The Shadow Price of Intermediary Constraints

The Shadow Price of Intermediary Constraints Chris Anderson and Weiling Liu∗ November 2, 2018 JOB MARKET PAPER Click here for most recent version Abstract Limits to the risk-taking activities of financial intermediaries are important for understanding market stability as well as asset prices, yet they remain difficult to pin down. We propose a novel measure of intermediary risk constraints called the interdealer broker (IDB) ratio, which is the percent of total trade volume conducted between dealers using an IDB. Theoretically, when aggregate risk constraints tighten, dealers will use IDBs more in order to redistribute idiosyncratic risk. Em- pirically, we test our measure in the U.S. Treasury market, where we find that the IDB ratio has a 0.72 correlation with interest rate risk, as proxied by Value-at- Risk. Furthermore, a one standard deviation increase in the IDB ratio forecasts a 1.8 percentage point higher annual excess return on a five-year bond. This return predictability holds across different fixed income classes, over varying maturities, as well as out-of-sample. ∗Weiling Liu (Job Market Paper) can be reached at [email protected] and Chris Anderson at chan- [email protected]. Harvard University. For helpful feedback we thank Malcolm Baker, John Campbell, Lauren Cohen, Richard Crump, Matteo Maggiori, Chris Malloy, Michael Fleming, Robin Greenwood, Sam Hanson, Derek Kaufman, Frank Keane, David Lucca, Or Shachar, Jeremy Stein, Adi Sunderam, Jonathan Wright, Zack Yan, as well as the participants in the HBS Finance Lunch Seminar, the LBS Transatlantic Student Conference, and the Federal Reserve Bank of New York's Research and Markets Group Seminars. 1 1 Introduction The financial crisis in 2008 demonstrated how limits to the risk-taking activities of financial intermediaries impact market stability as well as change real economic outcomes. It also sparked the intermediary asset pricing literature, in which the risk constraints of large intermediaries explain asset prices (Adrian et al., 2014; He and Krishnamurthy, 2013). These constraints may come from a number of sources, including internal risk tar- gets, limited funding capital, or external regulatory pressures. Today, a crucial question remains: how do we measure intermediary risk constraints? The risk-taking activities of large financial intermediaries are difficult to pin down, because their balance sheets are both expansive and complicated. For instance, the broker-dealers, which are financial firms that trade securities for their own accounts as well as for their clients, have strong incentives to veil their positions. Directly measuring dealers' risk exposure can be a Herculean task. In this paper, we take a novel approach and instead infer dealers' risk exposure from their trading behavior, following the principle of revealed preference. In doing so, we propose a novel measure of risk exposure relative to constraints called the interdealer broker (IDB) ratio. The IDB ratio captures the percent of total dealer trading volume that is conducted between dealers using an interdealer broker. While there are some existing proxies for intermediary risk-taking, they are either noisy or potentially biased. For example, Value-at-Risk (VaR) is an estimate of the maximum potential loss on a portfolio, which many dealers use to manage risk. However, VaR is released publicly by only a small number of firms; available for a short time period; and usually supplemented by other stress tests, which are non-public. Another popular proxy is leverage, which measures the ratio of a firm’s debts to its assets. Yet, in practice, broker-dealer leverage is roughly measured, captured only once a quarter, and released with a lag. To our knowledge, none of the empirical proxies show the tightness of dealer risk constraints, which is only internally observed. 2 The IDB ratio circumvents many of the issues with existing measures, because it does not rely on accurate nor complete disclosure of complicated holdings, and it can be constructed from high-frequency trading volumes. Furthermore, in the U.S. bond market, which is one of the largest and most liquid markets in the world, these trading volumes are consistently reported by a group of the largest intermediaries: the primary dealers. Perhaps most importantly, the IDB ratio tracks the tightness of dealer risk constraints, a theoretically important quantity which is almost never directly reported. Intuitively, in periods where risk constraints are binding, dealers are less likely to fulfill customer orders directly from their own balance sheets. Instead, they are more likely to resell parts of the order to other dealers, redistributing risk throughout the system. In order to transact with other dealers anonymously and without incurring high transaction costs, the dealers use the interdealer brokers (IDBs). We summarize this intuition using a stylized model of dealer trade and risk-sharing, making two central predictions. First, periods of higher risk exposures and tighter risk