (2005), who show that the

8 Acharya, Amihud, and Bharath (2009), Goyenko and Ukhov (2009) and Baele, Bekaert, and Inghelbrecht (2010). The primary motivation for using the CRSP data is to have a long enough Treasury bond illiquidity time series to be able to study the connection between economic environment, liquidity conditions, and equity prices. CRSP is the only data source that allows for the use of a sufficiently long period to subsume a variety of economic events. B. Stock Illiquidity An important determinant of choice of the liquidity measure is the long time period of our study. The high frequency microstructure data that is used to compute effective and quoted spreads are not available for the whole time period of our analysis. To measure illiquidity in the stock market the paper uses Amihud s (2002) illiquidity measure. Amihud (2002), Hasbrouck (2006), and Goyenko et al (2009) argue that Illiquidity is a good measure of the liquidity environment in the stock market. As defined by Amihud (2002), the illiquidity of stock i in month t is where i R td and i R ILLIQ DAYS, DAYS i t i 1 td t i i t d 1 Vtd i V td are respectively the return and dollar volume (in millions) on day d in month t, and DAYS i t is the number of valid observation days in month t for stock i. This measure has the following intuition. A stock is illiquid (i.e., has a high value of ILLIQ i t ), if the stock price moves a lot in response to little volume.3 For convenience, the ratio is multiplied by daily correlation between quoted and effective spread changes in the bond market is 0.68 over their nineyear sample period. Thus, quoted spreads are reasonable liquidity proxies. 3 ILLIQ i t is computed for NYSE/AMEX common stocks with at least 5 observations on return and volume during the month t.

9 Table 1 Panel B presents summary statistics for stock and bond illiquidity and funding liquidity measured with TED. Bond illiquidity has low mean and high standard deviation compared to its mean. The low mean is attributed to the analysis of short-term Tbills which have the highest liquidity. Although, high volatility of bond illiquidity indicates that this series captures a lot of information. TED spread achieves the highest value of almost 50 basis points in July 1974 during oil crisis. The second highest value is 39 basis points reached in October 2008 during the beginning of credit crisis. It should be noted that these are monthly data for TED spread which are less volatile. The daily data exhibit more extreme values. For example, on September 17, 2008, TED spread jumped to 300 basis points. Panel B reports correlation matrix between illiquidity measures and FED. FED is used in the analysis since it can indirectly affect TED via its effect on 3-month Tbill rate. Bond illiquidity is highly correlated with TED, This is the first indication of close link between these two variables. Stock and bond illiquidity also have positive and significant correlation of However, the correlation between Amihud-Illiquidity and TED is substantially lower, 0.24, then for bond illiquidity. FED has lower correlation with other variables. Given high correlation of bond illiquidity level with other variables of interest, in subsequent analysis though out the paper Bond ILLIQ is measured as residuals from bond illiquidity level AR(2) process. This is similar to approach of Pastor and Stambaugh (2003), and Acharya and Pedersen (2005) for stock market illiquidity, who use a (modified) second order autoregression to calculate unexpected innovations of illiquidity. The residuals from AR(2) regression show little autocorrelation and very low correlation with other variables.

10 3. Vector Autoregression Analysis The purpose of this section is to establish the link between market illiquidity as easiness to trade and funding liquidity as the ease with which traders can obtain funding. Given that there are reasons to expect cross-market effects and bidirectional causalities, as in Goyenko and Ukhov (2010), we adopt a four-equation vector autoregression specification that incorporates four variables: FED, Stock Illiquidity, Bond Illiquidity and TED spread. Therefore, consider the following system: (1) X t a j X t j (2) Yt a j X t j K K b u 1 1 j t j t and j 1 j 1 K K 2 b2 jyt j t, j 1 j 1 Where X Y is a vector that represents monetary policy and market (funding) liquidity. The number of lags, K, in equations (1) and (2) is chosen on the basis of the AIC and Schwarz Bayesian Information Criterion. The VAR with 2 lags is identified to by optimal. TED spread is set in the end of the VAR ordering since this is a variable of interest. However, the results reported below are not sensitive to VAR ordering. Figure 1, Panel A, illustrates the response of TED spread to a unit standard deviation change in a particular variable, traced forward over a period of 10 moths. Positive shock to FED increase TED spread and this impact is quite persistent. The market illiquidity effect on TED spread is different for stock and bond illiquidity. While stock illiquidity has no significant impact on TED spread bond illiquidity has significant and persistent for 6 months positive impact on funding liquidity. This result suggests that while positive shock to the market wide stock illiquidity has no information about availability of speculative capital in the economy, positive shock to bond illiquidity indicates an immediate and long-lasting decrease in funding liquidity. This effect is independent of monetary policy effect. Panel B further describes the differences between stock and bond illiquidity. While both stock and bond illiquidity increase with respect to increase in TED, bond illiquidity Y

