Now, in the previous episode, we talked about the idea of diversification and we basically said that the total risk of any portfolio consists of two parts. One part is the individual, or sometimes it's called idiosyncratic, but for us, it's important that it's diversifiable risk. And there is a certain floor, that's the market risk that cannot be diversified away by any combination of securities in the portfolio. Now, this episode contains some fundamental ideas how this portfolio approach can lead us to very classic, and I would say usable results. And I would not spend much time on that. I will just pronounce them because in order to study them in detail does require some more attention to the material and you just have to think about that, let's say, more than once. I'll just pronounce how this works. So the whole idea is that we would like to know what contributes to the portfolio risk. And here we know that the idea is that's only the market risk of the portfolio. And we would like them to find some sensitivity, with respect to sensitivity of any security, with respect to the market portfolio. Well, for the first time I produced this important idea of the market portfolio. Well, what is it? In the vast majority of cases, people use some stock market portfolios like the S&P 500 in the U.S. as a proxy for the market the portfolio. Although, this is not perfectly true because clearly there are all other securities that must be also included in that. All fixed income securities, all mortgages, all real estate, and even all human capital that people do not know how to properly evaluate. So this whole idea of the composition of the market portfolio remains one of the few most fundamental questions in corporate finance that although have been widely studied in the last couple of decades, but unfortunately, these studies have not produced any final result, if you will. So people keep thinking about that and they keep recognizing that this is a huge challenge, but unfortunately, they have not come up with any mutual except the way to quantify it. And all that ideally, is that this sensitivity of insecurity has a special name that all of you heard about, that's called beta, and for any security I. And well, you've seen the formulas about that. The beta, in general, is equal to covariance between this asset and the market. And then, divided by variance of the market which is the same as the correlation coefficient with Rho_I_M, and then, the ratio of standard deviations. We now understand why the market portfolio plays such an important role because everything else can be diversified away. Again, the logic here goes that, if for any reason the people would like to hold any portfolio of securities that is different from the market portfolio, it can be shown that they can do a better job by holding the market portfolio and doing something else. About that, we will talk in just a few minutes. But for now, I would just say that this coefficient beta is widely known. Unfortunately, it's difficult to come up with, in the correct way, because clearly these betas are not only expected in reality, they are known only from the pairs, but also they contain many series of returns to find them. And that does create some problem. Well, for now, I would like to draw your attention to just one thing. Then, clearly from this formula, there are two special portfolios. One portfolio is the market. Because see what happens with the market if this becomes one, this is the same, so we can see that beta market is clearly one. Because, here again, sigma MM is the same as Sigma M squared. Well, there is another special portfolio that is called beta of the risk-free portfolio. Well, for risk-free portfolio, sigma is zero and therefore, the beta is zero. So, these two special portfolios will play a very important role in our further discussion. And from now on, we will move ahead and say a few other words about portfolios that were specified by Markovitz, and that will lead us to the wrap up of this first, let's call it a theoretical part of this week and then, we will move on to some more practical aspects.
