### CFA Practice Question

A portfolio contains securities from five regions of the world, with one security from each region The probability that each security would go up in a year is 68%. The joint probability that all securities would go up in a year has been estimated at 18.9%. It can be concluded that the five securities are ______.
A. independent.
B. correlated.
C. neither independent nor correlated.
Explanation: For securities to be independent, their joint probability should equal the product on probabilities of each security going up in a year. Under the assumption of independence:

Joint probability = (0.68)5 = 0.145, or 14.5%

Since the estimated joint probability = 18.9% > 14.5%, the claim of independence can be rejected.

### User Contributed Comments9

User Comment
RCCFA why is it correlated???
wollogo Because they are not independent. If the securities were independent there would be no correlation between them, i.e. the probability of A increasing would not be affected by B, C, D or E increasing.
dimanyc wollogo, thx!
steved333 yes. correlated means that they somehow affect eachother. independent means that they don't. that being said, they can only be either correlated or independent. if p^n does not = the joint prob, then they are correlated, as p^n= joint prob is the definition of independent events.
dcsmith yawn
boddunah nice analystnotes. you got me . but there very good questions that can be tested
Ayodele waoh
CalebMast Independence and mutual exclusivity seem to be helpful here. These things could happen at the same time (what mutually exclusive actually means), but truly joint probabilities are multiplied by one another. There could be some that are anticorrelated (highly low correlation of .01, etc.) and effectively never occur together, thus not independent but actually anti-dependent. There seems to be a correlation that values are inverse - if one is up (or happening), the other cannot. In this case, independence simply means (per formula) that P(AB) = P(A) * P(B), which applied would mean that all of the happenings (each having the same probability individually) would be multiplied together, thus a pentic (5th power) as baseline. Since probability is more than the independence formula calculates (5th power), the items are not truly independent - some happen to occur with others, even if small. True independence is a high standard - even .01 over the formula calculation indicates lack of independence and answer should be the same.
chesschh There could also be a combination of independent and correlated securities