Life cycle consumption and portfolio choice under real interest rate risk

We set up a life cycle model with real interest rate risk to demonstrate that real interest rates have implications for optimal household consumption and investments. Lower interest rates lead to higher optimal stock investments and lower consumption. Ignoring the time-varying nature of real interest rates leads to overconsumption and underinvestment into stocks when interest rates are high and, ultimately, substantial welfare costs. Being exposed to an extended period of low interest rates even leads to substantial welfare losses when behaving optimally - particularly when being exposed to it at around retirement age when savings peak.