The slow adoption of residential energy-efficiency retrofits continues to hamper the energy transition. We study incentives for adoption by proposing a model of optimal investment under uncertainty where the wealth-maximising agent has the option to delay. Stochastic portfolio returns and energy prices are taken into account. An extension of the model where the energy carrier is switched, e.g. from gas to electricity, is also considered. Exercise boundaries for the optimal stopping problem are estimated numerically for recent case studies of German buildings. Investment is generally not optimal at current energy prices and market conditions. Increasing correlation between gas and electricity prices erodes the value of technology switching. Comparative statics reveal that energy-efficiency investments become optimal at relatively lower energy prices as wealth, income, and savings behaviour increase, and portfolio drift and volatility decrease. Consequently, incentive to invest in retrofits is far more heterogeneous along wealth dimensions than standard discounted cash flow analyses suggest. An examination of retrofit subsidies demonstrates how free-riding by wealthier agents occurs when subsidies are not appropriately targeted. We show that the pursuit of economic efficiency in subsidy design might have regressive effects on the wealth distribution.