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Arbitrage and Optimal Portfolio Choice with Financial Constraints

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Abstract

We analyze the pricing of risky income streams in a world with competitive security markets where investors are constrained by restrictions on possible portfolio holdings. We investigate how we can transfer concepts and pricing techniques from a world without frictions to such a more realistic situation. We show that basically two new aspects arise: First, portfolio constraints can lead to situations where not all arbitrage opportunities are necessarily eliminated in equilibrium. For a world with portfolio constraints the concept of no arbitrage has to be replaced by a weaker concept which we call no unlimited arbitrage. Second, though we can characterize prices which allow no unlimited arbitrage by the existence of certain state prices as in the unconstrained case, additional computational work is needed for deriving from this fact a pricing theory for contingent claims. We propose a technique which can achieve this task and which renders itself for a computationally simple implementation for many constraint situations which are of practical interest. The power of no arbitrage techniques is preserved in the sense that no specific assumptions about utility functions of investors have to be made. We relate our analysis to the optimal decision problem of an investor and show the various relations between the properties of an optimal solution to this problem and the arbitrage-free values of risky income streams. This opens a unified view on the different approaches to asset pricing under portfolio constraints used in the literature and conveys their common underlying logic.

Suggested Citation

  • Helmut Elsinger & Martin Summer, 2001. "Arbitrage and Optimal Portfolio Choice with Financial Constraints," Working Papers 49, Oesterreichische Nationalbank (Austrian Central Bank).
  • Handle: RePEc:onb:oenbwp:49
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    1. Pesaran, M. H. & Smith, Ron P., 1998. "Structural Analysis of Cointegrating VARs," Cambridge Working Papers in Economics 9811, Faculty of Economics, University of Cambridge.
    2. Diamandis, Panayiotis F. & Georgoutsos, Dimitris A. & Kouretas, Georgios P., 2000. "The monetary model in the presence of I(2) components: long-run relationships, short-run dynamics and forecasting of the Greek drachma," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 917-941, December.
    3. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, pages 283-306.
    4. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    5. Baillie, Richard T. & Pecchenino, Rowena A., 1991. "The search for equilibrium relationships in international finance: the case of the monetary model," Journal of International Money and Finance, Elsevier, vol. 10(4), pages 582-593, December.
    6. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    7. Meese, Richard, 1990. "Currency Fluctuations in the Post-Bretton Woods Era," Journal of Economic Perspectives, American Economic Association, pages 117-134.
    8. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    9. Dornbusch, Rudiger, 1976. "Expectations and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 84(6), pages 1161-1176, December.
    10. M. Hashem Pesaran & Ron P. Smith, 1998. "Structural Analysis of Cointegrating VARs," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 471-505, December.
    11. Ronald MacDonald & Ian W. Marsh, 1997. "On Fundamentals And Exchange Rates: A Casselian Perspective," The Review of Economics and Statistics, MIT Press, pages 655-664.
    12. Doornik, Jurgen A & Hendry, David F & Nielsen, Bent, 1998. " Inference in Cointegrating Models: UK M1 Revisited," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 533-572, December.
    13. David Backus, 1984. "Empirical Models of the Exchange Rate: Separating the Wheat from the Chaff," Canadian Journal of Economics, Canadian Economics Association, vol. 17(4), pages 824-846, November.
    14. Juselius, Katarina, 1995. "Do purchasing power parity and uncovered interest rate parity hold in the long run? An example of likelihood inference in a multivariate time-series model," Journal of Econometrics, Elsevier, vol. 69(1), pages 211-240, September.
    15. Cheung, Yin-Wong & Lai, Kon S, 1993. "Finite-Sample Sizes of Johansen's Likelihood Ration Tests for Conintegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 55(3), pages 313-328, August.
    16. Meese, Richard A & Rogoff, Kenneth, 1988. " Was It Real? The Exchange Rate-Interest Differential Relation over the Modern Floating-Rate Period," Journal of Finance, American Finance Association, vol. 43(4), pages 933-948, September.
    17. Goldberg, Michael D., 1995. "Symmetry restrictions and the semblance of neutrality in exchange rate models," Journal of Macroeconomics, Elsevier, pages 579-599.
