### CFA Practice Question

Consider the stock XYZ with the following returns in one year's time:

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

The Standard Deviation for XYZ is:
A. 9.63%
B. 8.63%
C. 7.63%
Explanation: Weight returns by probabilities and add 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 Comments5

User Comment
safash can some one show me the calculations plz
steph73 1)(5%*40)+(8%*40%)+(20%*25%) =6.2%
2)6.2%-5%=11.2 squre = 125.40 *35% =43.9
6.2-8%=-1.8 SQURE =3.24 *40% =1.29
6.2 -20% =-13.8 SQUARE =190.44 *25%=47.61
3)43.9+1.29+47.61=92.39 SQUARE ROOT =9.63%
aayush87 thanks steph!
hoyleng thanks steph..
welchdan To fix up Steph's

Step 1. (-5*.35)+(8*.4)+(20*.25)=6.45
Step 2a) 6.45 - (-5) =11.45. Square it > = 131.10 *.35 =45.89
Step 2b) 6.45-8 = (-1.55). square it > =2.4*.4 = 0.96
Step 2c) 6.45-20=(-13.55). square it > =183.60*.25=45.90

Step 3) 45.89+0.96+45.90=92.74
Step 4) take the square root of 92.74. = 9.63