Problem 3: Normal Distribution After Facebook\'s earnings announcement we have t

Question

Problem 3: Normal Distribution After Facebook's earnings announcement we have the following distribution of returns. First, the stock beats earnings expectations 75% of the time, and the other 25% of the time earnings are in line or disappoint. Second, when the stock beats earnings, the probability distribution of percent changes is normal with a mean of 10% with a standard deviation of 5% and, when the stock misses earnings, a normal with a mean of-5% and a standard deviation of 8%, respectively. (a) Ahead of the earnings announcement, what is the probability that Facebook stock will have a return greater than 5%? (b) Do you get the same answer for the probability that it drops at least 5%?

Explanation / Answer

expected return =0.75*10+0.25*(-5) =6.25

and std deviation =((0.75*5)2+(0.25*8)2)1/2 =4.25

a) probability that stock will have a return greater than 5% =P(X>5) =P(Z>(5-6.25)/4.25) =P(Z>-0.1529)=0.5608

b) No as expected return is not centered at 0 therefore we will not get same answer as we have received in part a.

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