Hello, everyone. Welcome back and thanks for joining us again. In this lecture, we're going to learn about the first main insight of the Capital Asset Pricing Model. We're going to show that in equilibrium only investors will hold the market portfolio. Maybe in different proportions but they will all hold the same risky portfolio which will turn out to be the entire market portfolio of risky assets. Let's see how this works. Remember the efficient frontier? Which we've seen before. So remember that I have the mean volatility space here. So let's suppose that there are many, many risky assets. Many, many risky individual assets. Each with the mean and volatility. And let's suppose there is the risk free way. The risky assets, which basically goes on the y axis because it has no risk. So we know from previous lectures that mean variants investors will diversify a way of risk when they can. They will construct portfolios, they will put together a combinations of acids in a way to diversify a way any unsystematic risk. In fact they will, they're going to prefer the best portfolios, efficient portfolios. Which lie on the upper part of the main variance efficient frontier. So just remember that this is the low cost of portfolios that have the minimum risk for a given level of return. Again, remember, given this possibility of course nobody would hold on to an individual asset, everybody would prefer to hold an efficient portfolio, a portfolio that has the least risk for a given level of return. And again, we know from mean optimization from previous lectures that an investors now who wishes to maximize her mean variance utility will choose to hold a combination of the safe asset, the risk free asset with the best possible risky portfolio along this frontier, the one that maximizes the Sharpe Ratio, which will turn out to be the Excuse my drawing here, but imagine that's a tangency point. So this is going to be this tangency portfolio. Which we called a mean-variance efficient portfolio. So then, basically, the efficient frontier simply becomes the capital allocation line. And all investors will basically hold a mix of the risk free assets and this mean variance efficient portfolio. So based on the evaluation risk of course. So this is all from mean variance optimization that we've before. Now, let's add some assumptions. So assumptions that come from the Capital Asset Pricing Model, the CAPM. So CAPM assumes that investors are all risk averse just like in mean variance optimization. And they are maximizing their expected mean variance utility. They are rational mean variance optimizers. And they're all competitive, they're individual price takers. In other words, no single investor can influence our prices. Now, of course these are assumptions. We make these assumptions to get to the results. Then we can go back and relax any assumption that we don't like and see how it affects our results. But just bear with me for the moment. What else? Well, there are no taxes or transaction cost, basically no frictions. Everybody can borrow and lend at the risk free rate, everybody has the same information, there is no information asymmetry and most importantly all investors has the same expectations, how much is this expectations? What does that mean? Well, what that means is they all agree on the inputs to the optimization problem that they face. They agree on the expectations of returns, variances, correlations, etc. That and here is the important point. So if everybody is acting as a mean-variance optimizer, facing the same frontier What must the tangency portfolio be in order for markets to clear? Think about it. Well, here is the result. If they all have the same expected returns, volatilities, correlations, etc., all inputs, then the solution, the tangency portfolio that delivers the highest Sharpe Ratio, the mean-variance efficient portfolio an equilibrium will have to be the entire market portfolio of risky assets. Think about it, everyone is solving the same problem. And choosing the same tangency portfolio and then holding combinations of that tangency portfolio and the risky asset. Some borrowing, some lending in the risky asset. Which via revile will cancel out. But the positions in the risky portfolio right, should in equilibrium aggregate to be the entire market portfolio of all risky assets. And again, remember if any asset is excluded in equilibrium as we've seen before with the IBM example in the last lecture, then it's price we'd have to change so that in equilibrium investor demand exactly equals the supply of securities. So basically market portfolio is mean variance efficient. So another way to state this same Insight is to say that in a CAPM world the capital allocation line that goes through the risk, the tangency portfolio. In a CAPM world the capital allocation line goes through the market portfolio. And it's called now The capital market line. So the efficient frontier now becomes the set of portfolios that you can construct with the risk-fee asset and market portfolio. Now, this has a very important implication. It means that holding the market portfolio is efficient. What this means this passive investing is efficient. All we need to invest in basically, it's an index fund that replicates the market portfolio and choose how much we want to allocate in this index fund and a safe asset. That's consistent with an efficient portfolio allocation. So in this lecture, you'll learn the first insight of the Capital Asset Pricing Model. In the CAPM world, the entire market portfolio, risky assets, is mean variance efficient. In other worlds, it is the optimal risky portfolio that provides the highest sharp ratio. Therefore, all investors, in equilibrium, will hold the market portfolio. They may be holding it in different proportions, but they will all hold the market portfolio as their risky portfolio. Basically what that implies is holding on to index fund that replicates the market portfolio is efficient. Passive investing is efficient.