Investments in energy technologies are substantially governed by climate policy. We demonstrate analytically that price-based instruments, such as carbon-taxes, and quantity-based regulations, like emission trading systems, have distinct effects on the (co-)variance of power plant profits. If investors are risk-averse, these differ- ences lead to divergent investment portfolios, breaking the equivalence of price- and quantity-based policy instruments under risk-neutrality. Using the European power sector as a case study, we calibrate an electricity market model with stochastic de- mand and find that, compared to a carbon tax, emissions trading pushes up the share of fossil fuel assets in a representative investor's portfolio since counteracting effects of permit and electricity prices reduce the covariance with other technologies, thereby enhancing the diversification value of these assets. Uncertainty about the stringency of carbon taxes leads to lower shares of fossil fuel assets with increasing risk aversion.