Hostname: page-component-5d84bcc8dc-6bbr8 Total loading time: 0 Render date: 2026-09-09T09:38:19.797Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic General Equilibrium and T-Period Fund Separation

Published online by Cambridge University Press:  02 February 2010

Anke Gerber ,
Thorsten Hens  and
Peter Woehrmann
Anke Gerber
Affiliation:
University of Hamburg, Department of Economics, Von-Melle-Park 5, 20146 Hamburg, Germany. anke.gerber@wiso.uni-hamburg.de
Thorsten Hens
Affiliation:
Swiss Finance Institute and Swiss Banking Institute, Plattenstr. 32, CH-8032 Zurich, Switzerland and Norwegian School of Economics and Business Administration, Helleveien 30, 5042 Bergen, Norway. thens@isb.uzh.ch
Peter Woehrmann
Affiliation:
Swiss Federal Institute of Technology Zurich, KPL F 38.2, Kreuzplatz 5, 8032 Zurich, Switzerland. pwoehrmann@ethz.ch
Get access Rights & Permissions [Opens in a new window]

Abstract

In a dynamic general equilibrium model, we derive conditions for a mutual fund separation property by which the savings decision is separated from the asset allocation decision. With logarithmic utility functions, this separation holds for any heterogeneity in discount factors, while the generalization to constant relative risk aversion holds only for homogeneous discount factors but allows for any heterogeneity in endowments. The logarithmic case provides a general equilibrium foundation for the growth-optimal portfolio literature. Both cases yield equilibrium asset pricing formulas that allow for investor heterogeneity, in which the return process is endogenous and asset prices are determined by expected discounted relative dividends. Our results have simple asset pricing implications for the time series as well as the cross section of relative asset prices. It is found that on data from the Dow Jones Industrial Average, a risk aversion smaller than in the logarithmic case fits best.

