[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 variance 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 loss distribution, so P and L distribution are always symmetric. Remember modern portfolio theory put forward by the Nobel Prize winner, Harry Markowitz, when you want to invest in financial assets, you should do a trade-off between risk and reward, 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 probability of getting a positive return or the probability of getting a negative return are roughly the same. So, this assumption is indeed correct if you look at investment in standard asset like for example when you invest in the portfolio like the Standard and Poor. Indeed the probability to have a positively return on the Standard and Poor and the probability to have a negative return on the Standard and Poor is roughly the same. But now, if you look at more complex assets like option, and you want to invest in these option, then that assumption of symmetry is not really collect. So if you remember what I'd talked about in basic concept in finance. When you look at the histogram, so the distribution of the return can be symmetric or asymmetric. And when we have an asymmetry we speak of about skewness. So when you look at investment in option typically what you will have is asymmetric distribution. So for example, when you invest in your call, so you buy your call, so 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 unlimited potential gain. So here clearly you have an asymmetric 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 button shell is limited to the premium that I receive. But I might have an unlimited downside and an unlimited loss. Okay, so in that case clearly the assumption of a symmetry distribution in not correct, because the probability to get enough movement and the probability to get a down movement are another thing. So what are the learning outcomes of this session? So we have two, in fact three learning outcomes. The first learning outcome is the 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 the case for example if you invest in options, but it will also be the case for example in, 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, their profit and loss distribution will be asymmetric. So the third learning outcome is that when you look at asymmetric profit and loss distribution, you should pay particular attention to negative outcomes or very large extreme negative returns. So in the next session about the valued risk and expected short form, we'll see the two type of this measure are particularly suited to that type of asymmetry distribution when you want to have a good measure of risk. [MUSIC]