Describing the Terminal Wealth of a Predetermined Schedule of Investments and Withdrawals
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Authors
Brown, Hayden T.
Issue Date
2024
Type
Dissertation
Language
Keywords
Annuities , Dollar Cost Averaging , Leveraged ETF , Portfolio Optimization , S&P 500
Alternative Title
Abstract
The terminal wealth of a predetermined schedule of investments and withdrawals is described in various settings. A lower bound is given for the terminal wealth of a schedule of investments in a single asset having a geometric Lévy alpha-stable wealth process. By means of a transformation, the lower bound is used to construct an upper bound on the probability to complete a schedule of withdrawals following an initial investment. For multiple investable assets, the probability to complete a schedule of investments and withdrawals is optimized over time-adapted portfolio weight functions. Lastly, the return of a daily leveraged ETF is bounded using simple characteristics of the underlying index's daily log-returns. Results are applied to portfolios involving the S&P Composite Index and an inflation-protected bond.
Description
Citation
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License
Creative Commons Attribution 4.0 International