# Mean-Variance Portfolio Axis Description

I'm currently looking into the mean-variance approach to portfolio theory and I wonder, why the standard deviation $$\sigma$$ is graphed on the x-axis and not the variance $$\sigma^2$$ as a measure of volatility (as the name would indicate). Does anybody know the reason for that?

Suppose you have a risk-free security R and a risky security B. A portfolio with a 0.50, 0.50 combination will have a standard deviation of $$0.5 \sigma_B$$, but a variance of $$0.25 \sigma_B^2$$. So if you draw it in Standard Deviation space it will be half way between R and B, in Variance space it won't be. This linearity is the reason it is more convenient to draw (std dev, return) space rather than (variance, return) space.