Welcome to Edhec-Risk Institute. Today we are going to talk about carbon footprint measures and we are going to talk about different ways to normalize carbon emissions as a function of company size. The first way that we use to normalize carbon emission is to divide carbon emission by the revenues of the firm. This is called carbon intensity. In the definition of carbon intensity, the task force on climate-related financial disclosure, TFCD, which we have already talked about recommends to use scope 1 and 2 only because of the already discussed limitations of scope 3 estimates which are obviously desirable in principle but which are much harder to do and therefore tend to be more noisy proxies for the aggregate emission of the firm. Carbon intensity is a quantity that can be measured at the level of a single company and then it can be aggregated at a portfolio level, where we use the portfolio weights as a weighting factor to aggregate the intensity of individual stocks and therefore to obtain carbon intensity of a portfolio. As opposed to using carbon intensity, one could also use carbon footprint measure where total emissions are normalized, not with the revenues of the film but with the market cap. Now, the expression here gives you the carbon footprint of a portfolio, whereby the carbon footprint of each company again, are weighted with the portfolio weight Wi and sum over all the portfolios, and then it's multiplied by a factor of $1 billion. Now, the key advantage of this very measure is that it gives us a sense of how much or how many tons of emissions are being involved in a $1 billion investment. That makes for a more tangible way for investors to understand their contribution or their footprint or the footprint of their portfolio. Now, this is good but there's a problem with this measure and the main drawback of this measure is that it tends to have lots of volatility because obviously as market prices move every day then the market cap of the company moves as well and therefore, the carbon footprint measure moves even if nothing has changed about the company impact in terms of emission. It's a highly volatile measure that fluctuates on a daily basis while carbon intensity because it's normalized by revenues, it's only revised when revenues are revised, say on an annual basis. Now, if you take a look at the universe of European Stoxx, we're looking at the 600 companies that are part of the European Stoxx 600 index. We're actually looking at fewer company than 600 for which we are able to obtain data, for example, 519 for scope one, and that goes down to 423 for scope 1, scope 2, and scope 3, suggesting again that we're having a bit more difficulty in estimating scope 3 for some of these companies. Now, what you can see is that there's of course, an increase in carbon emission measured in terms of million tons of CO_2. There are an increasing pattern as you move on from scope 1 to scope 1 and 2 and scope 1, 2, and 3. Obviously, there's a factor of five in this case where the mean value of scope 1 emissions is around four, it's 3.87 in this sample, while the mean value for scope 1, 2, and 3 reaches 20 million tons of CO_2 in this case. There's lot of dispersion as well, in particular when we're looking at including scope 3. This is what the distribution looks like. We see that there's a bulk of the distribution of companies that have a relatively low emission level and then there is a long dispersion, long tail on the right-hand side with some companies having a lot of carbon emissions. If now we switch to carbon intensity where again, we normalize in terms of intensity, we find that the mean value of this normalized quantity is 17 percent. Again, in terms of million tons of CO_2, divided by the revenues of the firm, and it goes all the way to 61 percent when we also account for scope two and scope three. Again, a pretty high standard deviation when it comes to the inclusion of scope 3 in this analysis, and again, we see a wide dispersion of firms including some firms that have an extremely high-intensity level for some of them. Now the last one that we're going to look at his carbon footprint where we divide carbon emissions by the market cap of the firm. In this case, the mean for scope one is 26 percent. It goes all the way to 89 percent when we include scope 1, 2, and 3. Here again, we find some fair amount of dispersion especially when scope three is included, and again the distribution of those carbon footprint measures suggests that they are firms outliers, firms that have a very high carbon footprint. This, by the way, suggests that any attempt at decreasing the carbon footprint of a portfolio will typically involve reducing the weight allocated to the stocks that tend to have a much higher than average carbon footprint.