Learning outcomes. After watching this video, you will be able to write the capital asset pricing model, CAPM, explain market risk premium, discuss what type of risk beta measures. The CAPM. Last time we saw the preliminaries necessary to understand the CAPM better. In this video, we will see the mathematical form of the CAPM. The CAPM is returned as follows. The expected return of any risky asset i equals the risk free rate of return plus the beta of the risky asset I, times the difference between the expected return on the market portfolio and the risk free rate. In notations the expected return of the risky asset is denoted by E(ri). The risk free rate of return is denoted by rf. The beta of the risky asset is denoted by beta sub i. And the expected return of the market portfolio is denoted by E(rm). We had defined the market portfolio last time. Beta is the measure of risk in the CAPM. Later, we will discuss what type of risk it measures. In plain English, the CAPM says that the expected return of any risky asset over and above the risk-free rate of return equals the sensitivity of its return with respect to the market portfolio, which is denoted by beta times the expected market risk premium. The expected market risk premium is the difference between the expected return on the market portfolio and the risk free rate of return. It tells us how much return in excess of the risk free rate of return. An investor expects to earn from holding the market portfolio. In other words, what is an investor's compensation for holding the risk of the market portfolio. So what is beta measure? We talked about diversifiable reducing credit risks and non-diversifiable, systematic risk. The market portfolio is mean variance efficient. This says that idiosyncratic risk to the extent possible has been diversified away. So whatever risk remains in the market portfolio is systematic risk. This means that beta is a measure of systematic risk. The more important implication is that investors expect to be compensated only for holding nondiversifiable systematic risk, and not for holding diversifiable idiosyncratic risk. Investors are expected to be smart enough to diversify away idiosyncratic risk by forming portfolios. How do we calculate an asset's beta? Beta sub i equals the covariance between the risky asset's returns and the market portfolio's returns divided by the variance of the market portfolio's return. The covariance is denoted by Cov(ri,rm) of i, of m. And the variance of the market portfolio's returns is denoted by sigma m squared. What can we say about the beta of the market portfolio? If we use the formula we will have the co-variance between the market's returns and the market's returns. Which is simply the variance of the market's returns divided by the variance of the market's returns. Thus, the beta of the market portfolio is one. An asset that has a beta greater than 1 is riskier than the market portfolio, while that with a beta less than 1 is less riskier than the market portfolio. The risk-free asset, by definition, has no risk and so, its beta is 0. Can beta be less than zero? What does it mean to have a negative beta? The answer is yes beta can be negative. This means that the asset's return will move in a direction opposite to that of the market's returns. If the market return is positive, the asset with a negative beta will have a negative return. And vice versa. Next time we will use the formula for beta to calculate the beta of a risky asset.
