Interest in measuring the GHG footprint and the GHG intensity of investment portfolios is growing! On the one hand, it's not saying much since so few investors cared in the first place. Still, it's enough to sustain a growing industry for generating these carbon metrics such as Trucost (and CAMRADATA?). In fact, Bloomberg terminals (computers for traders) now have a Carbon Risk Valuation Tool. For the investors that don't care, activist organizations such as 350.org have started calling for them to divest from fossil fuels. There are also (maybe?) individuals who want to better understand the carbon impacts of their own savings, investments, and retirement plans.
There are several different ways to calculate the footprint for investments, often referred to as financed emissions. There are then several different ways to calculate the carbon intensities of investments, where the carbon intensity is the carbon footprint normalized by something such as revenue. This report by the 2 Degrees Investing Initiative presents a good overview of these different metrics.
Really, the metric one uses depends on what it is being used for, what decision it is informing. These decisions depend on the investor (activist's) theory of change and ethics. For example, an investor making decisions on how to allocate funds might be purely motivated to minimize exposure to carbon risks. In other words, it is an investment strategy based on the theory of change that regulations and other future events will make carbon intensive companies less profitable. The investor behavior is not based on the ethic that it is immoral to invest in carbon intensive companies. It makes economic and professional sense that this investor should use a metric that will highlight the exposure to carbon risk.
An individual whose money is managed by said investor might think that it is immoral to invest in carbon intensive companies just as they might think it's immoral to invest in tobacco companies. Then, regardless of what investment strategy was actually pursued, they might care about how much emissions his or investments are "responsible for."
I am working on a report that claims that the carbon metric used by investors to allocate investments doesn't have to be and in fact probably shouldn't be the same one used to evaluate the ethical (social?) responsibilities of the investments.