Funding liquidity, market liquidity and TED spread: A two-regime model

Transcription

1 Funding liquidity, market liquidity and TED spread: A two-regime model Kris Boudt Ellen C.S. Paulus Dale W.R. Rosenthal February 15, 2013 Abstract We investigate the effect of market liquidity on equity-collateralized funding accounting for endogeneity. Theory suggests market liquidity can affect funding liquidity in stabilizing and destabilizing manners. Using the broker call rate and the average fee on stock loans that are attributable to shifts in the shorting demand curve, as central-bank-based and market-based proies for funding liquidity, we confirm the eistence of both regimes on a 13 year sample period, and show that we can separate them using the yield spread of Eurodollars over T-bills (TED spread). We find destabilizing funding responses for stock loans when the TED spread eceeds 50 bp, and a similar, but less pronounced effect for the central-bank-set rates when the TED spread eceeds 80 bp, suggesting market participants respond faster to crises and that the TED spread is an important market barometer for policy makers. Keywords: equity-collateralized funding liquidity, market liquidity, two-regime model, financial distress. We thank Jef Boeck, Christophe Crou, Stephen Schaefer, Nitish Sinha, Gunther Wuyts, and participants at the London Business School 2011 Transatlantic Doctoral Conference and the 22nd (EC) 2 Conference on the Econometrics of Policy Analysis after the Crisis and Beyond for helpful suggestions. We also thank Data Eplorers for providing us with institutional lending data. Financial support from the Dutch National Science Foundation (NWO) and the National Bank of Belgium is gratefully acknowledged. This is work in progress. Comments and suggestions are very welcome. K.U. Leuven and V.U. University Amsterdam; kris.boudt@econ.kuleuven.be London Business School; epaulus.phd2010@london.edu University of Illinois at Chicago; daler@uic.edu 1

2 1 Introduction Secondary markets are considered liquid if an investor can quickly eecute a significant quantity at a price near fundamental value. Such market liquidity is of great importance: it allows investors to enter and eit trading positions, rebalance portfolios, and smooth consumption. For market makers and other traders to provide liquidity in secondary markets, however, they need to raise capital from financiers in the primary market. This capital is often borrowed against collateral. We refer to the willingness of financiers to provide such collateralized loans as funding liquidity. Intuitively, when market makers and traders post more valuable securities collateral, financiers are more willing to lend out funds. Thus, the market value of the assets serving as collateral plays a pivotal role in the smooth functioning of capital markets. Moreover, these collateral values might well depend on their market prices, on the uncertainty of those prices (i.e. volatilities), and also on their market liquidities. So, asset market liquidity affects funding liquidity and vice versa. This paper empirically demonstrates the effect of asset market liquidity on financier behavior, and also shows how financial crises change this effect. Using a 13-year sample period ( ), we show that a deterioration of S&P 500 stock market liquidity only causes (equity-collateralized) funding liquidity to decrease when credit risk is high, and otherwise has no effect or slightly improves funding liquidity. Our results hold after accounting for the bidirectional causality between market liquidity and funding liquidity and controlling for endogenous stock volatility. Despite a longstanding interest in the determinants of market liquidity initiated by Stoll (1978), Amihud and Mendelson (1980), Kyle (1985), Glosten and Milgrom (1985), among others, the role of limited market-maker capital in asset market liquidity has been relatively uninvestigated. Even less is known on how asset market liquidity ultimately feeds back into the supply of funds. Recent theoretical work by Gromb and Vayanos (2002), Gromb and Vayanos (2010) and Brunnermeier and Pedersen (2009) suggests linkages between collateral values and funding can lead to virtuous cycles of increasing funding and market liquidity on one hand and vicious cycles of decreasing funding and market liquidity on other hand. However, data limitations have impeded efforts to confirm and 2

3 eplore these two regimes empirically. Indeed, to directly assess the cost of equity-collateralized funding requires a combination of equitycollateralized loan rates and haircut requirements. Unfortunately, such data is not readily available. A description of the institutional features of the secured lending market and the data challenges involved in monitoring lending conditions and systemic risk in repo and securitised lending markets can be found in Adrian et al. (2012). In the absence of comprehensive margin data, Mancini-Griffoli and Ranaldo (2011) draw on earlier work by Coffey et al. (2009) and Gorton and Metrick (2010) to measure capital constraints in the secured lending market by using the spread between Agency Mortgage Backed Securities and General Collateral repo rates. In this paper, we introduce and test two measures for funding liquidity, or rather funding illiquidity. The robustness of our estimations indicates these approimations are of good quality; and, the different measures create a scope for policy implications. First, we proy for funding illiquidity on a given day using a value-weighted average of fees for S&P 500 stock loans that are attributable to demand shifts for shorting S&P 500 stocks. As shown by Cohen et al. (2007), an outward shift in the demand curve for shorting stocks, leads to a significant negative abnormal return in the following month. This naturally implies that stock is poor quality collateral going forward, i.e. its funding liquidity decreased. By tracing inward and outward shifts of the shorting demand curve, we are effectively tracing decreases and increases, respectively, in equity-collateralized funding illiquidity. Second, we measure funding illiquidity through the surplus of the broker call rate over the 3-month US Treasury Bill rate. The broker call rate is the rate commercial banks charge to broker-dealers on short-term margin loans, and is usually steadied at a fied spread above the Federal Funds rates. Therefore, we posit that the latter measure is a central-bank-based measure, and the former measure is a market-derived measure. In addition, we establish an instrumental variables identification strategy that, for the first time, allows us to capture the endogeneity between market liquidity and funding liquidity. While our objective is to estimate the effect of market liquidity on funding liquidity, a causal relationship 3

