Interview Question: Three-Way Relations

Sample Question #201 (probability theory)

We have three random variables X, Y and Z. The correlation coefficient between X and Y is a>0, and that between Y and Z is b>0.

1) Let c be the correlation coefficient between X and Z. Is c > 0?

2) Given a and b, what can you say about c?

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2 Responses to Interview Question: Three-Way Relations

  1. Brett says:

    ANSWER (partial)
     
    1) No. c can be negative. We see this all the time in asset correlation matrices.
     
    2) (Not sure…)
     

  2. heath says:

    a_sq + b_sq + c_sq < 1 + 2abcthis follows from positive definiteness of the portfolio correlation matrix.Now that being said, a>0,b>0 doesnot impose any other condition on c. Only c has to be bounded by (-1/2ab). Thats the lowest it can go.

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