2. For two particular stocks A and B, let RA and RB denote their annual returns,

Question

2. For two particular stocks A and B, let RA and RB denote their annual returns, respectively. Suppose that RA is uniformly distributed between 12% and 26% and that RB is normally distributed with µ = 15% and 2 = 73.96%2 . Further, suppose the probability that both stocks A and B have positive annual returns is 0.67.

(a) In a given year, find the probability that stock A has a negative return, given that stock B has a positive return.

(b) In a given year, find the probability that both stocks A and B have negative returns

Please explain your working. I want to understand how you come to your answer. Thanks very much

Explanation / Answer

(a) P(RB>0) = P(Z>(0=15)/SQRT(73.96)) = P(Z>=1.74) = 0.9591

Using Total probability law,

P(RA<0|RB>0) = P({RA<0} {RB>0}) / P(RB>0) = [P(RB>0)-P({RA>0} {RB>0})] / P(RB>0) = (0.9591-0.67) / 0.9591 = 0.3014

(b) P(RA<0) = [0-(-12)] / [26-(-12)] = 12/38 = 0.3158

P({RA<0}{RB>0}) = 0.9591-0.67 = 0.2891 (Using results from part (a))

P({RA<0} {RB<0}) =P(RA<0)-P({RA<0} {RB>0})= 0.3158-0.2891= 0.0267

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