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Contents : Intermediary Asset Pricing By Zhiguo He and Arvind Krishnamurthy We model the dynamics of risk premia during crises in asset markets where the marginal investor is a financial intermediary. Intermediaries face an equity capital constraint. Risk premia rise when the constraint binds reflecting the capital scarcity. The calibrated model matches the nonlinearity of risk premia during crises and the speed of reversion in risk premia from a crisis back to precrisis levels. We evaluate the effect of three government policies: reducing intermediaries borrowing costs injecting equity capital and purchasing distressed assets. Injecting equity capital is particularly effective because it alleviates the equity capital constraint that drives the model's crisis. JEL: G12 G2 E44 The performance of many asset markets e.g. prices of mortgage-backed securities corporate bonds etc. depend on the financial health of the intermediary sector broadly defined to include traditional commercial banks as well as investment banks and hedge funds. The 2007-2009 subprime crisis and the 1998 hedge fund crisis are two compelling data points in support of this claim.1 However traditional approaches to asset pricing ignore intermediation by invoking the assumption that intermediaries' actions reflect the preferences of their clientinvestors. With this assumption the traditional approach treats intermediaries as a "veil " and instead posits that a representative household is marginal in pricing all assets. Thus the pricing kernel for the S&P500 stock index is the same as the pricing kernel for mortgage-backed securities. Yet many crises such as the subprime crisis and the 1998 episode play out primarily in the more complex securities that are the province of the intermediary sector. The traditional approach cannot speak to this relationship between financial intermediaries and Respectively: University of Chicago Booth School of Business and NBER 5807 South Woodlawn Avenue Chicago IL 60637 zhiguo-he@chicagobooth.edu Northwestern University Kellogg School of Management and NBER 2001 Sheridan Road Evanston IL 60208 a-krishnamurthy@northwestern.edu. We thank Patrick Bolton Markus Brunnermeier Doug Diamond Andrea Eisfeldt Vadim Linetsky Mark Loewenstein Pablo Kurlat Tyler Muir Amir Sufi Annette Vissing-Jorgensen Neng Wang Hongjun Yan and seminar participants at UC-Berkeley Boston University UCSB-LAEF conference University of Chicago Columbia University ESSFM Gerzensee FDIC University of Maryland NBER Asset Pricing NBER Monetary Economics NBER EFG NY Fed SF Fed and Yale for their comments. We also thank an anonymous referee for advice. 1 There is a growing body of empirical evidence documenting the effects of intermediation constraints (such as capital or collateral constraints) on asset prices. These studies include research on mortgagebacked securities (Gabaix Krishnamurthy and Vigneron 2005) corporate bonds (Collin-Dufresne Goldstein and Martin 2001) default swaps (Berndt et. al. 2004) catastrophe insurance (Froot and O'Connell 1999) and index options (Bates 2003 Garleanu Pedersen and Poteshman 2005). Adrian Etula and Muir (2010) show that an intermediary pricing kernel based on intermediary balance sheet information can explain the cross-section of asset returns. 1 2 THE AMERICAN ECONOMIC REVIEW AUGUST 2012 asset prices. It sheds no light on why "intermediary capital" is important for asset market equilibrium. It also does not allow for a meaningful analysis of the policy actions such as increasing intermediaries' equity capital or discount window lending which are commonly considered during crises. We offer a framework to address these issues. We develop a model in which the intermediary sector is not a veil and in which its capital plays an important role in determining asset market equilibrium. We calibrate the model to data on the intermediation sector and show that the model performs well in replicating asset market behavior during crises. The striking feature of financial crises is the sudden and dramatic increase of risk premia. For example in the hedge fund crisis of the fall of 1998 many credit spreads and mortgage-backed security spreads doubled from their pre-crisis levels. Our baseline calibration can replicate this dramatic behavior. When intermediary capital is low losses within the intermediary sector have significant effects on risk premia. However when capital is high losses have little to no effect on risk premia. The asymmetry in our model captures the non-linearity that is present in asset market crises. Simulating the model we find that the average risk premium when intermediaries' capital constraint is slack is abiyt 3%. Using this number to reflect a pre-crisis normal level we find that the probability of the risk premium exceeding 6% which is about twice the "normal" level is 1.33%. Another important feature of financial crises is the pattern of