4 operating in the opposite direction is likely also present. We rely on three natural instruments to isolate the eogenous variation in market liquidity: (i) a tick size dummy for the transition of the NYSE and Nasdaq to decimal pricing in the first quarter of 2001, triggering an eogenous drop in bid-ask spreads, (ii) a variable capturing the trend in average time between trades, allowing us to eploit the well-established correlation between trading activity and market liquidity as in George and Longstaff (1993), and (iii) the change in yields for short-term AAA-rated corporate bonds versus change in LIBOR. The latter spread is typically used to capture liquidity-driven action within the bond market independent of credit-risk as in Chen et al. (2005) and Almeida and Philippon (2007). We show these instruments have strong eplanatory power in asset market liquidity. Moreover, as financiers desire to supply liquidity is typically a function of the collateral asset s fundamental volatility, we control for S&P 500 market volatility by adding the VIX as a control variable. To account for the possibility that funding liquidity could feed back into asset market volatility, we add lagged volatility to our set of instruments to serve as an internal instrument in line with Bloom et al. (2007). Finally, we put forward a two-regime estimation procedure to distinguish between the stabilizing and destabilizing financier behavior featured in the aforementioned theoretical literature. On the one hand, when a financier believes a fall in market liquidity is temporary and could recover shortly, he might charge lower rates in response to decreased market liquidity of the stock collateral. This behavior has a stabilizing effect on market liquidity. On the other hand, financiers may destabilize market liquidity by increasing rates in periods of reduced market liquidity, forcing traders to unwind positions at unfavourable prices in order to meet the higher interest payments on their loans. Our approach to distinguishing between these two distinct regimes relies on Brunnermeier and Pedersen s (2009) proposition that a flight to quality, in the form of aggregate desire to move from investments of lower to higher credit quality, would be part of the spiral effect of a destabilizing reduction in market liquidity. Thus, we are able to associate the absence (presence) of a flight to quality with a stabilizing (destabilizing) regime. Episodes of flight to quality are usually detected using credit spreads. As noted by Brunnermeier 4

5 (2009), many market observes have focused on the TED spread, defined as the difference in yields between US Eurodollar futures, based on three-month USD LIBOR, and US Treasury bills. Thus, by construction, this spread captures the difference in yields between top-rated interbank and government riskless credits. 1 In times of uncertainty banks increase the interest rates on unsecured loans, driving up the LIBOR. A flight to quality would then manifest itself as a widening of the TED spread which in turn, as per Brunnermeier and Pedersen (2009), would suggest a destabilizing spiral between the liquidity of the equity market and the liquidity of the margin loan market. That a flight to quality is part of such a destabilizing spiral is crucial: it allows us to investigate the transition between stabilizing and destabilizing regimes based on the TED spread. We emphasize that our approach of using the TED spread as an eplanatory variable for equity-collateralized funding liquidity is not inconsistent with recent articles using the TED spread as a proy for funding illiquidity Brunnermeier (2009). In fact, we predict a strong positive relationship between the TED spread and funding illiquidity, through the credit risk and flight to quality channels. For the purpose of eposition, we begin our analysis with more simple estimation strategies fail to account for the endogeneity of market illiquidity and/or fail to distinguish between stabilizing and destabilizing market states. We point out where those specifications disagree with economic intuition or the data. We then report results of a two-regime, two-stage least squares estimation where the threshold for the transition between stabilizing and destabilizing states is estimated by the methods of Hansen (2000) and Caner and Hansen (2004), facilitating statistical inference on the estimated threshold. Our results provide direct evidence of the eistence of stabilizing and destabilizing financier behavior in response to decreased market liquidity and we show that we may separate these regimes using the TED spread. We further show that financiers and central bankers usually set stabilizing rates that encourage market liquidity to increase after it has decreased. However, for TED spreads above 50bp, financiers set destabilizing rates for their stock loans; and, for TED spreads above 80 bp, central bankers cease providing stabilizing rates for loans to brokers. Thus we not only provide evidence in support of Brunnermeier and Pedersen s (2009) hypothesis 1 These banks were once AAA-rated credits; however, that is no longer the case. 5

6 regarding the contemporaneous observation of destabilizing financiers and a flight to quality, but we also show that the TED spread is an important monitoring tool for policy makers and that policy makers actions in crisis lag those of market participants. The rest of this paper is organized as follows. Section 1.1 reviews related literature, and Section 2 motivates the regression specification and estimation methodology. Section 3 provides a description of the data. Section 4 discusses empirical results for both the market-, and central bank -based funding liquidity proies, robustness checks, and possible policy implications. Section 5 concludes. 1.1 Related Literature This paper belongs to a nascent empirical literature investigating the interplay between limited intermediary capital and asset market liquidity. Until now, this literature has focused on the effects of funding tightness on asset market liquidity and disregarded the endogeneity between the two. Comerton-Forde et al. (2010) eamine time-variation in market liquidity and provide evidence that liquidity-supplier financing constraints matter. In particular, they proy for funding liquidity in a sample using a panel of daily revenue and inventory data of NYSE specialists, and find that negative shocks to these variables reduces stock market liquidity. Mancini-Griffoli and Ranaldo (2011) consider the effect of secured versus unsecured borrowing by arbitrageurs during the financial crisis and confirm that funding liquidity affects market liquidity. Hameed et al. (2010) show that changes in the value of equities (collateral) affect market liquidity; they also find effects suggestive of reduced funding liquidity and show that there are economically significant returns for providing stabilizing market liquidity. Jensen and Moorman (2010) show that monetary policy, and thus funding liquidity, affects market liquidity. This is particularly relevant since one of our funding liquidity measures is based off of the Fed Funds rate. While these papers provide evidence for some aspects of the relationship between funding liquidity and market liquidity, they only cover one direction of causality. We depart from these eisting works 6

