So now we've introduced the concept of a model as a deliberate simplification of reality. You've had a look at the London Underground map, that world-famous image, which is a nice sort of introduction to this world of modeling. 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 our sort of more formal modeling, 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. 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. Now, 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 and 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 models are only as good as the model itself, which includes the assumptions we attached to them. So although we will make simplifying assumptions because other things equal, we value simplicity over complexity, beware, if we make wrong assumptions, this could lead to very dire consequences. 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 victim such as the collapse of Lehman Brothers, Bear Stearns or takeovers of these and others. Indeed in billions of dollars being wiped off global financial markets. 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 you to a single factor or a single group of people. Nevertheless, for the purposes of this short session on modeling and the assumptions attached to models, 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 credit, 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 the subprime mortgages. Collateralized debt obligations, CDOs. Sorry if 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 property up markets, and really an assumption which many people made. Call it hubris if you will, but really there was an assumption that house prices 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 a 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 property prices. Hence a lot of the models which people built to price accurately, I use that term loosely. These CDOs and other financial instruments are really based on this assumption of ever-increasing housing prices. Indeed for a period of time, the housing market, the prices were going up and up and up and it seemed these assumptions and 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 oversupply of houses onto the market, the lack of demand for people to buy them. If supply exceeds demand, the price, of course, is going to be plummeting. Really this realized event of falling prices was not something that the models created by some very clever people, people with PhDs in maths, statistics, physics, etc, is not something that they typically had anticipated. Well, maybe they have 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 very severe. Perhaps just another one I'll offer up, also perhaps finance related, later on in this course, we will look at some common probability distributions. Now, if I mention the normal distribution to you, if you've heard of it, great, if you haven't please don't be concerned, it's to be formally introduced later on. But this is sort of familiar bell-shaped curve. Now, modeling, trying to simplify reality. As we shall see in due course, the normal distribution, a very useful one to work with. Many statistical models will have an underlying assumption of normality. So apply it to finance, a lot of people may be willing to assume that the returns on say, stocks, may follow a normal distribution. A lot of models about whether to invest or not to 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 a modeling environment. However, as we know, as we further simplify reality, we increasingly depart from reality. In fact, 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 indeed very bad returns, like losing money, these sorts of events tend to occur with higher probabilities than say the normal distribution would predict. Now, we've got to consider these sorts of issues of probability distributions and the 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- In fact, the real world consists of perhaps more Black Swan events than a 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 of a victory in that election based on an assumption of popularity say of the party or the policies proposed, and maybe they have an electoral campaign which reflects the assumptions they've made or 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 the completely opposite outcome to which you had anticipated. So assumptions. Do we like them? Are the things equal? Yes, we simplified 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.