recovery of spreads. In the 1998 crisis most spreads took about 10 months to halve from their crisis-peak levels to pre-crisis levels. In the subprime crisis the half-life of most bond market spreads was about 6 months. As we discuss later in the paper half-lives for recovery of between 6 months and extending over a year have been documented in a variety of asset markets and crisis situations. We note that these types of recovery patterns are an order of magnitude slower than the daily mean reversion patterns documented in the market microstructure literature (e.g. Campbell Grossman and Wang 1993). A common wisdom among many observers is that this recovery reflects the slow movement of capital into the affected markets (Froot and O'Connell 1999 Berndt et. al. 2004 Mitchell Pedersen and Pulvino 2007 Duffie and Strulovici 2010). Our baseline calibration of the model can replicate these speeds of capital movement. We show that simulating the model starting from an extreme crisis state (risk premium of 12%) the half-life of the risk premium back to the unconditional average risk premium is 8 months. From a risk premium of 10% the half-life is 11 months. We also use the model as a laboratory to quantitatively evaluate government policies. Beginning from an extreme crisis state with risk premium of 12% we trace the crisis recovery path conditional on three government policies: (1) Infusing equity capital into the intermediaries during a crisis (2) Lowering borrowing rates to the intermediary as with a decrease in the central bank's discount rate and (3) Direct purchase of the risky asset by the government financed by debt issuance and taxation of households. These three policies are chosen because they VOL. XX NO. XX INTERMEDIARY ASSET PRICING 3 are among those undertaken by central banks in practice. In comparing $205bn of equity infusion to $1.8tn of risky asset purchase we find that the equity infusion is far more effective in reducing the risk premium. This occurs in our model because the friction in the model is an equity capital constraint. Thus infusing equity capital attacks the problem at its heart. We find that the interest rate policy is also highly effective uniformly increasing the speed of crisis recovery. This policy is effective because the financial intermediary sector carries high leverage and reducing their borrowing rates translates to a large subsidy to the intermediary sector. The contribution of our paper is to work out an equilibrium model of intermediation that is dynamic parsimonious and can be realistically calibrated. The paper is related to a large literature in banking studying disintermediation and crises (see Diamond and Dybvig (1983) Holmstrom and Tirole (1997) and Diamond and Rajan (2005)). We differ from this literature in that our model is dynamic while much of this literature is static. The paper is also related to the literature in macroeconomics studying effects of collateral fluctuations on aggregate activity (Kiyotaki and Moore (1997)). In much of the macro literature equilibrium is derived by log-linearizing around the steady-state. As a result there is almost no variation in equilibrium risk premia which does not allow the models to speak to the behavior of risk premia in crises. We solve a fully stochastic model that better explains how risk premia vary as a function of intermediary capital. In Bernanke and Gertler (1989) credit spreads are linked to the net worth of the entrepreneurial sector. However the action in credit spreads is due to default risk and bankruptcy costs rather than due to changes in economic risk premia. Brunnermeier and Sannikov (2010) is another recent paper that develops a macroeconomic model that is fully stochastic and links intermediaries' financing position to risk premia. Our paper is also related to the literature on limits to arbitrage studying how impediments to arbitrageurs' trading strategies may affect equilibrium asset prices (Shleifer and Vishny (1997)). One part of this literature explores the effects of margin or debt constraints for asset prices and liquidity in dynamic models (see Aiyagari and Gertler (1999) Gromb and Vayanos (2002) Geanokoplos and Fostel (2008) Adrian and Shin (2010) and Brunnermeier and Pedersen (2008)). Our paper shares many objectives and features of these models. The principal difference is that we study a constraint on raising equity capital while these papers study a constraint on raising debt financing. Xiong (2001) and Kyle and Xiong (2001) model the effect of arbitrageur capital on asset prices by studying an arbitrageur whose risk aversion varies based on a wealth effect arising from log preferences. The effects that arise in our model are qualitatively similar to these papers. An advantage of our paper is that intermediaries and their equity capital are explictly modeled allowing our paper to better articulate the role of intermediaries in crises.2 Finally many of our asset pricing results 2 The paper is also related to Vayanos (2005) who studies the effect of an open-ending friction on asset-demand by intermediaries. We study a capital constraint rather than an open-ending friction. 4 THE AMERICAN ECONOMIC REVIEW AUGUST 2012 come from assuming that some markets are segmented and that households can only trade in these markets by accessing intermediaries. Our paper is related to the literature on asset pricing with segmented markets (see Basak and Cuoco 1998 Alvarez Atkeson and Kehoe 2002 and Edmond and Weill 2009).3 Our paper is closely related to a companion paper He and Krishnamurthy (2011). We solve for the optimal intermediation contract in that paper while we assume the (same) form of contract in the current analysis. That paper also solves for the equilibrium asset prices in closed form while we rely on numerical solutions in the present paper. On the other hand that paper has a degenerate steady state distribution which does not allow for a meaningful simulation or the other quantitative exercises that we perform in the present paper. In addition the present paper models households with labor income and an intermediation sector which always carries some leverage. Both aspects are important in realistically calibrating the model. Apart from these differences the analysis in He and Krishnamurthy (2011) provides theoretical underpinnings for some of the assumptions we make in this paper. The paper is organized as follows. Sections I and II outline the model and its solution. Section III explains how we calibrate the model. Section IV presents the results of the crisis calibration. Section V studies policy actions. Section VI concludes followed by a short mathematical appendix. An online appendix provides further details of the model solution. I. The Model: Intermediation and Asset Prices Figure 1 lays out the building blocks of our model. There is a risky asset that represents complex assets where investment requires some sophistication. In our calibration we match the risky asset to the market for mortgage-backed securities as a representative large asset class that fits this description. Investment in the mortgage-backed securities market is dominated by financial institutions rather than households and sophisticated prepayment modeling is an important part of the investment strategy. The calibration is also appropriate for analyzing the financial crisis that began in 2007 where mortgage-backed securities have a prominent role. There are two groups of agents in the economy households and specialists. We assume that households cannot invest directly in the risky asset market. There is limited market participation as in Mankiw and Zeldes (1991) Basak and Cuoco (1998) or Vissing-Jorgensen (2002). Specialists have the knowledge to invest in the risky assets and unlike in the limited market participation literature the specialists can invest in the risky asset on behalf of the households. This investment conduit is the intermediary of our model. In our model the households demand intermediation services while the specialists supply these services. We 3 Our model is also related to the asset pricing literature with heterogenous agents (see Dumas (1989) and Wang (1996)). VOL. XX NO. XX INTERMEDIARY ASSET PRICING 5 RISKY ASSET MARKET Ht EQUITY HOUSEHOLDS SPECIALISTS/ INTERMEDIARIES RISKLESS ASSET MARKET Figure 1. Agents in the economy and their investment opportunities. are centrally interested in describing how this intermediation relationship affects and is affected by the market equilibrium for the "intermediated" risky asset. We assume that if the household does not invest in the intermediary it can only invest in a riskless short-term bond. This is clearly counterfactual (i.e. households invest in the S&P 500 index) but simplifies the analysis considerably. Households thus face a portfolio choice decision of allocating funds between purchasing equity in the intermediaries and the riskless bond. The intermediaries accept Ht of the household funds and then allocate their total funds under management between the risky asset and the riskless bond. We elaborate on each of the elements of the model in the next sections. A. Assets The assets are modeled as in the Lucas (1978) tree economy. The economy is infinite-horizon continuous-time and has a single perishable consumption good which we will use as the numeraire. We normalize the total supply of intermediated risky assets to be one unit. The riskless bond is in zero net supply and can be invested in by both households and specialists. The risky asset pays a dividend of Dt per unit time where Dt follows a geometric Brownian motion (GBM) (1) dDt gdt + dZt Dt given D0 . g 0 and 0 are constants. Throughout this paper Zt is a standard Brownian motion on a complete probability space ( F P ). We denote the processes Pt and rt as the risky asset price and interest rate processes respectively.

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