Well, we have now arrived to the final episode of the fourth week in which we talk about risk. Let me briefly recap what we did and then I'll tell you where we will go from here. Well, we said that the overall approach to risk, it deals with the ideology around the variables and it contains the following steps. Again, step 1, this is R is a random and, normally, with normal distribution. And from here, we got all these Rs for portfolios, Rs and Sigmas. Now, step 2, here, from these portfolios, we got diversification, beta, co-variances, and all the stuff. Then came step 3 that I will call special portfolios namely that was RF RM. And then from here, we also talk about efficiency and from here, we get to CAPEM saying that CAPEM is equivalent to saying that the market portfolio is efficient. And then, step 4 was this weighted average cost of capital. Basically, that's about how this goes. Now, what's good and what's bad about all that? We know that the general set of challenges dealt with the idea of expected versus factual and also, we dealt with the idea of all the ability of measuring some of these parameters, primarily, the beta and also the important objection was the composition of the market portfolio. That is not crystal clear for anyone right now. Then there are some other objections in this area. One objection is this normal distribution of the famous ideal of black swan sthat was so nicely put in the famous books of Dr. Nassim Talem, is about the fact that when we ignore the fact that some of these extremely unlikely but potentially damaging events may indeed occur and they do occur every now and then. Then the whole fabric of finance changes. And the important thing to observe here is that indeed, in many cases, there are certain areas in which we do have to take these black swans into account. But in the vast majority of more simplistic cases, especially in the evaluation of real projects, not of the evaluation of really very risky, the root of securities, that's a nice approximation. And so the idea is always like that. You have to realize every time when you deal with evaluation of certain instruments to what extent the overall set of assumptions is adequate with respect to them. In most cases, it is. And in these exceptions, they oftentimes just support the rule in general. Now, the other thing that must be taken into account and from here, we are sort of building a bridge to our next week is so far, with all these objections dealt with the idea when we said that the MPV is not on the best criterion but the uniform thing to come up with the value of the project. And now we can ask a big question. Are there areas in which MPV does not hold and why? And in order to come closer to that, I will introduce the following idea. Remember, we said that we make a decision now with point zero. But then maybe at some future point in time, some piece of important information arrives. What if we had an opportunity to adjust our project at the later point to this newly arrived information? And will that the ability would be extremely valuable? And that introduces the whole general idea of an option. And although options are widely known as popular financial instruments that are traded in huge volumes, but for us, we will use this idea but we'll apply that to, let's say, the projects that deal with something real. Actually, it oftentimes will be even more challenging and we will see that in the areas where these options are important, and there are quite a few, oftentimes, we will see that the question of how we can the value this option, that becomes a crucial point. And unfortunately, the approach to option evaluation is much more advanced than the approach that uses MPV. We will study that in week 5 in quite some detail trying to avoid the most intimidating formulas but still trying and realizing not only the ideas but the mechanics behind them. And then we'll see that sometimes, in option evaluation, the MPV formula fails. But we will be able to see how the combination of MPV without an option plus valuable option may result in a better and more adequate project evaluation. So now, I will close this week and as always, I wish you good luck with your assignments with regard to risk. And I'll see you next week in the interesting and more advanced, if you will, week that deals with options and options evaluation.
