A stock owned by a portfolio has a bankruptcy probability of 1% per year.Using a Poisson distribution,what is the probability that this firm will not declare bankruptcy over the upcoming 10 years?

Question

Quizplus · Accepted Answer

The Poisson distribution can be used to model the probability of a certain number of events occurring in a fixed interval of time, given the average rate at which they occur. In this case, the interval of time is 10 years, and the average rate of bankruptcies per year is 1%, or 0.01.

The probability of no bankruptcies over 10 years can be calculated as follows:

P(no bankruptcies) = e^(-lambda) * (lambda^k / k!)

where lambda = 0.01*10 = 0.1, k = 0 (since we are looking for the probability of no bankruptcies), and e is the mathematical constant e (approximately equal to 2.718).

Substituting these values, we get:

P(no bankruptcies) = e^(-0.1) * (0.1^0 / 0!) 
                  = e^(-0.1) * 1 
                  = 0.9048

Therefore, the probability that the firm will not declare bankruptcy over the upcoming 10 years is 90%, which is closest to option D (90%).

A Stock Owned by a Portfolio Has a Bankruptcy Probability