- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 8. Probability Concepts
- Subject 7. Covariance and Correlation

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**CFA Practice Question**

Which of the following statements is incorrect?

B. Cov(X,X) = Var(X)

C. Cov(X,Y) = E[(x - Ex) x (y - Ey)]

D. -1 <= Cov(X,X) <= 1

A. Cov(X,Y) = Cov(Y,X)

B. Cov(X,X) = Var(X)

C. Cov(X,Y) = E[(x - Ex) x (y - Ey)]

D. -1 <= Cov(X,X) <= 1

Correct Answer: D

-1 <= Cov(X, X) <= 1 is incorrect. A correct statement would be: Cov(X, X) = Var(X) and they >= 0. The variance is never negative and is not bounded above by 1.

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**User Contributed Comments**
8

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

fedha |
Good question coz it summarizes all the facts about covariance |

8thlegend |
Can someone explain why Cov(X,X) = Var(X) is correct? |

nike |
easy. correlation (X, X) = Cov(X,X)/(SD(X) * SD(X)). Since correlation (X, X) = 1 and (SD(X) * SD(X)) = VAR(X), so Cov(X,X) = VAR(X) |

bhaynes |
Key point to remember.......the covariance of a random variable with itself = the variance of the random variable. |

azramirza |
Dont understand this..it is said that covariance can be = 0, -ve or +ve????/ |

papajeff |
Corr cannot be negative, Cov can. |

Bududeen |
papajeff got it wrong...corr can be negative ...also cov can be negative but Var cannot be negative |

Rachelle3 |
Variance is the square but stan dev is the sq root so 3 * 3 is 9 the variance but the sq root would be 3 or the Stn dv. I am only using this small example to explain why variance is never negative so -12 sq = positive 144 and -123 sq = positive 15,129 when a negative is sq it turns POSITIVE try it!!! VARIANCE ALWAYS POSITIVE BCOZ VARIANCE IS SQ OF SOMETHING!!! |