- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 7. Expected Value, Variance, Standard Deviation, Covariances, and Correlations of Portfolio Returns

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**CFA Practice Question**

Suppose that the future short-term outlook for the economy is favorable, with probability 0.6, and unfavorable with probability 0.4. For two stocks, F and G, the return is 0.25 and 0.2, respectively, in favorable conditions, and 0.01 and 0.02 in unfavorable conditions. Calculate cov(Rf,Rg).

A. 0.0041472

B. 0.0062208

C. 0.010368

**Explanation:**E[Rf] = 0.6*0.25 + 0.4*0.01= 0.154

E[Rg] = 0.6*0.2 + 0.4*0.02 = 0.128

Cov(Rf,Rg) = E[{Rf - E(Rf)}*{Rg - E(Rg)}] = 0.6 * [{0.25-0.154}*{0.2-0.128}] + 0.4 * [{0.01 - 0.154}*{0.02-0.128}] = 0.010368

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**User Contributed Comments**
8

User |
Comment |
---|---|

eddeb |
computing exactly the explanation given, i get 0.00628 ?? |

bj90392 |
There are a lot of calculations to this. In the end I got .010348 so I think C is right |

RichWang |
Can BA II Plus Professional calculate COV(X,Y)? |

riouxcf |
RichWang, nope. |

jpducros |
Already explained in a previous question, use here the shortcut : cov (xy) = E (xy)-E(x)E(y) It is less confusing. I think that this is the type of question that you can make the difference with other CFA candidates...it is not that complex...and cov calculations scares a bit at first sight. |

cleopatraliao |
The use of the short cut here requires one to know E(xy) which is impossible to compute here so the short cut is not an option here. |

PeterL |
thank you, short cut is worthless |

elmagico10 |
Like jpducros explain, use the shortcut formula: COV (FG)=E(FG)-E(F)E(G) E(FG)=0,6*0,25*0,2+0,4*0,01*0,02 E(F)=0,6*0,25+0,4*0,01 E(G)=0,6*0,2+0,4*0,02 |