Abstract:
Dynamic investment strategies are widely popular within portfolio and risk management practice. Investor preferences, regulatory provisions and portfolio risk management require optimal financial portfolios to ensure minimum capital guarantee as well as risk measure constraints. Kraft & Steffensen (2013) introduce an innovative refinement of the seminal paper of Merton (1969) which is able to derive optimal investment strategies for either minimum capital guarantees or risk measure constraints in closed form via the dynamic programming principle (DPP) as alternative to the martingale approach. We provide an extensive overview on the DPP approach introduced by Kraft & Steffensen (2013) and introduce optimal unconstrained, stand-alone Value at Risk (VaR) constrained and minimum capital guaranteed portfolio strategies. We derive a dynamic investment strategy analytically, simultaneously fulfilling a minimum capital guarantee as well as a terminal VaR risk measure constraint. We refine the existing methodology and additionally conduct sensitivity and wealth-equivalent loss analysis of the derived optimal investment strategy, comparing it with the stand-alone constrained portfolio strategies. Based on our analysis, we suggest that optimal portfolios under risk and capital constraints may be beneficial for investors in some cases, but they usually come with additional costs or without significant additional benefits. Finally, we evaluate the applied methodology and suggest further research ideas.