Security design without verifiable retention

Abstract

This paper studies security design with adverse selection when verifiable retention is impossible due to market segmentation and price opacity across market segments. Rather than signaling through retention, sellers in the model signal quality through posted prices, which is feasible because the posted price affects buyers' search behavior and the equilibrium probability of selling. The optimal security design, in this case, is to break up the cash flow of an asset into several debt securities of increasing seniority. The size of senior relative to subordinated debts is affected by the equilibrium markup. Search frictions, as determinants of the markup, shape the endogenous creation of financial securities.

Introduction

The literature on security design with adverse selection often focuses on verifiable retention and its signaling effect.² Specifically, it is often assumed that a seller can promise to retain a state-contingent cash flow of his asset (a residual tranche, hereafter), and, more importantly, the seller's promise of retention can be verified by buyers. Since sellers with a worse asset typically incur a larger cost to keep a residual tranche, the size and shape of the residual tranche can, therefore, be used by buyers to infer asset quality. What is less known in the literature is the alternative scenario where buyers cannot verify retention. This paper, by focusing on security design without verifiable retention, is a step to fill the gap.

The lack of verifiable retention is a plausible characterization of many financial markets, in particular, the market for residential mortgage-backed securities (RMBS) and collateralized debt obligations (CDO). While verifiable retention may be consistent with reality in the corporate debt business, the evidence does not support that sellers can commit to retaining residual tranches in RMBS or CDO sectors. The offering process of RMBS and CDO is distinct from the traditional corporate syndication process where securities are sold on a predetermined day. With RMBS and CDO, primary market trades can occur over time, so sellers can hardly assure early buyers that residual tranches will not be sold later. Selling residual tranches is also facilitated by the creation of bankruptcy-remote special purpose vehicles in securitization processes. In practice, numerous examples exist where residual tranches of RMBS or CDO were sold, mostly to hedge funds.³ Not only is the sale of residual tranches rampant, it is also hard to detect since buyers do not observe sellers' holdings of individual securities.⁴ These features of RMBS and CDO sectors support my assumption of no verifiable retention.

In my model, the lack of verifiability is a result of market segmentation and price opacity across segments, which allow a seller to market each security, including the residual tranche, to a segment of buyers without being detected by the rest. The introduction of price opacity is motivated by the fact that in RMBS and CDO sectors, price quotes are often communicated bilaterally rather than publicly. With bilateral communication, a seller does not have to truthfully report the price he posts to a segment of buyers (say, hedge funds interested in high-risk securities) to another segment of buyers (say, pension funds interested in low-risk securities).

This paper explores market segmentation in the context of competitive search. In my model, each seller has one of two assets that differ in cash flow distribution. From the cash flow of his asset, a seller can design (at most) M securities and a residual tranche of arbitrary (weakly increasing) shapes. Each security, including the residual tranche, can be presented to a segment of uninformed buyers along with an ultimatum price. Buyers decide whether to search and for which type of contract. The selling probability is determined by demand over supply (also known as market tightness) through a matching function: a larger demand per unit of supply implies a higher probability of selling.

Since buyers cannot verify retention, sellers in equilibrium always attempt to sell the residual tranche. Still, non-trading arises out of rationing. In equilibrium, the selling probability is affected by sellers' choice of securities and prices. For a given security, good sellers (sellers with a better asset) will post a higher price and trade with a lower probability vis-a-vis bad sellers. Intuitively, rationing has to be more severe when the posted price is higher so that bad sellers do not overprice their securities. Good sellers self-select into posting a higher price because holding the security is less costly to them. In this way, prices help sellers to signal quality even if signaling through retention is unavailable.

The equilibrium explored in the paper features a surprisingly rich security structure: a set of $(M+1)$ increasingly senior debt securities (“multitiered debts”). Each debt security is characterized by two (possibly degenerated) flat regions: the debt security pays zero when the cash flow is too low and a fixed amount when the cash flow is sufficiently high. Between the flat regions, payment from the debt increases 1-to-1 with the cash flow. (See Fig. 1 for an illustration when $M=2$.) The security structure predicted by my model is consistent with market reality: issuing multitiered debts is prevalent in RMBS and CDO sectors.

The reason for issuing multitiered debts can be better understood if we discretize the cash flow state into a set of N points, with $N\gg M$. We can split the cash flow into N increasingly senior debts that positively span the space of weakly increasing securities (“basis debts”). The security design problem boils down to sorting N basis debts into $M+1$ bundles. Sellers want to bundle basis debts with similar information sensitivity because doing so alleviates rationing. In general, bundling basis debts reduces trade because it makes signaling harder by forcing sellers to sell each component with the same probability. Bundling basis debts of similar information sensitivity minimizes the reduction in trade because the selling probabilities of these debts are similar in the first place. When cash flow distributions are hazard rate ordered, the information sensitivity of basis debts monotonically decreases with its seniority. Thus, basis debts with consecutive seniority are grouped together, which again forms a set of increasingly senior debt securities.

The paper also speaks to the endogenous creation of senior debt through tranching. In the model, a reduction of markup makes signaling informationally-sensitive securities relatively easier because it reduces bad sellers' incentive to imitate. Consequently, sellers facing a low-markup environment will move marginal cash flow from a senior debt to a subordinated debt, as the latter is now easier to sell. Through this channel, economic shocks and policies that change the equilibrium markup affect the composition and the quality of primary markets. For example, a decline in aggregate matching efficiency that lowers markup will reduce the size of senior debts and, at the same time, improve their quality.

The remainder of this paper proceeds as follows. Section 2 discusses the related literature. Section 3 develops a model of security design with adverse selection and market segmentation. Section 4 demonstrates that the issuance of multitiered debt securities arises endogenously in equilibrium. Section 5 analyzes the effect of markup and search frictions on optimal security design. Section 6 discusses price transparency and endogenous market segmentation. Section 7 concludes.