Illiquid Assets and Optimal Portfolio Choice

The presence of illiquid assets, such as human wealth, housing and proprietorships substantially complicates the problem of portfolio choice. This paper is concerned with the problem of optimal asset allocation in a continuous time model when one asset cannot be traded. This illiquid asset, which depends on an uninsurable source of risk, provides a liquid dividend. In the case of human capital we can think about this dividend as labor income. The agent is endowed with a given amount of the illiquid asset and with some liquid wealth which can be allocated in a market where there is a risky and a riskless asset. The main point of the paper is that the optimal allocations to the two liquid assets and consumption will critically depend on the endowment and characteristics of the illiquid asset, in addition to the preferences and liquid wealth of the agent. We provide what we believe to be the first analytical solution to this problem when the agent has power utility of consumption and terminal wealth. We also derive the value that the agent assigns to the illiquid asset. The risk adjusted valuation procedure we develop can be used to value both liquid and illiquid assets, as well as contingent claims on those assets. ∗The Anderson School of Management, University of California at Los Angeles; 110 Westwood Plaza, Los Angeles, CA, 90095-1481 †University of Verona and University of California at Los Angeles. Permanent Address: Università degli Studi di Verona, Dipartimento di Scienze Economiche, Via Giardino Giusti, 2 37129 Verona, Italy. The present paper has been completed while the author was a visiting scholar at the Anderson School of Management, Faculty of Finance. C.T. gratefully acknowledges the Anderson School, the Finance Faculty and in particular Prof. Schwartz for the kind invitation and warm hospitality. C.T. would like to thank Marina Di Giacinto for constant support and many valuable comments, Martino Grasselli and the colleagues of the SAFE center in Verona for several insights and helpful discussions.