I do know, just unsure of how.
Maybe and example to clarify?
An investment over 3 years returned 12%, 4%, 6%.
The mean is 7.3%
The Stdev is .042
Where Standard deviation = risk, the risk-adjusted return is 7.3 /.042
We assume these returns are investor profits, unless something else detracts from them.
Something does.
It is required that over the same 3 years.
Year 1: 25% of 12% return is taken, leaving a net return of 9
Year 2: 20% of 4% is taken, leaving a net return of 3.2
Year 3: 10% of 6% is taken, leaving a net return of 5.4
The amount taken is independent of the returns.
The amount taken over three years has a SD of .076
Since this standard deviation (or variance also represents a risk to returns. Just ask we cannot know our returns, we cannot know how much will be taken year to year.
Because of this, our risk-adjusted net returns must account for this standard deviation as well as the former. How do I express this?