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Optimal Risk Taking with Flexible Income

Jaka Cvitani, Levon Goukasian, Fernando Zapatero

Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, California 91125
Business Division, Pepperdine University, Malibu, California 90263
Finance and Business Economics Department, Marshall School of Business, University of Southern California, Los Angeles, California 90089
cvitanic{at}hss.caltech.edu
levon.goukasian{at}pepperdine.edu
fzapatero{at}marshall.usc.edu

We study the portfolio selection problem of an investor who can optimally exert costly effort for more income. The possibility of generating more income, if necessary, increases the risk-taking appetite of the investor. We find the optimal allocation to the risky security as a proportion of financial wealth and as a proportion of the total wealth, defined as the combination of the financial wealth and the human capital of the investor. When the investor's objective is the maximization of the terminal wealth, we show that the optimal allocation to the risky security is a hump-shaped function of the investment horizon. However, when the investor maximizes utility from intertemporal consumption, the optimal allocation in the risky security is a constant proportion of the total wealth of the investor.

Key Words: utility maximization; optimal portfolio selection; intertemporal consumption; optimal effort
History: Received: March 6, 2006;