Cost-benefit analysis is only applicable if the variances of both costs and benefits are finite. In the case of climate change, the variances of the net present marginal costs and benefits of greenhouse gas emission reduction need to be finite. Finiteness is hard, if not impossible to prove. The opposite is easier to establish as one only needs to show that there is one, not impossible representation of the climate change with infinite variance. The paper shows that all relevant current variables of the FUND model have finite variances. However, there is a small chance that climate change reverses economic growth in some regions. In that case, the discount rate becomes negative and the net present marginal benefits of greenhouse gas emission reduction becomes very large. So large, that its variance is unbounded. One could interpret this as an indication that cost-benefit analysis is invalid. Alternatively, one could argue that the infinity is present in both the base case and the policy scenario, and therefore irrelevant; in that interpretation, cost-benefit analysis is a valid tool.