[MUSIC] In the previous videos, we have looked at how to construct a portfolio by using the effect of diversification to reach a low level of risk for a given level of expected return. Now we're going to move onto a slightly different perspective on this portfolio allocation problem. We are going to look at the implication of this type of decision at the market level. And the first step in doing that is to look at a result related to this literature on portfolio allocation. In the mean variance framework, which is called the Two Fund Separation Theorem. So what is it about? You'll see it's very simple. Let's start again with our description of the optimal diversification effects depicted here through the efficient frontier. We have a risk free asset, and the three risky securities. The red line is the efficient frontier with the risk free asset, the green line is the efficient frontier with only the risky security. Remember that these portfolio denoted tangency, is the only portfolio that belongs simultaneously to the two efficient frontiers. We know that this portfolio, because it also belongs to the green frontier, is only composed of risky assets. So how are investors going to choose their portfolio if they have access to the risk-free security? They're going to choose the portfolio along the green line. Not everyone will choose the same portfolio, because not everyone has the same target of the same tolerance to risk. An individual that is very risk averse will like to have a low level of risk in his portfolio. So he will choose to reach maybe a level of standard deviation of 5% and his portfolio will be located on the red line because he will optimally diversify. But his portfolio will be located close to the level of RF. Another investor who is more tolerant to risk and we seeking a better expected retail. Might choose a portfolio located to the right of the tangency portfolio, above the tangency portfolio in the red line. For example, with a target of 15%, we could reach something around 8% in expected returns for a target of 15% in risk. And this new portfolio would be above the tangency portfolio. What is very important to understand about the composition of these two different portfolios the risk averse and the very risk Tolerance. Is that they are actually composed of two funds. We could view each of these portfolio as a combination between only two portfolios. These two underlined portfolios would be the following. One, is just 100% in the risk free asset. And the other one is 100% in this tangency portfolio. So the actual choice of portfolio allocation, comes down in this framework to choosing the relative weight of these two portfolios. The risk averse investor who is looking for a low level of risk will have a large proportion in the risk free asset. And a small proportion in the tangency portfolio. The more risk tolerant investor, will have a large proportion in the tangency portfolio and a small proportion in the risk free rate. To actually be above the tangency portfolio, so to the right. An expected return which is larger than the tangency portfolio. We will have a negative investment in the risk-free, right? So, borrowing, leverage the position and more than 100% in the tangency portfolio. But, even these portfolios which include leverage are only combined of these two underlying funds, these two underling portfolio. One, the tangency portfolio composed only of risky security, and one composed only of the risk free asset. So this two-fund separation result, is the first step in understanding what this type of portfolio allocation. What type of impact it has on capital market equilibrium. On the equilibrium link between risk and return. [MUSIC]