In any stock market the market exhibits a bull market a bear

In any stock market, the market exhibits a bull market, a bear market or a stagnant market trend during a given week. Consider a stock market under the following; a bull week is followed by another bull week 90 % of a time, a bear week 7.5 % of a time, and a stagnant week 2.5% of a time. A bear week is followed with another bear week 80 % of a time, a bull week 15 % of a time, and a stagnant week 5 % of a time. A stagnant week is followed with another stagnant week 50 % of a time, a bull week 25 % of a time, and a bear week 25 % of a time. a. The market exhibits a bull market trend this week. What is the probability the market will not be in bear trend after four weeks ? Justify your answer.

b. What is the probability that the market will not be in a bear trend any of the next four weeks, given that the market is in a bull trend this week ? Write your answer in details.

Solution

if bull today , 0.90 bull week, 0.075 bear week . 0.025 stagnant week

if bear today , 0.80 bear weak, 0.15 stagnant week. 0.05 bull week

if stagnant today, 0.50 stagnant week, 0.25 bull week, 0.25 bear week

a) today its bull

we have to get the probability that it is not bear after 4 weeks

so after 4 weeks probability of bull = 0.90^4 = 0.656( as bull gives 0.90 times bull)

and after 4 weeks probability of stagnant = 0.075^4 = 0.003 ( same reason as above)

hence probability it wont be bear = 0.656+0.003 = 0.659

b) probability of not bear in any 4 week = all bear or all stagnant = part a + 2*(probability of bull and stagnant)

= 0.659 + 2(0.90*0.90*0.075*0.075) = 0.659+ 0.009 = 0.668