11 also immediately increases in response to monetary tightening (positive shock to FED) while stock illiquidity reacts to change in monetary environment with one month lag. Moreover, positive shock to bond illiquidity increases stock illiquidity and this effect persist for almost six months while the reverse is not true. This is consistent with Goyenko and Ukhov (2009) result: bond illiquidity is affected fist by monetary policy and then transmits these shocks into the stock market. Overall, the evidence shows that bond illiquidity similar to stock illiquidity is affected by TED. Hence both illiquidity variables are affected by funding liquidity. However, bond illiquidity contains more information. Unlike stock illiquidity, it predicts future changes in funding liquidity. This can be attributed to some extent to the ability of bond illiquidity to reflect macro-economic shocks which also have direct impact on funding liquidity. Therefore, positive shock to bond illiquidity reflects among other things decrease in funding liquidity. According to Brunnermeier and Pedersen (2009) this should have a direct effect on asset prices which the paper explores in the next section. 4. Cross-Section of Stock Returns Portfolio Evidence This section investigates whether a stock s expected return is related to the sensitivity of its return to the innovation in bond illiquidity. That sensitivity, denoted for stock i by its bond illiquidity beta BIlliq i, is the slope coefficient on Bond Illiquidity in a multiple regression in which the other independent variables are additional factors considered important for asset pricing. Bond illiquidity beta of assets is estimated in a five-factor model that includes bond illiquidity, the three Fama and French (1993) factors (the CRSP value-weighted market (MKT) portfolio, high-minus-low (HML) book-tomarket equity portfolios, and small-minus-big (SMB) market capitalization portfolios) and Carhart (1997) momentum factor (UMD). Bond illiquidity betas are estimated through a first-stage time-series regression r 0 BIlliq M S H U i, t i i BondILLIQt i MKTt i SMBt i HMLt i UMDt i, t (3)

12 where BIlliq r i, t denotes asset i s excess return. This definition of i captures the asset s comovement with bond illiquidity that is distinct from its comovement with other commonly used factors. Every month stocks are ranked according to their bond illiquidity beta, BIlliq i, using the past 36 months of data. Based on this past illiquidity beta, using data from t-36 to t-1, the asset is allocated to one of twenty portfolios. The portfolios are formed in month t+1 thus allowing for one month between stocks assignment to a portfolio and portfolio formation. Table 2 presents these portfolios average value-weighted returns and their Fama- French-Carhart (FFC) alphas with the corresponding t-statistics. The returns and riskadjusted returns (alphas) are increasing from low to high bond illiquidity beta portfolios, i.e., stocks with higher bond illiquidity betas have higher risk adjusted returns after accounting for Fama-French-Carhart factors. The spread between high and low beta portfolios is statistically and economically significant. The risk adjusted return difference between high and low bond illiquidity beta portfolios is 49 basis points per month with t=1.97. Table 3 presents similar analysis for sub-periods. As before, for each sub-period, portfolio returns are increasing in bond illiquidity betas. However, first sub-period ( ) fails to produce significant spread between extreme portfolios. In the second subperiod ( ) the risk adjusted spread between high and low bond illiquidity beta portfolios increases to 78 basis points with t=2.01. Thus, there is evidence that bond illiquidity risk is priced in the stock market and this effect is more pronounced in the last half of the sample. Higher bond illiquidity means tighter funding liquidity and therefore higher risk for stocks with higher trading constraints. This in turn causes higher expected returns for stocks with higher bond illiquidity betas. To separate further funding liquidity as the availability of trading capital and market liquidity as the ease to trade, Table 4 presents results of portfolio sorts on size (or stock illiquidity) and bond illiquidity. Size is commonly used as a first-hand characteristic of how liquid stock is and how easily it can be traded and Amihud (2002) price impact measures is a commonly used stock illiquidity measure.

