Bidding With Securities: Comment

Peter DeMarzo, Ilan Kremer and Andrzej Skrzypacz (2005, henceforth DKS) analyzed auctions in which bidders compete in securities. They show that a steeper security leads to a higher expected revenue for the seller, and also use this to establish the revenue ranking between standard auctions. In this comment, we obtain the opposite results to DKS’s by assuming that a higher return requires a higher investment cost. Given this latter assumption, steeper securities are more vulnerable to adverse selection, and may yield lower expected revenue, than flatter ones. Peter DeMarzo, Ilan Kremer and Andrzej Skrzypacz (2005, henceforth DKS) analyzed auctions in which bidders compete in securities, i.e., the winning bidder’s payment includes a share of cash flow or (ex-post) value generated from the auctioned object. With attention restricted to “feasible” securities, their main finding concerns the role of the “steepness” of securities in determining the seller’s revenue. They show that the steeper the payment to the seller as a function of the realized value, the higher is the seller’s expected revenue. A shift from a security, say a debt, to a steeper one, say equity or call option, “flattens” the surplus accruing to a bidder as a function of his future realized value, and this levels the competitive gaps between bidders. Hence, the competition becomes intensified. In this comment, we wish to add to DKS’ analysis a caveat — that the adverse selection problem should be an important part of security and auction design consideration. Unlike cash bids, security bids are difficult to evaluate when the seller does not know the buyer’s exact type. For instance, a 40% share of an asset managed by a buyer may be less valuable than a 30% share of the same asset managed by a different buyer, if the latter is much more competent. Lacking such information, a seller may fall victim to adverse selection, choosing a wrong bidder. This problem has been noted by several authors such as William Samuelson (1987), Simon Board (2007) and Charles Zheng (2001) in the context of a fixed security design. Our concern here is its relevance for security design: We show that the adverse selection problem may lead to the rankings of alternative security designs and auction formats that are quite different from, and in fact opposite to, those found in DKS. In particular, under a reasonable circumstance, a steeper security is more vulnerable to adverse selection, and could result in a poorer revenue performance, than a flatter security. To illustrate, suppose there are two buyers, 1 and 2. Buyer i = 1, 2 has a project which requires initial investment of xi and generates a (gross) return of xi + vi. Suppose v1 > v2 ≥ 0 and x1 > x2. That is, buyer 1’s project generates a higher return (so is efficient to select) but requires a higher investment than buyer 2’s project. This assumption is reasonable. A financially distressed or bankrupt firm will more likely turn profitable again under the management willing to infuse more cash, for instance. Or a firm that can generate a greater value from a under-performing target is more likely to have a higher opportunity cost (e.g., of pursuing other target) or stand-alone values. The assumption is equally compelling in other contexts, such as the government sale of oil leases. A security is feasible if the shares accruing to the payee and payer are both nondecreasing in the realized gross return. As DKS observe, all standard financial claims satisfy this monotonicity condition. This insight originates from Robert Hansen (1985) and is further developed by Matthew Rhodes-Kropf and S. Viswanathan (2000).