# tracking a portfolio's annualized return

I’ve created a spreadsheet that analyzes the total return of my portfolio in various ways. Among the metrics: A graph that tracks the annualized rate of return. For example a year ago the portfolio had an annualized return of about 6.7%. Now it’s around 8%. The figure changes slightly each day and produces an interesting line graph. I haven’t seen this type of graph (showing daily updates to annualized return) elsewhere and wonder if that is because it really is nonsense. Here’s why. One year after inception, if the portfolio gained 1% on a particular day, the annualized return also rose 1%. But now after three years, if the portfolio gains 1% in a day the change to the chart is maybe 1/3 of that. The sensitivity of the chart to the data is not constant. Doesn’t that invalidate the whole chart?

If you think about it, that makes sense because the older your portfolio is, the less that new data points are going to affect the lifetime average. If a portfolio is relatively flat for a year then jumps 1% on the last day of the year, then the portfolio would have a 1% gain for the entire year. If the portfolio is flat for 3 years then jumps 1% ,then the annualized return would be `1.01^(1/3) = ~0.33%` per year. So the math checks out.