### CFA Practice Question

Consider the stocks UVW and XYZ with the following returns in one year's time:

State of the World | Probability | Return UVW | Return XYZ
Recession | 35% | 6% | -5%
Middle | 40% | 4% | 8%
Boom | 25% | 0% | 20%

Consider a portfolio with 35% weight on UVW and 65% weight on XYZ. The standard deviation of returns for the portfolio is:
A. 3.55%
B. 5.55%
C. 6.55%
Explanation: Find weighted returns for portfolio in each state. Then weight by probability to find expected return. Then subtract expected return to find deviations. Square and weight by probability for variance. Square-root for std dev.

### User Contributed Comments4

User Comment
bsm9 Boo. You suck. Show me the calc!
mary11 I get 7.88...
purich When Recession E(P)= -1.15%
When Middle E(P) = 6.6%
When Boom E(P) = 13%
Mean = 0.35*-1.15%+0.4*6.6%+0.25*13% = 5.4875%
then
Var = 0.35*(-1.15%-5.4875%)^2 + 0.4*(6.6%-5.4875%)^2 + 0.25*(13%-5.4875%)^2
=30.80%
Std dev = sqrt(30.80%)=5.55%
xstefxanx is there any short way with calculator?