constraints are also periods with higher IDB ratios. Second, in settings like the U.S. bond market where dealers are net long holders of the risky asset, expected returns should be higher in order to compensate dealers for bearing risk. Empirically, we test our predictions in the U.S. Treasury market, where the primary dealers serve as the dominant intermediaries. This is an ideal setting because Treasury bonds are: (1) issued in standard maturities and at predictable intervals (2) uniform in terms of credit risk (3) important assets, serving as a global risk-free benchmark as well as a key indicator of macroeconomic conditions (4) traded by the primary dealers, who consistently report their trade activity. Supportive of our first prediction, we find that the IDB ratio rises when they bear more interest rate risk, as measured by interest rate Value-at-Risk. The correlation between the IDB ratio and interest rate VaR is positive and strong: 0.72 in levels and 0.58 in one-year changes. Consistent with our second prediction, we find that that the IDB ratio significantly forecasts future returns. A one standard deviation increase in the IDB ratio predicts a 3 1.8% higher annual excess return on a five-year Treasury bond. The return predictability of the IDB ratio holds across a range of different maturities, is not spanned by the forward rates, persists after controlling for macroeconomic conditions, and performs well out-of-sample. We provide additional evidence supporting our theory using U.S. Treasury auctions as well as the cross-section of primary dealers. In our proposed model, the IDB ratio is higher when dealers face positive inventory shocks that push them closer to risk constraints. U.S. Treasury auctions provide a set of natural experiments in which dealers face significant inventory shocks, because the primary dealers are required to bid competitively, but the amount that they receive is determined by the strength of other bids. We find that when the primary dealers unexpectedly receive a larger portion of the Treasury auction, the contemporaneous IDB ratio increases. In our model, we predict that dealers who are closer to constraints are more likely to use the IDBs to offload risk. Using proprietary data, we then examine the IDB ratio across individual dealers. We find that the dealers who have the highest IDB ratios also have the highest risk exposures, and they are more likely to reduce risk exposure in the future. Dividing the dealers into two halves, we further compare the IDB ratios of larger, core dealers versus smaller, periphery dealers. We find that while all dealers rely on the IDBs in order to manage risk, the IDB ratio constructed from large dealers drives most of the return predictability. Finally, we examine whether IDB ratios created from different market segments pos- sess additional information. First, we look at IDB ratios created from bonds in different maturity buckets: one- to three-year Treasuries, three- to six-year Treasuries, and 11-30 year Treasuries. When we add these ratios to the aggregate IDB ratio in return-forecasting regressions, we find they can increase the R-squared almost five-fold| from 7% to 32% when forecasting two-year bond returns. Next, we study two additional markets in which primary dealers play a key role: non-mortgage agency securities and mortgage-backed securities (MBS). We find that the agency and MBS IDB ratios positively forecast annual 4 excess returns in their respective markets, even after controlling for contemporaneous Treasury returns. Combined, this evidence suggests that risk management is segmented, and IDB ratios from different markets add valuable information. In the remainder of Section 1, we discuss related literature and provide context for trading in the U.S. bond market. In Section 2, we outline a stylized model which shows how interdealer trade ratios can reveal dealer exposure in the presence of constraints. We calibrate the model and produce several testable predictions. Section 3 describes our data sources and time samples. Turning to empirical analysis, Section 4 presents our main findings that the IDB ratio is closely related to risk exposure and it robustly forecasts future returns. Section 5 provides supporting evidence from Treasury auctions as well as the cross-section of primary dealers. In Section 6, we examine IDB ratios created from different maturities and other fixed income markets, providing evidence that risk management is segmented. Finally, Section 7 concludes. 1.1 Related Literature Our work contributes to three main strands of research: intermediary asset pricing, forecasting bond returns, and the structure of bond markets. First, this paper most naturally relates to the literature on intermediary asset pricing. This literature is nascent but quickly growing, especially following the financial crisis. On the empirical side, Adrian et al. (2014) documents that innovations to a measure of broker-dealer book leverage can price the cross-section of asset returns.

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