With the stock market swinging up and down, everyone wants to determine how well their investments are performing. It is very easy to look at the numbers that your custodian provides you. In my case, I just have to look at the % return that Fidelity provides and I can easily see how things are going. But what if I wanted to do the computation myself? How would I compute my overall return?
There is a right way and a wrong way. What seems like the easy/right way is to perform an arithmetic mean calculation. Get your returns over the past few months. Add them together. Divide by how many samples. And tada, there is my average return. This would be wrong. Why? In order to explain, I will utilize a tragic example. If your investments lose 50% of their value in the first month and then gain 50% of their value in the second month, your computation of the arithmetic mean would show you as break even for the two month period. In reality, your investments went down 50% and the 50% increase is based on the lower value of your portfolio.
After explaining it this way, you would say, “Aha…I can do that math in my head, it is obviously a 25% decline for the 2 months.” (A 50% loss of $1 would give you $0.50, a 50% gain on $0.50 would equal $0.75, therefore giving you a 25% decline of your initial $1.)
However, the right way to calculate your financial return is to compute the geometric mean. The geometric mean return is a value that indicates the tendency of the measured returns. To calculate the geometric mean, you multiply the returns together and take the nth root. In order to show the proper return, subtract 1 from the result. For the example above, you would take the square root of the product of .5 and 1.5. The product of .5 and 1.5 is .75. The square root of .75 is .866. Subtracting 1 from .866 shows that for the 2 month period, your return would be computed as -13.4%.
So when you look at the financial returns as shown by your broker/dealer and wonder why your computations are different, you can use the geometric mean calculation to derive their return.