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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ANSWER (partial)

1) No. c can be negative. We see this all the time in asset correlation matrices.

2) (Not sure…)

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.