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Optimal investment for defined-contribution pension plans under money illusion

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Abstract

This paper examines the optimal asset allocation for defined-contribution pension plans in an inflationary economy under money illusion. The financial market consists of nominal bonds, inflation-linked bonds, and a stock index. The objective of the pension plan is to maximize the expected utility of a mixture of nominal and real wealth at retirement, as the plan member partially overlooks inflation and tends to think in terms of nominal rather than real monetary values. We obtain the optimal strategy and demonstrate the impacts of money illusion on asset allocation. In particular, money illusion significantly reduces investment in inflation-linked bonds. We also show that (even partially) overlooking inflation can lead to considerable welfare losses.

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Notes

  1. Direct investment in real estate is not allowed in DC plans. Nevertheless, plan members can gain exposure to real estate through real estate investment trusts (REITs). Notably, many REITs are included in the S &P 500 index.

  2. Employer-sponsored retirement plans are classified into two types: defined-benefit (DB) plans and defined-contribution (DC) plans. The investment strategy of DB plans is made by professional fund managers. However, for DC plans such as 401(k), plan members take on the investment risk and choose their own investment strategies (Baranoffet al. 2021) and hence are more likely to suffer from money illusion.

  3. For tractability, we assume the labor income and the contribution (in real terms) are deterministic. The main results of our paper remain valid if we allow the contribution rate to be stochastic but spanned by the assets in the market, which is a standard assumption in the existing literature to obtain explicit solutions. In this case, the uncertainty in the contribution rate can be perfectly hedged by appropriate positions in the tradable assets. This will affect the hedging portfolio \(h_t\) in Lemma 3.1 but not the optimal control \(\alpha _t\) in Theorem 3.1. Therefore, all our numerical results will be unchanged.

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No funding was received for conducting this study. The authors have no relevant financial or non-financial interests to disclose. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. The authors have no financial or proprietary interests in any material discussed in this article.

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  1. Division of Banking & Finance, Nanyang Business School, Nanyang Technological University, Singapore, Singapore

    Pengyu Wei

  2. Department of Finance, Florida Atlantic University, Boca Raton, FL, USA

    Charles Yang

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  1. Pengyu Wei
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Wei, P., Yang, C. Optimal investment for defined-contribution pension plans under money illusion. Rev Quant Finan Acc 61, 729–753 (2023). https://doi.org/10.1007/s11156-023-01169-w

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