I know this isnt 100% (no pun intended), but I just want to make sure I am at least looking at these numbers somewhat correctly.
If you wanted to determine the probability of returns for a portfolio using the expected return, standard deviation of returns and R Squared would it simply be
Expected return +/- 1STD = 68% probability
Expected return +/- 2STD = 95% probability
Expected return +/- 3STD = 99.7% probability
then use R squared somewhat like an additional error estimate like if R Squared is 99 then there is a 99%ish chance that the above probabilities are correct?
using actual numbers: Expected return is 11%, STD = 8% so
68% chance for 3% to 19%
95% chance for -5% to 27%
99.7% chance for -13% to 35%
Any clarification if I am wrong would be much appreciated!
R^2 is for regressions to test fit quality. For example, if you fit [y = a*x + b + error] to some data, R^2 tells you how much variability in y can be attributed to x, rather than random error or other variables. The example you described just shows a return distribution, without describing any explanatory variables.
If R^2 is 99%, that means that predicted variability of y is 99% of total variability. That is, x explains 99% of the variability of the dependent variable.
So assuming that R^2 explains 99% of the variability of x can I then say that the standard deviation will account for 99% of all variability? Will that make my return probabilities listed above pretty accurate because of R^2 being 99? I’m just asking to make sure i’m understanding this correctly