How Do One Year Returns Effect the Total?

I ran my investment calculator for an individual investing $7000 (adjusted for inflation each year) in the S and P 500 for 40 years in a 401k making $60000 a year. I looked at how much money this person was pulling out of the stock market, on every continuous 40-year span, and took the correlation between each nth period return and the final amount. In English, how much does each year's market returns affect the grand total?

I don't just want the correlation, I want a confidence interval. This way I can tell which correlations are significantly not 0 at the 95% confidence level. As the data is explicitly not i.i.d., most traditional methods will fail; hence I fell back on the statistician's favorite backup: bootstrapping. I started by looking at a single year; how much does the nth year affect the grand total, and is there evidence enough to show it is not zero?

Any year with red shading is significantly not 0 and any with the orange is almost not significant. Of course the last year before taking your money out matters, a lot. But the second to last year has little impact. We can only make any solid conclusions based on the 1st and 13th years before removing the money — we can't conclude that the other years have any effect on the end outcome. That's crazy! That means there's no evidence to support the idea that, aside from a couple years, any single year return has a meaningful impact on the final amount.

5 Year Moving Average

So almost no single year has any effect on the final amount of money pulled out of the S and P 500. What about the 5-year moving average? One year may be a fluke but 5 years could be a full-blown recession; surely half a decade of market conditions must affect the outcome of our investment?

This is looking at the correlation between the end amount and the average return over the next 5 periods for each period. If the next 5 periods are good and I'm 15 years away from retirement, that's significantly bad for my retirement fund. However, if I'm more than 20 years away from retirement, there is not enough evidence to support the idea that the next 5 years of returns have a significant impact on my retirement fund. In other words, if you're anywhere from just starting to save for retirement to 20 years from just starting and the 2008 financial crash happens again, don't worry. There's no evidence that it will affect your retirement fund.

Why did I do this? According to Seeking Alpha, "if you invest in 401(k) every paycheck, and still have more than 10-15 years to retire, you are getting less of a bargain each passing month." I would beg to differ — my numbers suggest this statement has no evidence, and is simply pulled out of thin air.

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