13 Panel A, Table 4 presents Fama-French-Carhart (FFC) risk-adjusted returns for each of 25 size-bond illiquidity beta portfolios. For the first three size quintiles the portfolio abnormal returns are increasing in bond illiquidity betas almost monotonically. This pattern somewhat reverses for two largest size quintiles. Bond illiquidity extreme beta portfolios (high-low spread) produce significant positive spread for the first and third size quintiles. The spread is higher for the first size quintile, 35 basis points per month (t=2.23) and lower for the third size quintile, 27 basis points per month (t=2.11). This suggests that funding liquidity risk is primarily concentrated in small and medium size stocks. This is expected since large market capitalization stocks have lower trading restrictions and hence lower funding liquidity risk. Size does not have any effect on high beta portfolios. Starting with the third beta portfolio and onward size quintiles do not generate any significant spread. In fact the return pattern of size portfolios for these beta quintiles is almost flat. The first beta quintile portfolio has quite unexpected pattern in size portfolio returns. For this beta quintile, the biggest-size portfolio outperforms the smallest-size portfolio which is contrary to small size premium. The only reasonable pattern in size portfolios is observed for the second beta-quintile portfolio where small size outperforms big size portfolio by 23 basis points. However, this difference is only marginally significant (t=1.76). Therefore, bond illiquidity risk or funding liquidity risk is different from the size effect and rather helps explain the difference between size portfolio returns. Panel B, Table 4 presents the risk-adjusted returns for portfolio quintiles sorted first on Amihud (2002) Illiquidity and then on bond illiquidity beta. As before, one month is omitted between portfolio ranking and portfolio formation. For each stock illiquidity quintile, with the exception of the first quintile, the risk-adjusted returns are increasing in bond illiquidity beta portfolios. The highest spread between high/low beta portfolios is generated for the fifth, the highest, stock illiquidity quintile. It is also economically significant: 49 basis point per month, t=2.95. Stock illiquidity quintile portfolios produce significant spread with the expected sign for the second beta quintile portfolio. As expected, more illiquid stocks have higher returns than less illiquid stocks. The difference between high/low stock illiquidity portfolios is 37 basis points with t=3.08. However, the results for the first beta quintile

14 portfolio are quite striking. For this portfolio, low stock illiquidity portfolio outperforms high illiquidity portfolio by 37 basis point with t=2.22. This result goes opposite to positive stock illiquidity premium and suggests negative illiquidity premium. While negative illiquidity premium is not plausible for the assets with positive net supply and no short selling, it is quite possible for the assets in positive net supply like stocks and with short-selling allowed (Bongaerts, De Jong and Driessen, (2010)). According to Bongaerts et al (2010) if short selling constraints are lifted than the illiquidity premium can be either positive or negative. The sign will be determined by whether the marginal investor has long or short position. If the representative investor has long position (Acharya and Pedersen, 2005) than illiquidity premium is positive, and it is negative if the marginal investor holds short position. Bond illiquidity is a proxy for funding liquidity and funding liquidity in turn means the easiness to obtain capital or lower marginal requirements for trading in any given asset. Stocks with lower bond illiquidity beta are therefore easier to trade and easier to short-sell. Therefore, it is reasonable to expect that marginal investor has short position in these stocks. This might be one of the reasons we observe negative illiquidity premium for low beta quintile in Panel b and negative size premium in Panel a. Overall the results suggest that bond illiquidity contains information beyond stock illiquidity proxied by size and Amihud (2002) illiquidity measure. Cross-Sectional Regressions The paper next estimates the pricing of bond illiquidity risk controlling for other risk factors and firm characteristics. The asset-pricing models tested here are of the form R i 0 t tz i, t 1 i t E,, (4) where E R i denotes the expected return of stock i (excess of risk-free rate), i are factor loadings, is a vector of premiums, and Z i,t is a vector of firm characteristics for asset i observed at time t-1. Because loadings are unobservable, they are pre-estimated through a multiple time-series regression, (5) R i, t 0, i i f t i, t

