Welcome to Module 4. It has a focus on regime analyses and implication for portfolio decisions. Well, we have reasons to believe that frees can return parameters of various assets are actually not constant full time. We have reasons to believe they're time varying across the business cycle, and obviously an ability to capture these time changes would be of critical importance in portfolio decisions. For example, it is very intuitive that we should increase risk-taking when risk-taking is more rewarding for example. Now, capturing those time changes is little bit complex, and there are many different approaches that one can try and follow to estimate how those parameters, those risk can return parameters evolve over time. It turns out that the monks those many different approaches, there exists one which is more parsimonious and tends to provide pretty robust results which sees to model these time dependencies by trying to relay them to actually a small number of different regimes. Well, what is a regime in the first place? Well, a regime is a period of time in which precisely the characteristics of these assets would tend to be very stable, or reasonably stable. So the cost of oversimplifying we believe we would assume that risk and return parameters they constant within a given regime, and whenever we switch to a different regime, then these will involve some time variation in the parameters. These economic regime should be as distinct as possible from each other, and they will have this degree of homogeneity within the given regime that could help us try and characterize what the asset class behavior will be. Now there are many different ways John to think about what regimes could be and how we could characterize them. One way would be to think about two regimes; normal and crash. We could expand that a little bit and think about query regimes normal, transition, and crash, and we could have more regimes as well. We could think about a world in which we have a low volatility regime and a high volatility for example, and obviously that would have relations with respect to the aforementioned categorization in terms of normal and the crash. The key point is first to being able to evaluate the regime separately, and then to be able to provide a portfolio construction framework that allow us to take into account the different regimes and the fact that eventually throughout time, we will have with a given probability, we'll have to live for those different regimes. Well, this is precisely the task for which we have reasons to believe that Machine Learning techniques could be of some use, and that's what John is going to talk about. Thanks Lidel. Let's go back to the beginning of portfolio construction. The traditional portfolio model developed by Harry Markowitz was assuming a multinomial distribution. In this graph, we see the red probability distribution coming from a multinomial, and the blue lines to probability density function for historical performance of the Stock Market. The differences are quite evident. On the left side, we see much larger losses that have occurred had you been a normal distribution. In fact, October 19th 1987, we saw a 22 percent drop in one day that would be 22 standard deviations off as a normal distribution. In fact, I was at a conference into Wharton and Hurry Marcos was there that day giving a presentation. So you also see much tighter distributions around the central medium. This kind of historical performance is very different from a multinomial. Therefore, when we look at or looking models, we want to model that in a way that gives us better estimates going forward. Here's another view of that. This is called a Q-Q chart, and if the numbers historically, the dots in there represent historical return performance. If the multinomial distribution is accurate, we'd see all dots at current on that straight line. However, you see on the left side and somewhat the right side we have deviations. That means that the normal distribution is not really a very good estimate going forward. We have these conditions which are called contagion, and that should be modeled in a very different way as we will look at in this module. Here we see the GDP changing over time in the United States since 1950. If you look at a long period of time, you'd see a very, well, it looks like a very smooth progression. But during crash periods where we see slightly darker areas here, you see much bigger drops in GDP, and that's what we want to model is what happens during those drops, and compare that against the periods where we have normal relationships. They gave another example. This graph looks at about a seven-year period, the return of the S&P 500 in the middle or the 4500 in the middle, and here we have a variety of hedge funds and how they performed. The blue circles here represent positive returns and the orange represent negative returns. We'd go back to our little graphical network, and in particular the correlations are represented through the darker lines versus the lighter lines. Correlations above 0.5 have darker lines, and correlation below that have either no lines if they're below 20 percent, and lighter lines between 20 and 50 percent. Here you see some diversification, but underlying it, you still see a major factor which is the equity risk in premium is built into me the hedge funds. Still there's some diversification. However, if we go to a crash period, it's the next chart here, we see high correlation across all asset. So hedge funds you would think ought to be diversified. However, during these periods of contagion, we see many crashes. We see many things dropping dramatically. So indeed, you don't have that diversification that you get during normal periods even with categories like hedge. You'd see many of them having problems during crashes. So we want to find a way to identify normal periods and crash periods. We're going to use Machine Learning for that, and then we're going to build a multi regime portfolio model which extends that, which allows us much more accurate estimates of the downside risks. The worst-case risks which of course is the most important thing for most investors.