7 by focusing on the reverse causality: effects that changes in market illiquidity have on funding illiquidity. We eplicitely account for endogeneity using an instrumental variables identification strategy. Our paper not only provides direct evidence that market liquidity affects funding liquidity, but also documents the etent to which financiers responses to decreased market liquidity can further destabilize asset liquidity in a high credit risk environment. Drehmann and Nikolaou (2010) construct a measure of funding liquidity risk, i.e. the possibility that over a specific horizon the bank will become unable to settle obligations with immediacy, based on the aggressiveness of banks bids in the main refinancing auctions conducted at the European Central Bank between June 2005 and October They show this measure correlates positively with asset market illiquidity during the financial crisis but is otherwise uncorrelated with asset market illiquidity. This observation supports our approach to distinguish between stabilizing and destablizing regimes on the basis of the TED spread. To study the aforementioned correlations, they further present univariate regression results of their funding liquidity measure on a market liquidity inde. Since they rely on estimation methods which can be biased by the endogeneity between funding and market liquidity, and endogeneity is central to Gromb and Vayanos s (2002) and Brunnermeier and Pedersen s (2009) theses, their results are difficult to interpret. 2 Hypothesis development Four working hypotheses lead to an eplanatory regression model for the relationship between (equity-collateralized) funding and market liquidity. We summarize these hypotheses as stating that: (i) funding rates are affected by the epected future value of collateral; (ii) tranquil and jittery regimes for funding liquidity may be discerned by the TED spread; (iii) in the tranquil regime, financiers lower rates in response to market illiquidity; and, (iv) in the jittery regime, financiers raise rates in response to market illiquidity. Hypothesis 1 A financier sets the loan rate on a collateralized loan given epectations for the value-evolution of equity collateral. These epectations are influenced by (i) market liquidity, (ii) 7

8 market volatility (volatility of equity collateral value), and (iii) the level of the TED spread (as an indicator of market stability). To test this hypothesis, we regress the ecess broker call rate and the value-weighted average stock loan rate on a market liquidity proy and control for asset volatility and market-wide credit risk. This is the simplest hypothesis and serves as a sanity check on our data. If these epectations are not met, we should be concerned about the data being representative of a range of market conditions. We account for potential feedback effects of funding liquidity into market liquidity and asset volatility by instrumental variable estimation, and take the TED spread to be an eogenous control variable proying for market-wide credit risk. To the etent that the cost of equity-collateralized margin lending is not the sole determinant of large financial institutions s solvency, we assume changes in our proposed funding illiquidity measures are not a source of variation for the TED spread. Hypothesis 2 We distinguish between two regimes: tranquil and jittery markets. These occur when the TED spread is below or above some threshold. The models of Gromb and Vayanos (2002), Gromb and Vayanos (2010) and Brunnermeier and Pedersen (2009) feature funding rates that can either be stabilizing or destabilizing to market liquidity. Guided by eploratory data analysis and consistent with evidence in Balke (2000) and Drehmann and Nikolaou (2010), we propose a two-regime parametrization. We claim financiers apply different pricing models to periods of low-to-moderate credit risk versus periods of high credit risk and that credit risk is related to market stability. Our use of the TED spread as regimeseperator mirrors market watchers beliefs that the TED is a barometer for market sentiment (e.g. Krugman (2008)); spreads below some threshold imply relative tranquility in the market and spreads eceeding that threshold imply jitteriness. While Krugman and others have advocated a 100bp threshold, we take no e-ante position on the threshold value. Rather, we estimate the critical value of the TED spread using the methods of Hansen (2000) and Caner and Hansen (2004). This methodology allows us to formally test for the presence of a threshold and thus the validity 8

9 of our two-regime specification. Hypothesis 3 In tranquil markets, a financier decreases rates charged to brokers in response to increased market illiquidity. This response is stabilizing for market liquidity. If a financier believes market liquidity fluctuates and more asset market customers may be enticed to arrive soon, he perceives an increase in market illiquidity as temporary. An increase in market illiquidity then causes financiers to lower rates to entice market participants to trade; this preserves the business of lending to intermediaries. We believe a financier only sees rises in market illiquidity as temporary when the TED spread remains below some threshold. Consequently, a financier will charge stabilizing rates when the general mood in the market is confident and positive. Hypothesis 4 In jittery markets, a financier raises rates charged to brokers in response to increased market illiquidity. This response is destabilizing for market liquidity. When distrust in financial markets eceeds a threshold, financiers become wary of fluctuations in market liquidity. An increase in market illiquidity then causes financiers to increase their safety buffer against fluctuations in the collateral value for broker loans. Hence, they trade stabilizing rates for destabilizing ones: an increase in market illiquidity yields an increase in the ecess broker loan rate. 3 Data description We use eight variables in our two-regime, two-stage least squares estimation procedure. We proy for funding liquidity as dependent variable with two different measures: a market-based measure based on stock loan rates for S&P 500 stocks, and a measure based on the Federal Funds rate. Our set of eplanatory variables consists of bid-ask spreads for the S&P 500, S&P 500 implied volatility and the TED spread. To account for the endogenous relationship of both market liquidity 9

