Expression of risk: variance vs. standard deviation

CFA Level II Portfolio Management
#1

Hi guys,

Risk is more conveniently expressed in terms of variance rather than in terms of standard deviations because variances of uncorrelated variables are additive. Why? What is the meaning of this statement?

Regards, Sharad

#2

If the correlation of asset A’s returns and asset B’s returns is zero, and portfolio C is, say, 50% A and 50% B, then,

σ2C = 0.5 σ2A + 0.5 σ2B

but, most likely,

σC ≠ 0.5 σA + 0.5 σB