C  The Journal of Risk and Insurance, 2008, Vol. 75, No. 4, 847-872 PORTFOLIO CHOICE AND LIFE INSURANCE: THE CRRA CASE Huaxiong Huang Moshe A. Milevsky Jin Wang ABSTRACT We solve a portfolio choice problem that includes life insurance and labor in- come under constant relative risk aversion (CRRA) preferences. We focus on the correlation between the dynamics of human capital and financial capital and model the utility of the family as opposed to separating consumption and bequest. We simplify the underlying Hamilton–Jacobi–Bellman equa- tion using a similarity reduction technique that leads to an efficient numer- ical solution. Households for whom shocks to human capital are negatively correlated with shocks to financial capital should own more life insurance with greater equity/stock exposure. Life insurance hedges human capital and is insensitive to the family’s risk aversion, consistent with practitioner guidance. INTRODUCTION AND MOTIVATION There is a glaring disconnect between the way most financial advisers sell life in- surance and how they sell or promote investment products such as mutual funds, stocks, or bonds. Aside from the regulatory environment and the different licenses required—namely, securities as opposed to insurance—these two financial decisions are presented as if there were a “separation theorem” that justified their relative in- variance. Moreover, although the concepts of risk tolerance, risk aversion, and utility are ubiquitous in the lingo and marketing material of the securities industry, the same terminology rarely enters the dialogue in the life insurance arena. This is quite odd since historically the economics of insurance was the breeding ground for much of the development in utility theory. This observation is more than just anecdotal. The insurance literature’s starting point for the optimal face amount of life insurance is the original work by Solomon Huebner Huaxiong Huang is a professor in the Department of Mathematics and Statistics. Moshe A. Milevsky is the executive director of the IFID Center and Associate Professor in the Schulich School of Business. Jin Wang was a research associate at the IFID Centre, York University, 4700 Keele St., Toronto, Canada, when this article was written. M. Milevsky can be reached at milevsky@yorku.ca. The authors would like to acknowledge helpful comments from the JRI editor and two anonymous referees. 847