Alpha is just the difference between a securities return and the return that's predicted by the security market line. The security market line is the visual representation and the graphing of the capital asset pricing model. So with the CAPM, we've got the expected return of security (Ri) is equal to the risk-free rate of return (Rf) plus beta for that security times the market risk premium. So we can say what is the beta for different securities and then what is the expected return for different securities and we plot them and that gives us a line that we call the security market line. We've written about that in a different article so I won't go on about it too much here but here we've got our security market line and we've got beta on the x-axis, we've got the expected return of the security on the y-axis and then we've got the risk-free rate here. So this line that we have going out that's the security market line.
Now if we have a situation where the market portfolio is efficient, let's say we're talking about Microsoft and Caterpillar and Walmart they'll all plot at a different point on the security market line. So we have different points here and they'd all represent different stocks. Now we got a point in the market line that might correspond to a beta of 1.24 and maybe that's Microsoft and the expected return let's say is 12%. Now as we go higher on the security market line, higher risk implies. There's going to be a higher expected return.
Then we might have a situation though where there's a point that's not on the line at all. For example, let's take a point right upper the security market line, and let's say that this corresponds to eBay. Let's say, that point corresponds to a beta of 1.51. We trace that up to the security market line and then we trace it over and let's say that it would come out to an expected return of 13% and yet eBay here with the beta of 1.51 it's not on the line so it's not coming over to an expected return of 13% instead it's coming over to an expected return of 15%. So the difference between this actual point here and where it should be on the line, the difference here that is 2%. This is 15% - 13%.
What does this mean? Look eBay has a beta of 1.51 that's a measure of its systemic risk based on the capital asset pricing model which is pictured with the security market line we've plotted out. Ebey should have an expected return of 13% because this is the point here where it would be on the security market line yet eBay is not on the security market line it is instead off upper to the security market line. Conversely, you could have a point here that's below the security market line. Here we have a point upper the security market line what is called a positive alpha because the return is higher than what is predicted by the security market line for eBay. So eBay would have an alpha of 2% this is a positive alpha for eBay. So it's having a return that is higher than that which is predicted by the capital asset pricing model and which is pictured with the security market line like I said conversely we could have some stock over here where actually the return is lower. So when we look at the distance between the point and where it should be on this security market line that is the Alpha.
Again if the market portfolio is efficient then all securities are going to be at some point along the security market line. They're all gonna end up on the security market line however if we might have a situation where we have some points that are off the security market line and so that's where we have these stocks that have a nonzero alpha. So if you think about it conceptually if you're an investor and you see that oh there's a stock that is not on the security market line if it has a positive alpha, if alpha is greater than zero then you could improve on the market portfolio instead just holding the market portfolio you could buy you could go and buy the stocks that have positive alphas. Then you could sell any of the stocks that have an alpha that is negative. So all the ones that are below any kind of any point that is below the security market line that's going to be a negative alpha stock and so you would want to sell those.
