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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- Weitzman, Martin L, 1979.
"Optimal Search for the Best Alternative,"
Econometric Society, vol. 47(3), pages 641-654, May.
- M. L. Weitzman, 1978. "Optimal Search for the Best Alternative," Working papers 214, Massachusetts Institute of Technology (MIT), Department of Economics.
- Hector Chade & Lones Smith, 2006. "Simultaneous Search," Econometrica, Econometric Society, vol. 74(5), pages 1293-1307, 09.
- Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
- James Albrecht & Pieter A. Gautier & Susan Vroman, 2006. "Equilibrium Directed Search with Multiple Applications," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 869-891.
- James Albrecht & Pieter Gautier & Susan Vroman, 2003. "Equilibrium Directed Search with Multiple Applications," Tinbergen Institute Discussion Papers 03-004/3, Tinbergen Institute, revised 14 Feb 2004.
- James Albrecht & Pieter Gautier, 2004. "Equilibrium Directed Search with Multiple Applications," Econometric Society 2004 Latin American Meetings 330, Econometric Society.
- Albrecht, James & Gautier, Pieter A. & Vroman, Susan, 2003. "Equilibrium Directed Search with Multiple Applications," IZA Discussion Papers 719, Institute for the Study of Labor (IZA).
- James Albrecht, Pieter Gautier, & Susan Vroman, 2003. "Equilibrium Directed Search with Multiple Application," Working Papers gueconwpa~03-03-02, Georgetown University, Department of Economics.
- 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.
- Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
- Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
- 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.
- Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-969, July.
- George J. Stigler, 1961. "The Economics of Information," Journal of Political Economy, University of Chicago Press, vol. 69, pages 213-213. Full references (including those not matched with items on IDEAS)
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