All right. Let's think about what premium do investors require for holding risky assets. In order to properly address this question, we have to think about kinds of risks that investors face. And what I will say in just a few moments is that the investors actually require this risk premium not for all the risk that they take, but only for part of that risk. Well that sounds strange, and it seems that investors sort of make the choices and they treat risks differently, and that doesn't seem to be very natural. But the idea is that there is a very simple procedure to reduce risk exposure by real distinguishing between two different kinds of risk. This procedure is very well known and this called diversification, and I will start with a funny example that shows its mechanics. Well, this example is used in the textbooks, but still I will reproduce it here. So I will analyze the behavior of a portfolio of two stocks with respect to a certain kind of risk. Well, the kind of risk will be weather, and these two stocks are one company that I will call sunglasses, and the other I will call umbrellas. And the portfolio will be, this is a portfolio, this will be well, let's say for simplicity, one-half of sunglasses plus one-half of umbrellas. Well, clearly you know that in the portfolio, we don't have fractions of stocks. But for simplicity, we'll say that you can take whatever 50 stocks and 50 stocks altogether will be 100, it doesn't really matter. And now, these are certain inputs. Well, we can expect certain weather conditions and those will be of three kinds; that'll be a sunny weather, normal, whatever it is, because clearly, normal depends, one way of normal is in California, the other is somewhere in Norway. And then we will say, this is a rainy year. Now, you don't have to be a wiz to realize what's going on here because clearly, in a sunny year, sunglasses feel great, in the rainy year, umbrellas feel great. And in the normal year, we would say that both of them behave sort of in an average way. So I will put some numbers. Let's say, the return for the sunglasses in sunny year will be plus 33 percent, the return in a normal year will be plus 12 percent which is about the same as the market. And in the rainy year, unfortunately, it's negative nine percent. Well, for umbrellas, it's all the other way around, here it's minus 9 percent, here it's plus 12 percent, and here is plus 33 percent. And see what happens, if you take this portfolio, you can see that in all cases the portfolio return will be the same and equal to 12 percent. So plainly speaking, we, by holding the portfolio of one half of sunglasses, one-half of the umbrellas, we've completely diversified away the risk of changing weather. So our portfolio is risk-free with respect to the kind of risk that is called weather here. Now, you cannot, by the use of diversification, make a portfolio of risky assets completely risk-free. But, you can indeed diversify away specific risks associated with this very asset. So this 12 here, shows to you the average return on the market that takes into account risks other than the weather. And clearly, we can say that if we proceed with this diversification, let's say, we will try to diversify away the exposure to whatever, some other things. But we cannot diversify away the exposure to global macroeconomic factors or many other important factors that affect the economy. So we can indeed proceed and see that now the words that they produced in the very beginning of this episode, they start to be a little bit more sensible and meaningful, because when I said that investors do not care about all kinds of risks. So here you can say that if I am an investor and say, I would really insist on holding just the stock of sunglasses, and then I take a risk with respect to weather, and this risk, unfortunately, forces me to require a premium. But, people say, "You can diversify this risk by holding a portfolio and therefore, you can not require a premium for that." So that is the way how diversification works. And I will just draw a very simple chart that shows to you that if for example, this is the number of securities in your portfolio, and this is the portfolio standard deviation, then it goes like this, the overall risk is like this, where this is the market risk. And if you increase the number of securities you remove this risk which is the individual risk. This is how it goes. And this number of securities does not have to be really high. Oftentimes, if we have a couple of dozens of securities, you can almost completely remove this individual risk. We will discuss how we can use that to proceed, starting the next episode.
