A Search-Based Theory of the On-the-Run Phenomenon
Social Science Research Network
We propose a model in which assets with identical cash flows can trade at different prices. Agents enter into an infinite-horizon, steady-state market to establish long or short positions. Both the spot and the asset-lending market operate through search. Short-sellers can endogenously concentrate in one asset because of search externalities and the constraint that they must deliver the asset they borrowed. As a result, that asset enjoys both greater liquidity, measured by search times, and a
... gher lending fee ("specialness"). Liquidity and specialness translate into price premia that are consistent with no-arbitrage. We derive closed-form solutions for small frictions, and can generate price differentials in line with observed on-the-run premia. , and seminar participants at LSE, New Orleans, NY Fed, NYU, and Oxford for helpful comments. questionable given that government bonds are among the most liquid assets. On-the-run bonds are indeed very liquid, with many transactions being executed almost instantly. Transactions in off-the-run bonds, however, can take significantly more time. In particular, it can be difficult to locate a large quantity of a specific off-the-run issue. Thus, while an investor needing to buy the issue can easily contact a dealer, the dealer might not have the issue in inventory and could take time to locate it. Another illustration of search frictions is the phenomenon of "fails," whereby traders do not deliver a bond they have sold or borrowed by the time they must settle. One source of fails is the difficulty to locate the bond. 4 We consider an infinite-horizon, steady-state economy with two risky assets paying the same cash flow. Trade occurs because agents experience hedging needs to hold long or short positions. Upon experiencing a need to hold a long position, an agent enters the market seeking to buy one of the assets. He then holds the asset until the hedging need disappears, and then seeks to sell. During the time he is holding the asset, he can lend it to a short-seller for a fee. This corresponds to a repo transaction in our model, and the fee to repo specialness. 5 Conversely, upon experiencing a need to hold a short position, an agent enters the market seeking to borrow one of the assets. She then seeks to sell the asset, and when the hedging need disappears, she seeks to buy the same asset back and return it to the lender. Both the spot and the repo market operate through search and bilateral bargaining. For simplicity, we abstract away from dealers and adopt the standard search framework (e.g., Diamond  ) where agents search for counterparties directly. 6 Our model has multiple equilibria: a symmetric one where short-sellers borrow both assets, and asymmetric ones where they concentrate in one asset, declining any opportunities to borrow the other. This is because of search externalities. The more agents short an asset, the greater the asset's seller pool becomes. The asset's buyer pool also increases because of the short-sellers who need to buy the asset back. A larger buyer and seller pool implies lower search times, and the enhanced liquidity attracts more short-sellers. Thus, our theory can explain differences in liquidity between otherwise identical assets, consistent with the on-the-run phenomenon. While the general notion of search externalities is well-understood, its application to the onthe-run phenomenon is subtle. Absent the short-sellers, there would be no differences in liquidity. phenomenon, they propose a search-based model. 4 Fleming and Garbade  report that fails in the US market averaged $7.3 billion per day during the first eight months of 2001. For comparison, the daily volume during that period was about $250 billion (Fleming  ). 5 We describe repo transactions at the beginning of Section 4. See also Duffie  and Fisher , among others, for more detailed descriptions. 6 Of course, the search framework is only an idealization of price formation in actual bond markets -but so is the Walrasian auction. We expand on this point and provide further arguments in support of the search framework in Section 4.1.