10 and volatility with the dependent variable, we introduce three natural instruments to isolate the eogenous variation in market liquidity: a tick-size-change dummy, a variable representing the trend in inter-trade duration, and a measure for the change in short-term AAA corporate bond yields versus the change in LIBOR. We also add lagged volatility as an internal instrument to handle any endogeneity of the VIX inde. Our sample period covers March 1998 December While we are able to construct the time series of both the market-based and the central-bank-based funding liquidity measures for the entire sample period, the latter is only relevant for the period before 17 March On this day the Federal Reserve made the announcement that the Primary Dealer Credit Facility (PDCF) would accept equities as collateral for overnight loans, causing a structural break in the time series. 2 Figure 1 illustrates the steep decrease in the ecess broker loan rates at the announcement date of the Primary Dealer Credit Facility. Despite the Federal Reserve closing the PDCF on 1 February 2010, we do not etend our analysis with the ecess broker loan rates past 17 March 2008 so that we maintain a uniform sample. 3 Throughout the paper, we speak of funding and market liquidity. However, the nature of these variables means that they measure funding and market illiquidity. Thus we refer to these illiquidities when working with the data. 3.1 Variables Funding illiquidity (central bank measure: ecess broker loan rate, in %). The broker loan rate on day t is the rate commercial banks charge to broker-dealers on short-term margin loans.the bank reserves the right to call (end) the loan at any time at which point the borrowing en- 2 The PDCF was created by the Fed on 17 March 2008 to provide overnight loans through the Fed s discount window to primary dealers. The funding was provided via a repurchase agreement with the securities acting as collateral. Prior to 14 September, only investment-grade (debt) securities were eligible for the facility; however, starting on that date the facility accepted any securities eligible for tri-party repurchase agreements including equities. 3 In earlier results, we included the active mandate of the PDCF between March 2008 and February 2010 in our study of the ecess broker loan rate. That analysis is less clearly interpretable; however, it may provide some information on the etent that the Federal Funds rate may have been adjusted in light of the PDCF. We leave this for further research. 10

11 Ecess Broker Loan Rate (%) Figure 1: Ecess broker loan rate (fundilliq C ) March 1998-December Shaded regions indicate time periods when the TED spread eceeds 50 bp (light gray) and 80 bp (dark gray). The black bar near the bottom ais shows when the Primary Dealer Credit Facility was active (March 2008 February 2010). tity receives a margin call. The broker call rate, charged on what are effectively stock-collateralized loans, is published daily, every day for the previous day, in the Wall Street Journal as the Call Money Rate. We take the time series data from Bloomberg. This rate less the closing yield of the three-month US Treasury bill is the ecess broker loan rate which we denote fundilliq C. We say this measure is a central-bank-based measure because the broker call rate has typically been held as a (rarely-changing) spread over the Federal Funds rate. Thus this variable is largely affected by the policy maker s actions to control the money supply through overnight loans to commercial banks which, in turn, make equity-collateralized loans to the broker-dealers. 4 Due to the unavailability of complementary margin data, fundilliq C is an indirect measure of equity-collateralized funding liquidity. Nonetheless, we think of this rate as revealing how the Federal Reserve steers the refinancing ability of banks, based on its perceptions of market fundamentals and (systemic) risk factors. Figure 1 displays the ecess broker loan rate for March 1998 December One can note spikes 4 The eistence of Federal Reserve journal articles like Fortune (2000) suggests that the Federal Reserve effectively considers how policy affects broker call loans. 11

12 for the 1998 LTCM crisis, the 11 September 2001 terrorist attacks, and the recent credit crunch. The steep decline on 17 March 2008 coincides with the announcement of the Primary Dealer Credit Facility, after which we no longer consider fundilliq C in our analysis. Funding illiquidity (market measure: value-weighted average of fees for S&P 500 stock loans, originated on that day, attributable to demand shifts for shorting S&P 500 stocks %). We construct our second measure of funding illiquidity on the basis of a panel data set with daily frequency, consisting of volume weighted average stock loan fees and quantities of stocks on loan for S&P 500 stocks. This data is aggregated by Data Eplorers, from July 2006 to December 2011, across all their clients. Using similar stock loan data from a single institutional investor, Cohen et al. (2007) document that an increase in shorting demand, on average, leads to a significant negative average abnormal return of 2.98% in the following month. They also show that the shorting market is an important mechanism for private information revelation. In fact, an outward (inward) shift of the demand curve for shorting a specific stock implies more (less) capital is betting that its price will decrease, implying that stock is bad quality collateral going forward. Consequently, we reason that an outward (inward) shift of the demand curve for shorting a stock can be related to an increase (decrease) in its funding illiquidity. We proceed with inferring, on a daily basis, and for every stock in our sample whether it has eperienced an increase or decrease in demand for shorting by eploiting price-quantity pairs. For eample, an increase in the reported volume weighted average loan fee (VWAF), our price measure, coupled with an increase in the total quantity of stock on loan (Total Balance Quantity or TBQ), our quantity measure, corresponds to an increase in shorting demand, as would be the case for any increase in price coupled with an increase in quantity. As Cohen et al. (2007) note, this is not necessarily the only shift that occurred. However, for a shift of price and quantity into this quadrant, a demand shift outwards must have occurred. Similiarly, we label a joint decrease of price and quantity from one day to the net as an inward shift of the demand curve. We keep only these demand shifts and disregard the observations corresponding to dominant shifts of the supply curve. For each day, we then weigh the volume weighted average stock loan fee from the 12

