A theory of optimal timing and selectivity

• Published in: Journal of economic dynamics & control 1999-06, Vol.23 (7), p.929-965
• Main Authors: Chacko, George, Das, Sanjiv Ranjan
• Format: Article
• Language: English
• Subjects: Access to information; Economic theory; Growth stocks; Income funds; Information; Investment; Learning; Mathematical economics; Mutual funds; Portfolio management; Stochastic models; Stochastic processes; Studies; Temporal dimension
• ISSN: 0165-1889; 1879-1743
• DOI: 10.1016/S0165-1889(98)00050-5

We solve an extended optimal portfolio problem in continuous time for any horizon, where we allow the mean and variance of returns to be stochastic, introduce fund flows to and from the portfolio, permit differential investor preferences for dividend versus growth stocks, and allow the investor to buy costly information on the random mean and variance of the portfolio to improve his portfolio choice set. This model provides analytical results especially useful in understanding the expenditure on timing and selection information a mutual fund undertakes in attempting to improve performance relative to a benchmark. We examine this proposition for growth and income funds, long and short investment horizons, and also account for fund inflows and outflows. We also combine our model of costly learning with the traditional model of incomplete information to understand the interaction between costly and costless learning. The approach taken is a purely theoretical one, and in this regard the paper is normative in spirit. We anticipate that the propositions in this paper will provide two byproducts: (i) a framework for fund managers to think about how to allocate information expenses between timing and selection skills, and (ii) give academics, especially empirical researchers, a theoretical backdrop against which to examine the mutual fund industry.