Crashes and Collateralized Lending

This paper develops a parsimonious static model for characterizing financing terms in collateralized lending markets. We characterize the systematic risk exposures for a variety of securities and develop a simple indifference-pricing framework to value the systematic crash risk exposure of the collateral. We then apply Modigliani and Miller’s (1958) Proposition Two (MM) to split the cost of bearing this risk between the borrower and lender, resulting in a schedule of haircuts and financing rates. The model produces comparative statics and time-series dynamics that are consistent with the empirical features of repo market data, including the dramatic change in financing terms for structured products during the credit crisis of 2007-2008. First draft: April 2010 This draft: April 2011 ∗Jurek: Bendheim Center for Finance, Princeton University; [email protected]. Stafford: Harvard Business School; [email protected]. We thank Joshua Coval, Victoria Ivashina, David Sraer, Chris Rogers, Andrei Shleifer, and seminar participants at EPF Lausanne, MIT Sloan, Northwestern Kellogg, Princeton University, the University of Oregon, the Spring 2011 NBER Corporate Finance Meeting and the 6th Princeton-Cambridge Exchange Workshop for helpful comments and discussions. An important service provided by financial intermediaries in the support of capital market transactions is the financing of security purchases by investors. Investors can buy securities with margin, whereby they contribute a portion of the purchase price and borrow the remainder from the intermediary in the form of a collateralized, non-recourse short-term loan. The risk of the loan depends crucially on three factors: (1) the distribution of economic states; (2) the state-contingent outcomes for the collateral value at loan maturity; and (3) the collateral haircut (or margin) between the market value of collateral and the loan amount. The framework we propose isolates the systematic crash risk exposure of different collateral types (equities, corporate bonds, and CDO tranches), and provides a simple mechanism for allocating the cost of bearing this risk between a financing intermediary (lender) and investor (borrower), resulting in a schedule of haircuts and financing rates. A typical loan is collateralized by the underlying security and protected by the borrower’s capital contribution – the collateral haircut, or margin. The haircut protects the lender from changes in the liquidation value of the collateral. Although the liquidation value of an individual security can be affected by myriad market frictions on a day-to-day basis, our focus is on the effect of large market declines (crashes). This approach is motivated by the notion that the intermediaries who provide financing are likely to be well-diversified and have access to relatively efficient hedging strategies enabling them to eliminate the effect of small (diffusive) market moves on collateral values. As such, our framework assumes borrowers post haircuts to immunize lenders against extreme systematic price shocks, or market crashes. This systematic credit risk channel has not been explored in the banking literature, despite the growing role of collateralized lending (e.g. repo market) in the economy, and the widespread interest in ensuring collateral robustness in adverse economic states. A pervasive feature of capital markets is that extreme price drops – measured relative to recent return volatility – occur with some regularity. Using daily value-weighted US stock market returns from 1926 through 2009, scaled by their lagged standard deviation to construct a time series of Z-scores, we find that observations less than -6 occur every 5 years, on average. These are the economically significant events that collateral haircuts must cover in order for the intermediary to be protected from bearing losses on its loan, and the component of the cost of capital that we investigate. Unlike most papers in the banking and collateralized lending literature, we specialize to the case where there are no information asymmetries, agency concerns, differences in preferences or beliefs, or other frictions.1 Formally, we assume that the intermediary (lender) is wholly owned by the investor Some prominent, early papers examining the effect of frictions include: Diamond and Dybvig (1983), Shleifer and Vishny (1992), Holmström and Tirole (1997), Bernanke, Gertler, Gilchrist (1996, 1999), Kiyotaki and Moore (1997). Geanakoplos (1997, 2003) emphasizes the endogeneity of haircuts and their sensitivity to perceptions of default. Gennaioli, et al. (2010) present a model of financial innovation based on biased investor beliefs.