15 where f t is a vector of factors. Equation (4) is estimated using the cross-sectional regression method of Fama and MacBeth (1973). However, since the factor loadings in (5) are likely to be estimated with much error for individual assets, i is estimated from portfolios. First, similar Fama and French (1992), each month all assets are sorted in ten size portfolios and then each size portfolio is sorted in ten bond illiquidity beta portfolios. Bond illiquidity beta is obtained as factor loading from the regression of excess stock returns on Fama-French-Carhart factors augmented with bond illiquidity (equation (3)) using preceding 36 months of data. One month is omitted between portfolio ranking and portfolio formation. The beta of size/ portfolio j is estimated using the entire time series of returns BIlliq i for that portfolio. While a portfolio s beta vector is held constant, an asset s beta vector can change on a monthly basis as its portfolio assignment changes. This is the same type of procedure used in Fama and French (1992). The cross-sectional regression (4) is estimated using individual stock data every month, resulting in a time series of estimates, ˆ t. The time-series means and standard errors of ˆ t are calculated and used for hypothesis testing. The model in equation (4) is tested for several factor specifications. First, the CAPM is examined using the Center for Research in Security Prices (CRSP) valueweighted market portfolio, denoted MKT, augmented with bond illiquidity beta. The results in Table 5 suggest that CAPM beta does not have an explanatory power on this cross section. However, bond illiquidity has positive and highly significant risk premium. The positive premium is consistent with portfolio sorting results in Table 2 and 3. The other specifications are Fama-French three factor and Fama-French-Carhart four factor models augmented with bond illiquidity risk. Bond illiquidity premium is always positive and highly significant. Among other factors, value premium is significant while size, market and momentum are not. The last row presents factor models estimated with firm characteristics such as size, book-to-market and Amihud-ILLIQ added to the set of right-hand side variables. Book-

16 to-market ratio is computed annually similar to Fama and French (2008). 4 While size and ILLIQ are 1-month lagged, B/M ratio is lagged 1 year. Bond illiquidity premium continue to remain significant after controlling for these characteristics. Value premium becomes insignificant. This provides evidence of bond illiquidity/funding liquidity being priced and having positive and significant risk premium on the cross-section of stock returns. The paper next turns to the application of above findings for mutual fund portfolio returns. 5. Active-Equity Mutual Funds and Funding Liquidity Funding liquidity can be an important source of risk to control for mutual fund managers. Although mutual funds are not allowed to short-sale and borrow on margin they can hold stocks which are highly exposed to trading constraints. The above results show that these stocks have an abnormal positive profit to compensate for funding liquidity risk. If funds hold part of their portfolio in these stocks their portfolios will have significant bond illiquidity factor loading and subsequently reward the investors with higher returns. However, this would also result in extra risk taken by a fund manager. When a fund without cash reserves underperforms and investors withdraw the capital than a fund manager needs to liquidate in asset fire sales (Coval and Stafford, 2007). Stocks with higher funding liquidity risk are more difficult to liquidate which would lead to even further decline in fund value. Therefore, the hypothesis here is that funds with higher bond illiquidity beta should have higher abnormal returns to compensate investors for higher asset liquidation risk. We test this hypothesis on the cross-section of openended active equity mutual funds. Mutual Fund data 4 Similar to Fama and French (2008), book-to-market ratio, B/M, is defined as the natural log of the ratio of book value of equity to the market value of equity. Book value is total assets for year t-1 minus liabilities plus balance sheet deferred taxes and investment tax credit if available, minus preferred stock liquidation value if available, or redemption value if available, or carrying value. Market equity is price times number of shares outstanding at the end of December of year t-1 from CRSP. Book value of equity is defined as of the end of fiscal year end in calendar year t-1.

