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Understanding saving and portfolio choices with predictable changes in assets returns

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Author Info
Gollier, Christian

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Abstract

We consider an expected-utility-maximizing consumer living two periods who can invest in two assets, one of which is risk free. We do not restrict relative risk aversion to be constant. We first examine the effect that a change in the opportunity set in the second period has on the optimal saving in the first period. We show that an increase in the future risk free rate (keeping the equity premium unchanged) reduces savings if relative risk aversion is uniformly larger than unity. An increase in the equity premium or a reduction in the volatility of the risky asset raises savings if the index of cautiousness, i.e., the derivative of absolute risk tolerance, is smaller than unity. In a second stage, we use these results to determine the sign of the hedging demand for the risky asset for the following three types of predictability: predictable changes in the interest rate, mean-reversion in stock returns, and predictable changes in volatility. Depending upon the type of predictability under scrutiny, what matters to sign the hedging demand is whether relative risk aversion or cautiousness is smaller or larger than unity.

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Publisher Info
Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 5-6 (April)
Pages: 445-458
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Handle: RePEc:eee:mateco:v:44:y:2008:i:5-6:p:445-458

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Web page: http://www.elsevier.com/locate/jmateco

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  2. Leonid Kogan & Raman Uppal, . "Risk Aversion and Optimal Portfolio Policies in Partial and General Equilibrium Economies," Rodney L. White Center for Financial Research Working Papers 13-00, Wharton School Rodney L. White Center for Financial Research. [Downloadable!]
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  14. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January. [Downloadable!] (restricted)
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  15. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March. [Downloadable!] (restricted)
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  17. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August. [Downloadable!] (restricted)
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  19. Gollier Christian, 1995. "The Comparative Statics of Changes in Risk Revisited," Journal of Economic Theory, Elsevier, vol. 66(2), pages 522-535, August. [Downloadable!] (restricted)
  20. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April. [Downloadable!] (restricted)
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  21. Dreze, Jacques H. & Modigliani, Franco, 1972. "Consumption decisions under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 308-335, December. [Downloadable!] (restricted)
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