- CFA Exams
- CFA Level I Exam
- Study Session 18. Portfolio Management (1)
- Reading 52. Portfolio Risk and Return: Part I
- Subject 2. Variance and Covariance of Returns

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**CFA Practice Question**

It is NOT possible to construct a portfolio with zero variance of expected returns from assets whose expected returns have positive variance individually. True or False?

Correct Answer: False

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**User Contributed Comments**
11

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

KD101 |
I thought variance is always always positive |

tony1973 |
It's possible to construct a portfolio with 0 variance of expected returns. Consider a portfolios of two assets(A and B). Asset A and B's expected returns are exactly opposite: when A's return is 5%, B's is -5%; when A's return is -8%, B's is 8%. If you have 50% in A and 50% in B, your portfolio's expected return will always be 0. The expected return, variance and standard deviation of your portfolio's return is always 0 as well. |

aabbcc |
that is, the correlation coefficient of A and B is -1. |

roark |
all tht matters is the COvariance n not individual variances n of crs as KD101 pointed out variances cant b negative |

DaGuy |
Variance is never negative to begin with. You can construct a zero variance portfolio from two negatively correlated assets. It's impossible to construct a zero variance portfolio when the assets move in the same direction (positive correlation) because there is no cancellation effect. |

Crown01 |
that is when Ra=Rb and cov(A,B)=-1 and A:B=50:50. Or any others set but the Covariance must be negative. (not only at -1) So the answer is "It is possible ..." |

magicchip |
That's a good question |

azramirza |
I agree with daguy..however..if this is true..the answe shd be true...If the indiviaal a/s have +variance how can the portfolio have 0 variance...zero variance can be more of a product of negative corelation...please help.. |

VenkatB |
Good question. Assets can have Zero or (only POSITIVE) Variance. For diversification, we need to look at COVARIANCE or CORRELATION between assets. There is nothing mentioned about Correlation or covariance in the question. So we can't assume their correlation is also positive.. So the answer is False==> ie , you can construct zero variance portfolio with two individually positive variance assets.. |

michlam14 |
while logically it made sense, it took me awhile to fully grasp the concept - just look at the formula, even though the weighted variances of the individual assets are always positive, if cov*weight is sufficent to cancel out the positive variances, then we can have o variance, meaning Cov will have to be negative. |

johntan1979 |
Agree with michlam14 and some other guys on this list of comments. Took me awhile too. But they got the correct reasoning. The only thing that can be negative in portfolio variance is the covariance, which possibly can cancel out the individual positive variances. |