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

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.