Now that we are familiar with the fundamentals of risk and return, modern portfolio theory, and the main implications of the Harry Markowitz theory based on two-fund separation. Now it's time to go further and consider the Capital Asset Pricing Model or CAPM, which is more frequently used by researchers and market participants in order to determine the relationship between the risk and return. At the beginning of our lecture will formally derive the Capital Asset Pricing Model based on the Markowitz model, and then we'll talk about the key theoretical implications of the CAPM. We'll then proceed by talking in detail about the main approaches to determining the key unknowns in this model, which we use in order to determine the expected return. Finally, we'll focus on the critical arguments against the CAPM and the empirical evidence for and against this model in order to see how the forecasts fit reality. Finally, we will talk about several modifications of the CAPM frequently used in practice, which may help us better estimate the expected returns based on this model. Let's get started. This is William Sharpe, the Nobel Memorial Prize in economic sciences winner in the year 1990. By the way he shared this award with Harry Markowitz. He's famous for his research papers on the Capital Asset Pricing Model published in 1960s, as well as the fundamental book called Investments, where he summarizes all of the theories in financial science which help us evaluate various types of financial assets, and he is also known as the developer of the Capital Asset Pricing Model we are going to talk about today. Sometimes this model is also called the Sharpe Model after William Sharpe. In order to start, let's remind ourselves about the key implications of the Harry Markowitz model. As we remember, the optimal set of portfolios lie on the capital market line, where all the investors hold the combination of the risk-free asset and the tangency portfolio, which is the optimal portfolio of risky assets available in the market. By the way, if all investors have homogeneous expectations, which is one of the assumptions of the model, then each investor will identify the same portfolio as having the highest Sharpe ratio in the economy, thus all investors will demand the same efficient portfolio of risky securities, which is the tangency portfolio, adjusting only their investment in risk-free securities to suit their particular appetite for risk. However, if every investor is holding the tangency portfolio then the combined portfolio of risky securities of all investors must also equal to the tangency portfolio. Furthermore, because every security is owned by someone, the sum of all investors portfolios must equal the portfolio of all the risky securities available in the market, which we define as the market portfolio. Therefore, the efficient tangent portfolio of risky securities or the portfolio that all investors hold must equal the overall market portfolio. The insight that the market portfolio is efficient is really just the statement that demand must equal supply. In other words, all investors demand the efficient portfolio and the supply of securities is the market portfolio hence these two must coincide. If a security were not a part of an efficient portfolio, then no one will be holding that and the demand for this security will fall. The security's price will fall, causing its expected return to rise until it becomes an attractive investment. In this way prices in the market will adjust so that the efficient portfolio and the market portfolio coincide and demand will equal supply. Here is the equation for the capital market line showing the relationship between the expected return, which is the dependent variable, and the standard deviation of the portfolio, which is the independent variable. We see that the standard deviation of the portfolio is multiplied by the Sharpe ratio, which determines the slope of the CML. In the current context, this equation is assumed to describe a closed system within which the value of a single dependent variable is precisely defined by the values attributed to four independent variables. The model drives its validity from the algebraic logic as opposed to the verifiability or plausibility of attributed values whether realized or expected. It explains the assumed risk return characteristics of efficient portfolios while providing a platform from which to derive the capital asset pricing model. As we see, the Capital Market Line contains only efficient portfolios and assets. However, there are many others available in the market. Efficient portfolios plot along the capital market line and are perfectly correlated with the market portfolio. In other words, we can say that the correlation ratio of such portfolio with the market portfolio equals one. However, as we know, there are many other assets which do not lie on the Capital Market Line. Now we're going to generalize these relationship and include any other assets which are available in the market. Let's extend our equation for CML in order to define the return on any portfolio as a function of its total risk. Now we introduce the correlation ratio between the return of a portfolio and the return of the market portfolio, which will be multiplied by the Sharpe ratio. Now, by doing some workings with this equation shown, we can finally result in the following equation where the expected return on the portfolio should be equal to the risk-free rate plus the difference between the market return and the risk free return which we will further define as the risk premium by the covariance of the returns of our portfolio and the market portfolio divided by the variance of the market portfolio. The last part of equation is called the Beta coefficient and this is the ratio which shows the sensitivity of return of the given portfolio to that of the market. Now we have worked out the basic equation for the capital asset pricing model, which may help us estimate the expected return of a given asset knowing it's relationship with the volatility of the market portfolio. Finally, let's remind the key assumptions of the capital asset pricing model which we'll use when defining the expected return of a security. The capital asset pricing model is based on the Markowitz model, which implies that all the assumptions behind the Markowitz model also hold for the CAPM. However, there are some extra assumptions that we need to make. For example, we need to state that now all investors carry diversified portfolios over a broad range of securities. In other words, the firm specific risk which is estimated in the Markowitz model along with the market risk is not priced by the capital asset pricing model. This is only the market risk which drives the expected return of the asset in the framework of the CAPM. We also need to keep in mind that all investors have perfect information and homogeneous expectations, which also drives their solutions and investment decisions just in the same way. We also need to mention once again, that all investors should be price takers and cannot influence prices on their own and can lend or borrow unlimited amounts at the risk-free rate which is the same and stable for all the investors who operate in the market. Finally, we also need to assume the infinite divisibility of all the assets available in the market and perfect liquidity. Here are all the assumptions of the CAPM which again drive us more towards the concept of a perfect market. However, we need to keep these assumptions in mind when talking about the theoretical implications of the CAPM.