Let's say you were thinking of investing in eBay and you want to know the total risk associated with eBay stock. So you could go and you could calculate the standard deviation in eBay's returns, that's its volatility and that's going to tell you the total risk. But you've got to remember that the total risk has two components it's got the
Unsystematic risk: That's firm-specific, that's something maybe eBay CEO gets fired or some news in the market that has just to do with eBay.
Systemic risk: which is market-wide conditions, the Federal Reserve in the U.S. decides to cut interest rates that are the market risk that's going to affect eBay.
We talked about in previous articles that unsystematic risk is diversified away. When you hold a number of firm stock, not just eBay but you also have let's say Amazon you've got Kroger you've got Alcoa you've got a number of firms here, and as your portfolio size increases your volatility decreases because the unsystematic risks are averaging out. What does that mean? That means that systematic risk is what is going to be used to determine the risk of a firm when you're thinking about what is the cost of equity capital and what kind of risk premium do I want as an investor for investing in eBay. Then the question is how do we measure systemic risk? How do we measure this market risk that could potentially affect eBay?
That's what beta is. Beta measures the market risk and so beta it's a little bit complicated I want to start simple and get a little more complex later. So beta is the percentage change in an asset's or stock's return given that you have a 1% change in the market portfolio. So you might be thinking well what is the market portfolio? The market portfolio is this theoretical portfolio of all firms and asset classes. It's basically just all firms together, now in reality, a lot of times of people use something with the S&P 500 or something that is more of kind of a theoretical construct, and the way to operationalize it would be to use some kind of market index. So basically you're saying "If the S&P 500 or some index or this market portfolio goes up 1% or goes down 1% what happens to eBay's return?" How tied in is eBay's return to general market conditions? That's really what beta is telling us.
And by virtue of doing that it's telling us how much systemic risk how much market risk that an asset has, the eBay stock for example has. That's all the risk we care about when we're trying to value eBay because again if we're going to hold a portfolio of firms, the firm-specific risk or that unsystematic component that's going to be averaged out and so really we just want to care about the systemic risk. That's what beta is.
So ultimately with the beta, we're getting an idea of the sensitivity of eBay or whatever stocks return to the return of the overall market portfolio for example the S&P 500. Now it can get pretty complex to calculate beta but there are simpler ways to do it and I don't want you to get tied in and think this is the only way, I'm just trying to show you something simple and in future articles, we'll talk about the capital asset pricing model which is a little more complex and so forth but for right now let's just do a real simple example of how you might go about calculating beta. Let's say that we have a company called Tom skydiving and Tom skydiving that there could be two things that could happen the economy could be good or the economy could be bad. Let's say if the economy is good then Tom skydiving has a return of 30% if the economy is bad then Tom skydiving has a return of negative 50%. The market portfolio or that theoretical portfolio of all the firms and all the asset classes let's say that in a good state of the economy if the economy is doing well the market portfolio has a return of 22%, if the economy is doing bad, however, the market portfolio has a return of negative 10%. Now using just these percentage percentages here we can go ahead and we can calculate the beta for Tom skydiving.
What we're going to do is, we are basically going to take the range which is {30% - (-50%)} so that's going to be 80%. So that'll be 80% we're going to have a fraction and so in the denominator, we're going to have the market return which would be {22% - (-10%)} which is going to be 32%. So now we've got 80% divided by 32% that is going to give us 2.5. The beta of Tom skydiving is 2.5, what does that mean? That means that given a 1% change in the market portfolio, the change that we could expect and Tom skydiving as an investor is a percentage change of 2.5%.
How do we interpret that? Well, we could say that Tom skydiving has more systemic risk than the average firm or the average asset class. Because just an average firm would just be 1%. If you think about the market going up 1% that firm goes up 1%. So you just say the average systemic risk by a firm would be 1 and Tom skydiving is 2.5. For practical purposes what that means is when the market portfolio does really well, Tom skydiving does even better but when the market portfolio does poorly tom skydiving does even worse. So it's very reactive to what the market portfolios returns are. Beta is measuring the sensitivity of the assets. It makes sense because you look and you see okay when the economy is bad if the market portfolio goes down 10% but Tom skydiving goes down 50% and then when the economy is good the market portfolio goes up 22% but Tom skydiving goes up 30%. So that explains why we have this beta of 2.5. Now you could have conversely could have firms that actually have a beta of less than 1, where they're not reacting there if they actually have less systematic risk than the average firm. We're going to talk in our next articles about some different betas and firms.