13 Log Transformed Average 1 day VWAF Figure 2: Trade-weighted average of fees for S&P 500 stock loans, attributable to shifts of the demand curve for shorting, July 2006-December Shaded regions indicate time periods when the TED spread eceeds 50 bp (light gray) and 80 bp (dark gray). The black bar near the bottom ais shows when the Primary Dealer Credit Facility was active (March 2008 February 2010). retained demand shifts for all stocks by the number of transactions initiated that day, to construct our daily measure of funding illiquidity for S&P 500 stocks. The market-derived measure of funding illiquidity, fundilliq M t, is then: fundilliq M t = log ( N ) i=1 T rades it V W AF it 1 DS,it N i=1 T rades, (1) it 1 DS,it where i indees the N members of the S&P 500 on a day t with stock loan activity, T rades it represents the number of transactions initiated for stock i on day t, and where 1 DS,it is an indicator variable for a shift of the demand curve for shorting stock i between day t 1 and day t, 1 DS,it = 1 if (V W AF i,t 1 < V W AF i,t ) (T BQ i,t 1 < T BQ i,t ); 1 if (V W AF i,t 1 > V W AF i,t ) (T BQ i,t 1 > T BQ i,t ); 0 otherwise. (2) 13

14 Log Transformed Bid Ask Spreads Figure 3: Log-transformed bid-ask spreads on the S&P 500 inde (mktilliq) March 1998-December Shaded regions indicate time periods when the TED spread eceeds 50 bp (light gray) and 80 bp (dark gray). The sharp decrease in 2001 was due to the move to decimal prices. Since the average stock loan rate is very right-skewed, we take the logarithm of the series to avoid etreme values from dominating the regression. The time series of fundilliq M is plotted in Figure 2. The plot shows a positive trend throughout the evolution of the credit crisis, indicating increased demand for borrowing stock as part of a short-sell strategy. Market illiquidity (bid-ask spread, in %). Pagano (1989) and Johnson (2006) define market liquidity as the average willingness of the market to accommodate trade at prevailing prices. This willingness may fluctuate as the underlying state of the economy changes. The bid-ask spreads, standardized by division by the midquote, are generally considered a good measure of market illiquidity as per Goyenko et al. (2009). The CBOE aggregates bid-ask spread data from the market for the S&P 500 inde members. The series is available through Bloomberg. We take the logarithm of the standardized S&P 500 bid-ask spreads to reduce the impact of etremes on estimation. We denote this illiquidity measure mktilliq since an increase in bid-ask spread corresponds to an increase in illiquidity. Since we epect a causal relationship of funding illiquidity 14

15 on market illiquidity, we treat mktilliq as an endogenous regressor in our key estimations. We plot mktilliq across time in Figure 3 and observe a widening of bid-ask spreads for the S&P 500 inde throughout the credit crisis. A relative widening of bid-ask spreads indicates an increase in illiquidity. The radical drop in bid-ask spreads observed in 2001 is due to decimalization of NYSE prices, completed on 29 January 2001 (Portniaguina, Bernhardt, and Hughson, 2006). The relatively calm period of ehibits low bid-ask spreads indicating liquid markets; tense times, such as after 11 September 2001 or the credit crunch, ehibit high bid-ask spreads indicating illiquidity. Figure 4 presents scatter plots of fundilliq C and fundilliq M on mktilliq in Panels A and C respectively. Observations when the PDCF was active (17 March February 2010) are plotted with red crosses while other observations are plotted with circles; light gray (black) circles correspond to stable (jittery) market conditions (based on a TED spread threshold). For both Panel A and C, we find that the light gray circles reveal a linear pattern with a modest inclination whose sign is difficult to discern on a visual basis. Nevertheless, this suggests that market illiquidity only has a limited effect on funding illiquidity when market conditions are perceived as stable and financiers willingness to lend funds seems little affected by asset liquidity. We further note that the black circles, corresponding to jittery market conditions, ehibit a distinctly different pattern. While the slope of this pattern is hard to discern for fundilliq C in Panel A, the black circles in Panel C show a steep positive slope. This implies that, at least for the case of fundilliq M (and likely fundilliq C ), higher market illiquidity goes hand in hand with higher funding illiquidity, when credit concerns are high (i.e.high TED spreads). 5 Thus, Panels A and C of Figure 4 demonstrate the importance of distinguishing between stable and jittery markets, when modelling the effect of market liquidity on equity-collateralized funding liquidity. 5 Figures 1 and 2 show that for more than half of the Primary Dealer Credit Facility s active eistence, the TED spread was high (relative to our estimated thresholds). Thus, the positively sloped linear pattern of the red crosses in Panels A and C, is consistent with the positive slope of the black circles in these panels. 15

