Modified Mean-Variance Risk Measures for Long-Term Portfolios

Hyungbin Park
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Hyungbin Park: Department of Mathematical Sciences and RIMS, Seoul National University, 1, Gwanak-ro, Gwanak-gu, Seoul 08826, Korea

Mathematics, 2021, vol. 9, issue 2, 1-23

Abstract: This paper proposes modified mean-variance risk measures for long-term investment portfolios. Two types of portfolios are considered: constant proportion portfolios and increasing amount portfolios. They are widely used in finance for investing assets and developing derivative securities. We compare the long-term behavior of a conventional mean-variance risk measure and a modified one of the two types of portfolios, and we discuss the benefits of the modified measure. Subsequently, an optimal long-term investment strategy is derived. We show that the modified risk measure reflects the investor’s risk aversion on the optimal long-term investment strategy; however, the conventional one does not. Several factor models are discussed as concrete examples: the Black–Scholes model, Kim–Omberg model, Heston model, and 3/2 stochastic volatility model.

Keywords: continuous-time factor model; modified risk measures; mean-variance analysis; long-term investment; optimal strategy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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