[MUSIC] Now, how much of a fund's performance is beta? [MUSIC] To examine this work, what we need to do is look for relationships. Does the fund tend to go up when the market goes up and vice versa? How strong is the correlation? So let's look at some examples. Here are some market excess returns and here are some fund excess returns. So one month the market was down 2.32%. The fund returned down 1.7%. And we move on to the next month, and the next month, and then we plot it. So we just plotted one month's return of the market and the fund on the scatter plot. Keep going. The next month's return. And then the subsequent month's return. And you will see the scatter plot filling up. You will see that there is a relationship between the market and the fund. And if you plot a straight line, a line of best fit through this scatter plot, you'll see. You'll see market beta. This fund has a lot of beta on average, if the market goes up, this fund goes up. If the market goes down, this fund goes down. You plot another graph, and you may see the slope being much stronger. In which case, like in this red line you'd say that the fund has a higher beta than the previous fund. Sometimes the relationship will be much less. A certain fund may move much less than the market, like in this orange graph here. And you would has less beta. And then there could be funds which have no correlation to the market, a zero beta. Beta is the slope of the line of best fit. Now what does the fund do when the market does nothing? This is the y-intercept, This red line here is alpha. What the fund does on average when the market does nothing is alpha. So the slope of the line is beta and the intercept is alpha. In this picture it looks like the alpha level is about 0.5. So this fund is not just meeting the market when the market does nothing. It is beating the market by 0.5% every month, on average. That is a very high number. But here's an example of another fund against the market, and you can see it's intercept is negative. This is what we'd call negative alpha. So what is the alpha measurement recipe? It's a scatter plot. Plot market excess returns against the fund's excess returns. Draw the line of best fit. Measure the slop for beta, and measure the y intercept for alpha. Fitting a line to a data is a classic and simple mathematical problem. So the math for an alpha recipe is simple, all you need to do is fit a line. And given the data points, you can dispense with the graph and simply calculate alpha and beta using formula. These are the technical formulae to calculate beta. It is simply the correlation times the ratio of the funds [INAUDIBLE] to the market's [INAUDIBLE]. And similarly alpha is just simply the average fund return minus beta times the average market return. I want to clarify the concepts, we have just gone through alpha and beta with some practical examples. And so we're going to go through these examples and try and figure out what's he alpha and the beta in each of these practical examples. So first one is cash. Cash just runs a risk less rate f return, it has a beta of 0 and an alpha of 0. If you're fully invested in the stock market you then have a beta 1 and there's no alpha. If you're leveraged two times Into the stock market your beta is 2 and your alpha is 0. And if you're delevered meaning to say 50% invested in the stock market and 50% in cash, then your beta is 0.5 and your alpha is 0. I wonder if you're fully invested in the stock market and you're able to make one smart trade a year. And the smart trade typically makes money. In that case your beta is 1, pretty close to 1. And the alpha is a little positive. Another example would be, if you have zero market exposure. And you still have one trade, one personal trade. In this case, your beta is 0 and alpha is slightly positive So I want to sum up by essentially decomposing returns into this following graphs. You always have the risk-free rate. You can get that by investing in a money market instrument. You can get beta by investing in a market instrument like an index fund. And then you may be able to layer alpha on top of beta if you know how to gain. [MUSIC]
