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The Existence of an Optimal Allocation Rate in a Dynamic Portfolio: Rebalancing

Author

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  • Fujio Takata

    (Graduate School of Economics, Kobe University)

Abstract

Rebalancing is based on the notion that the initially determined weights in a portfolio keep constant in future terms. Focusing on a portfolio consisting of a risky asset and a risk-free asset, and assuming that all funds from the portfolio are invested in every term, investors can choose an optimal weight, which decides the proportion of investment between the two assets in every term. The weight functions as an indicator of the investment ratio between the two assets, which results in automatically inducing investors to buy less when the price of the risk assets is high, and to buy more when it is low. However, this notion is based on the existence of an optimal weight. A risky asset is supposed to follow two events: up and down. These phenomena have a certain probability. The growth rate of the portfolio follows Bernoulli trials. Investors choose the ratio to maximize the expected value of the growth rate, which is a function with three arguments, namely the probability, the up ratio, and the down ratio. The optimal weight depends on these arguments. The combination among the three can influence the existence of the optimal weight. Still, we may ask, does an optimal weight exist? We derive a conclusion: the ratios of up and down respectively have an upper boundary and a lower one. This relationship prevails regardless of probability. JEL Classification: G-11; G-12; G-32.

Suggested Citation

  • Fujio Takata, 2025. "The Existence of an Optimal Allocation Rate in a Dynamic Portfolio: Rebalancing," Discussion Papers 2515, Graduate School of Economics, Kobe University.
    • Handle: RePEc:koe:wpaper:2515
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