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**CFA Practice Question**

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

Recession | 35% | -5%

Middle | 40% | 8%

Boom | 25% | 20%

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.

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**User Contributed Comments**
5

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 |