This study presents results supporting the need to price climate risks in real estate investment trusts. We approach this objective by conducting some empirical analyses for global, regional, and [US] sectoral REITs for want of wider coverage while we also consider variants of climate risks involving physical and transition risks. We first establish that climate concerns amplify the volatility of REIT returns. While our results are split for sectoral REITs, we find that both physical and transition risks magnify the volatility in the regional and global REITs market. However, when we consider the US sectoral REITs, we find contrasting evidence between the two variants of climate risks. While the transition risks seem to raise the REITs market volatility, perhaps owing to improved trading in the market as signalled by some level commitments towards addressing climate change, the physical risks associated with damages due to climate change tend to lower the REITs market volatility due to lower trading. Consequently, we formulate a framework that enables a profit-maximizing investor to observe climate risks when making investment decisions in the REITs market, and we further show that doing so provides higher economic gains than ignoring it. This outcome has implications for investors looking for the best hedging strategy against climate-related risks, especially as the world intensifies efforts towards de-carbonization.