### CFA Practice Question

There are 294 practice questions for this study session.

### 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?

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.