# Simple Standard Deviation of Returns

Hi all,

I know this isnt 100% (no pun intended), but I just want to make sure I am atleast 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.

“Visit the Water Cooler forum on Analyst Forum. It is the best forum.”

- Everyone

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

What? No - standard deviation is a general measure of volatility. R^2 is… it’s what I just described above.

Standard deviation measures probability distributions. R^2 is an attribution measure for explanatory variables in regression.

“Visit the Water Cooler forum on Analyst Forum. It is the best forum.”

- Everyone