[MUSIC] Hi, I'm Olivier, so I will talk today about risk as volatility. So we will mainly concentrate on two questions. So the first question is are you sure that the vacuums or the volatility is always a good measure of risk? And the second question that we will address is are you sure that profit and low distribution, so PNL distribution are always symmetric? Remember more input for your theory put forward by the Nobel Prize winner Harry Markowitz. When you want to invest in financial assets, you should do a tradeoff between risk and award. And how do you measure risk? You measure risk using the volatility or the variance, which is the square of the volatility. So this is perfectly correct to use the variance as a measure of risk. But when you do that you assume implicitly that the return distribution or the profit distribution or the loss distribution are symmetric. So the possibility of getting a positive return or the possibility to get a negative return are roughly the same. So this assumption is indeed correct if you look at investment in standard assets. Like for example, when you invest in the portfolio like the standard in pools. Indeed propriety to have a positive return on the Standard pools. And the propriety to have a negative return on the standard and pools is roughly the same. But now if you look at more complex asset like option and you want to invest this option, the assumption of symmetry is not really collect. So if I remember what I talked about in basic concept in finance, when you look at the histogram, the histogram, so the distribution of the return, can be symmetric or asymmetric. And when we have an asymmetry we speak about stillness. When you look at investment in option, typically what you will have is asymmetric distribution. So, for example, when you invest in a course or you buy in a course what do you do? You pay the premium today, and in the future you expect to have an upward movement in the stock so that you can benefit from a limited potential gain. So here, clearly, you have an asymmetry in the distribution because the loss are kept to the premium that you pay, and the gain, in fact, can be unlimited. If you look at the reverse position, so if I sell a call, so in that case what I will do is I will cash the premium. And so my upside potential is limited to the premium that I receive. But I might have an unlimited downside and an unlimited loss. So in that case clearly the assumption of a symmetry distribution is not correct. Because the priority to get an up movement and the priority to get a down movement are not the same. So what are the learning outcomes of the session? So we have two, in fact, three learning outcomes. The first learning outcome is that variance is indeed a good risk measure, but only if you look at symmetric distribution. The second learning outcome that we have, is that be careful in which asset you invest. Because the P&L distribution or the profit and loss distribution can be asymmetric. This is a case for example, in if you invest in options, that it will also be the case for example. If you invest in corporate bonds where you can have a default of the company and if you have a default of the company, obviously the profit and loss distribution will be asymmetric. So the third learning outcome is that when you look at asymmetric profit and losses distributions, you should pay particularly attention to negative outcomes, or very large extreme negative returns. So in the next session about the value at risk and the expected shortfall, we'll see that due time of this measure are particularly suited to that type of asymmetry distribution when you want to have a good measure of risk.