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That's a pretty simple idea, which is why CAGR is used.
You can't average annual returns and get meaningful results.

The more subtle thing is to realize that the ordering of returns usually matters in the real world.
CAGR considers all possible orderings of a given set of returns as equivalent.
But, for example, consider a typical portfolio which is getting continuous small additions (a saver) or withdrawals (a retiree).
An unusually poor result near start of period is far more important to one group than to the other.
There is some academic research showing that one optimal approach for retirees is to have a very
equities-heavy portfolio, but purchase equity put options to protect it for just the first few years after retirement.
That is when sequence of returns is most critical to risk of portfolio failure.

Also, some investment strategies are relatively steady long term but relatively volatile short term.
It can be argued that the slope of a [real log] trend line through this portfolio value history gives a better
idea of expected rate of return than a CAGR calculated from endpoints which might be unusually displaced from the trend.
Shorter version: if you're looking at the CAGR of a time series that ended with a really stupendous month,
depending on your intended use of the figures you're perhaps looking at an overoptimistic figure.
It's arithmetically correct, but perhaps not what you want or need.
e.g., if you're trying to assess the predictive return implied by a backtest.

And one which many people seem to forget.
The only metric which matters for a "save till retirement" portfolio is the real value of the portfolio on retirement day.
It does not matter how volatile the portfolio was, or how much time was in cash, or how diversified it was.
Those may (or may not) matter somewhat to selecting the best strategy to achieve the maximum balance goal, but it's only the final balance that matters.
It's very much better to have a rich retirement after a wild ride than an impoverished retirement after a smooth ride.
A corollary is that bonds with low returns are not risk free. The risk is the "dog food at age 90" problem.

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