Proceedings of The 11th International Conference on New Ideas in Management, Economics and Accounting
Year: 2023
DOI: https://www.doi.org/10.33422/11th-.imeaconf.2023.02.100
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The Dynamic Portfolio – The Minimum Risk and The Maximum Growth
Fujio Takata
ABSTRACT:
This paper deals with portfolio selection, especially from the viewpoint of dynamics. Markets composed of many agents, such as the security market and the currency market, feature price fluctuations over time, which are often caused by changes in anticipations about the future. Investors have considered this as unfavorable, since it entails risk. To deal with this, Markowitz contrived a static portfolio selection theory, and that theory has now been developed with a dynamic principle. We also follow this trend: Based on the Wiener process, we establish a dynamic portfolio and find two important issues that involve two crucial phenomena which coexist on an efficient frontier: one is a situation with minimum risk; the other is one with maximum growth rate of the portfolio. In the latter case, the price fluctuations are not unfavorable but desirable. The two can coexist, because they are on the same efficient frontier curve. Furthermore, the equal weight of assets included in the portfolio entails a situation with minimum risk. This idea has been adopted in mutual funds, but we demonstrate preconditions for this idea. Moreover, the portfolio with the maximum growth rate is determined only by risk assets. Our discussions are made based on rigorous mathematical calculations.
keywords: efficient frontier; maximum return point; minimum risk point; portfolio selection; Wiener process