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Dynamic consumption and asset allocation with derivative securities

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  • Yuan-Hung Hsuku

Abstract

This paper provides a model in which a long-term investor chooses consumption and optimal dynamic asset allocation, including a riskless bond, risky stock, and derivatives on the stock, when there is predictable variation in return volatility. We maximize a more general recursive utility function defined over intermediate consumption rather than terminal wealth in order to reflect the realistic problem facing an investor who is saving for the future. The paper obtains a solution to this problem which is exact for investors with unit elasticity of intertemporal substitution of consumption, and approximate otherwise. The optimal log consumption-wealth ratio is a function of stochastic volatility, and the consumption-wealth ratio is an increasing function of volatility for investors whose elasticity of intertemporal substitution of consumption is smaller than one, while it is a decreasing function of volatility for investors whose elasticity of intertemporal substitution of consumption is larger than one. Derivative securities are a significant tool for expanding investors' dimension of risk-and-return tradeoffs, being a vehicle for the additional risk factor of stochastic volatility in the stock market. Non-myopic investors can utilize derivative securities, which provide access to volatility risk, to capitalize upon the time-varying nature of their opportunity set.

Suggested Citation

  • Yuan-Hung Hsuku, 2007. "Dynamic consumption and asset allocation with derivative securities," Quantitative Finance, Taylor & Francis Journals, vol. 7(2), pages 137-149.
  • Handle: RePEc:taf:quantf:v:7:y:2007:i:2:p:137-149
    DOI: 10.1080/14697680601077959
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    3. Bety Agnany & Maria Jose Gutierrez & Amaia Iza, 2007. "R&D Policy in Economies with Endogenous Growth and Non-Renewable Resources," ThE Papers 07/09, Department of Economic Theory and Economic History of the University of Granada..
    4. Agnani, Betty & Gutiérrez Huerta, María José & Iza Padilla, María Amaya, 2007. "R&D Policy in Economies with Endogenous Growth and Non-Renewable Resources," DFAEII Working Papers 1988-088X, University of the Basque Country - Department of Foundations of Economic Analysis II.
    5. Wei, Pengyu & Yang, Charles & Zhuang, Yi, 2023. "Robust consumption and portfolio choice with derivatives trading," European Journal of Operational Research, Elsevier, vol. 304(2), pages 832-850.
    6. Li, Danping & Shen, Yang & Zeng, Yan, 2018. "Dynamic derivative-based investment strategy for mean–variance asset–liability management with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 72-86.
    7. Sebastian, Steffen P. & Steininger, Bertram I., 2021. "Real estate ETNs in strategic asset allocation," Working Paper Series 21/8, Royal Institute of Technology, Department of Real Estate and Construction Management & Banking and Finance.

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