17 The paper uses the CRSP Survivorship Bias Free Mutual Fund Database with the CDA/Spectrum holdings database and merges the two databases using Mutual Fund Links tables available at CRSP. The monthly mutual fund data are from January 1990 to December 2009 and include net returns after fees, expenses, and brokerage commissions but before any front-end or back-end loads, total net assets, the fund s turnover ratio, expense ratio, investment objective, and other fund characteristics. The CRSP database identifies each shareclass separately, whereas the CDA database lists only the underlying funds. The Mutual Fund Links tables assign each shareclass to the underlying fund. Whenever a fund has multiple shareclasses at the CRSP database, the weighted CRSP net returns, expenses, turnover ratio and other characteristics are computed for each fund. The weight is based on the most recent total net assets of that shareclass. The analysis employs only actively managed all-equity funds. Included are funds with investment objective codes from Weisenberg and Lipper to be aggressive growth, growth, growth and income, equity income, growth with current income, income, long-term growth, maximum capital gains, small capitalization growth, micro-cap, mid-cap, unclassified or missing. When both the Weisenberg and the Lipper codes are missing, Strategic Insight Objective Code to identify the style is applied, and if Weisenberg, Lipper and Strategic Insight Objective Code are missing, investment objective codes from Spectrum, if available, to identify the style is used. If no code is available for a fund and a fund has a past month/s with the style identified, that fund month is assigned the style of the previously identified style-month/s. If the fund style cannot be identified, it is not included in the sample. Overall there are nine style categories: (i) Aggressive Growth, (ii) Equity Income, (iii) Growth, (iv) Long term growth, (v) Growth and Income, (vi) Mid- Cap, (vii) Micro-Cap funds, (viii) Small cap, and (ix) Maximum Capital Gains. Index funds are eliminated by deleting those whose name includes the word index or the abbreviation ind, S&P, DOW, Wilshire and Russell. Also balanced funds, international funds, sector funds and funds that hold less than 70% in common stocks are excluded. Small funds with total net assets of less than $15 million at the end of the period preceding the test period are also eliminated. Addressing Evans s (2004) comment on incubation bias, observations before the reported starting year by CRSP are eliminated.

18 And, following Cremers and Petajisto (2009), funds with missing name in CRSP are deleted. Overall the cross-section of 2,546 funds is analyzed. Table 6 reports summary statistics. The control variables in the predictive crossfund regressions are those that commonly appear in studies of fund performance. For example, Cremers and Petajisto (2009) use Total Net Assets, TNA, ($mm); Expense, the expense ratio of the most recently completed fiscal year; Turnover, defined as the minimum of aggregated sales or aggregated purchases of securities divided by the average 12-month TNA of the fund; Fund Age computed as the difference in years between current date and the date the fund was first offered; and Manager Tenure, the difference in years between the current date and the date when the current manager took control. 5 An important predictor of future performance is lagged alpha or InfRatio which may reflect managerial skill and strategy and is known to be a significant predictor of performance (see Brown and Goetzmann (1995) and Gruber (1996). Similar to the stock analysis, mutual fund bond illiquidity betas are estimated through a time-series regression r 0 BIlliq M S H U i, t i i BondILLIQt i MKTt i SMBt i HMLt i UMDt i, t (6) where r i, t denotes fund s i s excess return. Bond illiquidity beta in month t-1 is estimated by using return data from month t-24 to t-1, and so forth using 24-month rolling window. In contrast to stocks, the shorter window of 24 months is used for mutual fund sample. This is consistent with the previous work that advocates estimating fund risk exposure over a short period (Brown, Harlow and Starks (1996), Chevalier and Ellison (1997), (1999)). The performance measure, excess return, is estimated as realized returns minus predicted returns, where predicted return is obtained using factor loadings estimated from the previous 24 months of the above regression. Fama-French-Carhartadjusted excess return (FFC-Alpha) is also estimated by regressing excess returns on MKT, SMB, HML and UMD factors. Table 7 presents portfolio sorting results based on bond illiquidity beta. Each month t-2 funds are ranked into 10 portfolios based on their bond illiquidity beta and then equally-weighted excess portfolio return is computed for month t. This procedure allows 5 The manager can be an institution with a long tenure.

