[MUSIC] The next question that we would like to address is whether we can write something similar for an asset, a stock for example, that is not on the red line. For example, we could take stock A or stock C. Is there a way to link expected return to the level of risk of a particular security? And intuitively, the first thing we can say is that the risk of asset C, for example, this 20%, some of it should not be compensated by expected return. Why? Because we know we can choose a portfolio with the same level of risk using the effective diversification, but same level of expected return, sorry, but with a lower level of risk. So part of the risk of asset C can be diversified away. And we shouldn't expect to receive an expected return, a reward for burying that risk that can be diversified away. So the correct measure of risk for an asset that is not on the efficient frontier is not the total level of risk, but another measure, a measure of risk that we cannot diversify. This measure of risk is called the beta. So, let's see exactly how this measure is defined. This equation is the relation between risk and return for an arbitrary asset such as asset A, B, or C that is not necessarily on the efficient frontier. This relation is called the capital asset pricing model, or CAPM for short. We see that the equation looks a little bit like the one we had before for efficient portfolios. We still have an expected return, E[Ri]. This is what we want to explain, the expected return of the stock. We have an intercept, a minimum level, which is RF. And then we have the difference between the expected return on the market and RF similarly to what we had before for the capital market line. But instead of having the level of risk of the asset, we have this measure of non-diversifiable risk, which is the beta. This quantity measures the amount of risk that we cannot get away from by just combining the asset with other asset in the economy. Some of the risk of each asset can be diversified away by combination with other financial security. That part is diversifiable. What's left and what should be rewarded by an increase in return is measured by the beta. How is this beta computed? Well, you have the equation here on the second line. It is the ratio between two quantities. The first one measures the dependence between the asset return and the market return. We know that we can measure this dependence using correlation or covariance. Here the beta is defined with covariance. This measure of covariance between Ri, the return of the financial security we're interested in, and RM, is the first element in the definition of the beta. The second quantity is the variance of the market return itself. Remember that the variance is a measure of risk, a measure of dispersion. It's the square of the standard deviation. So how do we actually use a formula like this one to construct some expectation of what we expect to see in terms of return for a particular financial security? Well first we have to measure the beta of the security, this can be done using statistical measures, covariance and variance. Historical data can be used to measure the level of covariance and to measure the level of variance of the market. Now if we look at the link between beta and return, we can see that again they should align on a straight line. So different level of beta correspond to different level of return. And the link between the beta and the return is linear. This relation between beta and return along a particular line also has a particular name, it's called the security market line. This is depicted here in a new example. So what's important here is that we have not changed the y-axis. It's still expected return, but we have modified what's on the x-axis. Instead of having the measure of total risk, the measure of standard deviation, we now have a new measure, the beta, the measure of non-diversifiable risk. And one particular level is important, it's the level of the beta of the market. And what is the beta of the market? Well if we come back to the definition of the beta, the covariance of the market with himself, which would be the denominator in this equation to compute the beta of the market, correspond actually to the variance. The covariance of a random variable with itself, is the variance. So the beta of the market Is exactly equal to 1. So on the security market line, the intersection here of the straight blue line with beta equals to 1, this is the expected return on the market. So, this is equal to RF, the level of the risk free rate, the intercept plus beta times expected return on the market, minus expected return on the risk free rate. Okay, so the security market line describes all the expected return we would like to see for the financial securities available in the market as they defer in terms of beta. So let's look at one example. A stock with a beta of 1.4, what do we expect its return to be? Well if the measure of beta corresponds to the non-diversifiable risk, we can use the previous equation to compute its expected return. So let's just use these inputs in the previous formula and compute the expected return. So the expected return should be equal to the risk free rate, RF, plus the product of the beta, 1.4. And the difference between the expected return on the market and the risk free rates, so here 8%- 2%. If we compute this equation, we obtain that the expected return for these assets with a beta of 1.4 is exactly equal to 10.4. What's important here about the security market line is that we can observe different securities located at the same point with the same beta which do not necessarily have the same level of total risk. Let me go back to this slide. This graph depicts the efficient frontier and the individual security. We see that asset C is located here at a total risk level of 20%, and its expected return is 8%. All the securities if we had other financial asset in this market, located on the horizontal line starting at the origin at the 8% on the y-axis and crossing through C. All the points located on this line would generate the same expected return but different level of total risk. What we can say is that all these points actually corresponds to financial securities which have the same beta. Why do they have the same beta? Because beta defines the level of expected return. So all these securities align on an horizontal line crossing C will have the same level of expected return. So according to this equation, they will have the same level of beta, okay. So in the security market line here, we could very well have many stock located at the same point with the same beta. On the other graph, all these points would be located on the same horizontal line. So to conclude, the measure of risk that we should take into account according to this model to measure expected return, the level of risk that really matters is the level of non-diversifiable risk. And this measure corresponds to the beta which is computed by taking the ratio of the covariance of the return with the market to the variance of the market. [MUSIC]