What is shocking, is how catastrophically wrong you are.
"I could not care less about an active manager with a standard deviation of 10% versus 20% for the corresponding index fund that it's trying to outperform. "
For long term wealth creation, which is what you are trying to achieve, the standard deviation of returns is often far more important than the returns themselves.
Take this for a hypothetical example:
Year
1
2
3
4
5
6
7
8
9
10
Average
1
Index
15%
8%
12%
13%
-25%
3%
25%
16%
-30%
14%
5.10%
2
Fund
12%
5%
10%
10%
-18%
7%
18%
14%
-20%
8%
4.60%
3
Relative
-3%
-3%
-2%
-3%
7%
4%
-7%
-2%
10%
-6%
-0.500%
In this example:
The fund underperforms in 7 out of the 10 years or 70% of the time (similar to your active vs passive return comparison).
The average return of the fund over the 10 years is 0.5% lower than the index, so the fund underperforms there as well.
But because the standard deviation of the funds returns is also lower, the compounding return of the fund is higher, and the fund outperforms the index as a result.
In finance, it is not the average return that matters, it is the compounding return.
Starting with $100 and compounding the above returns results in this:
Year
0
1
2
3
4
5
6
7
8
9
10
1
Index
$100.00
$115.00
$124.20
$139.10
$157.19
$117.89
$121.43
$151.78
$176.07
$123.25
$140.50
2
Fund
$100.00
$112.00
$117.60
$129.36
$142.30
$116.68
$124.85
$147.32
$167.95
$134.36
$145.11
The fund's compounding return is 3.8% versus the index at 3.5%.
(20min delay)