THE EXTREME WEIGHTS IN THE INDEX PORTFOLIO OF CONSTANT-PROPORTION STRATEGIES

This paper analyzes the optimal of constant proportion index portfolio strategies. They are also called passive strategies which are becoming more common in Russia and abroad. They are significantly cheaper to implement than active strategies. In addition, as practice shows, in the long term they are more profitable and less risky. The main problem in these strategies is the choice of the proportions in which the investor allocates his capital between risky and risk-free assets. In constant proportion index portfolio the weight of risk asset remains constant throughout investment period. For this purpose, the investor with a certain frequency restores the desired balance between risky and risk-free assets. Each period at the beginning of which such recovery occurs is called the re-balancing period. In the case of strategies with index portfolios, risky assets are the shares of the index fund, and risk-free assets are the deposits in reliable bank or government bonds. According on the daily value of units of these funds and the annual interest rate for the 11-year period, using a specially developed program optimal weight index funds in the portfolios has been found. Parameters of the analyzed portfolios are: length of the investment period (from one year to 10 years) and the frequency of weight rebalancing (month, quarter, year). The sequence of optimal weights and the corresponding optimum yield for consecutive investment periods with a specified frequency of re-balancing were determined for each fund. It was found that in almost all cases, the optimal weights of fund equals the extreme values 0 or 1. Also, the frequencies of these values in the selected sequence is about the same for all funds. This empiric fact can be conventionally called the principle of extremeness or “all or nothing” principle.

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