16 Panel A: fundilliq C versus mktilliq Panel B: fundilliq C versus vol Log Transformed Bid Ask Spreads Ecess Broker Loan Rate (%) Volatility (%) Ecess Broker Loan Rate (%) Panel C: fundilliq M versus mktilliq Panel D: fundilliq M versus vol Log Transformed Bid Ask Spreads Log Transformed Average 1 day VWAF Volatility (%) Log Transformed Average 1 day VWAF Figure 4: Scatter plots of funding illiquidity versus endogenous regressors market illiquidity (mktilliq) and volatility (vol). Panel A (B) shows the ecess broker loan rate versus market illiquidity (volatility), with circles for non-pdcf observations and crosses for PDCF observations (March 2008 February 2010). The circles are light gray (black) for observations when the TED spread is below (above) 80 bp. Panel C (D) shows the value-weighted average of fees for S&P 500 stock loans attributable to shifts of the demand curve for shorting, versus market illiquidity (volatility), with circles for non-pdcf observations and crosses for PDCF observations (March 2008 February 2010). The circles are light gray (black) for observations when the TED spread is below (above) 50 bp. The strong separation of light circles (low TED spread) from dark circles and crosses (high TED spread) reveal the presence of two distinct regimes, differentiable on the basis of a TED spread threshold. 16

17 Volatility (%) Figure 5: Daily volatility (in percent) as measured by the Chicage Board Options Echange volatility inde (VIX) March 1998-December Shaded regions indicate time periods when the TED spread eceeds 50 bp (light gray) and 80 bp (dark gray). Volatility of stock collateral (in %): For a measure of the volatility of equity collateral, we use the CBOE implied volatility inde (VIX) derived from options on the S&P 500 inde. The series is denoted vol and plotted in Figure 5. While we are interested in estimating the effect of asset volatility on our two funding illiquidity measures, we believe it is reasonable that funding constraints may feed back into asset market volatility. Consequently, we treat the VIX inde as an endogenous regressor in our key estimation. We analyze the relationship between our two funding illiquidity proies and the VIX inde by means of scatter plots of fundilliq C and fundilliq M on vol. These plots are represented in Panels B and D of Figure 4 and reveal that, if we do not distinguish between a normal and high credit risk regime, at least a quadratic function is needed to fit all data points well. Thus, we also include the squared series volsq in our model. TED spread (in %): The TED spread (ted) serves as a control variable in our funding illiquidity model. The TED spread is the difference in yields between three-month Eurodollar deposits (effectively LIBOR) and three-month US T-bills. Thus it represents the risk premium charged on 17

18 TED Spread (%) Figure 6: TED spread as an indicator for stabilizing and destabilizing funding liquidity cycles March 1998-December The lower dashed line marks a TED spread of 50 bp; the upper dashed line marks a TED spread of 80bp. Above these levels, market participants and policy makers actions (respectively) destabilize market liquidity. top-rated interbank loans versus risk-free loans to the US government. Historically, market observers have focused on the TED spread (Kawaller and Koch, 1992; Brunnermeier, 2009). Since both T-bills and Eurodollar futures are highly liquid and liquidity effects are pronounced at longer maturities, we believe the TED spread to be largely a measure of credit risk. Indeed, the TED spread is now generally used as an indicator of perceived credit risk in the economy. We use the TED spread as a state variable to help distinguish between stabilizing and destabilizing regimes in the Brunnermeier and Pedersen model. Figure 6 displays the TED spread series over the sample period with noticeable spikes for the crash of Long-Term Capital Management in 1998 and the recent credit crisis. The dashed lines mark the levels at which central bankers (80 bp) and market participants (50 bp) actions suggest they perceive a crisis. 6 6 These threshold estimates are obtained through a two-regime, two-stage least squares estimation procedure detailed in Section 4.1 and are statistically significant at the 95% level. 18

19 3.2 Instruments The seminal models of Gromb and Vayanos (2002), Gromb and Vayanos (2010) and Brunnermeier and Pedersen (2009) illustrate the presence of a feedback effect between market illiquidity and funding illiquidity. This requires that our estimation handles such a simultaneous relationship. A possible remedy lies in using instrumental variables. These variables should have a high correlation with market liquidity and zero correlation with the error in predicting funding liquidity using market liquidity and the control variables listed above. While little research eists on the determinants of funding liquidity, much more work has been done on market liquidity. This allows us to identify several natural instruments that isolate eogenous variation in the bid-ask spreads. Since asset market volatility is an important control variable in all our regressions, we account for the possibility that funding liquidity could feed back into asset market volatility by completing our set of instruments with lagged volatility terms. Hence, we obtain (at least) eactly identified models. Such lagged volatility measures have previously served as internal instruments for stock volatility in Bloom et al. (2007). Tick size dummy. Harris (1994) shows that a market s tick size is a determinant of the bid-ask spread. This is clear from Figure 3 where we observe a drop in bid-ask spreads in early 2001 due to the decimalization of prices on the NYSE and Nasdaq. The NYSE completed its move to decimal pricing on 29 January 2001 (Portniaguina, Bernhardt, and Hughson, 2006) which lowered the tick size from eighths and siteenths to pennies.the Nasdaq began its decimal test phase on March 12, 2001 and completed it on April 9, 2001 (Chung, Van Ness, and Van Ness, 2004). We intuit that the tick size should have little impact on funding liquidity. Therefore, an indicator variable (decdummy) for the post-29 January 2001 period is our first instrumental variable. Trend in inter-trade duration. We use the trend in the average time between trades on the Nasdaq as a second instrument. It is well known that there is a strong correlation between trading activity and market liquidity, see e.g. George and Longstaff (1993) and Chordia et al. (2001). Unfortunately, NYSE trade counts are not directly available, but for the purpose of constructing 19

