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Normal Asset Allocations and Their Statistical Properties

Author

Listed:
  • Luca Ghezzi

    (Department of Integrated Business Management, LIUC Università Carlo Cattaneo, Corso Matteotti 22, 21053 Castellanza, Italy)

Abstract

This study focuses on efficient asset allocations that properly include T-bills, T-bonds, and the S&P 500 stock index. It checks that their annual real rates of linear return are both normal and almost lognormal. It reexamines how efficient portfolios based on the rates of linear return may turn into efficient portfolios based on the rates of logarithmic return. It finds that each efficient asset allocation has the lowest possible standard deviation as well as the highest possible arithmetic and geometric means. It eventually reconsiders the relationship between the confidence interval of a geometric mean and an expected long-run capital accumulation. As a consequence, it bridges a gap in the scientific literature by enabling financial advisors to trade off the mean rate of return on a portfolio more rigorously against the value at risk.

Suggested Citation

  • Luca Ghezzi, 2024. "Normal Asset Allocations and Their Statistical Properties," IJFS, MDPI, vol. 12(3), pages 1-14, July.
    • Handle: RePEc:gam:jijfss:v:12:y:2024:i:3:p:69-:d:1434304
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    References listed on IDEAS

    as
    1. Henriksson, Roy D & Merton, Robert C, 1981. "On Market Timing and Investment Performance. II. Statistical Procedures for Evaluating Forecasting Skills," The Journal of Business, University of Chicago Press, vol. 54(4), pages 513-533, October.
    2. James Nguyen & Wei-Xuan Li & Clara Chia-Sheng Chen, 2022. "Mean Reversions in Major Developed Stock Markets: Recent Evidence from Unit Root, Spectral and Abnormal Return Studies," JRFM, MDPI, vol. 15(4), pages 1-20, April.
    3. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    4. Luigi Buzzacchi & Luca Ghezzi, 2023. "Mean Reversion Lessens Mean Blur: Evidence from the S&P Composite Index," IJFS, MDPI, vol. 11(1), pages 1-13, January.
    Full references (including those not matched with items on IDEAS)

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