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Start-to-Low Drawdown as a Risk Measure and its Application to Portfolio Optimization for Levered Investors under Solvency Regimes

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  • Maringer, Dietmar
  • Stähli, Philipp

Abstract

Drawdown is an important risk measure in both theory and practice. Most drawdown measures use the running peak as the reference point from which to calculate the drawdown. Instead, the start-to-low drawdown (SLD), which references the start of the period, is firstly proposed as a relevant measure for levered investors. Secondly, an application to a levered investor who is also subject to regulatory capital requirements, as seen in the banking or insurance industry, is proposed. Such an investor is faced with regulatory sanctions as soon as their own funds no longer cover capital requirements, i.e., even before equity is exhausted. Portfolio optimization objectives are developed that consider return, cost of capital, and cost of drawdown together: the solvency cost-adjusted return (SCAR) including the cost of drawdown (SCARD). This is applied to the European insurance industry, with capital requirement calculations following the Solvency II standard model. For the empirical analysis, models of life and non-life insurance companies are constructed using EIOPA market overview data, and their investments are optimized for SCAR and SCARD as objectives. The investment universe consists of equity, corporate bond, and government bond indices with data ranging from 2005 to 2024. The characteristics and performance of SCARD-optimal portfolios of the modeled companies are compared to those of SCAR-optimal and equally weighted portfolios. Out-of-sample SCAR and SCARD following both objectives are higher than those of the equally weighted reference portfolio. SCARD-optimal portfolios show lower cost of solvency capital and lower drawdown than their SCAR-optimal counterparts, but also lower returns. The differences in return outweigh those of the other components, resulting in the SCAR and SCARD of SCAR-optimal portfolios tending to be higher than those of SCARD-optimal portfolios.

Suggested Citation

  • Maringer, Dietmar & Stähli, Philipp, 2025. "Start-to-Low Drawdown as a Risk Measure and its Application to Portfolio Optimization for Levered Investors under Solvency Regimes," Working papers 2025/07, Faculty of Business and Economics - University of Basel.
    • Handle: RePEc:bsl:wpaper:2025/07
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    References listed on IDEAS

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    1. Alexei Chekhlov & Stanislav Uryasev & Michael Zabarankin, 2005. "Drawdown Measure In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 13-58.
    2. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    3. Roy Kouwenberg, 2018. "Strategic asset allocation for insurers under Solvency II," Journal of Asset Management, Palgrave Macmillan, vol. 19(7), pages 447-459, December.
    4. Ning Zhang & Jingnan Chen & Gengling Dai, 2022. "Portfolio Selection with Regularization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 39(02), pages 1-27, April.
    5. Mikica Drenovak & Vladimir Ranković & Branko Urošević & Ranko Jelic, 2021. "Bond portfolio management under Solvency II regulation," The European Journal of Finance, Taylor & Francis Journals, vol. 27(9), pages 857-879, June.
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    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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