20 Duration and TrendDuration Figure 7: Duration between US stock trades and its long-term trend March December The gray line shows the inter-trade duration; the black line shows the trend before and after the NYSE tick-size change in January an instrument, it suffices to proy the trading activity on the S&P 500 stocks by the monthly average time between trades (epressed in years) on the Nasdaq. 7 The time series of duration is plotted in Figure 7. It has two components: a long term trend, driven by eogenous technological innovation, and stationary deviations from that trend. 8 Because the latter may be correlated with changes in funding illiquidity, we only use the trend in duration as an instrument given. To etract the trend, we regress duration on the tick size dummy and a pre- and post-tick size change linear and quadratic trends. These deterministic variables were shown by Chordia et al. (2005) to be significant determinants of market liquidity as measured by the quoted spreads on NYSE stocks. The bold black line (durtrend) in Figure 7 is thus our second instrument. Change in AAA corporate bond yields versus LIBOR. We use the change in yields for shortterm (1-year or less) AAA-rated corporate bonds versus the change in three-month USD LIBOR as our third instrument. Since both are AAA-rated credits, this should control for fied-income 7 The monthly Nasdaq trade count can be retrieved from MonthlyMarketSummary. We measure the time between trades in years assuming 390 trading minutes per day and 252 trading days in a year. 8 The Augmented Dickey Fuller test with intercept and trend in the testing regression and lags selected by means of the AIC criterion rejects the presence of a unit root in the daily fundilliq, mktilliq, vol, volsq and ted series and the monthly duration series at a 95% confidence interval. 20

21 !AAA Corp Bond Yield!LIBOR Figure 8: Difference between changes in short-term AAA corporate bond yields and changes in LIBOR March December This difference captures bond market liquidity unrelated to credit issues. market liquidity effects (apart from credit effects) in market liquidity. If an investor is worried about upcoming liquidity needs, he might prefer to invest in a short-term corporate bond for which there is a secondary market than lend to a bank (locking up his money for 3 months). Thus we think this instrument (aaaliq) detects liquidity-driven action within the bond market, eogenous to variations in credit risk that would be reflected in collateralized funding rates. Such spreads have been used for similar purposes by Chen et al. (2005) and Almeida and Philippon (2007). The instrument is computed using the Bloomberg AAA corporate bond yield inde (C0011Y) and is shown in Figure LIBOR concerns Two of our variables, the TED spread and the change in short-term AAA corporate bond yields versus LIBOR depend on the LIBOR rate. Mollencamp and Whitehouse (2008) provides evidence that London banks have been manipulating the submissions which help determine LIBOR and Keenan (2012) gives anecdotal evidence of this happening as far back as For several reasons, we suspect that this does not greatly affect our analysis. First, initial indications are that the 21

22 sizes of the manipulations are on the order of a few basis points economically significant for the interest-rate swaps markets, but not compared to the thresholds we estimate. Second, these manipulations were not always of the same direction; therefore, we would epect the manipulations to add noise to LIBOR and our analysis. If anything, this would make our results appear weaker than they are. 3.4 Summary statistics We look at daily data from two sample periods corresponding to the data available for our two measures of funding liquidity. One sample period is March 1998 February 2008 for the central-bankbased measure (fundilliq C ); the other period is July 2006 December 2011 for the market-derived measure (fundilliq M ). Table 1 presents summary statistics for the si non-indicator variables. The statistics are presented for the full sample and subsamples for when the TED spread is below or above a threshold value; about 80 basis points for fundilliq C and about 50 basis points for fundilliq M. We observe that the transition from a tranquil (low or moderate TED spreads) to a jittery regime (etreme high TED spreads) is characterized by an overall increase in funding and market illiquidity as well as in volatility. These increases are both economically and statistically significant. Formally, the χ 2 test of median equality and the t-test of mean equality indicate that the median and mean of f undilliq, mktilliq, vol and ted are significantly different between the two regimes at a 99% confidence level. 4 Empirical analysis 4.1 Methodology A simple approach to analyze the relation between funding and market illiquidity is to estimate an Ordinary Least Squares model of funding illiquidity versus market illiquidity and the eplanatory 22

