How to Calculate the Beta of a Portfolio? Overview and Explanation

How to calculate the beta of an entire portfolio? Let's say that you invested $2,000 in Walmart stock $8,000 in Intel stock, and $10,000 in Amazon and you know that the beta for each of these firms. You can go to Yahoo Finance and look up and say the beta of Walmart is 0.38, Intel's 0.86, and Amazon's 1.46 right you can tell that but how do you calculate the beta for this entire portfolio that you have here right you want to know how much systematic risk the portfolio has not just the individual stocks right so how would you go about doing that?

Well, you can calculate a weighted average, and to do that we're going to need to first calculate what's the total amount you have invested here. If we add up the $2,000 the $8,000 and the $10,000 that gives us a total of $20,000. Now that we know you have a total of $20,000 dollars invested we can go and calculate the weighted average as follows. So Walmart is $2,000 of the entire $20,000 so 2,000 out of 20,000 is the same as 2 over twentieth (2/20). We're going to multiply that by Walmart's beta which is 0.38. So Walmart is (2/20) of your position, we're going to multiply that by Walmart's beta.

Now what we're going to do is we're going to do the same with Intel and add the answer which is $8,000 out of $20,000 is the same as 8 over 20 (8/20). Then we're going to multiply that by Intel's beta which is 0.86 and then we are going to add to that the weighted average part of Amazon. Here Amazon is $10,000 over $20,000 and we multiply that by Amazon's beta of 1.46. Now we go ahead and we just basically do the multiplication of each of these three parts to do the weighted average and then add them together. If you do the math here that's going to give you a beta of 1.11, actually 1.12 but I just rounded it here. Now that tells you how much systematic risk there is in this portfolio that you've put together and you notice that that 1.11 is greater than the average systematic risk or the systematic risk of an average firm because it's greater than 1.