Now I'll say few words about an extremely important feature of the portfolio, that is, its efficiency. Now the word efficiency is widely used in, not only in finance but in other areas of business disciplines, too. And clearly has lots of different meaning. So for portfolios however, it has a very special meaning. So I will produce a famous chart here that is in all textbooks and there's a lot of discussion of this. I will be very brief. So the chart shows that if this is a sigma of the portfolio, and this is the expected return of the portfolio. So basically this is risk and this is return. And clearly, we have some one special point here. This is risk free, because risk free sigma is zero. And so this is, well, you can always argue that. Strictly speaking, risk-free securities do not exist. But like I said, for many, not only decades but even centuries, people would use government securities, especially US government securities as a proxy for risk-free. Now any security here is represented by a star like this. And when I put these stars, you can say that basically it's difficult to say which one is better. But it seems that sort of this one seems to be a little bit better than this one, because there risks are close. And not only close, but the risk of this is lower, but the return is higher. So you can see that this portfolio or this security is better than that one. So you can put all of these stars and then you can create a certain envelope curve here. And the portfolios that are on this curve market it's called efficient portfolio. So the idea is that if you are here, Then you have certain risk and then certain return. So you cannot find a portfolio which has either for this level of risk, a higher return because all of them are here. And by the same token, if you fix this return, you cannot find the portfolio of low risk. So this is the best Investment for your combination of preferences in this risk and return. And then, well, clearly for example I put that in that line because for all these pieces there is a better portfolio. So basically you have to stop somewhere here. But now see what happens. If investors could only hold these portfolios and they could not borrow and lend. Then we would say that dependent of a personal [INAUDIBLE] preference, you can always find a portfolio on this envelope curve. And this is the curve of efficient portfolios and then you will be better off now. But if we introduce borrowing and lending, so that means that this is a straight line that goes through this point. And we can see that there may be some cases. On this line, you do not have any portfolio. Here you have many portfolios, and there is clearly a very special line that goes like this. And this is called a special tangency portfolio. So it just touches this envelope curve. And look what happens here, if you can borrow or lend, what you can do is for example for this level of risk. Before you would have to take this one. But now it can be shown that if you use this portfolio and then you would borrow some money, and you could come here. Now, this combination of risk free asset and this tangent portfolio shows you a way how to be better off than staying on this envelope. Now, the whole idea about the famous formulas like capital as a pricing model that we'll talk about in just a few moments. And so in the others they talk about the following idea that this portfolio, and you don't realize there is no magic in that, is not only tendency, but this is the market portfolio. So basically from here on, we will say that the way how people derive, or let's say prove the capital as a pricing model as the most widespread criterion for assessing the expected return on assets. This is tantamount to saying that the market portfolio is efficient. Now there is a set of combination of these portfolios and some logical ideas and how you proceed with that to prove that this is the case. But general idea is like this, if any investor holds any portfolio that is different from the market portfolio, and this is for any way is better off than everyone would like to hold this portfolio, and then as a result then all the people will hold this portfolio and then this portfolio will become the market portfolio. Something like that without going deeper because then some of this logic may seem to be sort of strange. But it is perfect logic and it is widely accepted conclusion. So here we can see that the progress of here basically says that the, I'll put it that the market portfolio, Is efficient. By the way empirical evidence show that the market portfolio if we use proxies as the US Stock Market is not perfectly efficient. But it remains an open question. Whether it's because this approach is not perfectly correct or the composition of the market portfolio is not complete. This is remains an open question and for that reason people still take this as the primary idea and from here they proceed. Now, I will wrap up this part that talks about how we come close to the derivation of the famous capital as a pricing model. And starting in the next episode, we will come up with that and see where it leads and how it can be used.