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Rounding as Discrimination - Price Clustering in the OTC Tax-Exempt Bond Market

45 Pages Posted: 17 Mar 2007 Last revised: 23 Dec 2007

Dan Li

Federal Reserve Board

Date Written: November 28, 2007


I find that municipal bonds trade frequently at rounded prices. Over 13.6% of customer trades in the secondary market are at whole dollar prices. Prices also cluster at halves, quarters, eighths, tenths, etc. Rounding is more prominent in trades that are smaller in size and below par, and in bonds that have larger coupon, lower price volatility and higher trading frequency. All of these characterize bonds that have greater retail interest. Clustering is also prominent in bond yields and dealer's markup, which indicates that customers tend to accept prices without haggling.

To explain the pervasiveness and cross-sectional differences in rounding, I model the price formation process in a search-and-bargaining setting in which an informed dealer sells a bond to an uninformed customer. Both search and bargaining are costly. Dealer uses rounding to strategically signal his value and perturb the price. The model shows how dealer's choice of rounding level varies with trade size and buyer's search cost, bargaining cost and bargaining power. Empirically, I show that larger pricing grids are indeed associated with higher transaction cost. In fact, buying at whole dollars costs the customer 45 cents more, and selling at whole dollars costs 25 cents more per $100 par bond. Dealers earn 35% more if they round on both the buy and sell sides.

Keywords: Price Clustering, Yield Clustering, Markup Clustering, Dealer's Market Power, Bargaining, Price Resolution, Over-The-Counter Market, Municipal Bond

JEL Classification: D40, G14, G24

Suggested Citation

Li, Dan, Rounding as Discrimination - Price Clustering in the OTC Tax-Exempt Bond Market (November 28, 2007). AFA 2008 New Orleans Meetings Paper. Available at SSRN: or

Dan Li (Contact Author)

Federal Reserve Board ( email )

20th and C Streets, NW
Mail Stop 89
Washington, DC 20551
United States

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