For S&P, or any time series for that matter. When doing analysis on the distribution of the yearly returns, should I be looking at 1) the daily year over year values, 2) pick some starting point like December 31st of year YYYY and then look at YoY, or 3) something else.
My intuition is that for 1) you are artificially creating many "YoY" values that look the same because the previous days YoY will not change much given a one day move, but at the same time 2) seems a little arbitrary because youre just selecting a single point as a reference point (you could have chosen first of year or middle of year) and in fact 1) contains 2)
Doing both for S&P returns from Yahoo from 1950s doesnt seem like it shows a big difference in terms of mean or vol parameters (the daily YoY has wider min/max as you would expect):
> smry dailyYoY yearly Min. -0.6699000 -0.4499000 1st Qu. -0.0120600 -0.0061320 Median 0.0937500 0.0834800 Mean 0.0724200 0.0736000 3rd Qu. 0.1783000 0.1681000 Max. 0.5222000 0.3274000 Std Dev 0.1555526 0.1487778
It seems like one could argue that the yearly is just a sampled version of the dailyYoY, but which should I be using? I'm leaning more towards dailyYoY, because the other method ignores information I already know