Your math is of course correct, but I would turn the interpretation around:
On a 100-year scale, a 'tiny' 0.5% drop in compound return is massively 'important' in effect. It's no consolation to the person with 40% less money that his annualized performance was only 0.5% worse; you own the $1320, not the 7.45%.
"8%" is often thrown around as a long-long-term guesstimate of stock returns; if in fact that's slipped to 'merely' 7.5% based on the last year, that's remarkable.
The hit against the annualized rate within timeframes more like the earning careers (or even lifespans) of News.YC readers is also big. Here's an interesting graph for S&P total return over the last 20 years:
My point is there are plenty of large swings in the history of the S&P 500. It's up 15.38% from 10/9/2002, and down 41.33% from 3/24/2000. The BMW World for Iceland is down 99.44% over the last year which drastically changes their long term returns. But picking a peak or valley is not the best way to calculate returns.
IMO picking a peak or valley is less informative than what happens when you invest one inflation adjusted dollar every month over the history of a stock exchange. Add in selling off 1-4% a year and you can see what the stock market does for normal peoples investments.
Long story short: you can't predict the market. If you buy all your stock on one day, and in hindsight it turns out to have been at a peak, we'll you're screwed aren't you. If you buy your stock in periodic roughly equal sized increments over a period of time, the average cost of the stock will correspond to the stock's average over the long term. (i.e. sometimes you get it "cheap" when the market is beaten down, sometimes you get it "expensive", but it all comes out in the wash.)
This is a common strategy for long-term investors.
EX: While buying 100$ in stock at 10$/share and 100$ in stock at 20$/share means the average price was 15$ you have 15 shares for 200$ which is 13.33$ / share.
