CFA Practice Question

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CFA Practice Question

You are considering a portfolio only of long positions not involving leverage and have the following information:

Stock | Expected Return | Variance | Correlation

1 | 15% | 100 | R1,2 = 0.6
2 | 18% | 64 | R1,3 = 0.2
3 | 24% | 400 | R2,3 = -1.0

Without doing any calculations, what is the correct statement about the risk of a portfolio consisting of these three stocks?
A. The portfolio standard deviation must be between 8% and 20%.
B. The portfolio standard deviation could be less than 8%.
C. The portfolio standard deviation could be larger than 20%.
Explanation: The portfolio's standard deviation could be less than the lowest individual security's standard deviation of 8% because the correlation coefficients are all less than +1.0.

User Contributed Comments 5

User Comment
tll936 don't understand, any one help?
ninad123 If correlation coefficient less than 1 then if we add stock with correlation less than 1 to portfolio the risk i.e S.D. will keep on reducing.
endurance the whole concept about MPT is about this question
viruss it only means that even if you add securities that have higher standard deviations, you will reduce the risk of your portfolio (diversification concept). You then take the lowest standard deviation and you know that it could be lower ...
farhan92 I used a calculator but the comment by endurance basically sums it up.
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