[MUSIC] So now we've introduced the concept of a model as a deliberate simplification of reality. We've had a look at the London Underground map, the world famous image, which is a nice sort of introduction to this world of modelling. But clearly in a course on probability and statistics, we need to consider not maps of the underground but rather probabilistic statistical models of the real world. Well before we start to do all sort of more formal modelling, something I'd like you to consider at this very early stage is the role of assumptions in model building. Now, we said a model is this deliberate simplification of reality. And as a tool to assist us in this simplification of that very complex real world we find ourselves in, we often try to choose assumptions which will act as simplifying assumptions. Although we'll be seeing various assumptions introduced later on in the course, I should at this juncture give you a bit of a health warning, namely the potential caveats to actually introducing assumptions to models. Because as in when we have a functioning working model, we'll use this to try and describe, or maybe predict some behavior in the real world and use this in order to make our decisions. For example, to invest, or not to invest in a particular stock. So the conclusions, the output of our module's are only as good as the model itself, which includes the assumptions we attach to them. So although we will make simplifying assumptions, because other things equal, we value simplicity over complexity, but where if we make wrong assumptions, this could lead to very dire consequences. And let's just perhaps consider an example. Now I'm sure many of you are familiar with the global economic and financial crisis erupting around about 2007, 2008. That laid claim and had numerous victims, such as the collapse of Laymen for all those turns or takeovers of these and others. And in dearly billions of dollars being wiped off a global financial up market. Now in a short recording such as this, it would be overly ambitious to try and explain what caused the financial crisis. Clearly, it would be naive to focus and claim it was just due to a single fact or a single group of people. Nevertheless, for the purpose of this short session on modeling and the assumptions attached to modules, let's focus on the subprime mortgage market which some of you may have heard of in the media. As I say, it would be naive to say the crisis was solely due to those subprime mortgages. One could attribute some blame the amount to attribute to different actors is highly subjective. But you could say it was due to ultra loose monetary policy, reckless consumer spending, trade imbalances, the list goes on. But to return to these subprime mortgages. Collateralized debt obligations, CDOs, some of you may have come across those terms previously. Well this is not a finance course, and I don't propose to give you an in depth tutorial on CDOs. But nonetheless, we use to sort of model the a la property markets, and really an assumption, which many people made, called it hubris if you will. But really there was an assumption that houses really only went in one direction in the US and that was really going up. So when people were pricing mortgages, when they were valuing the properties on which these mortgages were used to buy, there was really a sort of, common acceptance, a common assumption that the US housing market was really headed in one direction, which was upwards. It was unthinkable that there would be, really a collapse in our property prices. And hence a lot of the models which people built to sort of price, accurately, I use that term loosely, these CDOs and other financial instruments were really based on this assumption of ever-increasing housing prices. And indeed, for a period of time, the housing market, the prices were going up and up. And it seemed these assumptions in the models were reasonable ones to make because they were reflected in reality. But as we know, what goes up can and typically does come down eventually. And there was a collapse in the US property market, mainly due to lots of people defaulting on these subprime mortgages. The over supply of houses on to the market, the lack of demand for people to buy them. And if supply exceeds demand, the price of course is going to be plummeting. And really this event, this realized event of falling prices was not something that the models created by some very clever people, people with PhDs in math, statistics, physics, etc., is not something they typically had anticipated. Or maybe they had, but perhaps they mispriced the risk of this event and thought it was an event with an extremely small probability of occurrence, which perhaps did, was not a realistic assumption. So beware assumptions you make in models. Yes, they may work in the very short term and all maybe well but if you base maybe some very important decisions on flawed assumptions the consequences could be a very severe. Now perhaps this is another of also perhaps finance related. Later on in this course we will look at some common probability distributions. Now if I mentioned the normal distribution to you, if you've heard of it great, if haven't, please don't be concerned, it is to be formally introduced later on. But it's sort of a familiar bell shaped curve. Now, modeling, trying to simplify reality. And as we shall see in due course, the normal distribution, a very useful one to work with. And many statistical models will have an underlying assumption of normality. So applies to finance, a lot of people may be willing to assume that the returns or net say stocks may follow a normal distribution. And a lot of models about whether to invest or not invest in a particular stock may be based on such a simplifying assumption. So true on the plus side, we have the inherent beauty of simplicity. The normal distribution very well known and quite easy to work with in the modelling environment. However, as we know, as we further simplify reality we increasingly depart from reality. And in fact, as some studies have investigated, or many studies have looked at the returns on stocks. And have actually found that the chance, the risk, of getting very high returns, or any very bad returns by losing money, these sorts of event tend to occur with higher probabilities than say the normal distribution, which are predict. Now we've got to consider these issues of probability, distributions, and attributes, the characteristics more formally, as indeed we shall. But if you have a model based on perhaps a flawed assumption, in this case of normality attached to share prices. And in fact the real world consists of, perhaps, more black swan events than the normal distribution might predict, then there's potential for very dire consequences. Perhaps just to round off, even in the political sphere. If a politician calls an election with the expectation. Expectation of a victory in that election base on assumption of popularity state of the party or the policies proposed. And maybe they have an electoral campaign which are effects the assumptions they've made. There was an anticipation or perhaps a victory. Well, if you get your assumptions wrong, if they turn out to be flawed, then you may end up having a completely opposite outcome to which you had anticipated. So, assumptions, do we really like them? Are the things equal? Yes, we simplify reality but we must be conscious that flawed assumptions could lead to very incorrect predictions of the future and hence could lead to very bad decisions being made. So please indeed feel free to use assumptions but use them with caution. [MUSIC]