23 Table 1: Summary statistics of data used with the two funding liquidity measures. Key: The top subtable is for the central-bank-based measure, ecess broker loan rate, for March 1998 February 2008; the bottom subtable is for the market-derived measure, based on average stock loan rates attributable to demand shifts for shorting stock, for July 2006 December Both tables show covariates (funding and market illiquidity, volatility, TED spread) and instruments (inter-trade duration trend, change in yield spread of AAA corporates over LIBOR). The yield spread is in percent ( 0.5 = 0.5%); duration trend is in thousandths of years ( 1 = years). The omitted tick-size-change instrument is 0 before full decimalization (29 Jan 2001) and 1 otherwise. The χ 2 test of median equality and the t-test of mean equality indicate that the median and mean of fundilliq, mktilliq, vol and ted are significantly different between the two regimes at a 99% confidence level. Summary Statistics Mar 1998 Feb 2008 Full sample TED spread 77 bp TED spread > 77 bp (2445 obs) ( 2034 obs) ( 411 obs) med mean min med mean ma min med mean ma fundilliq C mktilliq vol ted durtrend aaaliq Jul 2006 Dec 2011 Full sample TED spread 54 bp TED spread > 54 bp (1263 obs) (756 obs) (507 obs) med mean min med mean ma min med mean ma fundilliq M mktilliq vol ted durtrend aaaliq variables: fundilliq t = β 0 + β 1 mktilliq t + β 2 vol t + β 3 volsq t + β 4 ted t + ε t. (3) This approach is followed by Drehmann and Nikolaou (2010) in a reduced form univariate setting. Our descriptive analysis of the funding and market liquidity proies, however, indicates that two 23

24 corrections are needed to properly decipher the connection between market and funding illiquidity. First, consistent with the evidence in Table 1 and Figure 4 and in line with Balke (2000), we allow for a regime change if credit conditions cross a critical threshold. We implement this idea with an indicator variable stress t (κ) that equals 1 when the TED spread on day t eceeds a threshold value κ and is zero otherwise. This variable represents the transition from a stable to a distressed market regime. Using this variable, we define the following two-regime regression model and estimate it naively by least squares fundilliq t = β 0 + β 1 mktilliq t + β 2 vol t + β 3 volsq t + β 4 ted t + β 5 stressmktilliq t + β 6 stressvol t + β 7 stressted t + ε t (4) where stressmktilliq t = mktilliq t stress t (κ), stressvol t = vol t stress t (κ), and stressted t = ted t stress t (κ). 9 Net, because of the endogeneity between f undilliq and the eplanatory variables mktilliq, vol, stressmktilliq and stressvol, we introduce an instrumental variables estimation. This yields the following set of first-stage equations mktilliq t = α 0 + α 1 ted t + α 2 stressted t + α 3 decdummy t + α 4 durtrend t + α 5 aaaliq t + α 6 vol t 1 + α 7 volsq t 1 + α 8 stressvol t 1 + η t, (5) vol t = γ 0 + γ 1 ted t + γ 2 stressted t + γ 3 decdummy t + γ 4 durtrend t + γ 5 aaaliq t + γ 6 vol t 1 + γ 7 volsq t 1 + γ 8 stressvol t 1 + ξ t, (6) 9 By not interacting volsq t with stress t, Equation (4) imposes a linear relationship between volatility and funding illiquidity when credit risk is high. Adding this interaction term would require adding a further instrument to the eisting set of instruments, for eample stressvolsq t 1, in order to obtain eact identification. This eacerbates the problem of multicollinearity among the stress-variables, to the etent that the standard errors on the estimated coefficients increase substantially. Nevertheless, our threshold estimates ˆκ are robust to the inclusion of stress t volsq t in the model. 24

25 volsq t = δ 0 + δ 1 ted t + δ 2 stressted t + δ 3 decdummy t + δ 4 durtrend t + δ 5 aaaliq t + δ 6 vol t 1 + δ 7 volsq t 1 + δ 8 stressvol t 1 + ζ t, (7) stressmktilliq t = α s 0 + α s 1ted t + α s 2stressted t + α s 3decdummy t + α s 4durtrend t + α s 5aaaliq t + α s 6vol t 1 + α s 7volsq t 1 + α s 8stressvol t 1 + η s t, (8) stressvol t = γ s 0 + γ s 1ted t + γ s 2stressted t + γ s 3decdummy t + γ s 4durtrend t + γ s 5aaaliq t + γ s 6vol t 1 + γ s 7volsq t 1 + γ s 8stressvol t 1 + ξ s t. (9) We then re-estimate the benchmark linear model (3) and the two-regime model (4) by instrumental variables, using the tick size change dummy, trend in trade duration, change in short-term AAA corporate bond yields vs. LIBOR, lagged volatility, lagged squared volatility and the lagged interaction between volatility and stressed market conditions, as instruments for mktilliq, vol, volsq, stressmktilliq and stressvol. 10 Thus we obtain four estimation approaches to relating market and funding liquidity: (i) the linear model in Equation (3) estimated by Ordinary Least Squares (OLS); (ii) the linear model in Equation (3) fit by Instrumental Variables (IV) estimation; (iii) the two-regime specification in Equation (4) estimated by OLS, and finally; (iv) the two-regime specification in Equation (4) by IV estimation. Regardless of whether we are estimating two-regime specification in Equation (4) by OLS or IV, the threshold ˆκ (and its confidence interval) is always estimated by the methods of Hansen (2000) and Caner and Hansen (2004). The threshold estimate is asymptotically consistent but non-normally 10 This leads to an eactly identified model in the case of fundilliq M, for which the available sample period (July December 2011) ecludes the decimalization date of the NYSE, and the etra instrument decdummy is thus unavailable. In the case when fundilliq C proies for funding illiquidity, the sample period under consideration does include the NYSE decimalization date. Hence, a total of 8 instruments for 7 eplanatory variables are then available. 25