Information

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 45 , Issue 2 , April 2010 , pp. 369 - 400
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Algoet, P. H., and Cover, T. M.. “Asymptotic Optimality and Asymptotic Equipartition Properties of Log-Optimum Investment.” Annals of Probability, 16 (1988), 876–898.CrossRefGoogle Scholar
Antonelli, G. B. “Sulla Teoria Matematica della Economia Politica.” Pisa, Italy: Nella Tipografia del Folchetto (1886). English translation by J. S. Chipman and A. P. Kirman in Preferences, Utility, and Demand, J. S. Chipman, L. Hurwicz, M. K. Richter, and H. F. Sonnenschein, eds. New York, NY: Harcourt Brace Jovanovich, Inc. (1971).Google Scholar
Barberis, N., and Huang, M.. “Mental Accounting, Loss Aversion, and Individual Stock Returns.” Journal of Finance, 56 (2001), 1247–1292.CrossRefGoogle Scholar
Black, F., and Scholes, M.. “The Effects of Dividend Yield and Dividend Policy on Common Stock Prices and Returns.” Journal of Financial Economics, 1 (1974), 1–22.CrossRefGoogle Scholar
Breiman, L. “Optimal Gambling Systems for Favorable Games.” Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1 (1961), 65–78.Google Scholar
Browne, S. “The Return on Investment from Proportional Portfolio Strategies.” Advances in Applied Probability, 30 (1998), 216–238.CrossRefGoogle Scholar
Campbell, J. Y., and Cochrane, J. H.. “By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior.” Journal of Political Economy, 107 (1999), 205–251.CrossRefGoogle Scholar
Campbell, J. Y., and Shiller, R. J.. “The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors.” Review of Financial Studies, 1 (1988), 195–228.CrossRefGoogle Scholar
Cass, D., and Stiglitz, J. E.. “The Structure of Investor Preference and Asset Returns and Separability in Portfolio Allocation: A Contribution to the Pure Theory of Mutual Funds.” Journal of Economic Theory, 2 (1970), 122–160.CrossRefGoogle Scholar
Cochrane, J. H. “A Cross-Sectional Test of an Investment-Based Asset Pricing Model.” Journal of Political Economy, 104 (1996), 572–621.CrossRefGoogle Scholar
Constantinides, G. M. “Intertemporal Asset Pricing with Heterogeneous Consumers and without Demand Aggregation.” Journal of Business, 55 (1982), 253–267.CrossRefGoogle Scholar
Dempster, M. A. H. Risk Management: Value at Risk and Beyond. Cambridge, UK: Cambridge University Press (2002).CrossRefGoogle Scholar
Dempster, M. A. H.; Germano, M.; Medova, E. A.; and Villaverde, M.. “Global Asset Liability Management.” British Actuarial Journal, 9 (2003), 137–195.CrossRefGoogle Scholar
Den Haan, W. J., and Marcet, A.. “Solving the Stochastic Growth Model by Parameterizing Expectations.” Journal of Business & Economic Statistics, 8 (1990), 31–34.CrossRefGoogle Scholar
Detemple, J., and Gottardi, P.. “Aggregation, Efficiency and Mutual Fund Separation in Incomplete Markets.” Economic Theory, 11 (1998), 443–455.CrossRefGoogle Scholar
Dickey, D. A., and Fuller, W. A.. “Distribution of the Estimators for Autoregressive Time Series with a Unit Root.” Journal of the American Statistical Association, 74 (1979), 427–431.Google Scholar
Dimson, E., and Marsh, P.. “The Demise of Size.” In Security Market Imperfections in World Wide Equity Markets, chap. 6, Keim, D. B. and Ziemba, W. T., eds. Cambridge, UK: Cambridge University Press (2000).Google Scholar
Evstigneev, I. V.; Hens, T.; and Schenk-Hoppé, K. R.. “Evolutionary Stable Stock Markets.” Economic Theory, 27 (2006), 449–468.CrossRefGoogle Scholar
Evstigneev, I. V.; Hens, T.; and Schenk-Hoppé, K. R.. “Globally Evolutionarily Stable Portfolio Rules.” Journal of Economic Theory, 140 (2008), 197–228.CrossRefGoogle Scholar
Fama, E. F., and French, K. R.. “Dividend Yields and Expected Stock Returns.” Journal of Financial Economics, 22 (1988), 3–25.CrossRefGoogle Scholar
Goetzmann, W. N., and Jorion, P.. “A Longer Look at Dividend Yields.” Journal of Business, 68 (1995), 483–508.CrossRefGoogle Scholar
Gollier, C. The Economics of Risk and Time. Cambridge, MA: MIT Press (2001).CrossRefGoogle Scholar
Grandmont, J. M. “Transformations of the Commodity Space, Behavioral Heterogeneity, and the Aggregation Problem.” Journal of Economic Theory, 57 (1992), 1–35.CrossRefGoogle Scholar
Hagiwara, M., and Herce, M. A.. “Risk Aversion and Stock Price Sensitivity to Dividends.” American Economic Review, 87 (1997), 738–745.Google Scholar
Hakansson, N. H. “Optimal Investment and Consumption Strategies under Risk for a Class of Utility Functions.” Econometrica, 38 (1970), 587–607.CrossRefGoogle Scholar
Hakansson, N. H., and Ziemba, W. T.. “Capital Growth Theory.” In Handbooks in Operations Research and Management Science, Vol. 9 (Finance), chap. 3, Jarrow, R. A., Maksimovic, V., and Ziemba, W. T., eds. Amsterdam: Elsevier BV (1995).Google Scholar