    18. Boothe, Paul & Glassman, Debra, 1987. "Off the Mark: Lessons for Exchange Rate Modelling," Oxford Economic Papers, Oxford University Press, vol. 39(3), pages 443-457, September.
    19. Goldberg, Michael D., 2000. "On empirical exchange rate models: what does a rejection of the symmetry restriction on short-run interest rates mean?," Journal of International Money and Finance, Elsevier, vol. 19(5), pages 673-688, October.
    20. Frankel, Jeffrey A, 1979. "On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differentials," American Economic Review, American Economic Association, pages 610-622.
    21. Osterwald-Lenum, Michael, 1992. "A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 461-472, August.
    22. Meese, Richard A, 1986. "Testing for Bubbles in Exchange Markets: A Case of Sparkling Rates?," Journal of Political Economy, University of Chicago Press, vol. 94(2), pages 345-373, April.
    23. Abuaf, Niso & Jorion, Philippe, 1990. " Purchasing Power Parity in the Long Run," Journal of Finance, American Finance Association, vol. 45(1), pages 157-174, March.
    24. Ken Froot & Kenneth Rogoff, "undated". "Perspectives on PPP and Long-Run Real Exchange Rates," Working Paper 32027, Harvard University OpenScholar.
    25. Cushman, David O. & Sang Sub Lee & Thorgeirsson, Thorsteinn, 1996. "Maximum likelihood estimation of cointegration in exchange rate models for seven inflationary OECD countries," Journal of International Money and Finance, Elsevier, vol. 15(3), pages 337-368, June.
    26. Hooper, Peter & Morton, John, 1982. "Fluctuations in the dollar: A model of nominal and real exchange rate determination," Journal of International Money and Finance, Elsevier, vol. 1(1), pages 39-56, January.
    27. Froot, Kenneth A. & Rogoff, Kenneth, 1995. "Perspectives on PPP and long-run real exchange rates," Handbook of International Economics,in: G. M. Grossman & K. Rogoff (ed.), Handbook of International Economics, edition 1, volume 3, chapter 32, pages 1647-1688 Elsevier.
    28. Lothian, James R. & Taylor, Mark P., 1997. "Real exchange rate behavior," Journal of International Money and Finance, Elsevier, vol. 16(6), pages 945-954, December.
    29. Gonzalo, Jesus, 1994. "Five alternative methods of estimating long-run equilibrium relationships," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 203-233.
    30. Charles Engel & James D. Hamilton, 1989. "Long Swings in the Exchange Rate: Are they in the Data and Do Markets Know It?," NBER Working Papers 3165, National Bureau of Economic Research, Inc.
    31. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    32. Johansen, Søren & Juselius, Katarina, 1992. "Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 211-244.
    33. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, pages 3-24.
    34. MacDonald, Ronald & Taylor, Mark P., 1994. "The monetary model of the exchange rate: long-run relationships, short-run dynamics and how to beat a random walk," Journal of International Money and Finance, Elsevier, vol. 13(3), pages 276-290, June.
    35. Papell, David H., 1997. "Cointegration and exchange rate dynamics," Journal of International Money and Finance, Elsevier, vol. 16(3), pages 445-459, June.
    36. Chinn, Menzie D. & Meese, Richard A., 1995. "Banking on currency forecasts: How predictable is change in money?," Journal of International Economics, Elsevier, pages 161-178.
    37. Jeffrey A. Frankel, 1984. "Tests of Monetary and Portfolio Balance Models of Exchange Rate Determination," NBER Chapters,in: Exchange Rate Theory and Practice, pages 239-260 National Bureau of Economic Research, Inc.
    38. Bilson, John F. O., 1979. "The deutsche mark/dollar rate : A monetary analysis," Carnegie-Rochester Conference Series on Public Policy, Elsevier, pages 59-101.
    39. Panayiotis Diamantis & Dimitris Georgoutsos & George Kouretas, "undated". "The Monetary Model in the Presence of I (2) Components: A Cointegration Analysis," Working Papers 9904, University of Crete, Department of Economics.
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    Cited by:

    1. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, pages 772-786.
    2. Jürgen Eichberger & Klaus Rheinberger & Martin Summer, 2014. "Credit risk in general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 407-435.
    3. Bernard Cornet & Ramu Gopalan, 2010. "Arbitrage and equilibrium with portfolio constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 227-252.
    4. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    5. V.F. Martins-da-Rocha & L. Triki, 2005. "Equilibria in exchange economies with financial constraints: Beyond the Cass Trick," Microeconomics 0503013, EconWPA.

    More about this item

    Keywords

    Arbitrage; Portfolio Constraints; Asset Pricing;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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