I wanted to follow up this morning to show how the trend analysis described below is superior to the naive method used by some financial planners whereby they simply calculate the historical annual return for the market and extrapolate that return into the future. What I found is actually a better method than the one described in the post below.
The chart above shows cumulative annual returns since 1880 vs. returns over the subsequent ten years. The line of best fit is y = -8.7698*x+0.1407, where y = annualized returns over the subsequent ten years and x = the annualized returns calculated from 1880 up to the date of calculation. So, since annualized returns since 1880 have equaled 1.7% (inflation adjusted), projected annual returns over the next ten years are -1.0%. So, naively extrapolating 1.7% real returns into the future would be an inferior assumption as it does not account for the mean reverting nature of the market.
The really shocking thing is that this simple regression has R^2=46%, which is incredibly high for a single factor model in relation to a system as random as the stock market.
It's even more shocking when comparing returns over the prior 20 years (rather than since 1880) vs. the subsequent ten years, which is shown in the second chart above. Here the R^2 is 59%. The market close as of 2/25/11 resulted in annualized returns over the prior 20 years of 3.96% (inflation adjusted). Based on this regression with standard error of 3.58%, real annualized returns over the next ten years are projected to be 1.7% with a 50% confidence interval ranging from -0.8% to 4.1%. The 90% confidence interval is -4.2% to 7.6%.
Personally, given the significantly higher R^2 for this regression, I'm inclined to favor this method over the one in the post below that's based on the close/trend metric.
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