19 for one month between portfolio ranking and portfolio formation. Excess returns of decile portfolios are reported in the first raw of the table and FFC adjusted excess returns are reported below. Excess returns and risk adjusted excess returns are monotonically increasing from low to high beta portfolios. The highest abnormal return is obtained for the high beta portfolio, 0.499% with t=2.29. Mutual funds with higher bond illiquidity risk portfolios earn on average 50 basis points per month in risk adjusted returns. This is economically meaningful number. Overall, high beta portfolios outperform low beta portfolios by 1.046% per month (t=2.87) on the risk adjusted basis. Holding stocks with restrictive trading constraints should involve a lot of portfolio rebalancing since in order to liquidate these risky positions mutual funds would need to sell before trading constraints tighten due to negative shocks in the market. Higher portfolio rebalancing causes higher expenses and higher portfolio turnover. Moreover these effects should be less pronounced among large funds who have the pressure to diversify more and more pronounced among smaller size funds who behave less like an index. Therefore, the hypotheses tested here are: H1: Small size funds with higher bond illiquidity beta portfolios have higher riskadjusted returns compared to medium and large funds with high/low beta portfolios H2: Funds with higher expenses and higher bond illiquidity beta portfolio have higher risk adjusted returns compared to funds with low expenses and low/high beta portfolios H3: Funds with higher turnover and higher bond illiquidity beta portfolio have higher risk adjusted returns compared to funds with low turnover and low/high beta portfolios To tests the above hypotheses all funds are first sorted into size/expenses/turnover quintiles and then each quintile is sorted into five bond illiquidity beta portfolios. As before, one month is omitted between portfolio ranking and portfolio formation. The Fama-French-Carhart adjusted excess returns (FFC-Alpha) and corresponding t-statistics are reported in Table 8.

20 Panel A of Table 8 presents the results for 25 size-beta portfolios. For each size quintile, the portfolio alpha monotonically increases from low to high beta portfolio. The alphas are predominantly negative and significant for the first three beta portfolio across all size quintiles. This supports the previous notion in the literature that on average the mutual fund industry underperforms across all size categories. However, the alphas are positive and significant for the highest beta portfolios for the first, second and fifth size quintiles. Therefore not only small size but also large size funds invest in funding liquidity risk. The return is the highest for the high-beta/low size portfolio. This extreme portfolio generates 43 basis points (t=2.38) per month in risk adjusted excess returns. However, the difference is the spread between low and high size portfolios for the high beta quintile is insignificant. Therefore the first hypothesis is partially rejected: while small funds with high beta portfolios have almost twice higher risk adjusted returns compared to medium-size funds they have statistically similar abnormal profits as large funds (38 basis points per month, t=2.73). Panel B presents the portfolio results for 25 expenses-beta sorted portfolios. For each expense quintile portfolio alphas are monotonically increasing with the beta. The higher beta portfolio have higher excess returns. The alpha is the highest for the highexpenses/high-beta portfolio, 0.52% per month, t=2.19. This abnormal return is more than twice higher compared to the low-expenses/high-beta portfolio, 0.23%, t=1.80, and the difference between two portfolios is statistically significant. Moreover, the abnormal returns are monotonically increasing from low expenses to high expenses for the highest beta portfolio. Therefore, the second hypothesis is supported by the data: funds with higher bond illiquidity beta need to rebalance more frequently which leads to higher expenses but also to higher abnormal returns. The returns reported in the panel are net after expenses and fees returns. Therefore these funds are able to earn positive and significant after fees alphas. Panel C presents the test of the third hypothesis: funds with higher betas need to rebalance frequently therefore resulting in higher portfolio turnover. Thus funds with higher turnover and higher betas should earn higher abnormal returns. This is what the Panel finds: the highest abnormal return is observed in the highest turnover and the highest beta portfolio, 0.55% per month, t=2.54. This is very close to the 0.52% return