Hens, T.; Reimann, S.; and Vogt, B.. “Nash Competitive Equilibria and Two-Period Fund Separation.” Journal of Mathematical Economics, 40 (2004), 321–346.CrossRefGoogle Scholar
Huang, C.-F., and Litzenberger, R. H.. Foundations for Financial Economics. New York, NY: North-Holland (1988).Google Scholar
Ingersoll, J. E. Jr. Theory of Financial Decision Making. Savage, MD: Rowman & Littlefield Publishers (1987).Google Scholar
Jagannathan, R., and Wang, Z.. “The Conditional CAPM and the Cross-Section of Expected Returns.” Journal of Finance, 51 (1996), 3–53.Google Scholar
Jarque, C. M., and Bera, A. K.. “A Test for Normality of Observations and Regression Residuals.” International Statistical Review, 55 (1987), 163–172.CrossRefGoogle Scholar
Judd, K. L.; Kubler, F.; and Schmedders, K.. “Bond Portfolios and Two-Fund Separation in the Lucas Asset-Pricing Model.” Discussion Paper 1427, Northwestern University, Center for Mathematical Studies in Economics and Management Science (2006).Google Scholar
Keim, D. B. “Dividend Yields and Stock Returns: Implications of Abnormal January Returns.” Journal of Financial Economics, 14 (1985), 473–489.CrossRefGoogle Scholar
Kelly, J. L. “A New Interpretation of Information Rate.” Bell System Technical Journal, 35 (1956), 917–926.CrossRefGoogle Scholar
Kocherlakota, N. R. “The Equity Premium: It’s Still a Puzzle.” Journal of Economic Literature, 34 (1996), 42–71.Google Scholar
Kraus, A., and Litzenberger, R. H.. “Market Equilibrium in a Multiperiod State Preference Model with Logarithmic Utility.” Journal of Finance, 30 (1975), 1213–1227.Google Scholar
Kydland, F. E., and Prescott, E. C.. “Time to Build and Aggregate Fluctuations.” Econometrica, 50 (1982), 1345–1370.CrossRefGoogle Scholar
Lettau, M.; Semmler, W.; and Woehrmann, P.. “Nonparametric Estimation of Time-Varying Characteristics of Intertemporal Asset Pricing Models.” Working Paper, New School University (2007).Google Scholar
Litzenberger, R. H., and Ramaswamy, K.. “The Effect of Personal Taxes and Dividends on Capital Asset Prices: Theory and Empirical Evidence.” Journal of Financial Economics, 7 (1979), 163–195.CrossRefGoogle Scholar
Litzenberger, R. H., and Ramaswamy, K.. “Dividends, Short Selling Restrictions, Tax-Induced Investor Clienteles and Market Equilibrium.” Journal of Finance, 35 (1980), 469–482.Google Scholar
Lucas, R. E. “Asset Prices in an Exchange Economy.” Econometrica, 46 (1978), 1429–1445.CrossRefGoogle Scholar
Magill, M., and Quinzii, M.. Theory of Incomplete Markets. Cambridge, MA: MIT Press (1996).Google Scholar
Mehra, R., and Prescott, E. C.. “The Equity Premium: A Puzzle.” Journal of Monetary Economics, 15 (1985), 145–161.CrossRefGoogle Scholar
Merton, R. C. “Optimum Consumption and Portfolio Rules in a Continuous-Time Model.” Journal of Economic Theory, 3 (1971), 373–413.CrossRefGoogle Scholar
Perold, A. F., and Sharpe, W. F.. “Dynamic Strategies for Asset Allocation.” Financial Analysts Journal, 44 (1988), 16–27.CrossRefGoogle Scholar
Quah, J. K.-H. “The Law of Demand When Income Is Price Dependent.” Econometrica, 65 (1997), 1421–1442.CrossRefGoogle Scholar
Roll, R. “Evidence on the ‘Growth-Optimum’ Model.” Journal of Finance, 28 (1973), 551–566.Google Scholar
Rubinstein, M. “The Strong Case for the Generalized Logarithmic Utility Model as the Premier Model of Financial Markets.” Journal of Finance, 31 (1976), 551–571.CrossRefGoogle Scholar
Russell, T. “Portfolio Separation: The Analytic Case.” Economics Letters, 6 (1980), 59–66.CrossRefGoogle Scholar
Samuelson, P. A. “Lifetime Portfolio Selection by Dynamic Stochastic Programming.” Review of Economics and Statistics, 51 (1969), 239–246.CrossRefGoogle Scholar
Spare, A., and Ciotti, P.. Relative Dividend Yield: Common Stock Investing for Income and Appreciation. New York, NY: John Wiley & Sons (1999).Google Scholar
Thorp, E. O. “Portfolio Choice and the Kelly Criterion.” In Stochastic Models in Finance, Ziemba, W. T. and Vickson, R. G., eds. New York, NY: Academic Press (1971).Google Scholar
Tobin, J. “Liquidity Preference as Behavior Towards Risk.” Review of Economic Studies, 25 (1958), 65–86.CrossRefGoogle Scholar
von Neumann, J., and Morgenstern, O.. Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press (1944).Google Scholar
Welch, I., and Goyal, A.. “A Comprehensive Look at the Empirical Performance of Equity Premium Prediction.” Review of Financial Studies, 21 (2008), 1455–1508.CrossRefGoogle Scholar
Wolf, M. “Stock Returns and Dividend Yields Revisited: A New Way to Look at an Old Problem.” Journal of Business and Economic Statistics, 18 (2000), 18–30.CrossRefGoogle Scholar
Ziemba, W. T., and Mulvey, J. M.. Worldwide Asset and Liability Modeling. Cambridge, UK: Cambridge University Press (1998).Google Scholar