Hello! Welcome back. In previous lectures we saw how combining securities in a portfolio is able to reduce portfolio risk, by diversifying away the idiosyncratic risk, the non-systematic risk. But even when we have a large and well diversified portfolio, there will be some variability in this return, right? Because of the systematic risk, right. The part of portfolio risk that we can't eliminate, right, because all securities more or less move together, right. With the general markets, right, because of marketing-wide risk sources, okay. So in this lecture, we're going to revisit the definition of systematic and non systematic risk. And then we're going to talk about beta, right, which you will see is a measure of the systematic risk, okay. Let's review what we mean by systematic and non systematic risk. Remember systematic risk, also called market risk, is the part of the security's total risk that is coming to all assets, right. You can think of it as, capturing an essence reaction, to general market risks, right. So, an asset with a lot of systematic risks, right? Will move widely with the general markets. [COUGH] And because the source of this risk is market wide, and common to all securities. Even when we put together a large well diversified portfolio, we cannot eliminate this systematic risk, all right? because it's common to all assets, right? Now non systemic risks or idiosyncratic risks on the other hand, all right. Is part of security total risk that is unrelated to another asset, right. Therefore it is not related to moves of the market portfolio in general. All right it is the fluctuation in asset return for reasons that are peculiar to that as it only. Maybe it's the new contract, maybe it's labor difficulties of the company. Maybe it's the discovery that the company is involved in some fraud. Or maybe you know a pharmaceutical company getting approval from FDA, right? So these are the kinds of things that cause idiosyncratic risk, right? It is the part of the total risk that is washed away when we hold assets together. And this is the whole point, of course, of portfolio theory, that we can eliminate all this idiosyncratic risk by combining securities in an asset. So, what is beta? Well beta basically is a numerical description of this systematic risk, all right? It essentially compares how an asset moves relative to the market portfolio. Okay? So let me give you an example, and then I'll tell you how we measure it. Okay so suppose an asset has a beta of 2. Okay, so if a stock has a beta of 2 what does that mean. Well that means that, on average right it's going to fluctuate twice as much as the market. So for example if the market goes up by 10%, let's say, right. This stock will, right, will go up by on average 20%, right? On the other hand, if a, let's say a stock has a beta of 0.5, right? It means that it's not going to move as much as the market, right? For example it will only rise or fall by 5%, right? If the market goes up or down by 10%, right? So if the market goes up by 10% an asset with a beta of 0.5, will only go up by 5%. Right, so professionals in the industry call high beta assets right aggressive instruments, aggressive investments right. And they label low beta assets as defensive assets right. Assets that sort of fluctuate highly with the market, versus assets that fluctuate sort of less than the market. Okay, so how do we measure the beta, right? Well, we measure an asset's beta, with the asset's return covariance with the market, divided by the total market variance. So what's the beta of an asset i. All right what is beta of an asset i. Well it's going to be the covariance of its return. With the return on the market, market portfolio. Divided by right, the total market's variants. All right, alternatively I can write it as, right. Remember that covariance can be written as the correlation between the market and the assets, times its standard variation, law of deviation, times the market standard deviation, right. Again divided by the variance of the market, right, well I can simplify these cancels with this. So we're left with the correlation between asset i, and the market return times the standard deviation of the assets, divided by the market volatility right. So this is the definition of the beta. Now here is the key arguments, we know investors should be compensated for taking on more risk, right, with higher expected returns, right? Stock prices will adjust to offer higher returns right? If they are riskier to ensure that all securities are held by someone right? So that market's clear. Well, what should that extra return be? What is the extra reward? Well, not all of the risk of an individual security will be relevant, right, in determining this reward, this premium, right? Investors will not be rewarded for the unsystematic risk, right, because they can diversify it away, right? The only part of total risk that investors should get paid for bearing, is the systematic risk, right, the risk that diversification can't help, right? Which is what we measured by the beta. And that will give us the capital asset pricing model in the next lecture.