21 reported in Panel B for high expenses-high beta portfolio. This also indirectly provides the support for the second hypothesis. Funds with higher betas have to trade more, have higher turnover, higher expenses and eventually earn higher abnormal returns. While results presented in Table 8 are based on double-sorting and fail to account simultaneously for all fund characteristics the panel regressions reported below address this issue by taking into account not only fund characteristics but also time effects. The model tested below is of the form Alpha j,t = γ t BondILLIQBeta t-1 + δ 1t Expenses j,t-1 + δ 2t log(tna) j,t-1 + δ 3t [log(tna)] 2 j,t-1 + δ 4t Turnover j,t-1 + δ 5t log(fund Age) j,t-1 + δ 6t log(manager tenure) j,t δ 7t Performance j,t-1 + n StyleDummy j, n, t 1 (7) n 1 The fund performance measure alpha j,t estimated in the test period t, is regressed on its Bond ILLIQ Beta from the preceding estimation period (month t-1). The control variables include fund characteristics that are known at the beginning of the test period, the fund s lagged performance, and nine style dummy variables. Alpha j,t is estimated as excess returns which is the difference between actual returns and predicted returns. Predicted return is obtained using factor loading from equation (6) and using preceding 24-month of returns before testing period. The equation (7) is estimated with panel regression which also includes time and style dummies and standard errors are clustered by both fund and year. Our hypothesis is that γ > 0. That is, fund with portfolios with higher exposure to funding liquidity risk should have higher abnormal returns. Table 9 reports the results. As expected Bond ILLIQ Beta t-1 has positive and significant impact on next period fund performance. This evidence is consistent with the findings in the stock market but now they are also confirmed on mutual fund portfolio level. Among other variables, size has negative and significant effect on fund performance confirming the previous literature that size destroys value. Past performance is persistent which is reflected in the

22 positive and significant coefficient of Alpha t-1. This is consistent with Bollen and Busse (2005) who report short term persistence in fund performance. The alternative hypothesis is that Bond ILLIQ Beta t-1 might be just capturing the effect of other factor loadings. The second column of Table 9 present equation (7) estimation augmented with factor loadings on Fama-French and Carhart factors. Bond ILLIQ Beta t-1 remains positive and significant while other factor loadings are insignificant. Moreover, size loses its significant and the only other significant variable in this regression is past performance. Table 10 presents results for the determinants of bond illiquidity betas. Bond illiquidity risk increases with turnover, age and past performance. Positive effect of lagged alpha on funds illiquidity risk suggests that funds which just had high alphas are less financially constrained and incline to load more on stocks with higher funding constraints. These funds can afford to take on more of illiquidity risk. This argument is also consistent with the age effect. Older funds which are more known among investors are facing lower risk of fund outflow and therefore lower cash constraints, and thus too can afford higher illiquidity risk. The effect of turnover is consistent with portfolio sorting results presented above. Finally, the last column of Table 10 also controls for factor loadings of Fama- French and momentum factors. Only momentum beta has significant effect on next period illiquidity risk, i.e. funds pursuing momentum strategies are also exposed to funding liquidity risk. This is consistent with momentum literature which suggests that momentum strategies involve trading a lot in illiquid stocks (Korajczyk and Sadka (2004), Lesmond, Schill and Zhou (2002)). However, this paper also suggests that among other risks mutual funds also take on funding liquidity risk. 6. Conclusion This paper links Treasury bond illiquidity and funding liquidity. It is shown that Treasury bond illiquidity while capturing and transferring monetary policy shocks into stock market illiquidity also predicts changes in Treasury-Eurodollar (TED) spread which is a commonly used proxy for funding liquidity. Stock market illiquidity is lacking these properties. Increase in bond illiquidity predicts increase in TED spread.

23 On the cross-section of stocks, stocks with higher bond illiquidity betas earn higher risk-adjusted returns compared to lower bond illiquidity beta stocks. Bond illiquidity beta is estimated to have positive and significant risk premium after controlling for Fama- French and Carhart factors and firm characteristics such as size, book-to-market and stock illiquidity. Further, active equity mutual funds with higher loading of their portfolios on bond illiquidity have higher abnormal returns after controlling for the past performance, styles and various funds characteristics. This effect prevails across all size categories and is accompanied with higher expenses and portfolio turnover. Yet, after controlling for expenses and turnover, high bond illiquidity beta funds are still able to outperform the benchmarks by significant amount. Overall, the paper provides empirical support to Brunnermeier and Pedersen (2009) theory not only on the cross-section of stocks but also on the cross-section of mutual fund portfolios.

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