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We introduce and solve a new class of static portfolio choice problems, where only the best realized alternative matters. A decision maker must simultaneously choose among independent ranked options, and the better alternatives have a lower chance of panning out. Each choice is costly, and just one option may be exercised. This often emerges in practice: • A student must make a costly and simultaneous application to many colleges, and is accepted with smaller chances by the better schools. • An economics department must decide which of several PhD job candidates to fly out, and the better recruits will be available with smaller probability. We show that such portfolio choice problems quite generally entail maximizing a submodular function of finite sets - which is NP hard in general. Still, we develop a marginal improvement algorithm that produces the optimal set for our binary option structure in a quadratic number of steps. Applying it, we then show that the optimal choices are less risky than the sequentially optimal ones in Weitzman (1979), but riskier than the best singleton college choices. We also give practical rules of thumb, such as: (i) don't insure, choosing a safety school; instead, take risks - unless success rates are positively correlated; (ii) apply to an upwardly diverse portfolio of schools. We also provide comparative statics on the chosen set.

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Paper provided by Department of Economics, W. P. Carey School of Business, Arizona State University in its series Working Papers with number 2168591.

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Handle: RePEc:asu:wpaper:2168591

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  1. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
  2. Kenneth Burdett & Shouyong Shi & Randall Wright, 2001. "Pricing and Matching with Frictions," Journal of Political Economy, University of Chicago Press, vol. 109(5), pages 1060-1085, October.
  3. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  4. Albrecht, James & Gautier, Pieter & Vroman, Susan, 2003. "Equilibrium Directed Search with Multiple Applications," IZA Discussion Papers 719, Institute for the Study of Labor (IZA).
  5. Hector Chade & Lones Smith, 2006. "Simultaneous Search," Econometrica, Econometric Society, vol. 74(5), pages 1293-1307, 09.
  6. M. L. Weitzman, 1978. "Optimal Search for the Best Alternative," Working papers 214, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Goldengorin, Boris & Tijssen, Gert A. & Tso, Michael, 1999. "The maximization of submodular functions : old and new proofs for the correctness of the dichotomy algorithm," Research Report 99A17, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
  8. George J. Stigler, 1961. "The Economics of Information," Journal of Political Economy, University of Chicago Press, vol. 69, pages 213.
  9. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-69, July.
  10. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
  11. Hector Chade & Greg Lewis & Lones Smith, 2006. "The College Admissions Problem Under Uncertainty," 2006 Meeting Papers 125, Society for Economic Dynamics.
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