Liquidity Preference under Uncertainty: a Model of Dynamic Investment in Illiquid Assets

The paper presents a mathematical model of optimal investment in illiquid assets. Specifically, the model addresses the problem of an investor with limited capital resources, who makes sequential decisions on long-term investments under uncertainty as to future opportunities. The model demonstrates that such an investor will optimally demand a higher rate of return on investments in long-term, unmarketable assets and that the size of the premium demanded is an increasing function of the duration of the illiquid investment. Liquidity Preference under Uncertainty: A Model of Dynamic Investment in Illiquid Assets I . Introduction The article presents a mathemetical model of liquidity preference in an uncertain environment. The model addresses the problem of an investor, with access to a limited pool of capital, who makes sequential decisions on long-lasting investments, under uncertainty as to future opportunities. Our results demonstrate that a rational investor will, under these circumstances, demand a higher rate of return (liquidity premium) on investments in long-lasting unmarketable assets than on marketable ones. The liquidity premium demanded is an increasing function of the duration of the illiquid investment. Lumpiness and limited reversibility are important characteristics of some types of investment decisions (particularly investments in real capital) . Yet, with few exceptions, financial models of optimal investment (portfolio allocation) and the equilibrium structure of returns, rest on the assumption that asset markets are fluid and frictionless . That is, it is generally assumed that no transaction costs or trading indivisibilities exist which would hamper individuals in their initial allocation of wealth or in the free revision of their portfolios, and it is extremely difficult to incorporate such effects (and retain analytic tractability) into these models. For this reason, our analysis begins at a different point: from the outset we define some investment opportunities to be illiquid, and from there proceed to consider optimal investment criteria for such assets (in a dynamic context ,. where accepting one illiquid investment may cause the investor to forfeit a better one in the future). Liquidity, in this analysis, is considered to be a time variable: