The Impact of Time Horizon on the Effect of Diversification

40 Pages Posted: 22 May 2017

See all articles by Yonatan Berman

Yonatan Berman

London Mathematical Laboratory

Ron Berman

University of Pennsylvania - The Wharton School

Date Written: May 21, 2017


Although investors are often advised to diversify their investment portfolios as well as to consider rebalancing them periodically, research has shown that they often ignore this advice. We try to determine if this behavior is rational by analyzing a risk-averse investor who chooses between buy-and-hold portfolios comprised of assets with dynamic uncertain returns. The assets in the portfolio evolve according to multiplicative random walks, distinguishing them from the traditional one-shot or additive models.

Solving for the optimal choice, we find an interaction between diversification and the time horizon an investor is facing. This interaction results in conditions for which an optimal portfolio in one time horizon becomes suboptimal in a longer (or shorter) horizon. Moreover, we find that rebalancing may be suboptimal if the portfolio is diversified enough. Such effects are a consequence of the non-ergodicity of the value of assets that follow multiplicative dynamics.

Thus we are able to provide a rational explanation for observed behavior of investors and subjects in lab experiments who choose to not diversify their portfolios or do not rebalance as often as the standard theory would prescribe.

Keywords: Portfolio Selection, Brownian Motion, Random Walks, Choice Under Uncertainty, Behavioral Economics, Diversification Heuristics, Stochastic Models

JEL Classification: D14, G11, D81

Suggested Citation

Berman, Yonatan and Berman, Ron, The Impact of Time Horizon on the Effect of Diversification (May 21, 2017). Available at SSRN: or

Yonatan Berman

London Mathematical Laboratory ( email )

8 Margravine Gardens
London, London W6 8RH
United Kingdom

Ron Berman (Contact Author)

University of Pennsylvania - The Wharton School ( email )

3641 Locust Walk
Philadelphia, PA 19104-6365
United States

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