# Total Return Variability?

Can someone explain what “Rolling ten-year annualized return variability of total US stock market” represents in exact statistical terms?

Saw this in a Vanguard piece and hope to replicate for certain benchmarks.

Thank you!

See how TagniFi is helping investment professionals streamline their valuation and analysis process in Excel. Sign up for a free trial today.

rolling means they did january 1, 2000, to january 1,2010 as 1 obs

2nd obs would be jnauary 2, 2000 to january 2, 2000 as 2nd obs. and so on.

annualized return means they took the total return which could be 159%, and just so you can do annual comparisons, the 10 year annualized return is 10%.

variability just means the range of actual returns from that time period. like from 2000 to 2019. etc etc.

I love my cheese. I got to have my cheddar.

Thanks… How might I replicate something of similar nature in Excel with a historical time series of S&P 500 total cumulative return?

I do the 10y moving average on the data series, or do I first derive the annualized return and then the 10y average (how is this done on a nominal series)?

Then what is the statistical function to arrive at variability expressed in % terms?

Many thanks.

I’ve done this usin to shillers data set which is monthly but has data going back to 1850. You first need the annualized 10 year return of every data, before you can find the average  of all your observations. If memory serves correctly, you need to find the 10 year total return for each obs from the raw data since they don’t give you total return. Then annualized the 10 year total return. Then you can find the overall average. Or even use percentiles to find the odds. I’ve done this for several types, 1 year, 3 year, all the way to 50 year. It’s very interesting what the percentages are.

I love my cheese. I got to have my cheddar.

It could be interpreted multiple ways.  Best way is to look for a footnote on exact definition or call them.

#FreeCVM #FreeTurd #2007-2017